Abstract
In this chapter I focus on De Volder’s treatment of hydrostatics, i.e. the core of his teaching activities at Leiden experimental theatre. The chapter is devoted to discussion of De Volder’s attempt to combine two main models in hydrostatics. First, the Cartesian – which Descartes expounded through his theory of gravity – according to which bodies (either solid or fluid) provided with the same specific weight constantly nullify their reciprocal pressure, so that, for instance, there is no increasing pressure in water. Second, the Archimedean model (assumed by Boyle) according to which the conditions of the floatation of bodies are determined by the different pressures exerted within a fluid. I show that these models are ultimately inconsistent with each other, so that in refraining from publishing his disputations, De Volder might have been partially justified by this problem. Moreover, I consider De Volder’s application of such models to the explanation of the effects of the pressure of air, and its partial overcoming by his assuming, as a key factor determining pneumatic phenomena, the idea of the elasticity of air. This was a notion that De Volder also applied to physiology, and which testifies to his assumption of the Boyle-Mariotte law.
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Notes
- 1.
“Quam suam firmiter persuasum fuerit omnibus ab omni antiquitate Philosophis, aërem nostrum, quem haurimus, gravem esse, vel ex eo coniici potest, quod hoc ipsum nequidem ab illis in controversiam vocatum fuerit. Imo tam certe id creditum fuit Aristoteli eiusque sequacibus, ut non dubitarint, huic fundamento, omnem de corporum sub Luna degentium cognitione doctrinam superstruere. Neque vero haec res dubia habita fuit, nisi postquam quam experimentis Galilaei, Torricellii, Robervallii, Pascalii, Guericke, Boylaei, Hugenii, aliorumque excellentium hac in parte virorum, gravitas ipsius aëris adeo manifestae demonstrata fuit, ejusque effectus adeo notabiles animadversi, ut qui eam nihilominus negare velit, non tantae demonstrationum Mathematicarum claritati tenebras offundat, quam quidem suam in certissimis ratiociniis percipiendis prodat ignorantiam, tarditatemque,” De Volder 1676–1678, disputation 1, thesis 1.
- 2.
“Qua in re, ut omnem verborum effugiamus controversiam, praemonendum censeo, non id agi ut quaeratur de gravitate levitateve aëris ad alia corpora comparati, an nimirum aër levis possit dici si ad aquam et terram aliave corpora graviora conferatur, licet et ille gravis forte dici quaeat si referatur ad ignem ipso Aëre leviorem; quae res tantae est evidentiae ut non minus ridiculum mihi videatur eam, (quasi tam ineptus quispiam foret qui de ea, dubium moveret,) experimentis aut rationibus operose, ostendere velle, quam aëris, de qua haec agemus, gravitatem certis ab experientia petitis ratiociniis demonstratam convellere. Quanquam enim hoc effugium prima fronte speciem quandam veri mentitur, qua ab errore Aristoteles eiusque sequaces salvari possint, cum ille multis in locis expressis verbis asserat, nec aërem nec aquam simpliciter graves esse, ἁπλῶς μὲν γὰρ οὐδ έτερον τούτων κοῦφον ἢ βαρύ γῆς μὲν γὰρ ἄμφω κουφότερα, πυρὸς δὲ βαρύτερα. Simpliciter enim neuter eorum aut levis, aut gravis, ambo enim terra leviores, igne vero graviores l. iv. de coelo c. iv. et passim alibi,” De Volder 1676–1678, disputation 1, thesis 2; cf. De coelo, 311a25–26.
- 3.
- 4.
“Those of our predecessors who have entered upon this inquiry have for the most part spoken of light and heavy things only in the sense in which one of two things both endowed with weight is said to be the lighter. And this treatment they consider a sufficient analysis also of the notions of absolute heaviness, to which their account does not apply. This, however, will become clearer as we advance. One use of the terms ‘lighter’ and ‘heavier’ is that which is set forth in writing in the Timaeus, that the body which is composed of the greater number of identical parts is relatively heavy, while that which is composed of a smaller number is relatively light. As a larger quantity of lead or of bronze is heavier than a smaller-and this holds good of all homogeneous masses, the superior weight always depending upon a numerical superiority of equal parts-in precisely the same way, they assert, lead is heavier than wood. For all bodies, in spite of the general opinion to the contrary, are composed of identical parts and of a single material. But this analysis says nothing of the absolutely heavy and light. The facts are that fire is always light and moves upward, while earth and all earthy things move downwards or towards the centre,” Aristotle 1922a, 308a30–308b15.
- 5.
“Facile tamen patebit attendenti quam frivolum id sit, et quam, si hoc admittatur, principia rerum sublunarium instabili nitantur fundamento. Eam enim ob causam si liceat Aëri levitatem assignare, quia levior terra, certe et licebit aquam levem dicere, quam tamen omnes gravem clamitant. Nec aqua solummodo levis erit, sed et terra, sed et metalla, et mineralia, imo omnia corpora excepto solo auro, utpote quod omnium hactenus cognitorum est gravissimum. Quo ipso si forte praeterea aliquod corpus reperiatur gravius, actum erit prorsus de auri gravitate, idque quod iam sua natura grave audit, mox post talis, si forte detur, corporis inventionem, licet natura sua neutiquam immutatum sit, iuxta hunc Philosophicum sc. loquendi morem de hoc gravitatis solio deturbabitur, et dicendum erit leve. Quo ipso non difficulter animadvertitur, gravitatem corporum hoc sensu sumtam nihil de eorum natura determinare, quippe qua manente eadem corpus possit ex gravi mutari in leve, et ex levi in grave: unde et illud clarum est, quam solidis et constantibus fundamentis superstruatur Aristotelis et Peripateticorum de elementis rerum sublunarium doctrina, utpote quae si non in totum, magna certe ex parte hac gravitate levitateve nititur, quae tamen, ut ostendimus, ipsorum corporum naturam non attingit,” De Volder 1676–1678, disputation 1, thesis 2. The use of the case of gold – whose properties cannot be reduced to any of the four elements – in order to discard the Aristotelian theory of elements can also be found in an anti-Aristotelian thinker such as David Gorlaeus, and later in Henricus Reneri: see Lüthy 2012, chapter 4; Buning 2013, chapter 5.
- 6.
In Torricelli’s esperienza, is worth recalling, a tube filled with mercury, and closed on one side, is put into a container full of mercury: at that point, the mercury present in the tube does not descend completely in the container, as it is sustained by the pressing air, and leaving a ‘void’ space in the upper part of the tube itself. Torricelli provided an account of his experiment in two letters to Michelangelo Ricci of 1644, in Galluzzi and Torrini 1975, volume 1, 122–123 and 130–132.
- 7.
“Hanc autem posteriorem partem multis experimentis quae vulgo commentitio cuipiam vacui metui ascribi solent confirmarunt recentiores. Inter quos primum Torricellius non in hunc quidem finem, sed ut spatium inane ostenderet, tubo usus est vitreo, trium pluriumve pedum longitudine, quem ab altera solum parte apertum et mercurio repletum, aperto orificio post repletionem digito obturato, inversoque tubo, in aliud vasculum eodem mercurio refertum immisit ea lege, ut orificium tubi, antequam aperietur, depressum foret intra superficiem mercurii in vase stagnantis. Quibus ita constitutis, remotoque digito, quid fit? Mercurius nonne quod expectandum videretur, sua gravitate ex Tubo aperto effluet omnis? Praesertim cum in vulgata opinione nulla vis sit in aëre, huic descensui resistendo, imo e contrario videatur aër potius ei adiumento fore quam impedimento; nam quo delabitur plus mercurii, eo plus ascendit Aëris, qui motus ipsi fingitur naturalis. An vero providae Naturae iussibus obsecundans, suìque ipsius boni negligens, summo hoc sapientiae gradu, quo plerique mortalium carent, praeditus Mercurius in ipsa haerebit summitate? Ne forte suo lapsu in summitate Tubi, ad quam Aëri aditus non patet, monstrum illud horrendum producatur, quod Inane vocamus? Alterutrum certe horum fieri oporteret, si vulgaris Philosophiae Natura inhaereret principiis. Verum illa harum legum prorsus oblita, nec sese ad commentitias Philosophorum regulas astringi permittens, mercurium deprimit, non quidem ad fundum usque, sed ad altitudinem 28. aut 29. digitorum circiter, ad quam eundem subsistere cogit. Quod profecto experimentum Scholasticae Philosophiae fundamenta non parum conquassat. Corpus enim tantae gravitatis quanta est mercurius aperto orificio, per quod possit effluere, ad eam altitudinem sustineri, sine ullo, quod sustineat, aequipondio, vel novae cuiusdam intelligentiae opus est, utpote quam, ut ex coelorum motibus addiscimus, eo in casu, quo causas rerum ignoramus, in subsidium vocandam suo nos exemplo docuit Aristoteles; aut forte nova quaepiam in hoc rerum statu forma mercurio adiumento est, ne lapsu graviore ruat,” De Volder 1676–1678, disputation 1, thesis 4.
- 8.
Aristotle 1922a, 311b5–15.
- 9.
Sic.
- 10.
De Volder 1676–1677, 130r–v.
- 11.
Probably, it was dictated in the quoted form during the experiment itself, as it is reported in Latin, and as it cannot be found in this form in the text of the disputation.
- 12.
See Fredette 2001.
- 13.
As I am going to show, it is cited in De Volder’s dictata: see Sect. 6.2.1.2, Huygens’s quantification of centrifugal force.
- 14.
- 15.
Owned by De Volder: see Bibliotheca Volderina, 5. The positions of the Conimbricenses on the heaviness and lightness of elements are reported in the Idea philosophiae naturalis (1652) of Franco Burgersdijk, without mentioning, however, the problem of the gravity of air on air. Burgersdijk reports the idea that levity and gravity are derived properties of elements (like being dense and rarefied), and that such properties ground the natural movement of elements (upwards or downwards), which, once they reach their natural place, naturally come to rest: Burgersdijk 1652, 41–44. As to the positions of the Conimbricenses, see the next footnote.
- 16.
“Caeterum non solum Archimedes et Ptolemaeus, sed etiam Simplicius, Themistus, Syrianus, Alexander, ac Peripatetici fere omnes contrariam sententiam amplexi sunt, quae hisce duobus assertionibus continetur. Prima. Nullum elementum in suo loco naturali constitutum gravitat aut levitat, si modo gravius subsideat, levius emineat. Probatur: quia ideo elementa tanto naturae impetu praescriptam sibi a natura sedem petunt, ut inibì tranquillitate adepta consistant, nec iam ulterius cieantur. Deinde, quia si aër et aqua in patria regione deorsum niterentur, degravaret nostra capita aëris pondus, et ii qui sub aquis natant, onus magnum sentirent, quod tamen experientiae repugnat. Cur autem adhibeamus moderationem illam, si modo gravius, et c. ex sequenti assertione constabit. Secunda assertio: corpora gravia supra minus gravia, aut supra levia, ubicunque sint, gravitant: similiterque levia infra minus levia, aut infra gravia, levitant. Hanc assertionem probat experientia. Videmus enim ubicunque gravia aut minus gravia ponantur, confestim superiorem locum levibus aut minus gravibus, si haec infra sint, deferre: quod certe non fit, nisi mutuo gravium descendentium, leviumque ascendentium conatu atque impulsu, quem gravitandi et levitandi actum diximus,” Conimbricenses 1603, In de Coelo, quaestio 2, article 1, columns 529–530.
- 17.
“Ego igitur respondendum puto gravitatem sumi posse duobus modis. Cum enim sit qualitas quaedam et propensio ad inferum locum, quam consequitur hic effectus, haec operatio, ad eum locum moveri, ideo accipi potest tum secundum se pro actu primo, tum pro operatione et actu secundo […]. Sed altero modo accepta augeri ac minui potest, et dicitur gravitatio potius quam gravitas. Cum enim nil aliud sit quam excessus virtutis motricis supra resistentiam medii, unde fit descensus et pressio substantis corporis resistentis, hic maior fit dum resistentia imminuitur. […] Ipsa vero gravitatis ac levitatis distinctio, quam posuimus, tum per se manifesta est, tum ab Aristotele posita, nam gravitatem pro gravitatione sumimus quando dicimus: grave in suo loco non est grave, id est, non gravitat, nec premit deorsum. Primo enim modo falsum diceremus, quoniam elementum grave habet ubique naturam gravis, etiam in loco suo, ob id Aristoteles in contextu 16 et 27 quarti libri De caelo sumit priore modo gravitatem et levitatem, dum dicit levissimum esse id quod omnibus supereminet, et gravissimum id quod omnibus substat. Sic enim etiam in locis suis dicit esse gravissimum atque levissimum. In contextu autem 29 et 30 eiusdem libri sumit gravitatem et levitatem secundo modo, dum dicit lignum unius talenti in aëre maiorem habere gravitatem quam plumbum unius librae, contra vero in aqua rem sese habere. Sumit enim gravitatem pro operatione, quae notat respectum ad externa corpora per quae fit motus. Eo namque respectu variato etiam gravitas variatur, non quidem natura ipsa, sed gravitatio. Dicit etiam in contextu illo 30 omnia elementa in suis locis aliquam habere gravitatem praeter ignem, nam aër quoque in suo loco existens facilius deorsum pellitur, quam sursum, quia magis gravitat, quam levitat; attamen secundum eius naturam magis est levis, quam gravis,” Zabarella 1617, 341–342; cf. De coelo, 309a26–309b17, 311a21–29 and 311b2–12. See also Zabarella 2016, 441–442.
- 18.
“Illud sane constat q[uod], non est idem penitus utrobiq[ue] gravitatis officium: namq[ue] extra proprium locum efficit motum; in proprio loco magis studet quieti, ut videatur naturae consilium potius esse, ut ibi maneat corpus, neque inde facile detrudi pariatur, quanq[ue] centri satagat, q[uod] cum in proprii loci latitudine versetur; bona etiam ex parte finem suum sit consecutum. Nunc pondus ex ea propensione cognoscitur quae cum motu coniuncta est, aut affinis est motus, velut oppressio, non ex ea quae cum quiete consistit, neq[ue] n[am] pondus rei quae in trutina appensa est, apparet, si quis ea sustineat, sed si liberae naturae suae dimittatur. Itaq[ue] et o[mn]e impedimentum {evariat} pondus. Hoc igitur, cum extra proprium locum eveniat; fit, ut gravitas extra proprium locum, non in ipso sentiat. Poterat igitur Alexander occurrere dubitationi, negans elementa in proprio loco gravitatem, levitatemve habere, et id ipsi dari poterat, si eam facultatem accepisset quae pondere deprehenditur; nos illam vim accipere voluimus, qua rerum natura definitur, et ei perpetuo manet affixa,” Buonamici 1591, 480. See Conti 1997.
- 19.
Cf. the full text: “[i]t is due to the properties of the elementary bodies that a body which is regarded as light in one place is regarded as heavy in another, and vice versa. In air, for instance, a talent’s weight of wood is heavier than a mina of lead, but in water the wood is the lighter. The reason is that all the elements except fire have weight and all but earth lightness. Earth, then, and bodies in which earth preponderates, must needs have weight everywhere, while water is heavy anywhere but in earth, and air is heavy when not in water or earth. In its own place each of these bodies has weight except fire, even air. Of this we have evidence in the fact that a bladder when inflated weighs more than when empty. A body, then, in which air preponderates over earth and water, may well be lighter than something in water and yet heavier than it in air, since such a body does not rise in air but rises to the surface in water,” Aristotle 1922a, 311b1–15.
- 20.
“Lignum ergo talenti unius, quod aëris in se, plus habeat, quam aquae, ac terrae, gravius est in aëre, quam plumbum eminae tantum unius in aquam, quod longe plus terrae quam aquae, et longe plus aquae quam aëris habeat plumbum ocissime mergetur: aquae extimam planiciem lignum vix attingit, et eamdem postquam attingerit, supernatans illico quiescet: ita ut eam ob rem maiorem levitatem praeseferre videatur. Id Aristoteles quarto libro de Caelo […] ideo verum esse est ratus, quod aër in suo proprio naturalique loco aliqua gravitate sit praeditus,” Borri 1576, 213.
- 21.
“[…] ad experientiam omnium rerum magistra, perinde ac ad sacram ancoram confugimus, et duobus adinventis, tum ligni, tum plumbi frustulus aequalis, ut ex aspectu coniicere licebat, ponderis, neque enim nos ad lancem illa expendere necessarium esse duximus, sed periculo quod facturi fueramus, sat esse rati fuimus, si ad oculum expenderentur, eadem ergo duo adinventa aequalis ponderis frustula, ex altiore nostrarum aedium fenestra par impulsu, eodemque tempore proiiciemus: plumbum segnius descenderet, super lignum enim, quod prius in terram ceciderat, omnes quotquot ibi, rei exitum expectabamus, illud praeceps ruere vidimus: idque non semel, sed saepenumero eodem successu tentavimus. Cuius rei experimento ducti omnes in eamdem nobiscum pedibus {iuere} sententiam. Ergo tum rationi, tum experimento, tum auctoritati consentaneum est, aëris in suo proprio, naturalique loco, nonnullam esse gravitatem quo fit, ut lignum in quo plus est aëris, quam in plumbo, aequalis ponderis per aerem medium velocius descendat, et super aquam natet, quod in aqua aër sit levius, perinde ac levis est in terra, levitate licet existente minore,” Borri 1576, 215.
- 22.
Conti 1997, 13.
- 23.
“Et, primo quidem, omnino inexcogitabile videtur, quomodo aër et aqua in proprio loco gravitent. Nanque aliqua pars aquae in loco aëris, hoc est in aëre ipso, gravitat, et deorsum quidem fertur quia gravitat; sed quis unquam mente concipiet, aliquam partem aquae in aqua descendere? Si enim descendet, quando erit in fundo, necesse est ut locus, in quem intrat, iam evacuetur ab alia aqua, quae coacta erit ascendere unde alia recessit; et sic iam illa pars aquae erit levis in proprio loco. […] Ad exemplum autem Aristotelis de utre, respondeo quod, si foramen utris seu follis inflati sit apertum, ita ut aër, non vi compressus, in folle detineatur, non erit iam uter gravior quam non inflatus: sed si vi multum aëris in eo comprimatur, cui dubium erit quod gravitabit? Aër enim tunc, vi constrictus, gravior est aëre libero et vaganti: sicut si uter lana repleatur, deinde vero alterum tantum lanae superaddatur, vi comprimendo, quis anceps erit an gravior fiet uter necne?” Galileo 1890–1909, volume 1, 286.
- 24.
Commandino’s version was based on Tartaglia’s. For a thorough account of the editorial history of Archimedes’s treatise, and of the rediscovery of the original Greek version in 1906 by Johan Ludvig Heiberg, see Archimedes and Fleck 2016.
- 25.
“Proposition 5. Of solids one which is lighter than the fluid, when thrown into the fluid, will sink down until a volume of the fluid equal to the volume of the immersed portion has the same weight as the whole solid. […] [L]et [HTEF] now be the given solid which is specifically lighter than the fluid, [RSQY] a volume of the fluid equal and similar to the immersed portion [BCHT]. If the fluid is at rest, the weight of [HTEF] must be equal to that of [RSQY],” Dijksterhuis 1987, 375–376. Cf. Archimedes and Commandino 1565, 4. As to David Rivault’s version, see Fig. 5.2, Archimedes and Rivault 1615, 496.
- 26.
Dijksterhuis 1987, 373. Cf. Archimedes and Commandino 1565, 1: “[p]onatur humidi eam esse naturam, ut partibus ipsius aequaliter iacentibus, et continuatis inter sese, minus pressa a magis pressa expellatur. Unaquaeque autem pars eius premitur humido supra ipsam existente ad perpendiculum, si humidum sit descendens in aliquo, aut ab alio aliquo pressum.”
- 27.
According to Paolo Palmieri, Galileo was then ultimately led to develop his own theory of buoyancy – which he could not justify in an Archimedean way, i.e. by considering the weight of water on water – and presented it in his Discorso intorno alle cose che stanno in su l’acqua o che in quella si muovono (1612): see Palmieri 2005.
- 28.
“Haec, meo iudicio, quicquid dicant alii, est vera problematis explicatio. Cum igitur nec aër nec aqua deorsum in suis regionibus ferantur neque sursum, ne dicantur esse aut gravia aut levia; cum gravia definiantur ea esse quae deorsum feruntur, levia vero quae sursum. Et cum de motu loquimur, semper non solum gravitatis aut levitatis mobilis, sed gravitatis et levitatis medii etiam, ratio est habenda: non grave deorsum movebitur, nisi medio per quod ferri debet gravius erit; nec leve ascendet, nisi levius fuerit medio per quod movetur. Quod cum ita sit, aqua non descendet in aqua, cum aqua gravior non sit quam aqua; et cum non descendat, non erit aqua in aqua gravis,” Galileo 1890–1909, volume 1, 289.
- 29.
“Grave et leve non nisi in comparatione ad minus gravia vel levia considerarunt qui ante Aristotelem; et hoc quidem, meo iudicio, iure optimo. […] Cum enim in omni medio gravium gravitates tantum imminuantur, quantum illius medii pars aequalis moli solidi ponderaret, patet quod in illo solum medio integrae et non imminutae solidorum habebuntur gravitates, cuius nulla fuerit gravitas: tale autem solum est vacuum,” Galileo 1890–1909, volume 1, 289 and 295.
- 30.
“[D]icimur gravari, quando super nos incumbit aliquod pondus quod sua gravitate deorsum tendit, nobis autem opus est nostra vi resistere ne amplius descendat; illud autem resistere est quod gravari appellamus,” Galileo 1890–1909, volume 1, 288.
- 31.
“Quomodo ergo solvetur problema, nisi dicamus, aquam et aërem non gravare in suis regionibus? […] Si autem in aqua existentibus aliquod corpus aeque grave ac aqua nobis immineat, neque ab illo gravabimur neque attollemur, quia neque sursus neque deorsum tale corpus feretur. At non invenitur corpus aliquod, quod magis aquae in gravitate aequetur quam ipsamet aqua: non ergo mirum est si aqua in aqua non descendat et gravet; diximus enim, gravari esse resistere nostra vi corpori deorsum petenti. Et eadem prorsus ratio de aëre habenda est. Haec, meo iudicio, quicquid dicant alii, est vera problematis explicatio,” Galileo 1890–1909, volume 1, 288–289. Galileo was responding to Borri’s solution to the problem of the absence of the feeling of pressure underwater; for Borri the mass of water behaves as a solid body: cf. Borri 1576, 232.
- 32.
Conti 1997, 20–21.
- 33.
“Ho preso un fiasco di vetro assai capace e col collo strozzato, al quale ho applicato un ditale di cuoio, legato bene stretto nella strozzatura del fiasco, avendo in capo al detto ditale inserta e saldamente fermata un’animella da pallone, per la quale con uno schizzatoio ho per forza fatto passar nel fiasco molta quantità d’aria; della quale, perché patisce d’esser assaissimo condensata, se ne può cacciare due e tre altri fiaschi oltre a quella che naturalmente vi capisce. In una esattissima bilancia ho poi pesato molto precisamente tal fiasco con l’aria dentrovi compressa, aggiustando il peso con minuta arena. Aperta poi l’animella e dato l’esito all’aria, violentemente nel vaso contenuta, e rimessolo in bilancia, trovandolo notabilmente alleggerito, sono andato detraendo dal contrappeso tant’arena, salvandola da parte, che la bilancia resti in equilibrio col residuo contrappeso, cioè col fiasco: e qui non è dubbio che ’l peso della rena salvata è quello dell’aria che forzatamente fu messa nel fiasco e che ultimamente n’è uscita. Ma tale esperienza sin qui non mi assicura d’altro, se non che l’aria contenuta violentemente nel vaso pesò quanto la salvata arena; ma quanto resolutamente e determinatamente pesi l’aria rispetto all’acqua o ad altra materia grave, non per ancora so io, né posso sapere, se io non misuro la quantità di quell’aria compressa: ed a questa investigazione bisogna trovar regola, nella quale ho trovato di potere in due maniere procedere. L’una delle quali è di pigliar un altro simil fiasco, pur, come ’l primo, strozzato, alla strozzatura del quale sia strettamente legato un altro ditale, che dall’altra sua testa abbracci l’animella dell’altro, e intorno a quella con saldissimo nodo sia legato. Questo secondo fiasco convien che nel fondo sia forato, in modo che per tal foro si possa mettere uno stile di ferro, con il quale si possa, quando vorremo, aprir la detta animella per dar l’esito alla soverchia aria dell’altro vaso, pesata ch’ella sia: ma deve questo secondo fiasco esser pieno d’acqua. Apparecchiato il tutto nella maniera detta ed aprendo con lo stile l’animella, l’aria, uscendo con impeto e passando nel vaso dell’acqua, la caccerà fuora per il foro del fondo; ed è manifesto, la quantità dell’acqua che in tal guisa verrà cacciata, essere eguale alla mole e quantità d’aria che dall’altro vaso sarà uscita. Salvata dunque tale acqua, e tornato a pesare il vaso alleggerito dell’aria compressa (il quale suppongo che fusse pesato anche prima, con detta aria sforzata), e detratto, al modo già dichiarato, l’arena superflua, è manifesto, questa essere il giusto peso di tanta aria in mole, quanta è la mole dell’acqua scacciata e salvata; la quale peseremo, e vedremo quante volte il peso suo conterrà il peso della serbata arena, e senza errore potremo affermar, tante volte esser più grave l’acqua dell’aria: la quale non sarà dieci volte altrimenti, come par che stimasse Aristotele, ma ben circa quattrocento, come tale esperienza ne mostra,” Galileo 1890–1909, volume 8, 123–124. For the letter to Baliani, see Galileo 1890–1909, volume 12, 33–37.
- 34.
See AT III, 484. Discussed in Cottingham 1997.
- 35.
- 36.
Riccioli 1651, volume 2, 652.
- 37.
Borelli 1670, 251. Please note that in Magalotti 1666, 254–255, is reported the value of 1 to 1,179.
- 38.
“We took then an Aeolipile made of Copper, weighing six ounces, five drachms, and eight and forty grains: this being made as hot as we durst make it, (for fear of melting the mettle, or at least the Sodar) was removed from the fire and immediately stopped with hard Wax that no Air at all might get in at the little hole, wont to be left in Aeolipiles for the fumes to issue out at: Then the Aeolipile being suffer’d leasurely to cool, was again weighed together with the Wax that stopt it, and was found to weigh (by reason of the additional weight of the Wax) six ounces, six drachms, and 39 grains. Lastly, the Wax being perforated without taking any of it out of the Scale, the external Air was suffered to rush in (which it did with some noise) and then the Aeolipile and Wax, being again weighed amounted to six ounces, six drachms, and 50 grains. So that the Aeolipile freed as far as our fire could free it, from its Air, weighed less than it self when replenished with Air, full eleven grains. That is, the Air containable within the cavity of the Aeolipile amounted to eleven grains and somewhat more; I say somewhat more, because of the particles of Air, that were not driven by the fire out of the Aeolipile. And by the Way (if there be no mistake in the observations of the diligent Mersennus) it may seem strange that it should so much differ from 2 or 3 of ours; in none of which we could rarefie the Air in our Aeolipile (though made red hot almost all over, and so immediately plung’d into cold Water) to half that degree which he mentions, namely to 70 times its natural extent, unless it were that the Aeolipile he imploy’d was able to sustain a more vehement heat than ours (which yet we kept in so great an one, that once the Soder melting, it fell asunder into the two Hemispheres it consists of.) The fore-mentioned way of weighing the Air by the help of an Aeolipile, seems somewhat more exact than that which Mersennus used, In that in ours the Aeolipile was not weighed, till it was cold; whereas in his, being weighed red hot, it is subject to lose of its substance in the cooling, for (as we have elsewhere noted on another occasion) Copper heated red hot,” Boyle 1660, 286–288. All these values are far from the proportion of 1 to 3,000 and 1 to 4,000 mentioned as erroneous in experiment 27; probably, De Volder was referring to the proportion of 1 to 400 given by Galileo.
- 39.
Von Guericke 1993, 156. Cf. the full explanation: “[f]or example, hang a glass of this kind from a balance and weigh it, (with the stopcocks open, however, so that you may be certain that the glass is filled with air). Then evacuate all air from it and you will discover that after this has been done, it weighs one or two ounces less than its capacity. Thus after my receiver has been exhausted and is surrounded by the pressure of the atmosphere, it will be found, when examined on the balance, to be two ounces lighter than before, being equal in weight to two imperial thalers. Then prepare to let air enter once again (only a little at a time, however, so that it does not rush in so forcefully that it breaks the glass) and not only will you hear air enter with a hissing sound but you will even see the glass gradually taking on its former weight. This is a very clear demonstration of the weight of air,” Von Guericke 1993, 156; cf. Von Guericke 1672, 100–101. In his Elementa matheseos universae (first edition 1713–1715), Wolff reported the De Volder’s measurement given in the 1681 editions of the Disputationes de aëris gravitate, stating that De Volder followed the method described first by Von Guericke: see Wolff 1733, volume 2, 369. On Von Guericke, see Slaby 1907; Van Helden 1991; Hackmann 1979; Bazerman 1993; Harsch 2007; Conlon 2011; Schneider 2013.
- 40.
It is described as experiment 27 (22 March 1677) and in disputation 5 of his De aëris gravitate (29 June 1678), where he refers to an experiment performed a little more than a year before.
- 41.
“Hoc autem experimentum, quod ante annum et quod excedit publice ostendi, eam ob causam propono lubentius, quia non tantum in genere gravem aërem demonstrat, sed et data cuiuscunque massa aërea certam gravitatem et definitum pondus determinat. Qua in re usus sum bilance accurata, quae etiam si vel 25., aut 30. et c. lb. utrique imponerentur lanci, grano uno alterove addito demtove, in hanc illamve partem manifeste propenderet. Nisi enim ex aëris utamur bilancibus frustra certe erimus in examine tantilli ponderis, quod exhibet nobis aër. Hisce itaque exploravi pondus binorum hemisphaeriorum cera occlusorum, idque aëre nondum educto, ut nimirum fi inter hocce sphaerae pondus aëre repletae, et eiusdem aëre vel in totum, vel maxima ex parte vacuae discrimen quoddam animadverteretur, certo constaret id aëri educto deberi. Sphaerae itaque aëre refertae pondus fuit lb. vii. ℥i. ʒ ii. gr. xlviii. Hinc nulla omnino re sive addita sive demta, ope Antliae Pneumaticae aërem eduxi, occlusamque, ut ante, sphaeram imposui uni lanci, dum alteri adderetur idem pondus, quod sphaerae aëre refertae aequiponderare exploraveram. Profecto si nullum aër obtineat pondus necesse foret ut rebus ita constitutis in aequilibrio haereret bilanx. Nihil enim sphaerae decesserat praeter aërem quem ponderis expertem volunt. Sed quid factum? Lanx illa, quae pondus continebat,. deprimi, illa vero, quae sphaeram, attolli coepit, manifesto indicio, cum altera lanx non facta esset gravior, alteram demto aëre factam esse leviorem. Aëremque idcirco gravitatis esse participem Neque vero ad aequilibrium reduci res potuit, nisi demta parte ponderis, quod in altera lance continebatur, et demere quidem oportuit ʒ i. gr. xvii. Huius quippe sphaerae aëre tantum non prorsus vacuae pondus exploratum, fuit in eadem bilance lb. vii. ℥ i. ʒ i. gr. xxxi. Differentia itaque est, ut dixi, ʒ i. gr. xvii. quod certe, pondus, fatis notabile est, si pauculam illam Aëris quantitatem spectes, quae in sphaera, cuius diameter vix viii. digitorum est, contineri potest. Tota enim haec sphaerae cavitas, si eam perfecte rotundam. Et penitus aëre exinanitam, vix accedit ad sextam pedis cubici partem, ut notum est geometris,” De Volder 1676–1678, disputation 5, thesis 2.
- 42.
Cf. experiment 27; see also and the conversion of the weights in grains reported in De Volder 1676–1678, disputation 5, thesis 6.
- 43.
“VII. Quae ut scopo nostro applicentur, concipiamus binos aëris cylindros, quarum latitudines et inter se, et cum ea quae est nostrae Spherae accuratissime aequales ponantur, ab ipsa Telluris superficie ad ultimos usque athmosphaerae limites extentos. Facile autem est percipere unamquanque horum aëriorum cylindrorum superficiem modo horizonti parallela sit, et in aequali altitudine, premi necessario aequaliter, cum aequalem aëris quantitatem et pressionem supra se undiquaque sustineant. Ponamus porro in horum cylindrorum altero suspendi duo haec sibi invicem cera coniuncta hemisphaeria, aëre adhuc dum referta. Manifestum est, utramque tam internam quam externam huius sphaerae superficiem aequaliter ab aëre premi, eo quod internus ille aër aeque ac externus condensatus sit. VIII. Neque obstat parvula illa aëris quantitas, quae in sphaera est, quae vix videtur tanta vi premere posse internam quanta immensa aëris externi moles externam premit sphaerae superficiem. Etenim si rem rite consideremus, nulla pars aëris agit in sphaeram, nisi ea quae eam tangit proxime, quae tamen eo agit efficacius, quo a mole superioris aëris validius comprimitur. Unde si artificio quopiam fieri posset, ut aër externe sphaeram ambiens aequaliter ac nunc comprimatur, etsi nullus aër superior eum comprimeret, nonne manifestum erit hunc aërem licet in minori copia, quia tamen aeque compressus supponitur ac si omne pondus totius athmosphaerae sustineret, aequali vi acturum in ipsam sphaeram. Ex quo sane conficitur non tam aëris quantitatem quam eiusdem compressionem magis minusque validam spectandam esse. Haec autem cum aequalis sit aëri in sphaera contento, cum eo, qui extra sphaeram est, quid est evidentius quam utriusque vim et actionem in sphaeram aequalem esse? Cui consequens est hoc, in rerum statu ad separationem efficiendam nihil aliud requiri, quam ut parvula ea, quae per ceram est connexionis vis et efficacia superetur vincaturque. Ea enim aëris superficies, quae infra sphaeram est, aequaliter premitur cum superficie aëris laterali, nisi quod sphaerae pondus addat hic cylindro aliquod praepondium,” De Volder 1676–1678, disputation 2, theses 7–8; “[u]t autem nunc porro ad alterum obiectionis caput accedamus, quo si vel maxime aër premat, eam tamen pressionem gravitatem male dici: quia scilicet omnis pressio non est à gravitate. Quis negat: Sed tamen hanc pressionem, gravitatem dicendam esse existimavi semper, quae oritur ex descensu corporum sublunarium versus centrum Telluris. Sic merito eam aquae vim qua descendendo deorsum aliam aquam minus pressam cogit aut ascendere aut Tubum saepius nobis memoratum superiora versus premere, gravitatem dici et eam pressionem qua aër lateralis deorsum ruens, aërem sphaerae orificio subiectum in sphaeram cogit, gravitatem merito vocari censui. Quod si tamen hanc vocem huic pressioni applicare quis nolit, cum eo litem non movebo, modo fateatur hanc qualemcunque pressionem motui aëris deorsum deberi,” disputation 3, thesis 9. See also experiment 27: “[l]astly to show how great the pression of the air was, he said that that globe whose hemispheres could not otherwise [139v] be separated with less than 700 lb weight, he could separate it, when full of air <when> with only his breath, the which he easily performed by blowing it asunder,” De Volder 1676–1677, 139r–v.
- 44.
See Chalmers 2017, 6: “[a] key difference between pressure in the common sense and pressure in the technical sense is that the former relates to forces on bounding surfaces between media whereas the latter refers to forces within the body of media. Another is that, from the technical point of view, pressure is a scalar not a vector. Directed forces, such as those that occur at the boundary of a liquid are determined by variations of pressure, the gradient of pressure in technical terms, rather than by pressure itself. The technical concept of pressure in fluids breaks from the directedness implicit in the verb ‘to press’ from which ‘pressure’ originally derived and which is presupposed in the concept of pressure in its common sense.” On the idea of pressure, see also Calero 2008.
- 45.
- 46.
See Knowles Middleton 1964. In the Experimenta, for instance, the air pump itself is labelled as ‘instrumentum Torricellianum’. Usually, however, the phrase ‘instrumentum Torricellianum’ was used to mean barometer. In the eighteenth century, a distinction between a ‘Boylean’ and a ‘Torricellian’ vacuum had been well established: see, for instance, Pieter van Musschenbroek’s Elementa physicae conscripta in usus academicos (1734): “[i]nventor Antliae Pneumaticae, circa elapsi seculi medium, in Germania fuit Otto Guirikius, qui pulcherrima cum ea fecit pericula. Haec impulerunt Nob. Boyleum, adiutum opera […] Hookii, et Papini, ad similem antliam in Britannia construendam, quacum plurima instituendo experimenta philosophiam naturalem summopere promovit, hinc machina, vel antlia Boyleana, saepe vocatur. Eadem tempestate Leydae a Cl. Voldero alia inventa fuit, quacum an. 1675 laboratorio physico experimenta instituta Leydae fuerunt. Hanc machinam, nostra tempestate Cl. s’ Gravesandius ad magnam perfectione et simplicitatem reduxit, ita ut levi opera, et brevissimo tempore, ex recipientibus maxima aëris copia exantliari possit,” Van Musschenbroek 1734, 381.
- 47.
De Volder 1676–1677, 134r. Morley refers to Carel de Maets, professor of chemistry at Leiden.
- 48.
The history of the invention of barometer has been duly reconstructed in Thirion 1907–1909; Knowles Middleton 1963, 1964; Taton 1963; Prager 1981; Zouckermann 1981; Jones 2001; Shank 2012; Grosslight 2013; West 2013. However, it is worth providing a brief summary of the early dissemination of the story of Torricelli’s esperienza. After Torricelli described his esperienza in his letters to Ricci of 11 June and 28 June 1644, the news of the esperienza was disseminated, and it was repeated, first, in Rome, where Ricci resided (February 1645). Then, it spread in France, via a report of some of the contents of the letters written by a friend of Ricci, François Du Verdus, who sent it to Mersenne in 1644 (see Mersenne 1977, volume 13, 177–183). Then, in 1644 Mersenne visited Torricelli in Florence and witnessed a repetition of the experience by Torricelli himself (Mersenne 1647, 216). Eventually, Mersenne himself unsuccessfully attempted to repeat the experience in Paris in July 1645, together with Pierre Chanut (see the letter of Pascal to Antoine de Ribeyre of 25 June 1651, in Pascal 1923, volume 2, 482). Hence, in November 1646 Pierre Petit – a correspondent of Mersenne – successfully repeated the experience (see Petit 1647, 1–24), and in the same year Pascal undertook various researches on the topic (see Thirion 1907–1909). Also, the experience was performed in Poland in the same year (see Petit 1647, 27–68). Up to this point, it seems that the main source for Torricelli’s own experience had been Du Verdus’s report, thus raising a debate over its actual, first author (see Shank 2012, 167). In March 1648, moreover, Mersenne received from Raffaello Magiotti (from whom he probably asked for information on Torricelli’s experiment) – a friend of Ricci – the report of a previous experiment, carried out by Gustavo Berti in Rome (around 1640–1643), in the presence of Athanasius Kircher, Emmanuel Maignan, and Niccolò Zucchi (who later included accounts of it in their books: see Zucchi 1649, 101–115; Kircher 1650, 11–13; Maignan 1653, volume 4, 1885–1940). This experiment was, in principle, the same one conducted by Torricelli, with water in place of mercury, and using a tube of circa 22 braccia. Eventually, in June 1648, Cornelio – correspondent of Torricelli – published the whole story of the esperienza, decisively contributing to its ascription to Torricelli. Later, Dati gave the final word on the issue. On Cornelio, see Torrini 1977.
- 49.
In fact, his direct source seems to be Pascal’s Traité de la pesanteur de la masse de l’air, chapter 3, where a similar experiment, carried out with a syringe, is used to criticize the fear of a vacuum.
- 50.
De Volder 1676–1677, 136r–v.
- 51.
“Le accennai già che si stava facendo non so che sperienza filosofica intorno al vacuo, non per far semplicemente il vacuo, ma per far uno strumento che mostrasse le mutuazioni dell’aria, hora più grave e grossa, et hor più leggiera e sottile. Molti hanno detto che il vacuo non si dia, altri che si dia, ma con repugnanza della natura e con fatica; non so già che alcuno habbia detto che si dia senza fatica e senza resistenza della natura. Io discorreva così: se trovassi una causa manifestissima, dalla quale derivi quella resistenza che si sente nel voler fare il vacuo, indarno mi pare si cercherebbe di attribuire al vacuo quella operazione, che deriva apertamente da altra cagione, anzi che, facendo certi calcoli facilissimi, io trovo che la causa da me addotta (cioè il peso dell’aria) doverebbe per sé sola far maggior contrasto che ella non fa nel tentarsi il vacuo. […] Noi viviamo sommersi nel fondo d’un pelago d’aria elementare, la quale per esperienze indubitate si sa che pesa, e tanto che questa grossissima vicino alla superficie terrena, pesa circa la quattrocentesima parte del peso dell’acqua. Gli Autori poi de’ crepuscoli hanno osservato che l’aria vaporosa e visibile si alza sopra di noi intorno a cinquanta, overo cinquanta quattro miglia, ma io non credo tanto, perché mostrerei, che il vacuo doverebbe far molto maggior resistenza che non fa, se bene vi è per loro il ripiego che quel peso scritto dal Galileo s’intenda dell’aria bassissima che ve praticano per l’homini e gli animali, ma che sopra le cime degl’ alti monti l’aria cominci ad esser purissima e di molto minor peso che la 1/400 parte del peso dell’acqua,” Galluzzi and Torrini 1975, volume 1, 122–123.
- 52.
“La mia intenzione principale poi non è potuta riuscire, cioè di conoscer quando l’aria fusse più grossa e grave e quando più sottile e leggiera collo strumento EC, perché il livello AB si muta per un’altra causa (che io non credevo mai) cioè per il caldo e freddo e molto sensibilmente, apunto come se il vaso AE fusse pieno d’aria,” Galluzzi and Torrini 1975, volume 1, 123. It may be that De Volder was referring to Boyle, who in experiment 33 of the New Experiments recalled that the variations in pressure of atmosphere can be related not only to different altitudes, but to different circumstances, such as seasons, and latitudes, “seeming capable to alter either the height or consistence of the incumbent Atmosphere,” which, “might most of them be more exactly try’d by the Torricellian Experiments, if we could get Tubes so accurately blown and drawn,” Boyle 1660, 123. Besides, no narration of a ‘casual’ discovery in variations of atmospheric pressure can be found among De Volder’s sources, nor it could have been, as Torricelli purportedly used his strumento as a barometer. On the various attempts to collect data on variations of pressure by means of ‘Torricellian tubes’, see, for instance, the communications of Wallis appeared in the Philosophical Transactions (see infra, n. 54).
- 53.
The idea that Torricelli casually discovered variations in the level of mercury can be found in Haven 2006, 18; Long 2012; Allaby 2014, 80. And yet, De Volder’s ‘popularized’ version of the esperienza of Torricelli corroborates the view of J. B. Shank that Torricelli did not actually ‘invent’ the barometer, as claimed in Knowles Middleton 1964, 29: see Shank 2012.
- 54.
Wallis’s measurements are provided in his Relation concerning the late earthquake neer Oxford; together with some observations of the sealed weatherglass, and the barometer both upon that phænomenon, and in general, communicated to the Royal Society on 29 January 1666, and published in the issue 10 of the first year of the Philosophical Transactions (following the English style, March 1665): “[i]n my Baroscope, I have never found the Quicksilver higher than 30. inches, nor lower than 28. (at least, scarce discernably, not 1/16 of an inch higher than that, or lower than this;) which I mention, not only to shew the limits, within which I have observed mine to keep, vid. full 2 inches, but likewise as an Estimate of the Clearness of the Quicksilver from Air. For, though my Quicksilver were with good care cleansed from the Air,” Wallis 1665, 169–170. The same data are reported in Wallis 1670–1671, volume 3 (which probably was not owned by De Volder), 728.
- 55.
Cf. De Volder 1676–1678, disputation 2, thesis 8: “[n]eque obstat parvula illa aëris quantitas, quae in sphaera est, quae vix videtur tanta vi premere posse internam quanta immensa aëris externi moles externam premit sphaerae superficiem. Etenim si rem rite consideremus, nulla pars aëris agit in sphaeram, nisi ea quae eam tangit proxime, quae tamen eo agit efficacius, quo a mole superioris aëris validius comprimitur. Unde si artificio quopiam fieri posset, ut aër externe sphaeram ambiens aequaliter ac nunc comprimatur, etsi nullus aër superior eum comprimeret, nonne manifestum erit hunc aërem licet in minori copia, quia tamen aeque compressus supponitur ac si omne pondus totius athmosphaerae sustineret, aequali vi acturum in ipsam sphaeram. Ex quo sane conficitur non tam aëris quantitatem quam eiusdem compressionem magis minusque validam spectandam esse. Haec autem cum aequalis sit aëri in sphaera contento, cum eo, qui extra sphaeram est, quid est evidentius quam utriusque vim et actionem in sphaeram aequalem esse? Cui consequens est hoc, in rerum statu ad separationem efficiendam nihil aliud requiri, quam ut parvula ea, quae per ceram est connexionis vis et efficacia superetur vincaturque. Ea enim aëris superficies, quae infra sphaeram est, aequaliter premitur cum superficie aëris laterali, nisi quod sphaera pondus addat hic cylindro aliquod praepondium.” Cf. De Volder 1676–1678, disputation 5, thesis 8: “[h]aec itaque fuit aëris gravitas circa Tellurem eo quo experimentum feci tempore. Quae addo eam ob causam, quia athmosphaerae gravitas atque ideo etiam aëris compressio vel maior vel minor est, prout vel in Terrae cavitatibus profundius descendimus, vel in montium cacuminibus altius assurgimus. Deinde, quia eadem illa athmosphaera, atque ideo et aër eius gravitatem sequens pro diversis tempestatibus, nunc gravior nunc levior est, ut ex barometris, quae Mercurio suspenso Aëris gravitati aequiponderant, liquere potest. Nonnunquam enim in ilis descendit mercurius si pondus athmosphaerae fiat minus, nonnunquam ascendit, si pondus aëris fiat maius. Quae tamen differentia gravitatis licet in tota athmosphaerae massa satis sit notabilis, in ea tamen quantitate pedis cubici, de cuius gravitate determinata hic loquimur, considerari vix meretur. Id etenim observatum est maximam altitudinis, ut Wallisius refert, differentiam fuisse duorum digitorum atque adeo, vix confecisse circiter 1/15 totius gravitatis. Ex quo sequeretur si ad illas minutias attendere velimus, maximam differentiam gravitatis, quae intercedit inter aërem levissimum, et gravissimum in pede cubico fore circite; drachmae dimidiae. Haec enim unciae quin tam decimam circiter conficit partem”.
- 56.
- 57.
Cf. the full title: Admiranda de vacuo, scilicet Valeriani Magni demonstratio ocularis de possibilitate vacui. Eiusdem altera pars demonstrationis ocularis. D. De Roberval Narratio de vacuo. Valeriani responsio ad D. de Roberval. Responsio eiusdem ad Peripateticum Cracoviensem. On it, see Nejeschleba 2017.
- 58.
- 59.
See Magalotti 1666, Esperienza 31. For a commentary, see Favino 2008.
- 60.
- 61.
See Fouke 2003.
- 62.
- 63.
Boyle 1669b, 114.
- 64.
Pascal 1663, 18–21.
- 65.
“It tempts me much to suspect, that Monsieur Paschall never actually made the Experiment, at least with a Tube as big as his Scheam would make one guess, but yet thought he might safely set it down, it being very consequent to those Principles, of whose Truth he was fully perswaded. And indeed, were it not for the impetus, the Quicksilver would acquire in falling from such a height, the Ratiocanation were no way unworthy of him. But Experiments that are but speculatively true, should be propos’d as such, and may oftentimes fail in practise; because there may intervene divers other things capable of making there miscarry, which are overlook’d by the peculator that is wont to compute only the consequences of that particullar thing which he principally considers,” Boyle 1666, 64–65. The writer of the Experimenta mentioned a tube of 20 feet, used by Pascal with regard to another experiment, described in chapter 4 (concerning the equilibrium of solids and fluids).
- 66.
“Torricellius was the first that found the ascension of mercury by the pression of the air: but Pascalius a very ingenious […] Frenchman by reason rather than expressa [sic] pretended to prove that in a tube of 20 foot long the mercury ought to ascend only thus, et thus, by the pression of the water. Boyle first found that he had never tried those experiment, as never being at the bottom of the water thereby to see how far it did ascend or not. Hence he refuteth Pascalius: v[id]e ipsum Boilium,” De Volder 1676–1677, 132r–v.
- 67.
- 68.
“Nachdem auch diese Beschreibung der Königl. Societät in Engelland zu Gesichte kommen, haben sie gleichfals die Würckung untersuchen wollen, und es dahero Herrn D. Dionysio Papino aufgetragen, welcher auch durch Verfertigung der Machine (Fig. IV) befunden, daß das Wasser über 30 Fuß gestiegen. Die Würckung von des Papini Heber, hat Herr Volderus, Prof. Phys. zu Leyden, Anno 1686 öffentlich gezeiget und erklähret, an Cruribus von 3 Schuh lang, hat aber nicht zugeben wollen, daß das Wasser über 30 Schuh hoch steigen könne; weil solches die Kräffte der Atmosphaer nicht zuliessen,” Leupold 1724, 11.
- 69.
- 70.
Cf. De Volder 1676–1678, disputation 4, theses 5–6: “V. Dum itaque, nullum corpus movetur a semet ipso, patet causam motus, qui in uno est corpore, necessario in alio corpore quaerendam esse. An enim, et quo pacto res incorporales motum dare possint inquirere huius loci non est, cum de motibus solummodo agamus corporeis. Ex quo sequitur, id quod movet, necessario quoque moveri. Nemo enim comprehendet, ut opinor, corpus quiescens aliud impellere, movereque ulla posse ratione. Etenim aut distabit corpus quiescens ab eo, quod in motum concitat, aut continget proxime. Prius certe non fiet, quia nulla actio in distans, ut vulgatum et certum habet axioma, dari potest. Neque posterius. Et si enim contingat proximne, cum tamen sua quiete in id non agat, non certe movebit. Nam quid certius, quam eodem ritu ac motus causa est omnis in corporibus mutationis, ita quietem causam esse, cur corpora in eodem statu perseverent. Ex quo illud conficitur, priores species tum attractionis, tum pulsionis, in quibus corpus quiescens aliud vel ad se allicit vel a se propellit, manifestae repugnare rationi. VI. […] Posteriorem vero quod spectat attractionis speciem ea facillima intellectu est, et revera a pulsione non differt, si duo corpora, quorum alterum alterum trahere et tractione ad motum concitare dicitur, vinculo quopiam inter se connexa sint. Nam quid clarius, quam si catenula duo corpora inter se vincta consideres, non posse alterum propelli, quin ea ipsa propulsione moveatur alterum? Quid praeterea manifestius quam hanc attractionem a pulsu non differre? Ut enim hic fiat motus necesse, ut alterum impellatur idque, ea efficacia, qua utrumque impelli et moveri possit. Hanc speciem attractionis si defensam velint, facile patior, sed alteram illam, quae proprie suctio appellatur, qua corpus quod movetur sequitur corpus movens, quocum nullo vinculo, nullaque communione coniunctum est, rerum naturam nullo modo pati firmiter assevero.”
- 71.
Cf. De Volder 1676–1678, disputation 4, thesis 4: “[q]uibus de rebus quid censendum sit, ut constet, considerari primum velim nullum corpus a semet ipso moveri, Nam cum in corporis natura motus non involvatur, cumque quodlibet corpus cuiuscunque figurae aut magnitudinis absque motu concipere valeam, quid certius quam ex nullius corporis natura motum fuere? Si enim ullum corpus sit quod causa sit sui motus, nonne ut effectum causam, sic motus huiusce corporis naturam sequeretur necessario? Cui rei consequens est illud corpus in perpetuum motum iri, nec sine motu concipi posse. Ut enim nulla res sine sua natura, aut esse aut omnino cogitari potest; sic certe nec corpus, si eius naturam sequatur, eamque ideo necessario comitetur motus, sine illo motu aut a se, aut percipi posset. Quae cum de corpore absurdissima sint, patet sane de natura corporis motum non esse, sed omnem, qui inest corpori ab alio, hoc est, a causa externa esse.”
- 72.
Cf. De Volder 1676–1678, disputation 4, thesis 7: “[…] [n]eque difficilis est demonstratio, si consideremus nullum corpus aliud movere posse, nisi cum eo partem quandam fui, quem habet, motus communicet, neque posse cum altero motus sui communicare partem, quin tantundem ei decedat. Si enim corpus quod habeat 10. gradus motus alterum moveat, cum nulla causa sit, quae motum augeat, manifestum est eosdem 10. gradus permanere, et cum antea uni deberentur corpori, nunc duobus illisi m partiri, atque adeo, quantum alteri accedit motus, tantundem priori decedere.”
- 73.
Cf. De Volder 1676–1678, disputation 4, thesis 8.
- 74.
Cf. De Volder 1676–1678, disputation 4, thesis 9. In commenting on Descartes’s criticisms of the possibility of vacuum in Principia II.16, in the series Hamburg 273 of his dictata De Volder mentions the raising of water in pumps up to 33 feet as evidence against the supposed efficacy of the metus vacui: “si concedamus vacuum posse dari, cum illum fingunt eius metum in natura? Illud fieret causis naturalibus, nisi ubiq[ue] velint assignare miracula, profecto stolidissima e[ss]et natura q[uae] produceret id q[uo]d metuit. Si vero dicant id fieri miraculo, possum ego dicere, eodem miraculo muros po[ss]e collabi, etsi fiunt causae naturales, cur illas natura metuit, si non, cur metuit ea q[uae] non sunt. Deinde experientia contrarium evincit, si e[nim] aqua assurgat in antliis propter metum vacui, ergo tandiu assurget, quamdiu natura metuit, sed notum est {embijlus} (belgicae [sic] dictus de {stijger}) non po[ss]e attolli ultra 32 a 33 pedes, neq[ue] ulterius ascendit aqua, unde ra[ti]o cur in fodinis, non una sed pluribus antliis indigeant quarum non indigerent, si vacuum natura metueret, nam si aqua tamdiu ascenderet, quamdiu {embijlus} attolleretur, certum e[ss]et aquam nonnunquam attolli po[ss]e ultra 100 pedes, q[uo]d repugnat ante dictis,” Hamburg 273, 89. None of this prevents Morley, however, from using the term ‘vacuum’ countless times in his notes, nor using the phrase “the vacuum within the cupping-glass, was not sufficient, or strong enough, to draw, retain or bear any longer the weight of the bladder, and its ring,” in experiment 13 (De Volder 1676–1677, 111r).
- 75.
Descartes discussed the matter with Pascal in a meeting on 23–24 September 1647, as reported in a letter by Jacqueline Pascal to Françoise Gilberte Périer, née Pascal (both sisters of Blaise) of 25 September 1647: see Pascal 1923, volume 2, 42–48. Cf. De Raey 1654, 193–197: Rohault 1671, volume 1, 73–74. Rohault devoted an experiment conducted with a syringe to demonstrate his thesis: he supposed that the hole of the syringe is closed, and that the syringe has no pores of any kind. In this case, the external air that would be displaced if the piston were raised, will not find any space to move to, as everything is filled. Therefore, no force in nature can raise such piston. Therefore, if the piston can be raised, we must admit that the syringe has some pores, allowing the passage of a matter subtler than air (discussed in Dobre 2013a). Boyle, in turn, devoted experiment 38 of his Continuation of New Experiments Physico-Mechanical (1669b) to attempt to ascertain the existence of subtle matter, without success: see Boyle 1669b, 127–132. Boyle’s experiment consisted in trying to ascertain whether a sheet, placed around a piston moving in a vacuum, is moved by the subtle matter displaced by the piston. As to this issue, see Chalmers 2009, chapter 6.
- 76.
See De Volder 1676–1678, disputation 3, thesis 4: “[e]t certe quis non miretur, huic demonstrationi, quae tam clare, si credere fas sit, ostendit nec sphaeram ab aëre nec tubum ab aqua premi, experientiam repugnare. Qua stolidus ego (qui, ut ingenue fatear quod res est, ratiocinii huius subtilitatem non assequor, aut si assequar, futilitatem simul deprehendo) perfusus opinabar, non secus ac ille tubus nullam ab aqua pressionem sentit, quando interne aeque aquam ac externe habet, ita quoque sphaeram ab aëre non premi, ubi tam ab interna quam ab externa parte aeque compressum habet aërem. Eademque stoliditate inductus aeque ac demta ex tubo aqua, succedente aëre ipsa aqua multo minus gravi, omni gravitate aquae premitur versus superiora tubus, credidi, demto aëre, succedenteque materia subtiliori ipso aëre multo minus gravi, (si modo ullius gravitatis sit particeps, quod hic non determino) hemisphaerium inferius omni gravitate aëris versus superius propelli. Quod superius cum ab eadem gravitate deorsum pellatur, putavi demens huic hemisphaeriorum ad se in vicem pressioni cohaesionem hanc deberi.”
- 77.
“Hence also he inferred, as above that it was not the metus vacui which did hinder the separation of the cylinders with this dilemma: aut non datur talis metus vacui, et coë[u]nt illa, talis metu [sic], cum non detur, nequit impedire avulsionem cylindrorum. Aut si datur, et ille sit qui impediat disiunctos, iam profecto disiunximus illos, et coë[u]ntes datur via, et modus, introducendi vacuii in na[tur]am: imo fecimus ipsi mo[do] vacuum, q[uo]d utrumq[ue] negare de[be]nt, qui vacuum tantopere abohrrere na[tur]am aiunt,” De Volder 1676–1677, 81v.
- 78.
Cf. De Volder 1676–1678, disputation 4, theses 10–11.
- 79.
See Sect. 4.1.3.1, Four factors of cohesion: vacuum, rest, pressure and entanglement.
- 80.
Reported in Schott 1657, 25–26; see Gorman 1994.
- 81.
Von Guericke 1672, 101–103 and 119.
- 82.
In fact, the cohering glasses or marbles are kept together, not only by the pressure of the air, but also by the Van der Waals’s force, i.e. forces of molecular cohesion. Senguerd performed measurements of the weights sustained by cohering cylinders disposed both vertically and horizontally, claiming that they could sustain the same weight in both positions (see Sect. 4.1.3, De Volder’s ideas on cohesion and divisibility). Locke would use this kind of evidence to criticize the recourse to atmospheric pressure as a factor of cohesion of bodies, which he found in the De gravitate aetheris (1683) of Jakob Bernoulli: see Sect. 6.2.2.3.2, De Volder’s Huygenian theory of weight (and its relation to the idea of cohesion).
- 83.
As I am going to show, his measurements were rather aimed at showing the ways in which fluids press: see Sect. 5.4.1, “[...] les liqueurs pesent suivant leur hauteur”. Notwithstanding this, his performance of experiments with the Magdeburg hemispheres were frequent. According to his Experimenta, once he came to measure the weight sustained by two void hemispheres, or by one hemisphere joined to a plate, he measured it as 700 pounds with hemispheres of a diameter of 8 inches, while by using hemispheres of 6 inches’ diameter he could hang a weight of 425 pounds (in experiments 3 and 27, and disputation 5). De Volder’s performance of the experiments with the hemispheres was also reported by Dalrymple, mentioning the cohesion of hemispheres capable of sustaining a weights of 655 pounds (Dalrymple 1686, 542), and by Van Musschenbroek in his Dissertationes physicae, referring to De Volder’s Disputationes (Van Musschenbroek 1729, 453).
- 84.
De Volder 1676–1677, 112r. De Volder appended to the bladder weights of 7 or 8, 10 and 17.5 pounds.
- 85.
Boyle 1669b, 118–121 and 122–124.
- 86.
“[…] Nobilissimus Robertus Boyle […] in meliorem, experimentorumque tentaminibus peragendis commodiorem formam redegit antliam, multisque accessionibus locupletavit. Hinc et aliis nata occasio inventis nova adiiciendi; novae fabricae, felicioris, atque expediti magis usus, antlias construendi. Donec tandem circa annum 1675 consummatae magis structurae, experimentis minori cum molimine, et periculo peragendis, antlia, ut et apparatus ad illa requisiti, in lucem prodiret. Antliae tubus perpendiculariter erectus erat, et immobilis; inferiori eius parti ad angulum rectum affixus erat minor tubulus, cui recipientia, campanulae, tubi, quaeque porro evacuanda veniebant, adaptabantur. Huius formae antliam illo tempore, ad experimenta molienda, adhibui. Verum, cum et illius: structurae, situs, ac constitutionis antliam multis obnoxiam difficultatibus, atque incommodis; exquisitissimae aëris evacuationi minus convenire experirer, (duplicis enim, quo gaudebat, verticilli usus, plus involvit molestiae, et vitio inficitur facilius, quam unius: binos ad experimenta tentanda requirebat operarios, alterum ad antliam agitandam, et aërem subducendum; qui versurae epistomii vacaret alterum) antliam, quae minorem exigeret apparatum, exquisitiori aëris exhaustui, validiori eius constipationi, pluribus experimentis perficiendis, quibus prior impar erat, inservire aptam, minusque vitiis obnoxiam, excogitavi, atque ut mihi construeretur, anno 1679 cum artifice conveni,” Senguerd 1715, 3–4.
- 87.
De Volder 1676–1677, 106r.
- 88.
Cf. Daumas’s explanation: “[t]he air-pump of Samuel van Musschenbroek. Figure I is a schematic representation of the air-pump. The single cylinder (a) is of brass. The piston A (Fig. II), of almost 9 cm diameter, is of cork, covered with three strips of leather, and held between two brass plates (c). The piston rod consists of an iron rack attached by means of a pin to a small cylinder fixed to the upper of the two brass plates of the piston, there are no valves. After each movement of the piston the stopcock B is opened or closed (Fig. III). In the position illustrated the pump is in communication with the air; in the reversed position, with the receiver. The tube (f) between the pump and the plate E is of copper. Near the receiver is a tap D. The junction of the tube (f) with the tube (e) of the pump is shown in Fig. IV. The interior of the end of the tube (e) is ground away in conical form to receive the conical end of the tube (f). The latter is held in place by means of a screw passing through the collar (h),” Daumas 1972, 86.
- 89.
See Sect. 2.2.3, The mid-1670s clash at Leiden and the foundation of the experimental theatre.
- 90.
De Volder 1676–1677, 107r.
- 91.
Plato 1892, volume 3, 501–502. Cf. Timaeus, 79a–e.
- 92.
Descartes 1982, 55–56.
- 93.
“Aër itaque in inspiratione pectus ingreditur, non propter fugam vacui attractus; cum attractio ob illius fugam nulla detur, nec dari possit: sed quia thoracis dilatatione vicinus aër […] de loco deturbatur, […] et cum omnia corporibus plena sint […] necessario aër a pectore et alio aëre sic pulsus, in thoracem dilatatum per asperam arteriam adigitur,” Regius 1640, thesis 9. Also in Regius 1654, 276–277. “Sciendum itaque, in rerum natura vel dari vacuum, et haec praetensa explicatio per fugam vel metum vacui, cessabit; vel non dari, id est, omnia corporibus plena esse. Si plena sint (uti revera sunt) non potest in universo dari locus aliquis novus, nisi qui vel aëris, vel alterius (locum complentis) materiae, eam recipiat quantitatem, quae capacitati ipsius sit commensurata. Itaque, thorax in maiorem molem distendi nequit, nisi tanta aëris portio, quanta ampliori isti (quem per distentionem suam, maiorem quam antea, in universo occupat) loco exacte respondet, in pulmones impellatur,” Van Hogelande 1646, 264–265. Regius’s and Van Hogelande’s texts were owned by De Volder (see Bibliotheca Volderina, 3, 10). Swammerdam, in his Tractatus physico-anatomico-medicus de respiratione usuque pulmonum (1667) (dedicated to Melchisédech Thévenot), provided a similar explanation: “[i]n inspiratione igitur pulmones explicantur, quia aër tum a pectore sursum moto, tum etiam ab extrorsum propulso abdomine, de loco propulsus, in ipsos impellitur. Minime vero movetur in pulmones, seu eos ingreditur aër, quia ipsi primo explicantur seu extenduntur; cum in tantum explicentur ac extendantur pulmones, in quantum a propulso abdomine, atque a dilatato simul pectore, aër de loco movetur ac in ipsos impellitur,” Swammerdam 1667, 17. Please note that in his Traité de l’homme (posthumous editions 1662 and 1664), chapter 16, Descartes does not focus on the movement of air in and out the lungs, but only on the causes of the movement of the thorax. On the ‘Cartesian circle’, see Ragland 2016; Schmaltz 2016, chapter 5.
- 94.
“L’eau des pompes monte avec le piston qu’on tire en haut, à cause que n’y ayant point de vide en la nature, il ne s’y peut faire aucun mouve ment qu’il n’y ait tout un cercle de corps qui se meuve en même temps,” AT II, 588–589. See Nonnoi 1994.
- 95.
Cornelio 1663, 122–123.
- 96.
Or, as Wiesenfeldt has put it, commenting upon this experiment: “[t]atsächlich erschienen Descartes und ,die Cartesianer’ in de Volders Experimentalvorlesungen nur sehr selten und wurden dann beständig dafür kritisiert, daß sie Phänomene, die de Volder vom Luftdruck verursacht sah, anders zu erklären versuchten,” Wiesenfeldt 2002, 115.
- 97.
In commenting upon Principia II.33 in his dictata, for instance, De Volder does not deal with the problem of metus vacui: rather, in both the series he criticizes the atomist theory (ascribed to Epicurus and Lucretius) according to which movement is not possible in a plenum; against this theory, De Volder opposes the idea that all movement is ultimately circular: Hamburg 273, 98–101; cf. Hamburg 274, 41–42.
- 98.
See supra, n. 52.
- 99.
Boyle 1660, 246–247.
- 100.
“[…] dum suctor retrahitur, quanto relictus locus major fit, tanto minus loci relinquitur aëri externo, qui retrusus a suctore moto versus externa, proximum sibi aërem similiter movet, et hic alium, et sic continue: ita ut necesse sit aërem tandem compelli in locum desertum a suctore, et intrare inter superficiem suctoris convexam et cylindri concavam. Supposito enim aëris partes esse infinite subtiles, impossibile est ut via illa, qua retrahitur suctor illae non se insinuent. […] Esto locus ille relictus plenus […] aëre puro, id est […] corpore aethereo,” Hobbes 1668, Dialogus physicus, sive de natura aëris, 12.
- 101.
Indeed, as I show below, it is discussed, through Boyle’s mentioning of it, in his dictata: see infra, n. 296.
- 102.
Cf. Boyle’s Examen of Mr. T. Hobbes his Dialogus Physicus de Natura Aeris (1662b): “Mr. Hobbs proves the space deserted by the Quicksilver or the Air to have no Vacuity, because according to his Supposition the World is full; and not by any sensible Phaenomena that prove the Space in Question to be perfectly full […]. For no less Fulness is requisite to the truth of his Hypothesis […]. From all which it seems probably deducible, That ’tis a very hard thing, by. Mr. Hobbs’s way of managing the Controversie, to prove that there can be no Vacuum, But as for the Cartesian’s more subtile and plausible way of asserting a Plenum, it concerns me not here to Dispute against it, or Declare for it,” Boyle 1662b, 8–9. As to the Boyle-Hobbes controversy, see Shapin and Schaffer 1985.
- 103.
“Respirationis plane aliud est negotium, sed cum hic de ea ex professo agere non possimus, quia nervos nondum vidimus, attendemus ad illa solummodo, quae experientia nos docet; videmus enim hic, ventrem intumescere, quod dicimus fieri ab aëre: sed quomodo ille hoc facit? Quia aër primo a ventre et thorace inflatis propellitur, et cum vacuum dari repugnet, debet ille aër ingredi pulmones, eosque inflat et deprimit sua gravitate, hi diaphragma, hoc viscera abdominis, illa ventrem, et sic porro. Alias causas respirationis videbimus, cum ad nervos respirationi inservientes pervenerimus: tunc videbimus, quod pulmones sint tantum passiva respirationis instrumenta, qui aërem propulsum solummodo excipiunt, eique repulso exitum concedunt. Activa vero instrumenta respirationis, dicemus, esse musculos tam abdominis, quam diaphragmatis, qua de re nemo medicorum unquam antehac cogitavit,” Craanen 1689, 264–265.
- 104.
Cf. mss. Sloane 1274–1276.
- 105.
“Prima sit, in fluido quovis stagnante unamquamque fluidi superficiem horizonti parallelam qualiter premi. Altera vero, si superficies quaevis fluidi horizonti parallela inaequaliter prematur, partem magis pressam expellere eam, quae premitur minus. Quae sane leges eius sunt evidentiae, ut eas Archimedes supponere sine ulla demonstratione veritus non fuerit. Sic enim ait in libro περὶ τῶν ὀχουμένων. ὑποτιθέσθω τοῦ ὑγροῦ τοι αύταν φύσιν εἶμεν ὥστε τῶν αὐτοῦ μερέων ἐξ ἴσου κειμένων, καὶ συνεχομένων ἐπ᾽ ἀλλήλων, ἔλαττον πεπιεσμένον, ὑπὸ τοῦ μᾶλλον πεπιεσμένου ἐκβάλλεσθαι, ponatur fluidi eam esse naturam, ut partibus eius aequaliter iacentibus, et continuatis inter sese, pars minus pressa a magis pressa expellatur. Hisque iisdem fundamentis usi sunt Galilaeus, Stevinus, Boylaeus in hydrostaticis, uno verbo omnes rerum Hydraulicarum scriptores,” De Volder 1676–1678, disputation 2, thesis 2; cf. Archimedes and Rivault 1615, 491: “Υποθεσiσ A. Υποτιθέσθω τοῦ ὑγροῦ τοιούταν φύσιν εἶμεν, ὥστε τῶν αὐτοῦ μερέων ἐξ ἴσου κειμένων, καὶ συνεχέων ἐπ᾽ ἀλλἠλων, έλαττον πεπιεσμένον, ὑπὸ τοῦ μᾶλλον πεπιεσμένου ἐκβάλλεσθαι. […] Positio I. Ponatur humidi eam esse naturam, ut partibus ipsius aequaliter iacentibus, et continuatis inter sese, minus pressa a magis pressa expellatur […].” De Volder also quotes the Greek version of the postulate, which Rivault had provided in his 1615 edition (which includes variations with respect to those of Tartaglia and Commandino), by re-translating the postulate from Latin into Greek. Archimedes’s treatise on floating bodies (Περί τών οχουμένων), indeed, was until the discovery of the Archimedes’s palimpsest by Johan Ludwig Heiberg (1906) known only in the Latin translation provided by William of Moerbeke, on which Tartaglia and his followers based their edition. Another important seventeenth century edition was the Latin edition of Isaac Barrow (1675). As I am going to show (see Sect. 5.3.2, A theory of matter for floating bodies), De Volder also relied on Rivault’s commentary on the postulate.
- 106.
Cf. disputation 2, thesis 4: “[s]uperficie imaginamur partibus pressis inaequaliter sese res habet ac cum duabus lancibus ex eadem libra suspensis. Ut enim earum altera non descendit nisi ascendente altera, ita in hoc vase stagnantis aquae, altera eius pars non labetur deorsum, nisi altera sursum moveatur. Ut autem ea lanx necessario descendit, alteramque assurgere efficit, quae maiori premitur pondere, sic sane et ea pars aquae, quae maiori efficacia deorsum pellitur, descendit, et per consequens ad ascensum cogit alteram aquae partem, quae utpote imbecillior huic alterius partis descensui non est resistendo. Ut denique tum demum statera in aequilibrio haeret, quando in utraque lance eadem est pressio, sic et aquae Superficies tunc demum in eadem ubique consistet altitudine, quando omnes eius partes aequaliter pressae sunt, nec potet idcirco altera alteram ex loco, in quo est, expellere.”
- 107.
“Et sane huius effati veritas ex fluidorum natura fluit evidentissime. Nonne enim ea horum proprietas est, ut vel minimae cuivis cedant pressioni? Immittat quis sine ulla vi aut impetu manum in aquam; nonne confestim aqua cedit manui, et contra suam, ut vulgo creditur, naturam adcendit?” De Volder 1676–1678, disputation 2, thesis 3.
- 108.
“Positio III. Humidum omne pondus habere. Σκολιον. Praeter Archimedis positiones, et hanc addendam putavimus, nequis iis quae dicentur deinceps inficias ierit. Quod autem pondus habeat humidum omne, et grave sit, ipsimet sensus docent, ut non sit alio recurrendum in hac veritate determinanda. Nam ipsemet aër gravis est: quod utribus inflatis deprehenditur, qui si aliquando Aeolios Ithacis inclusimus utribus Euros, ut habet Poeta, gravius pendent quam si vacui aëre sint, etiam teste Aristotele […] cap. 4. l. 4 De caelo,” Archimedes and Rivault 1615, 492.
- 109.
For a discussion, see Chalmers 2017, 2.
- 110.
- 111.
“Proposition 4. Of solids one which is lighter than the fluid, when thrown into the fluid, will not sink down altogether, but a portion of it will project above the surface of the fluid. […] Proposition 5. Of solids one which is lighter than the fluid, when thrown into the fluid, will sink down until a volume of the fluid equal to the volume of the immersed portion has the same weight as the whole solid,” Dijksterhuis 1987, 375–376. Cf. Archimedes and Commandino 1565, 2–4; Archimedes and Rivault 1615, 496. See Fig. 5.2, Archimedes and Rivault 1615, 496.
- 112.
“Sit humidum ABCD et aliqua magnitudo FE eadem mole levior quam humidum: et ipsius quidem FE pars BE ponderet ut HI. Humidum vero molis quidem ipsius BE ponderet ut GI. Tandem tota FE gravitet eodem pondere GI. […] Et quoniam cuilibet ponderi in premendo resistentiae est: quanta erit GH gravitas obnitetur, prementi vi, et demergenti in humidum magnitudinem FE ita ut si vis illa cessaverit, resiliat ex humido FE magnitudo eadem pressa gravitate GH quae quo maior fuerit eo celerior erit repulsio, donec CF pars, qua magnitudo levior est, ex humido sese extulerit, quod erat probandum,” Archimedes and Rivault 1615, 497. See Fig. 5.12, Archimedes and Rivault 1615, 497. Cf. Commandino’s version: “[s]it enim magnitudo a levior humido: et sit magnitudinis quidem a gravitas b: humidi vero molem habentis aequalem ipsi a, gravitas sit bc, demonstrandum est magnitudinem a in humidum impulsam tanta vi sursum ferri, quanta est gravitas c. Accipiatur enim quaedam magnitudo, in qua d habens gravitatem ipsi c aequalem. Itaque magnitudo ex utrisque magnitudinibus constans, in quibus ad, levior est humido: nam magnitudinis quidem quae ex utrisque constat gravitas est bc; humidi vero habentis molem ipsis aequalem gravitas maior est, quam bc: quoniam bc gravitas est humidi molem habentis aequalem ipsi a. Si ergo dimittatur in humidum magnitudo ex utrisque ad constans; usque eo demergeretur, ut tanta moles humidi, quanta est pars magnitudinis demersa eandem, quam tota magnitudo gravitatem habeat. Hoc enim iam demonstrandum est. Si autem superficies humidi alicuius abcd circunferentia. Quoniam igitur tanta moles humidi, quanta est magnitudo a gravitatem habet eandem, quam magnitudines ad: perspicuum est partem ipsius demersam esse magnitudinem a; reliquam vero d totam ex humidi superficie extare. Quare constat magnitudinem a, tanta vi sursum ferri, quanta deorsum premitur ab eo, quod est supra; videlicet a d, cum netura ab altera expellatur, sed d fertur deorsum tanta gravitate, quanta est c: ponebatur enim gravitas eius, in quo d ipsi c aequalis,” Archimedes and Commandino 1565, 4–5. See Fig. 5.13, Archimedes and Commandino 1565, 4v. Cf. Dijksterhuis 1987, 376. This theory can be exemplified by what we usually know as Archimedes’s principle, viz. “any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.” A formulation which was never provided by Archimedes himself, but which is the most widely present in contemporary textbooks of physics. I have taken it from Chacón Rebollo and Lewandowski 2014, 30.
- 113.
“Sumamus cylindrum concavum aëre plenum, altero orificio apert, altero obturato in aquam mitti, orificio obturato versus inferiora posito, nonne manifestum est, si hic tubus cylindricus, ad 5. pedes infra aquam deprimatur, superiori orificio aperto extra aquam eminente, magna vi, imo omni gravitate istorum 5. pedum ab aqua subiacente versus superiora premi oportere? Quod ipsum certe fieri non posset, nisi aqua proxime inferius: tangens orificium et fundum Tubi, omni vi et gravitate lateralis aquae versus superiora premeretur? Si enim nulla gravitate, prensioneve deorsum rueret aqua, quae à lateribus est, nec illa aqua, quae fundo subiacet, ulla vi superiora versus deduceretur,” De Volder 1676–1678, disputation 2, thesis 5.
- 114.
“Ex quo id notari velim, in fluidis corporibus motum gravitatis quasdam deprimendo fluidi partes alias attollere eadem vi, qua reliquas deprimit, unde conficitur non omném superiora versus motum gravitatem tanquam causam excludere,” De Volder 1676–1678, disputation 2, thesis 5.
- 115.
As Morley reports them in Latin, it is probable that he wrote them down as De Volder uttered them.
- 116.
In the sheets extant at Marburg, ending with a letter dated 11 May 1695, and describing also the collision apparatus, one can find the description of the use of the cube: “[l]’usage de cube. Mette le cube dans un vaisseau d’eau avec le tuyaux a en haut, et mette autant de grelle de plomb {…} petites pieces de fil de cuivre, par le tuyaux a dans le <{…}> cube jusque a quand que la superficie de l’eau est egale avec la poincte de cube aupres b. C’est evident que cette cube quand il est avec la pointe egale avec l’eau qu’il fait rejetter autant d’eau, qu’il est grande, otez le cube et pese le, autant qu’il pese, autant pese un demy pied d’eau. Cela est le plus exact maniere pour peser l’eau. En un coste de cette cube est un vis pour ouvrir le cube quand il est trop pesant pour oter le boules,” Hessisches Staatsarchiv Marburg, file UniA 305a Nr 5947, 13–14. See Fig. 5.14, Hessisches Staatsarchiv Marburg, file UniA 305a Nr 5947, 13.
- 117.
The cube of water weighed 7 pounds and 14½ ounces, as seen above. Archimedes’s postulate is used to justify the condition of equilibrium between the cube of brass and a certain volume of water. Cf. the text of experiment 15: “[t]his he explicated with the comparison of an exact balance, or pair of scales. Presupposing that the element of water, was a thing, so easily loco mobilis, so easily fluid one way, as other, and so easily giving way to the least poise, or weight, as the exactest pair of scales, could be: the which he said was grounded for a principle in hydrostatic matters among the ancients: nim[irum] aërem circumambientem premere superficiem aquae s[ecun]d[um]m o[mn]es p[rop]ter aequale: nisi ii ita prement illa loco cederet, et fieret commotio, et perturbatio, et inaequalitas in superf[ici]e acquae, cum {I} nimirum {violet9} cedat imaginabili,” De Volder 1676–1677, 115r. In his Tweede deel op de Wiskonstige rekening (1680), Dirk Rembrandtsz van Nierop reported that De Volder weighed ½ cubic foot of water, namely 7 pounds and 14½ ounces: see Van Nierop 1680, 156.
- 118.
See his Dissertationes Taurinenses epistolicae physico-medicae (1712), where is provided a summary of the experimental lectures of Pierre Polinière, among which is mentioned De Volder’s ascertainment of the weight of 1 cubic inch of water: “Tent. 21. […] [n]os simul incidenter viam ostendimus, qua Clar. Volderus in specificam aquae et dehinc aliorum corporum gravitatem inquisivit, per aequilibrationem scil. cubi pollicaris aenei exacte aequilibrati per plumbeos globulos immissos cum aqua et c. quae plenius tum deducta sunt,” Camerarius 1712, 362. The experiment cannot be found among Polinière’s Expériences de physique (1709). Most probably, Polinière referred to the usual cube of ½ foot side.
- 119.
Cf. experiment 17: “he inferred the same which in the first hydrostatic experiment: viz. q[uo]d tantumdem aquae exacte o[mn]i[n]o illud vas loco suo pepulerat, quantum ipsum vas ponderabat: et coë[u]ntes in o[mn]ibus granib[u]s quae in liquida immittunt, tantumdem sc[ilicet] liquidi illa loco suo pellere, qua[nt]um ipsa ponderent. Which by the by he said was the only way, and fundament for the gaging of ships or measuring how much weight they carry et cetera,” De Volder 1676–1677, 118r. This experiment is comparable to experiment 15: in experiment 17, however, De Volder used glass containers instead of the cube of brass, and filled them with sand.
- 120.
“This experiment was made with mercury: relating to the former ones, viz. the equiponderosity of material things with water, or rather as Volder printed these days in some theses which he presided, omnia corpora, quae innatant liquori, t[antu]m h[ab]ent ponderis, quantum liquor a corpore suo ex loco expulsus ponderat. As also this experiment did relate, unto this thesis likewise then printed by him: aquam, et aërem esse corpora gravia, cum r[ati]o, tum exper[ienti]aa [sic] docet, ac proinde falsum est, elementa in suis locis non esse gravia,” De Volder 1676–1677, 130r–v.
- 121.
See Sect. 5.3.4, Stevin’s ‘geometrization’ of hydrostatics, and Boyle’s experimental approach.
- 122.
De Volder 1676–1677, 127v–129v.
- 123.
De Volder 1676–1677, 120r. A “big [writing] slate” is indeed mentioned in the 1705 inventory of the theatre.
- 124.
De Volder 1676–1677, 120v.
- 125.
See Crombie 1996, chapter 10. A set of balls aimed at performing this experiment was sold by Johannes Joosten van Musschenbroek, who duly describes this method to Johannes Dorstenius in a letter of 13 March 1702: Hessisches Staatsarchiv Marburg, file UniA 305a Nr 5947, unnumbered page. This letter is extant in two copies (apparently by two different hands).
- 126.
It is worth noting that the reporter provides wrong data on the weight that the different bodies have in water. Indeed, according to the manuscript, in water the ball of brass weighs 5 ounces, 4 drams, 5 grains; that of lead weighs 5 ounces, 6 drams, 5 grains; their league weighs 5 ounces, 4 drams, 3 grains. However, in water the ball of brass, which has the lowest specific weight, would lose more weight than the league, which is specifically heavier than the brass, and lighter than the lead.
- 127.
Cf. the text quoted supra, n. 105.
- 128.
Galileo, Pascal and Boyle repeatedly used the idea of specific gravity or weight (for Galileo, gravità in specie), a notion which is also theorized in Rivault’s commentary on Archimendes – namely, in his scholium to the postulate that Rivault added to the original text (see supra, n. 108): “[c]aeterum hoc humidi pondus, non tam metimur quantitate molis, quam genere naturae: nam, ut ait Vitruvius [De architectura, book 7, chapter 8], non amplitudine ponderis, sed genere singularum rerum gravitatem esse, non est negandum. Et hoc deinceps erit animadvertendum cum dicemus aliquod grave se habere ad humidum in gravitate in aliqua ratione. Sensum enim erit, de densitate et rei expositae naturali compactione, secundum quam aestimamur ipsius humidi gravitas, et cuius causa res ipsa et humidum paris molis, vel differunt vel aequantur in ponderositate,” Archimedes and Rivault 1615, 492. Stevin used this concept in the third definition of his De hydrostatices elementis (1605, first Dutch edition as De beghinselen des waterwichts, 1586): “[m]ateria ponderosius corpus, quod magnitudine aequalibus praeponderat,” Stevin 1605, 111.
- 129.
In what follows, I assume a systematic rather than a chronological perspective on these topics. For a more comprehensive account of the historical evolution of the theories of floatation between the sixteenth and seventeenth centuries, see Chalmers 2017.
- 130.
For a full account, see Palmieri 2005.
- 131.
“Sunt et caussae gravitatis, aut levitatis per se: huiusmodi […] sunt naturae elementorum, quae quattuor modis variatae efficiunt et quattuor simplicia corpora, et quattuor item affectiones, sive habilitates ad motum quae per gravitatem, et levitatem menti nostrae subiiciuntur: nam gravia levia quae sunt corpora simplicia, et singula ex his, vel absolute, vel aliqua ex parte, sed et multae sunt aliae caussae comites propter quas haec enatant, illa merguntur. Principem vero locum inter ipsas corporis figura sibi vendicavi: illa n[am] quae latiora sunt, per aërem difficilius cadunt, aegriusq[ue] merguntur in aquis, et si terrae plurimum habent, veluti ferrum. […] Ac primi quidem caussas explicat Arist. hae vero resolvuntur in duo principia patiens et efficiens; patiens autem est corpus continuum, quod dividitur ab eo quod per ipsum fertur; illud aute[m] humidum esse oportet; na[m] sic facile ab alio terminos accipit: prout igitur magis minusve dividuum fuerit: sic et magis minusve aditum praebet corporib[us] quae feruntur: ita per aërem citius, q[uam] per aqua aliquid fertur; propterea q[uia] aqua minus humida est, et terminatur difficilius, q[uam] aër, quo plus fuerit, aut minus, ita quoq[ue] facilius, aut aegrius se dividi patitur,” Buonamici 1591, 491. On Aristotle’s definition, see De generatione et corruptione, 329b30–31.
- 132.
“Huc accedit q[uod] perspicue veteres confutavit Arist. [cf. De caelo, book 1] quia corporum levium motus sursum ad suum locum ex graviorum pulsione fieri contenderent, et profecto videret illud necessario consequi, ut omnia corpora naturalia forent gravia secundum naturam, nulla omnino levia, {q[ui]n} prorsus evenire idem, si aër et ignis in ima aquae sede collocarent. Et quamvis ab Arist. pulsio concedat in elementis, unde terrae partes contrahant in orbem, non est, mea quidem sententia, talis, ut de suo loco naturali gravia pellat, sed ut magis centrum versus deducat,” Buonamici 1591, 494.
- 133.
“[L]a cagione per la quale alcuni corpi solidi discendono al fondo nell’acqua, esser l’eccesso della gravità loro sopra la gravità dell’acqua, e, all’incontro, l’eccesso della gravità dell’acqua sopra la gravità di quelli esser cagione che altri non discendano, anzi che dal fondo si elevino e sormontino alla superficie. Ciò fu sottilmente dimostrato da Archimede, ne’ libri Delle cose che stanno sopra l’acqua. […] Io con metodo differente e con altri mezzi procurerò di concludere lo stesso, riducendo le cagioni di tali effetti a’ principii più intrinsechi e immediati,” Galileo 1890–1909, volume 4, 67.
- 134.
“[…] intendendo d’un vaso di terra, inferisce contro Archimede così: Tu di’ che i solidi che galleggiano, sono men gravi dell’acqua; questo vaso di terra galleggia; adunque tal vaso è men grave dell’acqua, e però la terra è men grave dell’acqua. Se tale è la illazione, io facilmente rispondo, concedendo che tal vaso sia men grave dell’acqua, e negando l’altra conseguenza, cioè che la terra sia men grave dell’acqua. Il vaso che soprannuota, occupa nell’acqua non solamente un luogo eguale alla mole della terra della quale egli è formato, ma eguale alla terra e all’aria insieme nella sua concavità contenuta; e se una tal mole, composta di terra e d’aria, sarà men grave d’altrettanta acqua, soprannoterà, e sarà conforme alla dottrina d’Archimede: ma se poi, rimovendo l’aria, si riempierà il vaso d’acqua, sì che il solido posto nell’acqua non sia altro che terra, né occupi altro luogo che quello che dalla sola terra viene ingombrato, allora egli andrà al fondo, per esser la terra più grave dell’acqua; e ciò concorda benissimo con la mente d’Archimede,” Galileo 1890–1909, volume 4, 81–82; cf. Buonamici 1591, 494–497.
- 135.
“[…] quello che in questo caso discende e vien locato nell’acqua, non è la sola lamina o tavoletta d’ebano, o di ferro, ma un composto d’ebano e d’aria, dal quale ne risulta un solido non più in gravità superiore all’acqua, come era il semplice ebano o ’l semplice oro. E se attentamente si considererà, quale e quanto sia il solido che in questa esperienza entra nell’acqua e contrasta con la di lei gravità, scorgerassi esser tutto quello che si ritrova sotto alla superficie dell’acqua; il che è un aggregato e composto d’una tavoletta d’ebano e di quasi altrettanta aria, una mole composta d’una lamina di piombo e dieci o dodici tanti d’aria,” Galileo 1890–1909, volume 4, 98–99.
- 136.
“[…] parermi che ’l Sig. Buonamico imponga ad Archimede e deduca dal suo detto più di quello ch’egli ha proposto e che dalle sue proposizioni si può dedurre: avvegnaché Archimede né neghi né ammetta la leggerezza positiva, né pur ne tratti, onde molto meno si debbe inferire ch’egli abbia negato che ella possa esser cagione e principio del moto all’insù del fuoco o d’altri corpi leggieri; ma solamente, avendo dimostrato come i corpi solidi più gravi dell’acqua discendano in essa secondo l’eccesso della gravità loro sopra la gravità di quella, dimostra parimente come i men gravi ascendano nella medesima acqua secondo l’eccesso della gravità di essa sopra la gravità loro; onde il più che si possa raccorre dalle dimostrazion d’Archimede è che, sì come l’eccesso della gravità del mobile sopra la gravità dell’acqua è cagion del suo discendere in essa, così l’eccesso della gravità dell’acqua sopra quella del mobile è bastante a fare che egli non discenda, anzi venga a galla, non ricercando se del muoversi all’in su sia o non sia altra cagion contraria alla gravità. […] Sieno dunque indirizzate l’armi del Sig. Buonamico contra Platone e altri antichi, li quali, negando totalmente la levità e ponendo tutti li corpi esser gravi, dicevano il movimento all’insù esser fatto non da principio intrinseco del mobile, ma solamente dallo scacciamento del mezo; e resti Archimede con la sua dottrina illeso, poi che egli non dà cagion d’essere impugnato,” Galileo 1890–1909, volume 4, 84–85.
- 137.
“[…] io piglio dalla scienza meccanica due principii. Il primo è, che pesi assolutamente eguali, mossi con eguali velocità, sono di forze e di momenti eguali nel loro operare. Momento, appresso i meccanici, significa quella virtù, quella forza, quella efficacia, con la quale il motor muove e ’l mobile resiste; la qual virtù depende non solo dalla semplice gravità, ma dalla velocità del moto, dalle diverse inclinazioni degli spazii sopra i quali si fa il moto, perché più fa impeto un grave descendente in uno spazio molto declive che in un meno. […] Come, per esemplo, due pesi d’assoluta gravità eguali, posti in bilancia di braccia eguali, restano in equilibrio, né s’inclina l’uno alzando l’altro; perché l’egualità delle distanze di ambedue dal centro, sopra il quale la bilancia vien sostenuta e circa il quale ella si muove, fa che tali pesi, movendosi essa bilancia, passerebbono nello stesso tempo spazii eguali, cioè si moverieno con eguali velocità, onde non è ragione alcuna, per la quale questo peso più di quello, o quello più di questo, si debba abbassare; e per ciò si fa l’equilibrio, e restano i momenti loro di virtù simili ed eguali. Il secondo principio è, che il momento e la forza della gravità venga accresciuto dalla velocità del moto; sì che pesi assolutamente eguali, ma congiunti con velocità diseguali, sieno di forza, momento e virtù diseguale, e più potente il più veloce, secondo la proporzione della velocità sua alla velocità dell’altro. Di questo abbiamo accomodatissimo esemplo nella libra o stadera di braccia diseguali,” Galileo 1890–1909, volume 4, 68. On Galileo’s theory of momento, see Galluzzi 1979.
- 138.
“[…] la mole dell’acqua che s’alza nell’immersion del solido, o che s’abbassa nell’estrarlo, non è eguale a tutta la mole del solido che si trova demersa o estratta, ma a quella parte solamente, che nell’immersione resta sotto il primo livello dell’acqua, e nell’estrazione riman sopra simil primo livello,” Galileo 1890–1909, volume 4, 72.
- 139.
“Séguita in oltre che, posto un solido men grave dell’acqua in un vaso di qual si voglia grandezza, e circunfusagli attorno acqua sino a tale altezza, che tanta acqua in mole, quanta sia la parte del solido sommersa, pesi assolutamente quanto tutto il solido, egli da tale acqua sarà giustamente sostenuto, e sia l’acqua circunfusa in quantità immensa o pochissima. […] Il che a molti potrebbe, nel primo aspetto, aver sembianza di grandissimo paradosso, e destar concetto che la dimostrazione di tale effetto fosse sofistica e fallace; ma per quelli che per tale la reputassero, c’è la sperienza di mezo, che potrà rendergli certi: ma chi sarà capace di quanto importi la velocità del moto, e come ella a capello ricompensa il difetto e ’l mancamento di gravità, cesserà di maravigliarsi, nel considerare come all’alzamento del solido M pochissimo s’abbassa la gran mole dell’acqua ABCD, ma assaissimo ed in uno stante decresce la piccolissima mole dell’acqua ENSF come prima il solido M si eleva, benché per brevissimo spazio; [...] E per amplissima confermazione e più chiara esplicazione di questo medesimo, considerisi la presente figura [...] nella quale al vaso larghissimo EIDF, vien continuata l’angustissima canna ICAB, ed intendasi in essi infusa l’acqua sino al livello LGH; la quale in questo stato si quieterà, non senza meraviglia di alcuno […]. Ma tal meraviglia cesserà, se noi cominceremo a fingere l’acqua GD essersi abbassata solamente sino a QO, e considereremo poi ciò che averà fatto l’acqua CL. la quale, per dar luogo all’altra che si è scemata dal livello GH sino al livello QO, doverà per necessità essersi nell’istesso tempo alzata dal livello L sino in AB, ed esser la salita LB tanto maggiore della scesa GQ, quant’è l’ampiezza del vaso GD maggiore della larghezza della canna LC, che in somma è quanto l’acqua GD è più della LC. Ma essendo che il momento della velocità del moto in un mobile compensa quello della gravità di un altro, qual meraviglia sarà se la velocissima salita della poca acqua CL resisterà alla tardissima scesa della molta GD?” Galileo 1890–1909, volume 4, 76–77.
- 140.
See, for instance, his treatment of Archimedes’s proposition 5, which I summarized above: “[h]is stantibus apparet XO et OP humidi partes ex aequo positas esse et continuatas, non premi vero similiter, quod XO premitur a magnitudine EHTF et a residuo pyramidis. OP vero premitur a solido RSQV, quod est aequale ipsi BHTC parte ipsius EHTD, et ab altero residuo superiori residuo aequali. Magis ergo premitur OP. Itaque altera pars OP ab ea pelletur. Non igitur consistet humidum, quod tamen consistere ponebatur. Proinde ex humidi superficie nihil extat ipsius EHTF magnitudinis. Verum neque demensa descendet inferius: necesse est enim, ut in descensu pariter expellantur: at ibi solum expulsio succedit, ubi una pars premitur magis, quam proxima; sed hic cum solida magnitudo et humidum sint aeque gravia, nulla pressio maior, propterea neque pulsio, neque descensus igitur,” Buonamici 1591, 493. See Fig. 5.1, Archimedes and Commandino 1565, 4r.
- 141.
“[…] ab experientia significamus nempe vas, quod caeteroquin eminebat in aquis, ubi plenum aqua fuerit, nihilominus ad imum proficisci, quod sane difficiles extricatus habet; q[ui]n neque id vasis naturae po[ssi]t adscribi, quod {et} si dissolvatur ex aqua extabit; nec illae aquae, quae recipitur, cum ipsa propter aequalem potestatem, quam habet cum reliqua, in eadem superficie manere debeat. […] Arbitror […] quam aqua per illud vas, a quo continetur, a toto segregata est: ideoque totius beneficio non {polles}, tanquam aliud quid, ab aqua diversum, per proprium pondus habet, et reliquam aquam, tanquam medium per quod feratur, opprimit, simul dividit, neque vas, ut lignum simpliciter descendit, sed tanquam unum quid cum eo factum, quod continet, in aqua pondus habet figurae beneficio quae multum alieni comprehendit,” Buonamici 1591, 494–495.
- 142.
“Io non dico già che non si possano, di legno che per sua natura galleggi, far barche, le quali poi, piene d’acqua, si sommergano; ma ciò non avverrà per gravezza che gli sia accresciuta dall’acqua, ma sì bene da’ chiodi e altri ferramenti, sì che non più s’avrà un corpo men grave dell’acqua, ma un composto di ferro e di legno, più ponderoso d’altrettanta mole d’acqua. Cessi per tanto il Sig. Buonamico di voler render ragioni d’un effetto che non è,” Galileo 1890–1909, volume 4, 83.
- 143.
“Può ben l’ampiezza della figura ritardar la velocità, tanto della scesa, quanto della salita, e più e più secondo che tal figura si ridurrà a maggior larghezza e sottigliezza: ma ch’ella possa ridursi a tale, ch’ella totalmente vieti il più muoversi quella stessa materia nella medesima acqua, ciò stimo essere impossibile. […] Che se l’incremento e ’l decremento della tardità o velocità non avessero altro rispetto che alla grossezza o sottilità de’ mezzi, ogni mobile, che scendesse per l’aria, scenderebbe anche per l’acqua: perché qualunque differenza si ritrovi tra la crassizie dell’acqua e quella dell’aria, può benissimo ritrovarsi tra la velocità dello stesso mobile nell’aria e qualche altra velocità; e questa dovrebbe esser sua propria nell’acqua: il che tuttavia è falsissimo,” Galileo 1890–1909, volume 4, 88 and 130.
- 144.
“Ricevasi, dunque, per vera e indubitata conclusione, che l’acqua non ha renitenza alcuna alla semplice divisione, e che non è possibile il ritrovar corpo solido alcuno, di qualunque figura esser si voglia, al quale, messo nell’acqua, resti dalla crassizie di quella proibito e tolto il muoversi in su o in giù, secondoché egli supererà o sarà superato dall’acqua in gravità, ancorché l’eccesso e differenza sia insensibile,” Galileo 1890–1909, volume 4, 108.
- 145.
Problemata, 931a38–931b8.
- 146.
“Ratio positionis seu assumpti huius a natura, qualitatibusque humidi dependent. Ea enim ipsius natura est, ut facile mobile sit: tum ut facile cedat, quia non partibus constat arcte compactis, quin potius leviter divisibilibus, similis fere aëri, cuius flexibilitatis ergo, dixit Aristoteles, ἑπ’ οὔτε ἐστὶν ἓν σῶμα συνεχές. Propterea si prematur quocumque modo etiam levissime, facile […] disiungitur […]. Tum si motu […] extima illa superficies facta […] inaequalis, nativo pondere restituetur, donec ad aequilibrium ierit. Imo id acciderit […] si totius corporis non disiuncta fuerit series,” Archimedes and Rivault 1615, 491. Cf. Problemata, 931b, 4–5.
- 147.
De Volder 1676–1677, 115r.
- 148.
“Et sane huius effati veritas ex fluidorum natura fluit evidentissime. Nonne enim ea horum proprietas est, ut vel minimae cuivis cedant pressioni? […] Cum enim agatur solummodo de separatorum […] corpusculorum motu et agitatione, quis non videt hunc illumve motum facile quibusdam fluidi partibus imprimi posse, qui non imprimatur aliis, a prioribus omnino seiunctis avulsisque?” De Volder 1676–1678, disputation 2, thesis 2.
- 149.
Gorlaeus 1620, 332–333; Reneri 1635, disputation 4, thesis 29; Regius 1646, 155 and 158; De Bruyn and Posahazi 1654, thesis 5; De Raey 1666, thesis 3. Traditionally, air was labelled as humid and hot, while water was humid and cold; by considering air as dry, Gorlaeus was dismantling the traditional, four-fold theory of the elements, following Girolamo Cardano and Henricus de Veno, who claimed that air cannot truly mix with other bodies: see Lüthy 2001.
- 150.
Descartes 1982, 69–70. De Volder does not provide a relevant variant of Descartes’s account in his dictata on II.54, as he remarks only that fluid bodies can be easily separated as their particles move in all directions: cf. Hamburg 273, 113–144; Hamburg 274, 47–48. Moreover, for Descartes – and for his followers – there is no dichotomy between fluids and solids: rather, they are ‘different states’ of matter, and there are degrees of solidity and fluidity, as in a spectrum. This idea is expressly given in Le monde, chapter 3. I discuss Descartes’s theory of floatation – which was part of his theory of gravity – in Sect. 5.5, De Volder’s Cartesian hydrostatics: a mixed approach.
- 151.
See supra, n. 66.
- 152.
“[…] si un Vaisseau plein d’eau n’a qu’une seule ouverture, large d’un poulce, par exemple, où l’on mette un Piston chargé d’un poids d’une livre, ce poids fait effort contre toutes les parties du Vaisseau generalement, à cause de la continuité et de la fluidité de l’eau: mais pour determiner combien chaque partie souffre, en voicy la regle: Chaque partie large d’un poulce, comme l’ouverture, souffre autant que si elle estoit poussée par le poids d’une livre (sans compter le poids de l’eau dont je ne parle pas icy, car je ne parle que du poids du Piston), parce que le poids d’une livre presse le Piston qui est à l’ouverture, et chaque portion du Vaisseau plus ou moins grande, souffre precisément plus ou moins à proportion de sa grandeur, soit que cette portion soit vis à vis de l’ouverture ou à costé, loin ou prez; car la continuité et la fluidité de l’eau rend toutes ces choses là égales et indifferentes […]. Voicy encore une preuve qui ne pourra estre entenduë que par les seuls Geometres, et peut estre passée par les autres. Je prends pour principe, que jamais un corps ne se meut par son poids, sans que son centre de gravité descende. D’où je prouve que les deux pistons figurez en la Figure VII. sont en Equilibre, en cette sorte; car leur centre de gravité commun est au point qui divise la ligne, qui joint leurs centres de gravité particuliers, en la proportion de leurs poids; qu’ils se meuvent maintenant, s’il est possible: donc leurs chemins seront entre eux comme leurs poids réciproquement, comme nous avons fait voir: or, si on prend leur centre de gravité commun en cette seconde situation, on le trouvera precisément au mesme endroit que la premiere fois,” Pascal 1663, 8–11. Pascal refers to Torricelli’s principle, dealt with in Sect. 4.2.2, Huygen’s laws of collision. This explanation, notably, will be assumed also by Rohault, who in chapter 10 the first part of his Traité de physique (1671) addresses the equilibrium of fluids in an asymmetrical, inverted syphon (in § 11) exactly after having treated the principle of the lever (§ 10).
- 153.
“Nous voyons par là que l’eau pousse en haut les corps qu’elle touche par dessus; qu’elle pousse en bas ceux qu’elle touche par dessous; et qu’elle pousse de costé ceux qu’elle touche par le costé opposé: d’où il est aisé de conclure que, quand un corps est tout dans l’eau, comme l’eau le touche par dessus, par dessous et par tous les costez, elle fait effort pour le pousser en haut, en bas et vers tous les costez: mais comme sa hauteur est la mesure de la force qu’elle a dans toutes ces impressions, on verra bien aisément lequel de tous ces efforts doit prevaloir. Car il paroist d’abord que comme elle a une pareille hauteur sur toutes les faces des costez, elle les poussera également; et partant ce corps ne recevra aucune impression vers aucun costé, non plus qu’une giroüette entre deux vents égaux. Mais comme l’eau a plus de hauteur sur la face d’en bas que sur celle d’en haut, il est visible qu’elle le poussera plus en haut qu’en bas, et comme la difference de ces hauteurs de l’eau est la hauteur du corps mesme, il est aisé d’entendre que l’eau le pousse plus en haut qu’en bas, avec une force égale au poids d’un volume d’eau pareil à ce corps. Un corps dans l’eau est contrepesé par un volume d’eau pareil, de là vient que quelques corps y tombent. […] D’autres y montent. S’il est de bois, ou d’une autre matière plus legere que l’eau en pareil volume, il monte avec toute la force dont le poids de l’eau le surpasse,” Pascal 1663, 25–26.
- 154.
Stevin’s De beghinselen des waterwichts was published as part of his De beghinselen der weeghconst, together with a treatise De weeghdaet and an appendix. These were all later included in the Hypomnemata as the section on statics (as tome 4). In 1634, a French edition of Stevin’s Hypomnemata was published as Oeuvres mathématiques.
- 155.
- 156.
“It is true that the force on a lock gate follows from Proposition XI, but it does so only because the relevant knowledge has been assumed in its proof. As we have noted, Steven assumes that the force on a vertical surface of a given area at some level is equal to the force on a horizontal surface of the same area at the same level,” Chalmers 2017, 40.
- 157.
This topic is considered in Sect. 5.4.1, “[...] les liqueurs pesent suivant leur hauteur”.
- 158.
Cf. supra, n. 128.
- 159.
See definition 7: “[v]as superficiarum est superficies corporis cogitatione ab eo separabilis,” and postulate 3: “[p]ondus a quo vas minus alte deprimitur, levius; quo altius, gravius; quo aeque alte, aequipondium esse,” Stevin 1605, 111–112.
- 160.
See proposition 2: “[s]olidum corpus materia leviore quam sit aqua non omnino mergitur, sed eminet aliqua sui parte. […] Demonstratio. Cum igitur A ex hypothesi materiam habeat leviorem aqua GF, et haec dato corpori A sit aequalis, GF necessario ipsi A praeponderabit, iam in vase superficiario loco aquae substituitur corpus A ipsi congruum, nam ex fabrica parti GF aequale est et simile, cumque A corpus levius sit aqua effusa propterea vas superficiarum EF […] non tam alte mergetur ab A atque ab FG: atqui quanto minus alte corpus superficiarum EF subsidit, tantum corporis A supra aquam extare necesse est. Conclusio. Quamobrem corpus solidum materiae levioris quam aqua non totum mergitur, sed aliqua sui parte supereminet. Quod demonstrasse oportuit,” Stevin 1605, 114.
- 161.
Boyle 1666, Preface, 6 (unnumbered). Please note that in his Paradoxes Boyle deals with the positions of Stevin only; Galileo and Ghetaldi are mentioned only in this passage.
- 162.
See Sect. 5.4.2.2, Boyle’s experimental approach to the paradox.
- 163.
Boyle 1666, Preface, 7–15 (unnumbered).
- 164.
“[…] [the] difficulties making the Experiments propos’d by Monsieur Paschall more ingenious then practicable, I was induc’d on this occasion to bethink my self of a far more Expeditious Way, to make out, not only most of the Conclusions wherein we agree, but others that he mentions not; and this with so much more ease and clearnesse,” Boyle 1666, 6. See also the scholium to paradox 3.
- 165.
Or, in Boyle’s own words: “[t]his postulatum or Lemma, consists of three parts; the first of them more, and the two last, less principal. Suppose we then, (First) That if a Pipe open at both Ends, and held perpendicular to the Horizon, have the lower of them under Water, there passes an Imaginary plain or Surface, which touching that Orifice is parallel to the Horizon; and consequently parallel as to sense to the upper Surface of the water, and this being but a help to the Imagination will readily be granted. Secondly, To this it will be consonant, that each part of this designable surface, will be as much, and no more press’d, as any other equal part of it, by the water that is perpendicularly incumbent on it. For the water or other Fluid being supposed to be of an homogeneous substance, as to gravity, and being of an equal height upon all the parts of the imaginary Surface; there is no reason why one part should be more press’d by a perpendicular pillar of that incumbent fluid, then any other equal part of the same Surface by another perpendicularly incumbent pillar of the same or equal Basis and height, as well as of the same Liquor. But Thirdly, Though whilst our imaginary Surface is equally press’d upon in all parts of it, the Liquor must retain its former position; yet if any one part comes to have a greater weight incumbent on it, then there is upon the rest, that part must be displac’d, or depress’d, as it happens, when a stone or other Body heavier then water sincks in water. For wherever such a Body happens to be underneath the water, that part of the imaginary plain that is contiguous to the lower part of the stone, having on it a greater weight then other parts of the same Surface, must needs give way, and this will be done successively till the stone arrive at the Bottom; and if, on the other side, any part of the Imaginary Surface be less press’d upon then all the rest; it will by the greater pressure on the other parts of the Surface be impell’d upwards, till it have attain’d a height, at which the pressure (of the rais’d water, and the lighter or floating Body (if any there be) that leans upon it, and gravitates together with it, upon the subjacent part of the Imaginary Surface) will be equal to that which bears upon the other parts of the same Surface,” Boyle 1666, 8–11.
- 166.
“From what has been hitherto shewen, we may safely infer the Proposition, upon whose occasion all this has been delivered. For since the oyle in a Pipe, open at both Ends, may be kept suspended in any part under water, as at Q, because it is there in an Aequilibrium with the External water; and since being lifted up in the water, as from Q to S, the oyle can no longer be kept suspended, but by its own gravity will runne out. And since, in a word, the deeper the water is, the greater weight and pressure is requir’d in the Cylinder of oyle, to be able to countervail the pressure of the water, and keep it self from being lifted up thereby; there seems no cause to doubt but that the parts of the water incumbent on the Superficies G H, do more press that Superficies, than the parts of the water contiguous to the Superficies J K do press that; and consequently, that the parts of the water that are under the uppermost Surface of it, are press’d by those of the same Fluid that are directly over them: As we saw also that the upper parts of the oyle, whil’st the pipe was in raising from Q to S, depress’d the lower so much, as to force them quite out of the Pipe; there being in these cases no reason why the lowermost parts of a Liquor should press more, or have a stronger Endeavour against any other Liquor (or any other Body) the higher the Liquor incumbent reaches, if these inferiour parts deriv’d their pressure only from their own particular Gravity, (which is no greater then that of the other Homogeneous parts of the Liquor) and therefore they must derive the great force wherewith they press from the weight of the Incumbent parts, which consequently must be allow’d to press upon them,” Boyle 1666, 33–35.
- 167.
Boyle 1666, 67. See also 8–23
- 168.
Boyle 1666, Preface, 16 (unnumbered).
- 169.
“This may be prov’d by what has been already delivered in the Explication of the first Experiment: For where ever we conceive the lowest part of the Body, which is either totally, or in part, immers’d in water, to be there the imaginary Superficies being beneath the true Superficies, every part of that imaginary Superficies must be press’d upwards, by vertue of the weight of the water incumbent on all the other parts of the same Superficies, and so that part of it, on which the immers’d Body chances to leane, must for the same Reason have an endeavour upwards. And if that Endeavour be stronger then that wherewith the weight of the Body tends downwards, then […] the Body will be buoy’d or lifted up. And though the Body be heavier then so much water, and consequently will subside, yet that Endeavour upwards of the water, that touches its lower part, is onely rendred ineffectual to the raising or supporting the body, but not destroyed; the force of the heavy Body being from time to time resisted, and retarded by the water, as much as it would be if that Body were put into One Scale, and the weight of as much water, as is equal to it in bulk, were put into the other,” Boyle 1666, 67–68.
- 170.
“[…] this pressure of the perpendicular Cylinder doth really urge the oyle in the shorter leg to flow out; you may learn by slowly lifting the Syphon (without changing its, former posture) towards the Surface of the water. For as the lower leg comes nearer and nearer to that Surface, (to which, as I newly intimated, it is still to be kept parallel) the oyle in the Horizontal leg will be driven out in drops, by the pressure of the other oyle in the perpendicular leg. That likewise before you begin to raise the Syphon, the lateral pressure of the water against the lower Orifice of it is, at least in such Experiments, near about the same with what would be the perpendicular pressure of a Cylinder of water, reaching from the same Orifice G (or some part of it) to the top of the water, may be gather’d from hence, That the Surface of the oyle in the longer leg will be a litle higher then that of the external water, as (by reason of the often mention’d comparative levity of the oyl) it would be, if we suppose, That a pipe of Glass of the same bore, and reaching to the top of the water, being fitted to the Orifice of the Horizontal Leg (as in the annex’d figure the Cylinder, G H) were fill’d with water,” Boyle 1666, 144–145.
- 171.
- 172.
“Si fundo EF plus ponderis insideat aquae GHFE, id erit ab aqua finitima, atque ideo si fieri possit est ab AGED et HBCF, quibus positis fundo DE quoque, propter aquam finitimam GHFE (cum utrobique sit par ratio) plus ponderis incumbet quam sit aquae AGED, perinde quoque basi FC plus insidet ponderis quam aquae HBCH; quare toti fundo DC maius quoddam pondus insidet quam aquae totius ABCD, quod tamen, cum ABCD corpus rectangulum sit, absurdum fuerit. Eadem ratione evinces fundo EF non minus pondus sustentari quam sit aquae GHFE; quare tantundem duntaxat ponderis necessario ipsi incumbet,” Stevin 1605, 119. See Schuster 2013, chapter 3.
- 173.
See supra, n. 152.
- 174.
Boyle 1666, 117.
- 175.
“Take a slender Glass pipe, of an even Bore, turn’d up at one end like the annexed Syphon. Into this Syphon suck oyl of Turpentine till the Liquor have fill’d the shorter leg, and be rais’d 2 or 3 Inches in the longer. Then nimbly stopping the upper Orifice with your finger, thrust the lower part of the Syphon so farre into a deep Glass full of water, That the Surface of the oyle in the longer leg of the pipe, may be but a little higher then that of the External water; and, upon the removal of your finger, you will find the Surface of the oyle to vary but little, or not at all, its former Station. And as, if you then thrust the pipe a little deeper, you will soe the oyle in the shorter leg to begin to be depress’d; so, if afterwards you gently raise the pipe toward the top of the water, you shall see the oyle not only regain its former station, but flow out by degrees in drops that will emerge to the Top of the water. Now, since the water was able, at first, to keep the oyl, in the longer leg of the pipe, suspended no higher, then it would have been kept by a Cylinder of water equal to the Orifice of the shorter leg of the pipe, and reaching directly thence to the Top of the water; (as may be easily cried, by making a Syphon, where the shorter leg may be long enough to contain such a Cylinder of water to conterpoize the oyl in the longer;) & since, when once, by the raising of the pipe, the height of the incumbent water was lessen’d, the oyle did more then Counter-ballance it; (as appears by its flowing out of the Syphon,) we may well conclude; That, though thence were in the Vessel a great deal of water, higher then the immers’d Orifice of the Syphon, (and it would be all one, though the Syphon were placid at the same depth in a pond or lake;) yet, of all that water, no more did gravitate upon the Orifice, then that which was plac’d directly over its, which was such a pillar of water, as the Paradox describes,” Boyle 1666, 121–123.
- 176.
Boyle 1666, 125.
- 177.
Please note that the 1705 inventory includes a more complex U-shaped instrument to show the pressure exerted by the height of water: i.e. a hydrostatic lever: “a big glass with a copper lid, with a pipe [attached] at the side, to sustain the weight of the water in this side-pipe standing [rising] above the weight.” See Molhuysen 1913–1924, volume 4, 106∗.
- 178.
Probably: “m[od]o.”
- 179.
De Volder 1676–1677, 133r.
- 180.
See supra, n. 152.
- 181.
“Impleatur vas ABC aqua per A in elatiori loco: possitque per C effluere aqua si abundaverit, totumque vas censeatur plenum: certissimum est vase existente pleno, aquam fore elatiorem in A quam in C et propterea, ut novimus ex quotidiana experientia, effluxuram aquam per C quousque superficies aquae quae in A redierit ad D quod est in eodem plano cum C ut sic aqua tota sua elatiori superficie stet ad libramentum. Et hoc quidem contigerit, licet sit maior, licet minor sit, moles aquae in parte vasis AB quam in BC. Unde aqua non censetur habere vim premendi alias corporis sui partes, nisi ea quantitate, qua ad perpendiculum libramento supereminet. Eo etenim constituto, totum corpus quiescit et subsidet. Quod de omni humido intelligendum est,” Archimedes and Rivault 1615, 492.
- 182.
Descartes 1982, 193.
- 183.
“Incumbunt. Id vult iuxta Stevinum, aquam omnem pressionem exercere secundum lineas perpendiculares, et singulas partes fundi sustinere aquam perpendiculariter incumbentem,” Hamburg 273, 235. In the other series of dictata Descartes does not consider this issue.
- 184.
“[…] no more drops than {are in the cylinder} 1, 2, 3, 4, or others equivalent, press upon this same part B of the vessel; because at the same moment of time at which this part B can descend, no other drops can follow it,” Descartes 1982, 193; see Fig. 5.57, Descartes 1644a, 203. This is a dynamical rendering of a static situation, which is used by Descartes to explain the hydrostatic paradox, which I discuss in Sect. 5.5.1, An introduction to Descartes’s hydrostatics.
- 185.
“Possunt. Id vult, si q[ui]s utatur infundibulo (Belg. e[ss]e trechter) sive tubo aequali, cuius orificium aequale sit angustissimae parti infundibuli, pari celeritate aquam aliumve liquorem per utrumq[ue] descensurum, concipiamus ex. gr. infundibulum ABCD et tubum EBFD dico aquam aeq[ue] cito descensuram per tubum EBFD ac per infundibulum ABCD. Nec e[nim] q[uo]d q[ui]s dicat aquam lateralem G a H in infundibulo premere[,] quia id falsum e[sse], sola e[nim] perpendicularis premit, itaq[ue] s[e]mp[er] respicienda altitudo, [n]o[n] vero latitudo,” Hamburg 273, 235.
- 186.
Please note that both Descartes and De Volder accepted the principle – first treated by Benedetto Castelli – according to which a fluid passing from a large to a narrow passage increases its speed (I discuss it in Sects. 6.1.2, Descartes’s cosmogony and cosmology and 6.2.2.1, Newton’s critique of Descartes’s vortex theory). This might not be at odds with the arguments provided here, because the principle of Castelli applies to the continuous movement of fluid, which takes place in several instants, while in a Cartesian framework a static condition, such as that of the fluid in the funnel, is rendered as a dynamic condition by considering a movement taking place in the first instant. In Descartes’s perspective, this is as a tendency to motion rather than an actual movement (taking place in more instants): I deal with this in Sect. 5.5.1, An introduction to Descartes’s hydrostatics.
- 187.
“Een copere buys verdeelt in voeten om de perpendiculare pressie van ’t water als ook de snelheyt van die te wegen en te meten,” Molhuysen 1913–1924, volume 4, 105∗.
- 188.
Chalmers 2017, 59; cf. also the text quoted supra, n. 44. On the understanding of pressure, see also Bertoloni Meli 2006, chapter 6.
- 189.
See Sect. 5.5.3, De Volder’s Archimedeo-Cartesian hydrostatics: an impossible synthesis?.
- 190.
As in the case of the cohering marbles, discussed in Sect. 4.1.3, De Volder’s ideas on cohesion and divisibility, the hemispheres are also discussed in the pro gradu disputation of Johannes Franciscus de Witte van Schooten. Senguerd used hemispheres with a diameter of 4 inches and 4 lines – viz. those represented in the figure –, to which he managed to append a weight of 275 pounds, and of 8 inches and 6 lines, undepicted (maybe the same ones used by De Volder), to which he appended weights of 850 pounds: see Senguerd 1715, 166.
- 191.
De Volder 1676–1677, 86r. See supra, n. 83. In fact, the ratio 425/6 is 70.8: lower than the ratio 700/8, i.e. 87.5. De Volder does not relate this proportion to the weights of 450 pounds he appended, in experiment 2, to the cylinders of 2 inches and
$$ \frac{1}{3} $$diameter: see Sect. 4.1.3, De Volder’s ideas on cohesion and divisibility.
- 192.
De Volder 1676–1677, 85r. This kind of apparatus, probably a tripod, is not mentioned in the 1705 inventory.
- 193.
De Volder 1676–1677, 79r.
- 194.
See Molhuysen 1913–1924, volume 4, 105∗–106∗.
- 195.
“[…] Waer uit genoegh te besluiten is dat om den bodem reghthoekigh af te trekken so komt dit geheel met Symon Stevin over een: en nogh boven dit so is dit ook tuighwerkelijk ondersoght by den B. de Volder Professor in de Philosophia en Mathematise Konsten tot Leyden en is hier mee ook heel effen over een gekomen,” Van Nierop 1680, 153. Mentioned, in turn, in the Wiskonstige oeffening, behelsende eene verhandeling over veele voorname zaken van de mathesis (1718) of Pieter Hellingwerf: “[e]n de hoegrootheyt van de perpendiculare perssing tegens een scheve bodem, vint men by Dirk Rembrantsz. van Nierop aangetekent in zyn tweede deel van de Wiskonstige Reekening, pag. 153 dat de Heer Professor de Volder tot Leyden, door ondervinding heeft gemeeten en de uytkomst van die effen met de 10 Propositie, 3 Afdeeling, 1 Boek, bevonden over een te komen,” Hellingwerf 1718, 348.
- 196.
De Volder 1676–1677, 140r–141r.
- 197.
“Or puis que cette expérience a été révoquée en doute par tant d’habiles gens, je serai bien aise de dire ici en peu de mots ce que j’ai vû faire sur cela à M. de Volder, Prof. célebre en Philosophie & en Mathématique à Leyde, lorsque j’avois l’honneur d’étudier sous lui il ya sept ou huit ans,” Lufneu 1685, 384. Most probably, the experiments took place after 19 February 1675 (when Lufneu enrolled at the University), and before 20 June 1679 (when he graduated in medicine). Lufneu’s 1685 report was reprinted – without the last two paragraphs (quoted infra, n. 204, and infra, n. 253) – in volume 28 of the Nouveau choix de pieces tirées des anciens Mercures, et des autres journaux, published by Jean-François Marmontel (1759). The report was also included in the various reprints of the Nouvelles.
- 198.
“1 consectarium. Immitto in aquam ABCD huius propositionis solidum IKLM, materiae levioris quam aqua, quodque ideo ipsi innatet parte NOLM immersa, reliqua NOKI supereminente, ut in subiecta figura apparet. Iam solidum IKLM […] est aequale tantae aqueae moli, quanta est pars sui demersa NOLM. Quare solidum IKLM cum reliqua ipsum ambiente aqua pondere aequat corpus aqueum magnitudinis ABCD. Itaque etiamnum asserimus secundum propositionis sententiam, fundo EF inniti pondus aequale corpori aqueo magnitudinis columnae, cuius basis sit EF, altitudo perpendicularis GE a summa superficie aquae AB ad imum fundum EF demissa. Unde efficitur a materia qualibet aquae innatante fundum nec magis nec minus affici, quam ab aqua in eadem altitudine constituta,” Stevin 1605, 119.
- 199.
“2 consectarium. Secundo in aquam ABCD immititor corpus solidum, solidave quotcunque materia aquae aequipondia, inter quae, reliqua omnia aqua expulsa, tantum comprehendatur IKFELM; quae cum ita sint, haec corpora fundum EF nec aggravant necque relevant ab eo pondere quo aqua prius ipsum afficiebat. Quare etiamnum ex sententia propositionis dicimus, fundo EF insidere pondus aequale aqueo ponderi, magnitudine columnam aequante, cuius basis EF, altitudo perpendicularis GE ab aquae summo AB seu MI ad imum EF demissa,” Stevin 1605, 120.
- 200.
“3 consectarium. Si tertium ABCD mera aqua, et in ipsa EF fundum horizonti parallelum. Quibus positis, aqua sub fundo EF tam potenter ipsum sursum premit, quam aqua supra insidens deorsum; secus enim per 1 propos. infirmius validiori concederet, quod hic non fit quia utrumque loco suo permanet. Iam corpus solidum isti aquae pondere homogeneum ita collocator ut aqua IKEFLM ab inferiori parte presset fundum EF, ut hic. Quibus positis, aqua subter EF nunc tam valide premit fundum EF, sive ipsum solidum, quam prius ipsam aquam oppositam: sed impressio tanta tunc erat quanta superioris aquae ad EF depressio, ut supra patuit, superioris autem aquae depressio aequalis erat ponderi columnae aqueae cuius basis EF, altitudo perpendicularis GE, a superficie AB seu MI ad fundum EF demissa. Itaque aquae subter EF constitutae impressio erit quoque tanta,” Stevin 1605, 120.
- 201.
“4 consectarium. Corpora solida secundi tertiique consectarii istic ita firmentur, effusaque aqua spatium IKFELM vacuum nullo amplius pondere efficiet fundum EF; unde apparet aqua in vacuum locum rursum infusa fundum EF tam valide premi, ac si intregrum vas ABCD, sublato isto corpore solido, aqua repletum foret,” Stevin 1605, 120.
- 202.
“5 consectarium. At vero quia immissa solida 2 et 3 consectarii sunt suo loco defixa, ipsorum materia extrema nec gravitate nec levitate ulla afficiet fundum EF, quamobrem sublata omni aquam ambiente materia, relinquentur internae istae aqueae figurae MIKFEL, quales hic vides. Atque hic etiam ex sententia propositionis dicimus base EF subnixum esse pondus, aequale ponderi aqueae columnae cuius basis EF, altitudo perpendicularis ab MI aquae summo in fundum EF demissa. Atque ita in caeteris omnibus figuris quarum fundum sit in plano horizonti parallelo. Conclusio. Itaque in fundo horizonti parallelo, et c.,” Stevin 1605, 120–121.
- 203.
Stevin 1605, 145.
- 204.
“Avant que de finir, il faut que je dise encore que M. Boyle, dans l’endroit que j’ai cité de son paradoxe 6. remarque, que l’expérience que je viens de décrire est la seule des cinq de Stevin, qu’il sache avoir été examinée, et mise à l’essai. Mais je suis témoin qu’outre celle-ci, qui est la troisieme en rang dans l’Hydrostatique Pratique de Stevin, M. de Volder a executé la premiere avec un pareil succès,” Lufneu 1685, 389.
- 205.
Boyle 1666, 136–137.
- 206.
In the third volume of his Magia, Schott proposed five arguments against the idea that elements do not gravitate on elements: see Schott 1657–1659, volume 3, book 5, syntagma 3, erotemata 3–4. All these arguments – whose author is not disclosed by Boyle, are systematically criticized by Boyle in appendix 1 to his Hydrostatical Paradoxes. The arguments, in Boyle’s versions, are as follows: “(1) Because else the inferiour parts of the water would be more dense then the Superior,” (2) “Because Divers feel not, under water, the weight of the water that lyes upon them,” (3) “That ev’n the slightest Herbs growing at the bottom of the water, and shooting up in it to a good height, are not oppress’d or lay’d by the incumbent water,” (4) “That a heavy Body ty’d to a string, and let down under water, is supported, and drawn out with as much ease, as it would be if it had no water incumbent on it; nay, with greater ease, because heavy bodyes weigh less in water then out of it,” (5) “Because a Bucket full of water, is lighter in the water, then out of it; nor does weigh more when full within the water, then when empty out of it,” Boyle 1666, 202–206.
- 207.
“MNO libra esto, cuius lances M, O; atque M quidem figurae cylindraceae aequalis exposito GCD ideoque 10 librarum aquae capax; tum P solidum simile lanci M et minus, scapo affigatur ut hic vides. Inseratur igitur solidum P in lancem M, ut in secunda figura, lancique O imponatur pondus Q 10 lb; iam fundum M tam valide impinget in corpus P quam a 10 lb impelletur. sit autem corpus P decima parte minus quam M, ut vacuus inter utrumque locus 1 lb aquae expleatur, hoc est aquea mole aequante corpus EAB. Itaque 1 lb aquae in lancem infusa hanc deprimet, reliquamque attollet, id ipsum testante experientia, et 10 propositionis demonstratione approbante. Quare 1 lb aquae in lance M istic tantae erit potentiae, quam 10 lb plumbi ferrive aut alterius materiae solidae eidem lanci M affixae. Atque eadem ratione 1 lb aquae, huiusmodi partium dispositione maioris erit efficaciae, quam millae librae materiae alterius. Quae cum ita sint, aqua quae inter utriusque fundum, corporis P lancisque M intercessit, fundum M nunc tam valide pressat ac prius fundum corporis P, hoc est, ac 10 lb; cum pondus Q 10 lb in reliqua lance O immissum sit. Itemque contra aqua tanta vehementia premit fundum lancis M, quanta est efficientia 10 lb Q. Ponamus autem aquam in fundo M aequari ipsi KLBA, reliquam autem ipsi P circumfusam, reliquae IE. Quare aqua EAB tam potenter pressat fundum A B, quam haec aqua fundum M, ideoque EAB premit suum fundum AB aequivalenter 10 lb, sed tantus est item pressius aquae GCD contra fundum CD. Quamobrem, quod pragmaticè confirmare statueramus, aqua EAB pondere 1 lb suum fundum A B aequè validè premit, atque GCD 10 lb fundum CD. Pari ratione evinces, vel 1 lb pressare potentius mille libris,” Stevin 1605, 146.
- 208.
The letter was printed for the first time in the Florence edition of Galileo’s works of 1718.
- 209.
“Ma che dirà V. S. se io mostrerò che un vaso che galleggi sendo anco ripieno di acqua, non farà mutazione alcuna se con l’imposizione di un solido nel modo detto si scaccierà quasi tutta l’acqua che in esso vien contenuta? Ma per ben dichiarare il tutto, ed insieme accrescer la maraviglia, intendasi un cilindro solido AB, fermato e sostenuto in A, di poi intendasi il vaso CDE, capace della mole AB e di poco di più, il qual vaso, sendo separato e allontanato da esso cilindro AB, sia ripieno di acqua, della quale ne capisca, per esempio, 100 libre: di poi postolo sotto ’l solido fisso AB, lentamente s’innalzi verso esso solido, in guisa che, entrandovi egli dentro, faccia a poco a poco traboccar fuori l’acqua, secondo che esso vaso CDE si anderà elevando. Or io dico, che quella persona che anderà alzando detto vaso contro il solido AB, sempre sentirà il medesimo peso, ben che di mano in mano vadia uscendo fuori l’acqua; né meno si sentirà aggravare dopo che nel vaso non sarà rimasto più di due o tre libre d’acqua, di quello che egli sentisse gravarsi quando era del tutto pieno, ancor che il solido AB non tocchi il vaso, ma sia, come si è supposto, fissamente ed immobilmente sostenuto in A,” Galileo 1890–1909, volume 4, 306–307. See Fig. 5.39, Galileo 1744, volume 1, 263. For a thorough discussion, see Palmieri 2005.
- 210.
“Ciò potrà per esperienza esser fatto manifesto ad ognuno, ma oltre all’esperienza non ci manca la ragione. Imperocchè considerisi come la potenza sostenente il solido in A, mentre esso era fuori di acqua, sentiva maggior peso, che dopo che il solido B è immerso nell’acqua, perchè non è dubbio alcuno, che se io reggerò in aria una pietra legata ad una corda, sentirò maggior peso, che se alcuno mi vi sottoponesse un vaso pieno d’acqua, nel quale detta pietra restasse sommersa; scemandosi dunque la fatica nella virtù che sostiene il solido AB, mentre e’ si va immergendo nell’acqua del vaso CDE, che lo va ad incontrare, nè potendo il peso di questo andare in niente, è forza che s’appoggi nell’acqua, ed in conseguenza nel vaso CDE, ed in quella virtù che lo sostiene; e perchè noi sappiamo, che ogni solido più grave in specie dell’acqua, e che in essa si de merge, va di mano in mano perdendo di peso, tanto quant’è il peso d’una mole d’acqua uguale alla mole del solido demersa, facilmente intenderemo tanto andare scemando la fatica della virtù sostenente il solido AB in A, quanto l’acqua va scemando la gravità di esso solido: adunque il solido AB va gravando sopra alla forza sostenente il vaso CDE tanto quanto è il peso d’una mole d’acqua uguale alla mole del solido demersa: ma alla mole del solido demersa è di mano in mano uguale la mole dell’acqua che si spande fuori del vaso, adunque per tal’effusione d’acqua non si scema punto il peso che grava sopra la virtù che sostiene il vaso. Ed è manifesto che il solido AB, se ne scaccia l’acqua del vaso, nientedimeno con l’occuparvi il luogo dell’acqua scacciata vi conserva tanto di gravità, quanta appunto è quella del l’acqua che si versa,” Galileo 1890–1909, volume 4, 307–308.
- 211.
Bardi 1614, 16.
- 212.
See Schott’s Mechanica hydraulico-pneumatica, part 2, classis 1, machina 11.
- 213.
Schott 1657, 318–319. Cf. Ens 1636, 215 (i.e. 217)–218: “[m]irabile est aquam vase quolibiet conclusam, et violenter divisam tantum acquirere ponderis, ac si locus a corpore dividente occupatus uniformiter aqua refertus esset. Varia liceret ad propositionis huius probationem experimenta congerere, at egregia duo tantummodo in medium proferam; quae equidem vera esse nunquam crederem, nisi ipsemet eorum periculum fecissem. Primum est lapidem ingentem, locum 10, 100 aut 1000 librarum aquae occupantem, vel corda, vel catena suspensum, in vas aquae plenum dimittito; aut ferro alicui muro adhaerenti saxum immobiliter affigito, illique vas aqua refertum supponito: porro vas ita collocandum est, ut et saxum immissum summa ex parte contingat, et inter utrumque locus unius librae aquae intercedat; quae iniecta (si lapis locum 100 librarum aquae occupet) 100 libris gravior evadet; adeo, ut prae aquae ponderositate, vas suppositum aegre sustineri possit. Secundum longe mirabilius est. Bilancem communibus aliis simillimum parato, hoc tamen uno excepto, quod huius cratere licet aequalis ponderis, inaequalis tamen capacitatis sint, in uno quippe pondera ponenda, in alterum aqua infundenda erit. Affige igitur muro (ut antea dictum est) corpus aliquod, sive solidum, sive intus vacuum, capax locum 9 librarum aquae occupare: deinde imposito in craterem debitum 10 librarum pondere, et in oppositum infusa libra aquae; craterem libram aquae continentem dicto corpori submittito, ut corpus cratere, nulla ex parte contracto, comprehenduntur: quo peracto, libram aeque infusam, 10 libri plumbi aequipollere disces.”
- 214.
“Res haec est omnino mirabilis, sed verissima, et experientia saepius comprobata quam quilibet facile poterit facere. Affirmabat doctissimus mathematicus P. Ioannes Carolus la Faille, cum Panormi in disputatione publica predictam experientiam contra quendam discipulum meum, Terrae immobilitatem, non obstante continua centri gravitatis mutatione, mathematice demonstrantem attulisset; illam olim Serenissimo Alberto Belgii Gubernatori fuisse exhibitam; eumque, cum versatissimum esset in rebus mathematicis, et in sumendis experimentis curiosissimus, tantopere tamen obstupuisse, ut asseruerit, nunquam se rem mirabiliorem spectasse,” Schott 1657, 319.
- 215.
“Memini, cum Panormi in Sicilia in disputatione publica meus quidam in mathematicis discipulus demonstraret, Terram non ad quamlibet novi ponderis ex parte una additionem, et inde secutam centri gravitatis mutationem, titubare, nec locum mutare, nisis fortassis accederet pondus haemispherii terraquei pondere non minus […], memini inquam, virum doctissimum P. Joannem Carolum La Faille, Serenissimi Joannis ab Austria nunc Belgii Gubernotoris tunc vero Sicilia Proregis Mathematicum, opposuisse hoc Stevini Exemplum […] asseruisseque, summa omnium admiratione, vel unam libram aquae vasi praedicta ratione efformati conclusam sufficere, ad globum tarraqueum loco suo dimovendum,” Schott 1657–1659, volume 3, 455. On La Faille’s mentioning of Stevin’s sample 1, see infra, n. 218.
- 216.
As a matter of fact, indeed, in this way one can just measure the weight of the water in the containers, but not their internal pressure. This can on the other hand be revealed by the use of the libra mirabilis – in which the pressure of water in-between the bottoms of the solid and the container, keeps them separated, and can be measured with a balance. In the case used by Ventimiglia, indeed, the pressure exerted at the level of the bottom of the inverted T-shaped container is not revealed just by putting the container on a balance, because this pressure is also exerted upwards, so that its effects are nullified.
- 217.
“Aderat disputationi illustrissimum Dominus Carolus Vintimiglia, Eques Panormitanus nobilissimus, et eximius mathematicus, et statim absoluta disputatione fieri curavit duo vasa praedicto modo efformata, et me praesente experimentum fecit, sed sine ullo effectu; manifeste enim deprehendimus, vas ABE cum aqua sua non gravare tantum manum, aut bilancem sustentantem, quantum eam gravabat vas GCD, unde conclusimus, nec fundum utriusque aequaliter premi ab aquis inclusis. Fatebatur ingenue dictus P. La Faille […] nos in bilancibus vel manibus non totum illud vasis pondus sentire fundum tamen illo premi; sed non persuadebat, repugnante manifesta experientia,” Schott 1657–1659, volume 3, 455–456.
- 218.
“Aio itaque, propositionem, illam X Stevini, prout ab ipso ibidem proponitur et explicatur, veram esse, et bene ab ipso probari, et confirmari etiam experientia; at falsum esse allatum exemplum, et ex propositione illa nequaquam deduci, et insuper experientiae manifesto repugnare. Legatur proposito apud ipsum, et cum ea conferatur exemplum. Confirmare nititur Stevinus loco cit. libri 5 exemplum praedictum alia experientia, quam ibidem adducit, et nos ex ipso adduximus in Mechanica hydraulico pneumatica parte 2 classe 1 cap. 6 machina 2 et appellavimus libram hydrostaticam mirabilem. Eandem experientiam in citata paulo ante disputatione afferebat P. La Faille, experientia est verissima, et ab aliis saepius probata, sed non est ad rem: nec enim fundum ancis librae premit tam valide modica aqua, sed impetus ab aqua cylindro ligneo impressus, et a cylindro in aquam et fundum lancis reflexus, ut ibidem nos explicavimus,” Schott 1657–1659, volume 3, 456. Cf. Schott 1657, 319: “[q]uaenam igitur huius experimenti est ratio? An quia corpus P aquae lancis M immersum pellitur ab aqua sursum, utpote aqua levius, ut supponitur: et cum palo seu scapo affixum sit, et cedere non possit, impetus ab aqua ipsi impressus reflectitur in fundum vasis M, illudque deorsum premit tanta vi, quantae deprimeret aquae moles corporis P aequalis, nempe in casu posito moles aquae librarum novem? Scimus enim experientia, corpora aquae intrusa, si leviora sint quam aqua eiusdem molis, sursum pelli, et quidem tanta vi, quanto aqua molem habens corpori intruso aequalem gravius est ipso corpore, ut Archimedes demonstrat lib. I de iis quae vehuntur in aquis.”
- 219.
See supra, n. 206.
- 220.
- 221.
Boyle 1666, 140.
- 222.
See the third part of his Mechanica, chapter 14, De hydrostaticis. Wallis proposes a theory of floatation based on Archimedes’s postulate 1 (which is not overtly mentioned): see proposition 1 (“[s]i grave fluidum […] superne vel non prematur, vel aequaliter prematur ubique: retinebit illud, supernam superficiem quod spectat, situm horizontalem, seu potius sphaericum, Telluri concentricum […]. Atque inde deturbatum, suapte se gravitate eo restituet. Sin superne prematur inaequaliter, […] ea parte quae maiori pressu urgetur, descensus fiet; partibus ita pressis, alias, quae vel non pressae sunt, vel minus pressae, loco suo detrudentibus, quae itaque, pro illo descensu, assurgent,” Wallis 1670–1671, volume 3, 708. According to this theory, a body lighter than water, once put in water, is bounced upwards as the effect of the different pressure exerted on the (ideal) surfaces of water: see proposition 3: “[s]i illud D [i.e. a solid body] plus gravitet quam tantundem circumpositi aëris […], minus autem quam tantundem fluidi subiecti: innatabit D; sed depressis eousque partibus C subiectis, donec eum situm obtinuerit D, ut aequigravitet aggregato aëris et subiecti fluidi quorum locum occupat,” Wallis 1670–1671, volume 3, 711. Probably, Wallis found it difficult to justify, on such an Archimedean basis, the fact that the pressure of a fluid can be independent from the quantity of water which is above it. In fact, he does not even consider the case of floatation on a little water, and dedicates to the conditions of floatation only 7 of the 15 propositions of the chapter, the others being dedicated to the explanation of the suspension of mercury in Torricellian tubes.
- 223.
As to this point, one can also find it in Lufneu’s 1685 report. In the opening, Lufneu claims that physics had made little progress because of the lack of experiments, and, even if in recent times progress had been made by Stevin, Bacon, Galileo, William Gilbert, Descartes and Boyle, no agreement had ever been reached as to the explanation of the experiments they provided, nor on the conditions of the possibility of such experiments, namely, on the principles allowing for their very possibility. A foremost case, as to this, was the paradox of Stevin: see Lufneu 1685, 381–382.
- 224.
- 225.
“Vas ABCD aquae plenum, cuius fundum DC horizonti parallelum rotundo foramine pertundatur, quod ligneus tegat orbis GH materie quam aqua levior. Exponatur deinde vas alterum IKL superiori quidem aeque altum, sed minus et aquae item plenum, cuius fundum ad MN perforatum aequaliter antecedenti EF, et orbe quoque OP ipsi GH aequali obtegatur. Quibus positis, orbis GH contra communem ligni naturam vimque ingenitam ex aqua non emerget, sed foramini EF incumbens tam valenter premet quam columna aquea EFQR multatum differentia ponderum lignei orbis GH et aquae ipsi aequalis. Et qui experimento hoc cognoscas, orbi GH libram affigito, cuius pondus S ponderi dicto aequale sit, eritque orbis GH ipsi aequilibris. Similiter firmato ad orbem OP libram, cuius pondus T superiori S aequeponderet, orbisque hic OP ponderi T manebit aequilibris. auctis autem ponderibus S, T, orbes GH, OP attollentur, atque adeo hac via deprehendes orbes istos in funda subiecta aequalem impressionem facere; unde propositi veritas perspicitur videlicet minorem aquae molem IKL tam valide quam maiorem ABCD premere fundum sibi subiectum,” Stevin 1605, 147. He does not specify if the container is placed somewhere, or if its provided of some kind of support (as it was to be for De Volder’s instrument).
- 226.
In the Notato to the sample, Stevin specifies that if the moveable bottom GH is made, for instance, of lead, the weight S will counterbalance a weight equal to that of the column EFRQ plus the weight that the bottom GR has in water: “si discus GH esset e plumbo, ferrove, aut alia materia graviore quam aqua formatus, eius in subiectum foramen impressionem fore tantam, quanta sit columnae aqueae EFQR auctae differentia ponderis, quae inter H orbem dictum et aquae molem sibi aequalem intercedit,” Stevin 1605, 147.
- 227.
“[…] l’autre estroit, comme en la quatriéme; l’autre qui ne soit qu’un petit tuyau qui aboutisse à un Vaisseau large par en bas, mais qui n’ait presque point de hauteur, comme en la cinquiéme Figure; et qu’on les remplisse tous d’eau jusques à une mesme hauteur, et qu’on fasse à tous des ouvertures pareilles par en bas, lesquelles on bouche pour retenir l’eau; l’experience fait voir qu’il faut une pareille force pour empescher tous ces tampons de sortir, quoy que l’eau soit en une quantité toute differente en tous ces differents Vaisseaux, parce qu’elle est à une pareille hauteur en tous: et la mesure de cette force est le poids de l’eau contenuë dans le premier Vaisseau, qui est uniforme en tout son corps; car si cette eau pese cent livres, il faudra une force de cent livres pour soûtenir chacun des tampons, et mesme celuy du Vaisseau cinquiéme, quand l’eau qui y est ne peseroit pas une once. Pour l’éprouver exactement, il faut boucher l’ouverture du cinquiéme Vaisseau avec une piece de bois ronde, enveloppée d’étoupe comme le piston d’une Pompe, qui entre et coule dans cette ouverture avec tant de justesse, qu’il n’y tienne pas, et qu’il empesche neanmoins l’eau d’en sortir, et attacher un fil au milieu de ce Piston, que l’on passe dans ce petit tuyau, pour l’attacher à un bras de balance et pendre à l’autre bras un poids de cent livres: on verra un parfait Equilibre de ce poids de cent livres avec l’eau du petit tuyau qui pese une once; et si peu qu’on diminue de ces cent livres, le poids de l’eau fera baisser le Piston; et par consequent baisser le bras de la balance où il est attaché, et hausser celui où pend le poids d’un peu moins de cent livres,” Pascal 1663, 1–3. See Fig. 5.43, Pascal 1663, figures 4–5.
- 228.
See supra, n. 65.
- 229.
“We provided then a vessel of Laton, of the figure express’d in the Scheme, and furnished it with a loose Bottom C D, made of a flat piece of wood cover’d with a soft Bladder and greas’d on the lower side neer the edges, that leaning on the rim of wood G H, contiguous every where to the inside of the Laton it might be easily lifted from off this Rim; and yet lye so close, upon it, that the water should not be able to get out between them: And to the midst of this loose bottom was fastned a long string, of a good strength, for the use hereafter to be declared. The Instrument thus fitted, the water was poured in apace at the Top A B, which, by its weight pressing the false Bottom C D against the subjacent Rim, G H, contributed to make the Vessel the more tight, and to hinder its own passing. The Vessel being fill’d with water we took the forementioned string, one of whose ends was fastned to I, the middle part of the loose Bottom; and, tying the other end K to the extremity of the Beam of a good pair of Scales, we put weights one after another into the opposite scale, till at length those weights lifted up the false Botom C D from the Rim G H; and, consequently, lifted up the Incumbent water; which presently after ran down between them. And having formerly, before we poured in any water, try’d what water would suffice to raise the Bottom C D, when there was nothing but its own proper weight that was to be surmounted; we found, by deducting that weight from the weight in the scale, and comparing the Residue with the weight of as much water, as the cavity of the broad, but very shallow Cylinder B E C H G D F would have alone (if there had been no water in the pipe A I) amounted to; we found, I say, by comparing these particulars, that the pressure upon C D was by so very great odds more, then could have been attributed to the weight of so little water, as the Instrument pipe and all contain’d, in case the water had been in an uniform Cylinder, and consequently a very shallow one, of a Basis as large as that of our Instrument,” Boyle 1666, 137–140.
- 230.
“L’illustre M. Boyle, tout consommé qu’il est dans l’art de faire des expériences, a douté de celles de Stevin; car ayant prouvé la 10. proposition de Stevin dans son paradoxe 6. d’Hydrostatique, il y joint une remarque, par laquelle il rend douteux les corollaires de Stevin, & principalement le cinquieme, & il ajoûte que M. Wallis & quelques autres Savans en doutoient aussi. Il tâche pourtant d’éprouver s’il y avoit quelque chose de vrai dans l’expérience; & pour cet effet, il fit faire un vase semblable à celui de Stevin, mais le succès ne fut pas tel qu’il l’eût voulu. Il trouva bien à la verité que la pression étoit plus grande que celle qu’on pouvoit attribuer au poids de l’eau, mais non pas selon les proportions de Stevin, ainsi il laissa la chose pour être plus soigneusement examinée,” Lufneu 1685, 383–384.
- 231.
See infra, n. 242. The material was chosen in order to avoid leakages of water.
- 232.
“Il prit le tuyau ou cylindre ABCD de la hauteur d’un pied representé dans la 1. Figure, au bas duquel BD il y avoit en dedans une bordure d’environ six lignes, qui servoit à empêcher que le fond EF ne tombât hors du cylindre, au dedans duquel il pouvoit monter & descendre. Ce fond avoit un crochet au milieu pour les usages que nous dirons ci-dessous, & son diametre étoit presque aussi grand que celui du cylindre, aufin qu’il ne restât point d’intervale par où l’eau pût s’échaper; tous ceux qui resterent furent exactement bouchez avec de la cire. On appliqua à l’ouverture AC le couvercle HIM avec quatre vis bien fortes, pour empêcher que l’effort de l’eau enfermée dans le cylindre, ne le soûlevât. Au milieu du couvercle étoit le tuyau ML haut de cinq pieds, & large d’environ 6. lignes, autant qu’il m’en peut souvenir. On passa une corde par ce tuyau, laquelle étoit attachée d’un côté au crochet du fond EF, & de l’autre à l’une des branches de la balance OP. J’ai voulu décrire un peu amplement cette machine, parce que ni Stevin, ni M. Boyle ne l’ont point fait,” Lufneu 1685, 384–386.
- 233.
“Een copere cylinder met een ingesette boom van ½ voet diameter, met verscheyde kopere pypen en een kettingh gaande van de losse boom door de pyp naar boven tot de selfde eynde,” Molhuysen 1913–1924, volume 4, 105∗.
- 234.
The first figure is included in a catalogue probably sent as a letter dated 11 May 1695, where the cylinder aimed at demonstrating the hydrostatic paradox is extensively described (please note that a marginal note, in a different hand, refer to Valentini 1714, 43, commented in De Clercq 1991, 101–102): “[l]e cilindre de Monsr Le Profr de Volder. A. Le cilindre haut 1 pied. B. Le couvercle. CC. Quatre vis pour fermer le couvercle B. D. Un tuyaux de 6 <de> pied de longue. E. Cinq vis a chaque pied un. F. Un vis pour faire sortir l’air et remplir le cilindre. GGG. Trois pied. H. Un vis qui comprime l’instrument I pour tenir ferme le couvercle en bas. K. Le couvercle en bas en le quel est fonde un anneau, en le quel le crochet est attache en ce crochet et une chaine qui passe par le tuyaux D. L’usage. Applique le couvercle K qui est au fond avec un peu de cire dans le cilindre, attache le crochet a le couvercle, et mette l’anneau L a un bras de balance, et pese combien de poids qu’on faut pur attirer le couvercle quand il est soulement attaché avec cire. Mette derechef le couvercle avec de cire, et applique dans le cilindre, et attache l’instrument I qui on comprime avec le vis H, {est} sert quand on tourne le cilindre que le couvercle ne tombe car on faut bien fermer que l’eau ne puis sortir, <{…}> car on faut dehors aussi {graisser} le couvercle. Rempli le cilindre <{…} le tuyau> d’eau, <est> et applique le couvercle B avec le cire sur le cilindre et {ferre} bien avec le quatre vis CC, est <{…}> pese combien de poids qu’on faut pour attirer le couvercle K qui \est/ 6 pouces de diameter <est> et le cilindre est un pied de hauteur. Mais on faut de compter combien que le cire <{…}> a tenu la premiere fois. Mette pur le troisieme fois le couvercle K: et applique le tuyaux \D/ sur le couvercle B et rempli le tuyaux et le cilindre bien exact avec l’eau, vous verrez qu’on faut avoir autant de poids pour attirer le couvercle comme si le cilindre estoit egal{e}ment si haut que le tuyaux, le vis E de tuyaux {sont}, quand on veut remplir le tuyaux a trois pied on ouvre le vis a trois pied l’eau qui est dessus coule dessous, et on peut peser a chaque pied. Le chaine passe per le tuyaux quand on pese. C’est une chose incroyable si on ne voyait pas l’experience que c’est petit peu d’eau a autant de force, car il {n’y a} point de proportion entre le largeur de cilindre et de tuijau et le chaine passe encor. N.B. on ne fait pas oublier pour detacher l’instrument I quand on pese. Secondement on fait encor des autres experiences avec cette cilindre. Le couvercle en bas et en haut bien ferme et le tuyau applique mais le chaine extrait, rempli le cilind[re] et tuyaux plein d’eau et mette de poid sur le couvercle B et detache le vis CC que vous verrez que c’est petit peu d’eau qui est dans le tuyau a un incroyable force pour elever le couvercle avec tout le poid, mais si tost que seulement une gutte ou deux d’eau puis couler entre le couvercle et le bord de cilindre, la force est fait avec un pied de hauteur de tuyau il puisse elever le couvercle avec 40 <{…}> \livres/ si on prend donc 6 pied il fera un incroyable force,” Hessisches Staatsarchiv Marburg, file UniA 305a Nr 5947, 9–12. The description is repeated in the following, unnumbered sheets, which all end with a letter dated 11 May 1695 – so that one of the two descriptions is a copy (apparently, they are in two different hands). The file UniA 305a Nr 5947 contains two more unpaginated sheets (put at the end of the file), in which the apparatus is described two further times, in German: the second figure is provided in the last sheet. For a commentary, see De Clercq 1991, 104 (see also 90 and 101–102), and De Clercq 1989, 32–33.
- 235.
Valentini 1709, 59–60; cf. Valentini 1714, 43, 104. The instrument sold by Van Musschenbroek and described by Valentini had slightly different dimensions from the one described by Lufneu (see Table 2.2, De Volder’s natural-philosophical instruments). Valentini’s description was probably based on Van Musschenbroek’s manuscripts, as argued in De Clercq 1991.
- 236.
Lufneu only claims that it had, at the bottom, a border of around 6 lines to prevent the bottom to fall downwards.
- 237.
Where 12 lines = 1 inch, and 12 inches = 1 foot. I consider the Parisian ligne; the same duodecimal proportions were used in England, while in the Netherlands there were various kinds of conversion, based on proportions of 8, 10 or 12 lines (lijnen) per inch (duim).
- 238.
“En premier lieu M. de Volder remplit d’eau le cylindre jusques à l’ouverture AC. Il falut dix livres d’eau pour cela. Ensuite il remplit d’eau le tuyau LM jusques au bout L. Puis il chargea le plat de la balance QR de divers poids. Il falut y mettre 60 livres avant que le fond EF montât, ce qui montre évidemment que ce fond, qui ne soûtenoit que le poids d’environ 12 ou 13 livres d’eau (car le tuyau ML n’en contenoit qu’environ deux ou trois livres) étoit néanmoins aussi pressé que s’il eût soûtenu 60 livres, d’où paroît que l’expérience de Stevin est très-certaine. Pour mieux faire voir que l’eau contenuë dans le tuyau M L augmentoit extrêmement la pression, M. de Volder relâcha les quatre vis qui servoient à tenir ferme le couvercle, ayant mis premiérement au dessus de ce couvercle un poids de 20 ou de 30 livres. Je remarquai que les vis étant relâchées le couvercle s’éleva, & qu’il s’écoula de l’eau, preuve évidente qu’une assez petite quantité d’eau peut produire une fort grande pression,” Lufneu 1685, 386–387.
- 239.
“Il est donc constant que tout le fond BD de la 1 Figure est autant pressé par l’eau, qui est dans le cylindre ABCD & dans le tuyau ML, que si le cylindre s’élevoit selon toute sa largeur jusques au sommet du tuyau, & qu’on y versât 60 livres d’eau, d’où on peut recueillir ce principe universel, que l’eau y toutes les autres liqueurs pressent le fond qui les soutient, non pas selon leur masse ou leur pesanteur specifique, mais selon la hauteur qu’elles ont par-dessus ce fond, ce qu’il faloit demontrer,” Lufneu 1685, 388.
- 240.
“[…] iuxta […] Mariotti experimenta minima quoque fluidorum portio tubo gracilior CD dolio vastissimo AB aut cylindro perpendiculariter erectis annexo immissa vel emissa, non tantum omnem in dolio AB contentum humorem […] commovere, sed et magnam eius partem, cum pondere E in fig. 3 tab. V imposito, elevare, aut et operculum annexum vehementer attrahere valent, ut in Volderi cylindro tab. V fig. 2 delineato videre licet, cuius sequentes sunt enchireses: applica operculum KK (quod in fundo cylindri est) ipsi machinae mediante cera. Insere hamum catenae, per medium tubi D decurrentis, modo dicto operculo: annulum vero L in summitate catenulae applica bilanci et observa, quantum ponderis requiratur ad operculum attrahendum, quando cera tantum fundo agglutinatum est. Abhinc operculum de novo mediante cera applica cylindro, combinando simul fulcrum I verticillo HF comprimendum: hoc enim impedit, quo minus operculum, si machina invertatur, excidat. Optime enim obturandum est, ne aqua immittenda effluat, eumque in finem externe operculum quoque axungia quadam oblinendum erit. His ita praeparatis cylindrum aqua imple illique operculum superius B mediante cera applica omniaque bene claude firmaque quatuor verticillis CC. Pondera de novo, quantum ponderis requiratur ad operculum K (6 digitos in diametro habens) per cylindrum unius pedis attrahendum. Ubi tamen observetur, ut tantum de pondere detrahatur, quantum sola antea cera tenuerat. Applica porro tertia vice operculum K et desuper impone tubum aeneum D operculo B. Imple tubum aeque ac cylindrum aqua et videbis, quod tantum ponderis requiratur ad operculum attrahendum, ac si cylinder altitudine aequaret tubum D quod proportione quadam habita minuitur, si reseratis verticillis EEE plus minus aqua detrahatur. Admiratione sane dignum est, tantillum aquae adeo valide reniti, cum nulla sit proportio inter latitudinem cylindri et inter latitudinem tubi superimpositi, a catena transeunte iamdum ex parte occupatam,” Valentini 1709, 59–60. I discuss De Volder’s debt to Edme Mariotte below.
- 241.
See Guillemin 1868, 79.
- 242.
“Vidi primam machinam, quam conficiendam curaverat D. de Volder e quatuor asseribus sibi mutuo quam fieri potuit accuratissime coagmentatis, ne aqua efflueret. Fundo, ut in praecedenti experimento, rite disposito replebatur vas istud quadratum aqua. Sed nulla hactenus per commissuras effluebat aqua: operculo autem ei coaptato et tubulo aqua ad 5 pedum altitudinem repleto, tantam vim pressionis exercebat aqua in fundum et in vasis latera, ut undique per commissuras asserum efflueret. Quas dein pice accuratissime obturari, sed frustra, aqua nihilominus undiquaque perfluente, curavit; unde coactus fuit eam quam supra descripsimus e cupro fieri machinam. E quibus iterum evidenter constat aquae pressionem in fundum et latera (secundum leges hydrostatices) non ab elevatione fundi, sed ab aquae incumbentis pressione dependere,” Lufneu 1687, 242–243. In his criticism, Pujolas maintained that the upwards pressure of water on the upper part of the container was due to its being raised: so that it was not exerted but in this case: see Pujolas 1687, 26–27. Cf. Lufneu 1687, 242: “[n]otavi quippe postquam cylindrus ut et tubulus ML repleti erant aqua Cl. Virum D. de Volder operculo imposuisse 20 aut 30 libras, dein relaxasse quatuor cochleas, quibus operculum cylindro annectebatur, atque eo ipso aquam elevato operculo effluxisse. Quam circumstantiam si vel solam respexisset, qui potuisset D. Pujolasius negare veritatem experimenti, et hypothesin Stevini tanquam falsam reiicere? Et quonam pacto illius causa in sola fundi elevatione quaesivisset?”
- 243.
De Volder 1676–1677, 140v.
- 244.
“Fundum AB fundo CD similis esto et aequalis, itemque altitudo EF altitudini GH; sed pars IE insistens suiectae aquae KLBA minor sit, quam pars ipsius GCD sibi respondens, pendatque aqua EAB 1 lb, GCD 10 lb, sitque GCD cylindrus, is igitur ipsius EAB erit decuplus, huius tamen in fundum AB impressum esse tantum asserimus, quantus sit totius GCD in fundum CD,” Stevin 1605, 145. See Fig. 5.49, Stevin 1605, 145.
- 245.
“The Learned Stevinus, having demonstrated the Proposition we lately mention’d out of him, subjoyns divers consectaries of which the truth hath been thought more questionable, then that of the Theorem it self. And therefore he thought fit to add a kind of Appendix to make good a Paradox, which seems to amount to this. That If, in the Cover of a large Cylindrical Box, exactly closed, there be perpendicularly erected a Cylindrical Pipe open at both ends, and reaching to the Cavity of the Box; this Instrument being fill’d with water, the circular Basis of it will susteine a pressure, equal to that of the breadth of the Basis and height of the Pipe,” Boyle 1666, 135.
- 246.
“[…] ut luce meridiana clarius constet fundum, dum est in CD seu ante sui elevationem, actu premi ea gravitate ac vi, quam conatus sum probare, alteram, quam primo non annotavi, circumstantiam paucis apponam. Vidi primam machinam […],” Lufneu 1687, 242–243. See supra, n. 242.
- 247.
See supra, n. 195.
- 248.
Chalmers 2017, 59.
- 249.
“Je suppose pour fondement ce principe d’Hydrostatique, qu’aucune liqueur ne se répand sur un fond plat, sans le presser également par tout. Prenons garde dans la 2. Figure à la colomne CDE égale en hauteur au cylindre ABCD & au tuyau LM de la premiere. L’eau de cette colomne presse le fond DE par toute sa pesanteur, mais afin qu’ elle puisse demeurer en équilibre, il est nécessaire que la colomne d’à côté HD presse le fond GD de la même force que CDE presse DE, autrement l’eau qui est en CDE descendroit, & celle qui est en HD monteroit, ce qui est contre l’expérience, donc, &c. Par la même raison on prouve que l’eau de la colomne KEF presse le fond EF, de la même force que CDE presse DE, & la même chose faut-il dire de toutes les colomnes laterales,” Lufneu 1685, 387–388. At Leiden, Senguerd did not deal with the paradox, even if he maintained that the pressure of a fluid depends on its height, mostly by considering the case of Torricellian tubes disposed obliquely (in which the vertical component of the mercury reaches the same level): see his Philosophia naturalis (ed. 1685), chapter 8, and Rationis atque experientiae connubium, chapter 16.
- 250.
See Sect. 5.4.2.1, Early discussions of the paradox: Stevin, Galileo and Schott.
- 251.
“Nam cum diameter laminae ligneae KM partes 61 habeat quales diameter vasis HI habet 62, manifestum est quod superficies fundi vasis ad superficiem laminae se habet ut 3844 ad 3721; quorum differentia est 123. Itaque rotundum intervallum inter latera vasis et marginem laminae ligneae habet se ad aream laminae ut 123 ad 3721, hoc est, area laminae ligneae excedit aream dicti intervalli plus quam triginta vicibus. Ac proinde aqua incumbentem dicto intervallo inter margine laminae et later vasis plus quam triginta vicibus, pondusque, sive pressione huius alterius pondus pressionemque vincit plus quam triginta vicibus. Adeo ut impossibile sit ut aqua incumbens praedicto intervallo ita premat aquam ipsi subiectam, ut huius vi sublevetur lamina quam vis tricies maior deprimit. Quod aeque absonum atque absurdum phaenomenon esset, atque si pondus lanci iniectum alteri ponderi ipso tricies maiori in oppositam lancem imposito praeponderare,” More 1671, 155–156. More challenged Boyle also to the case of in which the quantity of water sustaining a body is more or less than the water displaced by the floating body (see More 1671, 169–170): in this case, however, Boyle did not answer. On More’s hylarchic principle, see in particular Hall 1990; Hutton 1990.
- 252.
“I thus argue: ’Tis manifested by Hydrostaticians after Archimedes, that in water, those parts that are most press’d, will thrust out of place those that are less press’d: which both agrees with the common apprehensions of men, and might, if it were needful, be confirm’d by Experiments. ’Tis also evident, that that part of the above-mention’d imaginary Plane, that is cover’d by the woodden Plate, must be pressed by a less weight than the other part of the same Plane; because the wood being bulk for bulk lighter than water, the aggregate of the wood and water incumbent on the cover’d part of the same Plane must be lighter in specie, than the water alone that is incumbent on the uncover’d part of the same Plane; and consequently this uncover’d part being more press’d than the other part of the Plane, the heavier must displace the lighter, which it cannot do but by thrusting up the board, as it does, when the external force that kept it down is removed. And, to add this upon the by, this greater pressure against the bottom than against the top of bodies immers’d in water specifically heavier than they, is a true reason of their emersion, as I have elsewhere shewn. So that there happens no more in this case than what usually happens in the ascension of bodies in liquors specifically heavier than themselves, on the account of the newly mention’d difference of Pressure. […] ’Tis true, that according to the Doctors supputation, if the solid Cylinder, consisting of the woodden Plate, and all the water directly incumbent on it, were put into an ordinary ballance, it would there many times out-weigh the hollow Cylinder of water alone that leans upon the uncover’d part of the imaginary Plane. And that is it that seems to have deceiv’d the Learned Doctor. But there are divers Hydrostatical Cases, wherein the Phænomenon depends not so much upon the absolute weight of the compared Bodies, as upon their respective and their specifick Gravity,” Boyle 1999–2000, volume 7, 111.
- 253.
“On pourroit déduire plusieurs choses de cette expérience, si la briéveté que je me suis proposée me le permettoit. J’ajoûterai seulement que l’on ruïne par là de fond en comble, l’objection qu’un célebre Théologien, nommé Henri Morus, a proposée contre les loix Méchaniques de l’Hydrostatique. Je ne m’arrêterai pas à le montrer, car tous ceux qui examineront la chose attentivement, pourront d’eux mêmes satisfaire à cette objection, & à toutes les autres qui sont répandues contre M. Descartes & M. Boyle, dans le Livre de ce Théologien,” Lufneu 1685, 388–389.
- 254.
De Volder owned the 1681 edition of Du Hamel’s treatise, so that his earliest source for Mariotte’s experiment seems to be the Journal (which he owned in a complete series): see Bibliotheca Volderina, 10 and 93.
- 255.
See Valentini 1709, plate 5, figure 3.
- 256.
“On voit un effet surprenant de l’équilibre dans l’expérience suivante: Aïez un tonneau de bois large de deux ou trois pieds ABCD, plein d’eau, enfoncé par les deux bouts: faites une ouverture au fond d’en-haut comme en E, pour y mettre un tuyau d’un pouce de largeur, si bien joint avec de la poix & de la filasse ou avec quelqu’autre matière, que l’air n’y puisse entrer, & que ce tuyau étroit, sçavoir EF, ait 12 ou 15 pieds de hauteur: emplissez d’eau le tonneau par quelques trous qu’on fera au fond supérieur, & posez sur le fond sept ou huitcent livres de poids, qui le feront courber en concavité, comme AMD. Si l’on met une marque blanche au dehors du tuyau, comme au point H, & à côté un peu plus haut une régle IL, plantée dans le mur voisin, & affermie de manière qu’elle demeure immobile; en versant de l’eau en suite peu à peu dans le tuyau étroit EF, vous verrez que quand il sera plein, le fond AMD sera élevé avec les poids de 800 livres dont il est chargé, non seulement à son premier état AED, mais même qu’il aura pris une courbure convexe, & que son élévation dans le milieu sera autant élevée par-dessus le point E, que le point M étoit au-dessous auparavant; ce que l’on connoîtra parce qu’on verra élever la marque blanche H, & passer peu à peu plus haut que la régle IL, dont on pourra mesurer la différence. Que si le tuyau est encore plus haut, l’élévation des poids sera encore plus grande: d’où l’on juge que le peu d’eau qui est dans le tuyau, a autant de force pour élever ce grand poids & courber le fond du tonneau en convexité, que si ce tuyau étoit de même largeur que le tonneau,” Mariotte 1686, 106–108. The report given by the anonymous reviewer is very synthetic, and does not include any explanation: “[e]n traitant de l’Equilibre des liqueurs d’où il prend occasion d’expliquer les Principes d’Hydrostatique, il rapporte une autre Experience de M. Mariotte, quia esté faite au College de Bourgogne en présence de grand nombre de personnes d’un tonneau AB dont le fonds chargé d’un poids de six cens livres fut élevé visiblement à la hauteur d’un pouce après qu’on eut fait couler dans ce tonneau 4 ou 5 livres d’ eau seulement par le moyen d’un tuyau CD assez étroit & d’une hauteur de 10. ou 12. pieds, comme on peut voir dans la 2. figure,” Anonymous 1678, 106.
- 257.
“Soit dans la figure suivante BCDE de l’eau dont la surface superieure soit BC, contenuë dans quelque vaisseau, & soit AFGH un corps cubique plus leger spécifiquement que l’eau, & plus pesant que l’air; je dis qu’il ne demeurera pas sur la superficie de l’eau: car la colomne quarrée d’eau KRLI seroit plus pressée qu’une colomne égale BEIK, puisque le poids du corps AH y seroit de plus. Donc le poids descendra, & entrera dans l’eau, mais il ne s’y cachera pas entièrement, parce qu’alors la colomne KRIL composée de ce corps & d’eau, seroit plus legére qu’une égale colomne d’eau BEIK. Soit donc son enfoncement jusques en KR, & que l’eau qui l’environne se soit élevée jusques en BC, qui sera plus haute qu’elle n’étoit auparavant à cause que la portion KGHR du corps occupe la place d’une partie qui est obligée de s’élever: je dis que l’eau contenue en KGHR, dont le corps occupe la place, sera d’un poids égal au poids de tout le corps, c’est-à-dire, que si une quantité d’eau égale en volume à KGHR pése autant dans l’air que le corps entier AFGH, il demeurera dans cette situation la portion KRGH de ce corps sera au total, comme la pesanteur spécifique de tout ce corps sera à celle de l’eau,” Mariotte 1686, 116–117.
- 258.
- 259.
Cf. Valentini’s commentary, supra, n. 240.
- 260.
- 261.
Cf. the French translation, L’existence de Dieu démontrée par les merveilles de la nature (1725, the treatise had many translations and editions): “M. Varignon, que tout le monde reconnoît pour un si grand Méchaniste, l’appelle un fameux Paradoxe; tous ne différent que quant à la maniere d’expliquer comment cela se fait dans les fluides. M. Mariotte l’appelle un effet surprenant de l’équilibre. M. Whiston, Prelect. Phys. pag. 247, dit, en parlant de cette Loi, qu’elle est parfaitement connuë dans l’ Hydrostatique; mais jusqu’à présent à peine en a-t-on trouvé aucune preuve naturelle ou Mathématique,” Nieuwentijt 1725, 594; see also 591–595. Cf. Varignon 1692; Whiston 1710, 247;
- 262.
“Quoi qu’il en soit, cette proposition est vraie, & elle est aujourd’hui admise si unanimement par tous les Méchaniciens, qu’il fa lieu d’etre surpris que quelques grands hommes en aient douté. On peut dire qu’en cela ils consultoient davantage leur imagination que les principes de l’Hydrostatique; car il est facile de démontrer la vérité dont on parle, à priori, ou du moins en s’appuyant seulement de la plus simple des expériences hydrostatiques; sçavoir l’équilibre qui se fait dans les branches d’un siphon d’inégal diametre, lorsque le fluide est dans l’une & l’autre à la même hauteur. S’il y avoit cependant encore quelques lecteurs peu convaincus de cette vérité, nous lui alléguerions une curieuse expérience que M. Mariotte faisoit à Paris vers le même-tems que M. de Volder faisoit la sienne en Hollande. Le Physicien François prie un tonneau de deux à trois pieds de diametre qu’il dressa sur un de ses fonds. Il perça celui de dessus d’un trou auquel il ajusta solidement un tuyau d’un pouce de diametre, & de plusieurs pieds de hauteur. Il chargea aussi ce fond d’environ sept à huit cens livres, ce qui le fit courber considérablement vers le dedans. Alors il mit de l’eau dans le tonneau, & quand il fut rempli, il en versa dans le tuyau; à mesure qu’il le faisoit, on la vit non-seulement redresser & soulever le fond avec les poids dont il étoit chargé, mais il fallut encore y en ajouter de nouveaux pour l’empecher de le courber en sens contraire,” Lufneu 1759, 198–199.
- 263.
I.e. a “glass with an opening in the middle to demonstrate the lateral pressure of the air,” and “several copper boxes of one and a half foot, with lids, for use in the wooden container, to measure the horizontal pressure of water, and at any angle.” See Table 2.2, De Volder’s natural-philosophical instruments.
- 264.
“[…] mais considérez-la en ceux qui, étant nés aveugles, s’en sont servis toute leur vie, et vous l’y trouverez si parfaite et si exacte qu’on pourrait quasi dire qu’ils voient des mains, ou que leur bâton est l’organe de quelque sixième sens qui leur a été donné au défaut de la vue. Et, pour tirer une comparaison de ceci, je désire que vous pensiez que la lumière n’est autre chose, dans les corps qu’on nomme lumineux, qu’un certain mouvement ou une action fort prompte et fort vive qui passe vers nos yeux par l’entremise de l’air et des autres corps transparents en même façon que le mouvement ou la résistance des corps que rencontre cet aveugle passe vers sa main par l’entremise de son bâton. Ce qui vous empêchera d’abord de trouver étrange que cette lumière puisse étendre ses rayons en un instant depuis le soleil jusqu’à nous; car vous savez que l’action dont on meut l’un des bouts d’un bâton doit ainsi passer en un instant jusqu’à l’autre, et qu’elle y devrait passer en même sorte, encore qu’il y aurait plus de distance qu’il n’y en a depuis la terre jusqu’aux cieux,” AT VI, 84. On Descartes’s treatment of the idea of tendency to motion, see Garber 1992, chapter 7; Schuster 2013, chapter 3.
- 265.
Descartes 1982, 193.
- 266.
“Premitur. I.e. expellitur,” Hamburg 273, 235.
- 267.
Descartes 1982, 193.
- 268.
“Verbi gratia, in fundo unius determinentur puncta g, B, h, in alterius i, D, l; dico omnia illa puncta aequali vi premi, quia scilicet premuntur lineis aquae imaginabilibus eiusdem longitudinis, nempe a suprema parte vasis ad imam. Neque enim fg linea hic longior censenda est quam fB vel aliae: non premit enim punctum g iis partibus quibus curva est et longior, sed iis tantum quibus deorsum tendit, quibus aequalis est aliis omnibus. Probandum autem est solum punctum f aequali vi premere tria puncta g, B, h atque tria distincta m, n, o premunt alia tria i, D, l. Quod fit hoc syllogismo: Res graves aequali vi premunt omnia circumquaque corpora, quibus expulsis aeque facile inferiorem locum occuparent. Atqui solum punctum f aeque facile occuparet inferiorem locum, si posset expellere tria puncta g, B, h atque tria puncta, m, n, o, si expellerent alia tria puncta i, D, l. Ergo solum punctum f aequali vi premit tria simul puncta g, B, h atque tria puncta distincta, m, n, o premunt alia tria i, D, l. Maior videtur esse tam clara et evidens ut possit esse principium scientificum. Minor ulterius probatur: Imaginentur omnia inferiora puncta g, B, h et i, D, l eodem momento aperiri vi gravitationis corporum suprapositorum, certe eodem instanti concipiendum erit solum punctum f triplo celerius moveri quam unumquodque ex punctis m, n, o. Illi enim tria eodem momento loca erunt explenda, quo momento unum tantum cuilibet ex punctis m, n, o erit occupandum. Ergo vis qua solum punctum f premit inferiora, aequalis est vi trium simul punctorum m, n, o,” AT X, 70–71.
- 269.
See Gaukroger and Schuster 2002.
- 270.
“Ie ne me souuiens pas de la raison de Steuin, pourquoy on ne sent point la pesanteur de l’eau quand on est dessous; mais la vraye est qu’il ne peut y auoir qu’autant d’eau qui pese sur le cors qui est dedans, ou dessous, qu’il y en auroit qui Pourroit descendre, en cas que ce cors sortist de sa place. Ainsy, par exemple, s’il y avoit un homme dans le tonneau B, qui bouchast tellement de son cors le trou marqué A, qu’il empeschast que l’eau n’en pust sortir, il sentiroit sur soy la Pesanteur de tout le Cylindre d’Eau ABC, dont ie suppose la EF base de mesme grandeur que le trou A, d’autant que, s’il descendoit en bas par ce trou, tout ce cilindre d’eau descendroit aussi; mais s’il est un peu plus haut comme vers B, en sorte qu’il n’empêche plus l’eau de sortir par le trou A et que ce trou soit bouché, il ne doit sentir aucune pesanteur de celle qui est sur luy entre B et C, d’autant que, s’il descendoit vers A, cette eau ne descendroit pas avec lui; mais au contraire une partie de l’eau qui est sous lui vers A, de même grosseur qu’est son corps, monterait en sa place, de façon qu’au lieu de sentir que l’eau le presse de haut en bas, il doit sentir qu’elle le soulève de bas en haut: et cela s’accorde à expérience,” AT II, 587–588.
- 271.
Descartes provides this theory in explaining his theory of gravity, which in his hands becomes a sort of branch of hydrostatics: “[t]hat is to say, just as one side of the balance can only be raised or lowered if the other side, at exactly the same instant, moves in the opposite direction, and just as the heavier always makes the other rise, so too the stone […], for example, is so opposed to the quantity of air above it, which is exactly the same size as it and whose place it would have to occupy if it were to move further away from the centre T [i.e. the centre of the Earth] that this air would of necessity have to descend to the extent that the stone rose. […] In this way you can see that every part of terrestrial bodies is pressed towards T, not indifferently by all the matter surrounding it but only by an amount of the matter exactly equal to the size of that part and which, being underneath the part, can take its place if that part moves down. This is the reason why, among the parts of any single body that we call ‘homogeneous’, such as those of air or water, the pressure on the lowest is not notably more than that on the highest, and why a man at the bottom of very deep water does not feel it pressing on his back any more than if he were swimming right on top,” Descartes 2004, 48–49. De Volder owned Descartes’s Le monde as well: see Bibliotheca Volderina, 9.
- 272.
“[…] je suppose que les petites parties, dont l’eau est composée, sont longues, unies et glissantes, ainsi que de petites anguilles, qui, quoiqu’elles se joignent et s’entrelacent, […] puissent aisément être séparées; et […] que presque toutes celles tant de la terre que même de l’air et de la plupart des autres corps ont des figures fort irrégulières et inégales, en sorte qu’elles […] se lient les unes aux autres, ainsi que font les diverses branches des arbrisseaux […]. Et lorsqu’elles se lient en cette sorte, elles composent des corps durs, comme de la terre, du bois, ou autres semblables; au lieu que, si elles sont simplement posées l’une sur l’autre, sans être que fort peu ou point du tout entrelacées, […], elles doivent […] composer des corps liquides fort rares et fort légers, comme des huiles ou de l’air,” AT VI, 233–234 and 236. De Volder owned the 1637 edition of Descartes’s Essais,: Bibliotheca Volderina, 4. In his Bibliotheca, no Latin edition of Descartes’s Essais, namely the Specimina, is listed. He owned the 1670 Latin edition of the Meditationes and Principia, namely the first two tomes of the fifth edition of Descartes’s Opera philosophica (1670–1672), printed in Amsterdam, in which the Meteora are printed in the third tome. Yet, De Volder referred to it several time in his dictata (for instance, as to the explanation of the elasticity of air: see infra, n. 333); as he refers to chapters (capita) of this treatise, rather than to discourses (in which the French editions are divided), he probably had a Latin version at his disposal. Latin editions of the Meteora appeared in 1644, 1650, 1656, 1664, 1672, 1685 and 1692.
- 273.
“45. What the nature of air is. […] [A]ir must be nothing other than an accumulation of particles of the third element, so thin and separated from one another that they obey all the movements of the heavenly globules; and that therefore air is a very rare, fluid, and transparent body and can be formed of particles of any figure at all. […] Since they are disunited, each one is moved independently of its neighboring ones; and thus occupies that whole small spherical space which it requires for its circular movement around its own center, and drives all neighboring particles out of that space. This is why it does not matter {for this effect} what figures the particles of air may have,” Descartes 1982, 203–204.
- 274.
- 275.
Descartes 1982, 70.
- 276.
“[…] as far as fluid bodies are concerned, even though our senses may not inform us that their particles move, since they are too small, this is nonetheless easily deduced from effects; especially in the cases of air and water, because many other bodies are destroyed by them: for no physical action of that kind can occur without {the fluid particles} moving […] Yet there is a difficulty here, because these particles of fluids cannot all move at the same time in every direction; […] In order to resolve this difficulty, we must recollect that it is not movement but rest which is contrary to movement; and that the determination of a movement in one direction is contrary to its determination in the opposite direction, as was stated earlier. Furthermore, [we must remember that] all moving bodies always tend to continue their movement in a straight line. Now from these things, it is obvious […] that as far as determination is concerned, the fact is that there are as many particles of D moving from C to B as in the opposite direction: for the same ones which come from C strike the surface of the body B and are driven back toward C. Although some of these particles, considered individually, strike B and drive it toward F (and thus more greatly impede its movement toward C than if they were at rest); an equal quantity of particles also move from F toward B, and drive B toward C. The result is that B is no more driven in one direction than in another, and therefore remains at rest, unless something else intervenes. No matter what we suppose the shape of B to be, it is always driven by exactly the same number of particles of the fluid coming from one direction as from the other. […] Thus far, however, we have been considering B to be at rest; if we now suppose it to be driven toward C by some force coming from elsewhere, this force, however slight, would suffice, not indeed to move, B by itself, but to unite with the [force of the] particles of the fluid body FD and to enable them to drive B toward C and to transfer to B some of their motion,” Descartes 1982, 70–71. In II.57, Descartes provides another demonstration of the same matter by considering more overtly the circles aeiouy described by the particles of the fluid. Please note that the particles do not ‘sustain’ the body in the fluid: its equilibrium is solely determined by its being equiponderant to water, i.e. of being exactly light as an equal volume of water, which thus does not displace it downwards.
- 277.
“From the preceding, it is clearly perceived that a solid body, immersed in a fluid and at rest in it, is held there as if in equilibrium. Further, no matter how large it may be, it can always be driven in one direction or another by the least force; whether this force comes from elsewhere […]. When this occurs, it is absolutely necessary for a solid body situated in such a fluid to be carried along with it: nor is this contradicted by the fourth rule; according to which, as I stated before, a body which is at rest cannot be set in motion by any smaller,” Descartes 1982, 75.
- 278.
On II.56: “[e]xigua. Haec regula est nobilissimi Hugenii,” Hamburg 273, 117; cf. Hamburg 274, 48: “[h]aec vis quantumvis exigua. […] [E]st idem cum regula nobiliss. Hugenii, qui affirmat nullum corpus quantumvis magnum in sua quiete permansurum, si aliud corpus, utut exiguum, occurrat.”
- 279.
“[…] l’obseruation que les pompes ne tirent point l’eau a plus de 18 brasses de hauteur ne se doit point rapporter au vuide, mais ou a la matière des pompes ou a celle de l’eau mesme, qui s’escoule entre la pompe & le tuyau, plutost que de s’eslever plus haut,” AT II, 382. For a discussion, see Nonnoi 1994.
- 280.
See Sect. 4.1.3.1, Four factors of cohesion: vacuum, rest, pressure and entanglement.
- 281.
“[…] imaginez l’air comme de la laine, et l’æther qui est dans ses pores comme des tourbillons de vent, qui se meuvent çà et là dans cette laine, et pensez que ce vent qui se joüe de tous costez entre les petits fils de cette laine, empesche qu’ils ne se pressent si fort l’un contre l’autre, comme ils pourroient faire sans cela; Car ils sont tous pesans, et se pressent les uns les autres autant que l’agitation de ce vent leur peut permettre; Si bien que la laine qui est contre la terre est pressée de toute celle qui est au dessus iusques au delà des nuës; Ce qui fait une grande pesanteur; En sorte que s’il falloit élever la partie de cette laine, qui est, par exemple, à l’endroit marqué O, avec toute celle qui est au dessus en la ligne OPq, il faudroit une force tres-considerable. Or cette pesanteur ne se sent pas communément dans l’air, lors qu’on le pousse vers le haut; pour ce que si nous en élevons une partie, par exemple celle qui est au point E, vers F, celle qui est en F va circulairement vers GHI, et retourne en E, et ainsi sa pesanteur ne se sent point; non plus que seroit celle d’une roüe, si on la faisoit tourner, et qu’elle fût parfaitement en balance sur son aissieu,” AT I, 205–206.
- 282.
“Mais dans l’exemple que vous apportez du tuyau dr, fermé par le bout d, par où il est attaché au plancher AB, le Vif-argent que vous supposez estre dedans, ne peut commencer à descendre tout à la fois, que la laine qui est vers r, n’aille vers O, et celle qui est vers O n’aille vers P et vers q, et ainsi qu’il n’enleve toute cette laine qui est en la ligne OPq, laquelle prise toute ensemble est fort pesante; Car le tuyau estant fermé par le haut, il n’y peut entrer de laine, ie veux dire d’air en la place du Vif-argent, lors qu’il descend,” AT I, 206.
- 283.
See the letters of Descartes to Mersenne of 13 December 1647 and to Carcavi of 11 June 1649, where Descartes claims that he himself had suggested to Pascal the performing of his experiment with mercury: AT V, 99 and 366.
- 284.
“Cuiuslibet figurae. Nonnulla certa et determinatur [sic] figura, {…} aquaeq[ue] particulae separatim moveatur, ab aliis, cuius cumq[ue] enim figurae sint, si modo nimia non impediat magnitudo, hoc pacto a globulis moveri potest, ita ut forma aeris non consistat in certa figura, sed tantum in tenuitate particularum, {earumdemq[ue]} a se invicem secretione,” Hamburg 274, 102.
- 285.
Descartes 1982, 172.
- 286.
“Sibi invicem sic adhaerent. Hoc sane in aere nostro locum habere ostendunt plurima effecta, q[uae] ex aeris gravitate dependent. Q[ua]lia sunt ascensus aquarum in antliis, ad pedes circiter 33, mercurii in tubis residentia ad pedes circiter 2½. Quae sane effecta tam notabilia non forent, nisi particulae ramosae in aere haerentes tota sui mole in ea corpora agerent, ac proinde non omnino disiunctim moveantur,” Hamburg 274, 82.
- 287.
“Componi. Si vulgatos philosophos qui in 4 elementis omnem operam pereunti consulamus, dabunt aere pro corpore simplici, humido, et calido, nec quid praeterea, ad haec omnia referunt q[uo]d ipsum praeterquam quod nil sit ab ere alienum aliis potius competit corporibus, in aqua enim est humiditas, in eadem calida, calor, in eadem simplicitas, unde sequeretur aerem idem esse quod aqua, quod falsum est. E contra, cum manifestum sit, si experientiam consulamus, solem omnia effluvia attollere ex corporibus q[uae] in aere haerent, quid certius et evidentius est, quam aerem non simplicem, sed omnino compositum e[ss]e, nec est q[uo]d dicant, se non dicere id de aere nos cingente, sed alio quem purum concipiunt, id e[nim] nil ad nos, is e[nim] si detur, imaginarius plane est, nullumq[ue] nobis usum prahebet. Quo itaq[ue] errore ut nos liberemus, videamus quidnam hic noster aer sit: si generationem aetheris antea descriptam videamus et respiciamus, constituunt aerem e[ss]e mobilia, et ex iis, q[uae] detruduntur, versus aquam et terram, calore attolli, frigore [n]a[m] rursus decidere, quodcunq[ue] enim sit attollitur, quamdiu est in illo motu, est aer, unde patet e[ss]e congeriem diversarum particularum et diversi generis, cum autem obsequantur motui globulorum caelestium constituere debent corpus valde rarum, cum globuli per quaelibet spatia moveantur, cumq[ue] omnia corpuscula q[uae] impedimento sunt, globulis expulsa sint, globuli ubiq[ue] sibi vias fecere, sicq[ue] aer factus est pellucidus, fluidus autem est ex eo, q[uo]d particulis crassioribus detrusis reliquae disiunctae et a {se} invicem remotae, cuilibet motui obsequantur. Figurae. Dicit particulas disiunctas e[ss]e, non quod una nos contingat alteram, et peculiarem habeat sphaeram, id e[nim] nec ex natura rei nec aeris fluit, separatae ergo sunt; et diversimode moventur, sed ita tamen ut se invicem tangant et premant: nonne enim antea ostendimus aetherem congregari circa sidus, quia globuli maiore habent recedendi vim eodem modo globulis premunt par[ticu]las ad motum in {eptas} deorsum, non itaq[ue] cohaerent, sed tamen sibi mutuo incumbunt, quemadmodum particulae in aqua quidem sunt separate, et tamen, se mutuo tangunt. Id itaque non concipiendum est quasi aer habeat particulas divulsas, sed ita, ut non cohaerentes tamen sibi mutuo incumbant, q[uo]d sequitur a priori ex natura generationis, et a posteriori, ex ipsa earum gravitate, si enim avulsae essent, non premerent se invicem, patet itaq[ue] quidem separatas esse, sed tamen sibi mutuo incumbere, et premere inferiora corpora,” Hamburg 273, 248–251.
- 288.
“[…] deduci potest istius vulgaris experimenti in quo enodando plurimi frustra insudarunt, cur nimirum fiat, q[uo]d urinatores aliisq[ue] homines sub aqua degentes nullum sentiant aq[uam] supra incumbentis pondus: huius enim ratio ex iis, q[uae] hoc §§ adferuntur, manifesta est. Etenim si homo constitutus in puncto ex. gr. 3, premeretur aqua 3 4 deorsum ut occuparet locum 2, necessario aqua, q[uae] in 2 est, eadem mole 1 est corpus hominis ascenderet versus 3, quae cum aeq[ua]li impetu huic ascensui resistat, efficit etiam, ut homo in 2 nullo pacto deorsum premi queat, unde nec mirum est, eum nullum suora se sentire pondus, quippe cuius tota vis in ea consistit pressione,” Hamburg 274, 100. See Fig. 5.57, Descartes 1644a, 203.
- 289.
“3. Propositio. Causam reddere cur homo alte infra aquam natans maximo eius pondere non opprimatur. Humani corporis planum occupet pedes 10, is infra aquam 20 pedes demersus, aquae pede cubico 65 lb aestimato, sustinebit per 10 et 11 prop. de Elem. Hydrostat. 13,000 lb. Quamobrem qui potest, ut tanto pondere pressus non opprimatur; Causa autem haec est: Omni pressu quo corpus dolore afficitur, pars aliqua corporis luxatur. sed isto pressu nulla corporis pars luxatur. Isto igitur pressu corpus dolore nullo afficitur. Assumptio syllogismi reipsa manifesta est, nam si pars aliqua ut caro, sanguis, humor aut quodlibet denique membrum luxaretur, in alium locum concedat necesse esset; atqui locus ille non est extra corpus, cum aqua undique aequali pressu circumfusa sit (quod vero pars ima per 11 propos. Hydrostat. paulo validius prematur superiore, id hoc casu nullius momenti est, quia tantula differentia partem nullam sede sua dimovere potest) neque item intra ipsum corpus concedit, cum istic corpore omnia oppleta sint, unde singulae partes singulis partibus aequaliter resistunt, namque aqua undiquaque eadem ratione corpus totum circumstat. Quare cum locus is nec intra neque extra corpus sit, absurdum imo impossibile fuerit partem ullam suo loco emoveri, ideoq[ue] nec corpus hinc afficietur ullo dolore. Sed in exemplo clarius ita intelliges, esto A B C D aqua cuius fundum D C, in quo foramen E habeat epistomium sibi insertum, cui dorso incumbat homo F. Quae cum ita sint, ab aquae pondere ipsi insidente nulla pars corporis luxari poterit, cum aqua ut dictum est, undique urgeat aequaliter. si vero eius veritatem explorare libeat, eximito epistomium E, tumque tergum nulla re fultum sustinebitur, ut in locis caeteris; ideoque istic tanto pressu afficietur, quantus 3 exemplo 2 propositionis huius demonstratus est, videlicet quantam efficit columna aquea cuius basis sit foramen E altitudo autem eadem quae aquae ipsi insidentis. Quo exemplo propositi veritas manifesto declaratur,” Stevin 1605, 148–149.
- 290.
Boyle 1666, 242.
- 291.
“[…] this subtil Philosopher: for whose Ratiocinations though I am wont to have much respect, yet I must take the liberty to confess my self unsatisfy’d with this. For haveing already sufficiently prov’d, That the upper parts of water press the lower, and the bodies plac’d beneath them, whether such bodies be lighter in specie then water or heavier; we have subverted the Foundation, upon which Monsieur Des Cartes’s ingenious, though unsatisfactory, Explication is built,” Boyle 1666, 231–232.
- 292.
“And yet I shall add ex abundanti, That supposing what he sayes, That in case the solid B should descend towards A, the incumbent water would not descend with it, but a part of the subjacent water, equal in bulk to the solid, would ascend, and succeed in its room; yet that is but accidental, by reason of the steinchness and fulness of the Vessel,” Boyle 1666, 232.
- 293.
“VVe took then a somewhat slender Cylindrical pipe of Glass, seal’d at one end, and open at the other; and to this we fitted a Rammer, which (by the help of some thongs of soft leather, that were carefully wound about it) did so exactly fill the pipe that it could not easily be mov’d to and fro; and would suffer neither water, nor aire, to get by betwixt it, and the internal surface of the Glass. VVe also provided some small Tad-poles (or Gyrini) about an Inch long or less; which sort of Animals we made choice of before any other, partly because they could, by reason of their smalness, swim freely to & fro in so little water as our pipe contain’d; & partly because those Creatures, being as yet but in their Infancy, were more tender, and, consequently, far more expos’d to be injur’d by compression, then other Animals of the same Bulk, but come to their full age and growth, would be, (as indeed such young Tad-poles are so soft and tender, that they seem, in comparison to the bigger sort of flies, to be but organiz’d Gelly.) One of these Tadpoles being put into the water, and some Inches of aire being left in the pipe, for the use anon to be mention’d; the water and aire, and consequently the Tadpole, were by the intrusion of the plug or rammer, with as great a force as a man was able to imploy, violently compress’d; and yet, though the Tadpole seem’d to be compress’d into a little less Bulk then it was of before, it swom freely up and down the water, without forbearing sometimes to ascend to the very top, though the Instrument were held perpendicular to the Horizon. […] And having repeated this Experiment several times, & with Tadpoles of differing ages; we may, I presume, safely conclude, That the Texture of Animals is so strong, that, though water be allowed to weigh upon water, yet a Diver ought not to be opprest by It: Since, whether or no water weighs in water, ’tis manifest that in our Experiment, the water, and consequently the Tadpole, was very forcibly by an External Agent compress’d betwixt the violently condens’d aire, and the rammer,” Boyle 1666, 243–246. The solution of Stevin and Boyle was followed also by Von Guericke, who provides a short statement on this issue in his Experimenta nova, book 3, chapter 1: “[b]ecause of its own weight, air presses not only upon itself but upon all things beneath it with an essentially constant pressure. We do not feel this because we live in this air which surrounds us with equal pressure on all sides and at the same time penetrates us. For as fish have no perception of pressure in the water, so animals perceive it even less in the air,” Von Guericke 1993, 113. The reference to the fact that air penetrates us, seems to rely particularly on Boyle’s idea that air makes us resisting to its pressure as it is provided with an elastic power, given in his New Experiments about the Differing Pressure of Heavy Solids and Fluids: “I have elsewhere proved by Experiments, that a cubick inch of Air, for instance, has as strong a spring as suffices to enable it to resist the weight of the whole Atmosphere, as far as it is exposed thereunto; for else it would be more compress’d than de facto it is. And 3. I have also shewn, that a very little portion of Air, though it will much sooner loose its spring by expansion than a greater, yet ’t will resist further compression as much as a greater: And 4. I have also shewn, that in the pores of the parts of Animals, whether fluid or consistent, as in their Blood, Galls, Urines, Hearts, Livers &c. there are included a multitude of Aereal corpuscles, as may appear by the numerous bubles afforded by such Liquors, and the swelling or expansion of the consistent parts in our exhausted Receiver. 5. To this we may add, that, besides the Bones, whose solidity is not questioned, a much greater part of the humane body than is wont to be imagined, does really consist of Membranes and Fibers, and the coalitions and contextures of these; and that these substances are by the Providence of the most wise Author of Things made of a much closer and stronger Texture, than those, that have not tried, will be apt to think; as I could make probable by the great force that Bladders will endure, and the very great weight that Tendons of no great thickness will lift up or sustain, and by other things that I shall not now insist on. Lastly, There is a far greater difference, than men are wont to suspect, between the effects of the Pressures made upon Bodies by incumbent or otherwise applied solid weights, and those that they suffer from heavy but every way ambient fluids; as will appear by the Experiments to be mention’d by and by,” Boyle 1999–2000, volume 7, 217.
- 294.
“[…] having met with a Learned Physician, that living by the Sea-side in a hot climate, delighted himself much in diving; and inquiring of him whether he felt no compression, when he passed out of the Air into the Water, he answered me, that when he div’d nimbly as others use to do, he took not notice of it, but when he let himself sink leisurely into the water, he was sensible of an unusual pressure against his thorax, which he several times observed. A man that gets his living by fetching up goods out of wrack’d Ships, complain’d to me, that if with his diving Bell he went very deep into the Sea, and made some stay there, he found himself much incommodated; which though he imputed to the coldness of the water, yet by the symptoms he related I was inclin’d to suspect, that the pressure of it upon the Genus Nervosum might have an interest in the troublesome effect. And I have been assured by an eminent Virtuoso of my acquaintance, that he was lately informed by a person, whose profession it is to fetch up things from the bottom of the Sea by the help of a diving Bell, that several times when he descended to a great depth under the surface of the water, he was so compress’d by it, that the blood was squeez’d out at his Nose and Eyes; which Relation seems to favour our conjecture, and would much more confirm it, if I were sure, that the effect was no way caus’d by some fermentation or other commotion in the blood it self, occasioned by the great density or other alterations of the Air he breath’d in and out, or by some other operation of the ambient Medium distinguishable from the compression of the water, though perhaps conjoyn’d with it,” Boyle 1999–2000, volume 7, 220–221.
- 295.
See the text quoted supra, n. 293.
- 296.
“Explicare. Id hac in re situm, po[ss]e hic rationem dari rei, de qua tam acriter disputatur, id q[uod]: cur urinatores non sentiant infra aquam eius gravitatem. Stevinus fingit vas quodpiam, et in eius fundo hominem horizonti parallelum, vasiq[ue] aquam infundit, q[uo]d fit? Non {sentis} o[mnin]o aquam, si vero in fundo sit orificium, per q[uo]d aqua descendere potest, idq[ue] si corpore tegat, o[mnin]o tunc demum sentiet aquam, is, eumq[ue] secutus Boijle, putat aquam premere quidem, sed quia undiq[ue] premit aequaliter, non sentire, q[uo]d si verosimile sit, {ea} et inverosimile erit, q[uo]d sc[ilicet] o[mnin]o a torculari pressus non sentiet pressionem, verum quidem {e[nim]} si c[or]pus solidum e[ss]et, non sensurum pressionem, {[n]a[m]} si o[mn]ia in homine e[ss]ent aqua repleta, {c[um]} vero cavum sit corpus. {X} non aqua sed aere repletum, o[mnin]o sentiet. Alia ergo causa e[ss]e debet, quam licet Boijle voluerit impugnare. Verissima tamen {e[st]}, et quamvis Boijle testatur sibi ab autore nostro {[n]o[n]} e[ss]e satisfacturum, nil tamen, q[uo]d aliquomodo urget, profert. Concipiamus itaq[ue] hominem in aquis mediis constitutum, non sentiet (si premeretur) aquam, nisi deorsum orientem, si vero ostendamus hanc pressionis vim, non ab o[mn]e sed alia aqua sustineri, causa certa {e[st]}, concipiamus ergo cylindrum, {aq[uae]} ipsi incumbentem, si {hic} descenderet, alius ipsi aequalis ascendere deberet, c[um] vero sint aequilibrio, non potest unus descendere, nec {prom} premere, si vero concipiamus ap[er]turam q[ua]m tegit o[mnin]o, sentiet pressionem quia tunc una aqua descendere potest non ascendente alia, sed aere, ut si 2 habeamus bilances, et utrisq[ue] imponamus 100 ll, si q[ui]s manui sustineat alterutram, non sentient pressionem, quia ab altera parte est aequalis, si vero, 100 ll addat ℥ 1 tunc demum sentiet, quia utraeq[ue] non amplius sunt in aequilibrio, sed una praevalet, et magis premet, quia proinde causa sequitur ex principiis mechanicis,” Hamburg 273, 235–236.
- 297.
As to II.57: “[m]utare. B ergo movebitur sed hoc motu non tolletur motus ab iis versus a, quia non opponitur huic motui, sed determinationi, nec est q[uo]d opponat quispiam, tales annulos authorem hic pro modulo fingisse, atq[ue] adeo hijpothesis usum e[ss]e. Moveantur. Ut haec difficultas tollatur, dico demonstrationem nostram non uti talibus circulis, sed fluidi aequilibrio, quod si non facere, pars q[uae] praevaleret, tolleret motum particularum, in contrarias partes motarum, unde haec aucta viribus reliquas secum aget, versus easdem partes, atq[ue] adeo non stagnans amplius, sed motum erit fluidum, sic quoscunq[ue] fingamus circulos, demonstratio sequitur. Si itaq[ue] ponamus 2 circulos, sive plures ambientes B s[e]mp[er] eadem erit demonstratio, si enim tot sunt par[ticu]lae, q[uae] impellunt versus orientem ac versus occidentem, necessario manebit eodem in loco. Si vero plures ab oriente, movebitur versus occ[identem]: q[uo]d in stagnante e[ss]e nequit. Res haec commodius explicari nequit quam exemplo bilancis,” Hamburg 273, 117–118. As to II.56–57, in the other series of dictata: “[…] ratio autem huius rei manifesta est, ut enim bilanx, in cuius utraq[ue] lance aequale sit positum pondus, manebit in aequilibrio; si vero alterutri addatur vel minimum pondus, statim ex ea parte praeponderabit. Sic etiam corpus B in fluido stagnante, sive cuius exiguae particulae non in hanc magis quam in illam feruntur partem, constitutum, pellitur a particulis q[uae] a {C} B versus F feruntur versus B, et idem corpus pellitur a totidem particulis aequali vi versus C, unde necessarium est, ut in eo loco, in aequilibrio quiescat, si vero alteri parti huius aequilibrii vis quaedam, licet minima addatur, {illae} vis efficiet ut nunc maiori vi propellatur B versus f quam versus C, cum autem maiores vires semper sortiatur effectus, necesse etiam est ut B versus F moveatur. §§ LVII. Hoc paragrapho autor aliq[ua]nto clarius explicat id quod priori proposuerat, et hunc in finem eligit in fluidi particulis certum quoddam motus genus, in quo evidentius id, quod prius universum demonstraverat, demonstrat, non tam existimandum est, autoris demonstrationem semper talibus hamulis fundatam esse, cum si accurate attendamus, tota vis {nitator illis}, q[uo]d partes fluidi in diversas aequali impetu ferantur partes, deinde quod omnis impetus vel sit circularis, vel circularibus aequipollere, tandem q[uo]d ex primo sequitur corpus B aequalibus viribus propelli versus C, quam versus F, ex quibus tribus, q[uae] in omni fluido locum habent, totam suam conficit demonstrationem,” Hamburg 274, 48–49. See Fig. 5.60, Descartes 1644a, 63.
- 298.
De Volder 1676–1677, 81r.
- 299.
De Volder 1676–1677, 83r.
- 300.
“Verum ut pateat simul et quam imperite de hisce rebus loquantur, qui aëris hancce pressionem et gravitatem impugnatam volunt, et quando pressio illa debeat animadverti, age excutiamus huius effecti manifestam causam. Consideremus hunc in finem bilancem ex aequilibrio suspensam, ita ut utrique lanci mille imponantur pondo. Supponat quis uni lanci manum. Proculdubio nullam pressionem sentiet, non quod illa lanx non omni suo pondere deorsum ruat, sed quod huic deorsum pressioni obsequi nequeat, quin altera lanx paribus ad descensum viribus pollens assurgat. Qua ratione dum hae vires sibi invicem impedimento sunt, neutra lancium vel ascendit vel descendit, neutra suppositam manum vel minimum premit. Eadem ratione aquae aut cuiuscunque alterius liquoris quae in vase stagnat, una pars nequit descendere, quin ex altera parte tantundem aquae ascendat, quae cum parium cum priori si virium, huic descensui obicem ponit, efficitque pressionis aequalitate, ut duae quaelibet aquae partes eiusdem altitudinis eiusdemque quantitatis suas invicem premendi vires tollant et in aequilibrio sint. Ponatur nunc porro infra hasce aquas corpus quodcumque, id sane descendere nequit ea pressione, qua aqua superior imminet, quia dum descendit tantundem inferioris aquae, et parium idcirco cum superiore virium ascenderet. Hinc si vel descendat vel ascendat, id non fiet a pressione ipsius aquae, sed ab excessu gravitatis levitatisve quo aquam illud corpus superat. Cui consequens est, hanc aquae pressionem cum in aequilibrio sit a manu aut corpore nostro aquis supposito nequaquam animadverti posse. Quae demonstratio non tantum in aquis locum habet, sed in fluidis quibuscunque corporibus aqua sive levioribus sive gravioribus, sive minus sive magis compressis. Non enim nititur ea peculiari aquae natura, sed universali lege gravitatis et natura fluidorum corporum,” De Volder 1676–1678, disputation 3, thesis 7.
- 301.
“I. Aquae partes superiores in inferiores gravitant. II. Premit deorsum, ad latera et sursum. III. Premit tantum secundum altitudinem unde sequitur, urinatores sub aquis nullum incumbentis pondus sentire,” Serrurier 1690, annexa 1–3.
- 302.
“[…] id notari velim, in fluidis corporibus motum gravitatis quasdam deprimendo fluidi partes alias attollere eadem vi, qua reliquas deprimit, unde conficitur non omnem superiora versus motum gravitatem tanquam causam excludere,” De Volder 1676–1678, disputation 2, thesis 5.
- 303.
Descartes 1982, 193.
- 304.
Descartes 2004, 49–50.
- 305.
See supra, n. 76.
- 306.
Descartes 1982, 192. Please note that De Volder does not address the role of air, in commenting upon this article: cf. Hamburg 273, 235; Hamburg 274, 99–100.
- 307.
See Sect. 5.1, The gravity of the air: a complex idea.
- 308.
“Quae demonstratio non tantum in aquis locum habet, sed in fluidis quibuscunque corporibus aqua sive levioribus sive gravioribus, sive minus sive magis compressis. Non enim nititur ea peculiari aquae natura, sed universali lege gravitatis et natura fluidorum corporum,” De Volder 1676–1678, disputation 3, thesis 7.
- 309.
De Volder owned the first two volumes of Lana de Terzi’s Magisterium naturae et artis (1684–1686; the third volume was published in 1692): see Bibliotheca Volderina, 1.
- 310.
Lana de Terzi established the ratio of the weights of air and water via the method proposed by Galileo in his Discorsi, quantifying it as 1 to 640, and then claimed that the diameter of the copper spheres capable of floating in air should be of 14 feet: see Lana de Terzi 1670, 53, 56–57.
- 311.
See Hooke 1679, 21–24. Lana de Terzi’s idea was also discussed in Leibniz’s Hypothesis physica nova (1671). In 1671 a review by Henry Oldenburg of the Prodromus appeared in the Philosophical Transactions, but no discussion of the idea of the aerostate is made. Johann Christoph Sturm labelled Lana’s flying chariot as realizable: Sturm 1676, 56–66.
- 312.
See, in particular, disputation 3, thesis 5: “[e]stne igitur aqua non gravis? An vero ea ipsa aëre minus coarctata compressave est?” Also, De Volder – as seen in the comparative table on the weights of air and water (Table 5.1, De Volder’s measurements in hydrostatics) – performed measurements on the weight of the water, ascertaining its changes.
- 313.
See Bertoloni Meli 2006, chapter 6.
- 314.
Further editions of Commandino’s translation, both owned by De Volder (see Bibliotheca Volderina, 5) appeared in 1583 and 1680. Another popular device, working by air compression, was the arquebuz, or wind-gun, allegedly invented by Hero’s master, Ctesibius. Before Commandino’s edition, Hero’s ideas were spread by their discussion given in Girolamo Cardano’s De subtilitate rerum (1550).
- 315.
“[A]ëris corpora inter sese quidem coaherent, non tamen ex omni parte, sed interiecta habent intervalla quaedam vacua, sicut arena, quae est in littoribus. Itaque minimo concipiendum est arenae particulas corporibus aëris similes esse, aërem vero, qui inter particulas arenae intericientur, similem vacuis intra aërem contentis. Quemombrem vi quadam accedente aërem densari contingit, et in vacuorum loca residere, corporibus praeter naturam inter sese compressis: remissione vero facta rursus in eundem ordinem restituitur, ob naturalem corporum contentionem, quemadmodum et in cornuum ramentis, et in spongiis siccis: quae si compressa remittantur, rursus in eundem locum redeunt, eandemque accipiunt molem. Similiter si aliqua vi aëris particulae a se invicem distractae fuerint, et maior praeter naturam locus vacuus fiat, rursus ad sese recurrunt,” Hero and Commandino 1583, 8–9. Descartes used the model of the sponge to explain rarefaction in Principia II.6–7. His idea of elasticity, however, does not rely on the comparison with the sponge.
- 316.
See Valleriani 2010, 173–176.
- 317.
Aristotle 2014, volume 1, 369; cf. Physica, 217a26–33.
- 318.
Aristotle 2014, volume 1, 369; cf. Physica, 217b11–19.
- 319.
- 320.
See Grant 1981, 72–73.
- 321.
Hero and Aleotti 1589, 8. For a thorough discussion, see Valleriani 2014.
- 322.
- 323.
Posthumously published in his Scripta in naturali et universali philosophia (1653). Discussed in Manzo 2003. See also Gemelli 1996.
- 324.
For a thorough discussion, see Gemelli 2002; Van Berkel 2013, chapter 4.
- 325.
See Mersenne 1644, Praefatio, 8 (unnumbered). In turn, in his Mechanica hydraulico-pneumatica Schott (who criticizes to the idea of interstitial or disseminated vacuum) traces back the resilience of air after compression to the resistence that bodies exert to their penetration by other bodies: see Schott 1657, 45–46.
- 326.
“Debet autem ad hoc intelligi aër hic noster quem respiramus, tantum possidere appetitum, seu tanta vi pollere ad sese dilatandum atque rarefaciendum, quanta est vis naturae elementaris ipsum comprementis seu condensantis. Quod etiam ipsius naturae legibus apprime quadrat, et constantissime servatur in omnibus illis corporibus quibus resiliendi facultas ab ipsa natura concessa est, ut in arcubus, et aliis innumeris: quae quidem omnia corpora, donec tenduntur aut vi comprimuntur, modo non ultra metas virium suarum, nunquam cessant reniti; ac tanta vi ad resiliendum feruntur innato appetitu, quanta ab aliis corporibus trahuntur, aut impelluntur: ita tamen ut initio sui resultus, vis illa fit maxima, inde vero sensim languescat fiatque minor ac minor, ac tandem nulla; postquam scilicet corpus resiliens ad debitum sibi statum redierit. Eodem modo, idem aër tubo inclusus, quandiu tubus ille clausus remanet ex utraque parte, tantum premitur atque condensatur quantus est nisus naturae elementaris ad premendum hunc nostrum aërem; ideoque ille idem vi rursus pari, tali compressioni renititur, dilatari appetens, ut locum ampliorem sibi naturaliter debitum acquirat. Neque enim ille tubo inclusus minus premitur aut condensatur quam extra; quia cum iam pressus atque condensatus assumptus sit, nullam exinde libertatem nactus est adhuc ut dilatari ac rarefieri posset,” Roberval 1923, 315. For an extensive account, see Webster 1965.
- 327.
“At vero, si praeter hydrargyrum aut aquam, admittatur in tubo portio aliqua hujusce nostri aëris pressi atque condensi, ut supra diximus, is aër libertatem nactus, ac suis omnibus partibus resiliens ad sese rarefaciendum, impellet ipsum hydrargyrum aut aquam, quae ideo deprimentur infra praedictam altitudinem, vel magis vel minus, prout aër ipse majores aut minores ad rarefactionem vires obtinebit. Eodem prorsus modo quo aqua in aequilibrio constituta: dum scilicet ejus superior superficies in mari vel stagno aliquo, vel etiam in vase, ad horizontem librata est,” Roberval 1923, 317–318. Cf. Noël 1648, 55–56. I owe most of the references to Webster 1965, who provides a full-fledged account of the first experiences on the elasticity of air.
- 328.
This text is included in Gassendi’s Animadversiones in decimum librum Diogenis Laertii: see Gassendi 1649, Appendix, iii–x. Gassendi had also reported and commented upon Roberval’s experiment with vacuum in a vacuum: see Mersenne’s De nupero circa inane coacervatum (April 1647): in Gassendi 1649, 424–444.
- 329.
See Gassendi 1649, Appendix, v–vi.
- 330.
See chapter 8: “[e]sse non pondus tantum, sed et rarefactorium aëri elaterem experimentis demonstratur,” Pecquet 1651, 48.
- 331.
“Hunc fingito tibi velut spongiosi vel lanei potius cumuli terraqueum orbem ambientis molem; cuius proinde partes superiores ab inferioribus, compressione gradatim incedente, sustineantur, sicut, quo Terris accedunt vicinius, eo etiam incumbentium nisu et pondere compactius opprimantur: et ob id spontaneo dilatatu (quem elaterem nuncupo) utcunque graviter aggestarum onus, subiectae nitantur, si libertas adsit, rarescere. Hinc infero eiuscemodi partium infimam, ut toti subiectam oneri, sic omnium esse maxime condensatam; et per hoc ab eadem non solo duntaxat Pondere, sed et elasteris, cuius tum validissimus ad rarefaciendum nixus est, virtute terraqueae sphaerae premi superficiem,” Pecquet 1651, 48–49. The idea of the wool can be found also in the letter of Torricelli to Ricci of 28 June 1648, where, however, no elasticity of the air is considered, but only its compression: see Galluzzi and Torrini 1975, volume 1, 130–132.
- 332.
“46. Why it is easily rarefied and made dense. Air, however, is easily made dense by cold and rarefied by heat: for, since almost all of its particles are flexible, like soft feathers or thin cords; the more rapidly they are driven, the more widely they extend themselves, and therefore require a larger sphere of space for their movement. […] 47. Concerning its forcible compression in certain machines. Finally, air which is forcibly compressed in some vessel has the {same} force to spring back {as was employed to compress it} and to extend itself immediately into a wider space. On the basis of this, machines are created […]. The cause of this is that, when air has thus been compressed, each of its parts does not have that small spherical space which it needs for its movement to itself, but other neighboring particles enter into that space. Since the same heat or the same agitation of these particles is meanwhile maintained by the heavenly globules constantly flowing around the particles of air, the latter strike one another with their extremities, and attempt to drive one another out of their place, and thus together produce the force to occupy a greater space,” Descartes 1982, 204–205.
- 333.
In the Hamburg 273 series, notably, De Volder makes recourse to the case of closed thermoscopes: “aeris phaenomenum est, quod frigore condensatur, et calore rarefit, ut patet in thermoscopiis, in quorum superiore parte est aer, in inferiore aqua fortis, colore q[uo]dam tincta, ubi enim aer calore maiore movet in latius se extendens premit aquam adeo ut effluere debeat, in frigore contra, contrarium fit in thermoscopiis clausis, non tam a rarefactione aeris, quam, aquae pendentibus. Duo enim eorum sunt genera, quorum prius solummodo huic nostrae rei confert, aer sc[ilicet] rarefit, et plus occupat spatii, quod ex natura eius evidentissime sequitur. Part[ticu]lae enim eius sunt flexiles et molles, quae flaccidae quidem haerent extenduntur et maius requirunt spatium, instar funiculi cuius exempli author utitur metor. c. 2. § 3. Sicq[ue] maior motus impellit corpuscula, aut per lineam rectam aut circularem q[uae] regula generalis est per circulare in orbem feruntur, si transferantur in maiori motu q[ua]m ut ei per lineam possunt obsequi, sic radii solares ita impingunt et movent corpora, cumq[ue] non possunt omnia obsequi motus per lineam rectam ferri debent per circularem, quod cum fit vim habent alia corpora excludendi, sicq[ue] maius spatium occupandi, ubi autem motus c[i]eat pori rursus sunt minores et aer condensatur,” Hamburg 273, 251–252. Cf. the other series: “[q]uo pacto molles plumulae et tenues folliculi celeri agitatione possunt rigiditatem acquirere, accurate explicatum vide in meteoris p. 3 cap. 2,” Hamburg 274, 102. Cf. Descartes’s Météores, Discours second: “[r]emarqués aussy que les vapeurs occupent tousiours beaucoup plus d’espace que l’eau, bienqu’elles ne soient faites que des mesmes petites parties. Dont la raison est que lorsque ces parties composent le cors de l’eau, elles ne se meuuent qu’assés fort pour se plier, et s’entrelacer, en se glissant les vnes contre les autres, ainsi que vous les voyés representées vers A. Au lieu que lors qu’elles ont la forme d’vne vapeur, leur agitation est si grande, qu’elles tournent en rond fort promptement de tous costés, et s’estendent par mesme moyen de toute leur longeur, en telle sorte que chascune à la force de chasser d’autour de soy toutes celles de ses semblables, qui tendent à entrer en la petite sphere qu’elle descrit. Ainsi que vous les voyés representées vers B. Et c’est en mesme façon que si vous faites tourner assés viste le piuot LM, au trauers duquel est passée la chorde NP, vous verrés que cette chorde se tiendra en l’air toute droite et estendue, occupant par ce moyen tout l’espace compris dans le cercle NOPQ, en telle sorte qu’on n’y pourra mettre aucun autre cors, qu’elle ne le frappe incontinent auec force, pour l’en chasser: au lieu que si vous la faites mouuoir plus lentement, elle s’entortillera de soy mesme autour de ce piuot, et ainsi n’occupera plus tant d’espace,” AT VI, 241–243.
- 334.
“Nam, quam afferunt, ratio futilis est. Penetrat, inquiunt, vitream aetherea subtilitas densitatem, et affusa quaquaversum complicatae vesiculae, per illius tandem poros intus irrepit, ac totam in pristinum distendit tumorem. Sed meminerint, quod autumant, pervium esse circumquaque vitrum ingressuro aetheris et proinde versus vesicam […], aetherem aequali undique radiorum irruentium impetu ferri; sic ut eam potius interceptam comprimat, opprimatque, quam eidem in seipsam reacturus, inutilem dilatationem curet imponere,” Pecquet 1651, 52.
- 335.
- 336.
Pascal 1663, 18–21; Senguerd 1681, 178; Mariotte 1686, 139–140. See also Charleton 1654, 55–57, discussed in Webster 1965.
- 337.
See Magalotti 1666, 31–34; Von Guericke 1993, 179; Sturm 1676, 22.
- 338.
- 339.
Boyle 1660, 22.
- 340.
Boyle 1660, 23.
- 341.
Boyle 1660, 25–27.
- 342.
I.e. to Line’s Tractatus de corporum inseparabilitate (1661). See Shapin and Schaffer 1985, chapter 5.
- 343.
“[W]e began to pour Quicksilver into the longer leg of the Siphon, which by its weight pressing up that in the shorter leg, did by degrees streighten the included Air: and continuing this pouring in of Quicksilver till the Air in the shorter leg was by condensation reduced to take up but half the space it possess’d (I say, possess’d, not fill’d) before; we cast our eyes upon the longer leg of the Glass, on which was likewise pasted a list of Paper carefully divided into Inches and parts, and we observed, not without delight and satisfaction, that the Quicksilver in that longer part of the Tube was 29. Inches higher then the other. Now that this Observation does both very well agree with and confirm our Hypothesis, will be easily discerned by him that takes notice that we teach, and Monsieur Paschall and our English friends Experiments prove, that the greater the weight is that leans upon the Air, the more forcible is its endeavour of Dilatation, and consequently its power of resistance, (as other Springs are stronger when bent by greater weights.) For this being considered, it wil appear to agree rarely-well with the Hypothesis, that as according to it the Air in that degree of density and correspondent measure of resistance to which the weight of the incumbent Atmosphere had brought it, was able to counter-balance and resist the pressure of a Mercurial Cylinder of about 29. Inches, as we are taught by the Torricellian Experiment; so here the same Air being brought to a degree of density about twice as great as that it had before, obtains a Spring twice as strong as formerly,” Boyle 1662a, 58–59.
- 344.
“We will further suppose each of these so coyled up to have such an innate circular motion […]. By this Circular motion the parts of the laminae endeavouring to recede from the Centre or Axis of their motion, acquire a Springiness outward like that of a Watch-Spring, and would naturally flye abroad untill they were stretch’d out at length,” Boyle 1662a, 94–95.
- 345.
For instance, in his The Origins of Forms and Qualities (1666). As detailedly reconstructed in Clericuzio 1998, Huygens criticized Boyle’s explanation in a letter read at the Royal Society on 30 July 1662, in which he objected to the idea that the particles of air are provided with an innate movement. To it, Huygens opposed the Cartesian theory of elasticity. In his answer, read in the same day, Boyle pointed out that the theory was Hooke’s, and that the printers omitted his name.
- 346.
The Discours or Essay de la nature de l’air dates back to 1676, and it was printed as the second of his Essays de physique (1679–1681). Cf. “[…] il faut avoir un tuyau recourbé, dont les deux branches soient parallèles, et dont l’une soit d’environ huit pieds de hauteur, et l’autre de douze pouces; la grande doit être ouverte en haut, et l’autre scellée exactement. On commencera à verser un peu de mercure pour remplir le fond où est la communication des deux branches, et on fera en sorte que le mercure ne soit pas plus haut dans l’une que dans l’autre, afin d’être assuré que l’air enfermé n’est pas plus condensé ou dilaté que l’air libre. On versera ensuite peu à peu du mercure dans le tuyau, prenant garde que le choc ne fasse entrer de nouvel air avec celui qui est enfermé; et on verra, comme je l’ai vu plusieurs fois, que, lorsque le mercure sera élevé à quatre pouces dans la petite branche, le mercure sera dans l’autre quatorze pouces plus haut, c’est-à-dire, dix-huit pouces au-dessus du tuyau de communication; ce qui doit arriver, si l’air se condense à proportion des poids dont il est chargé, puisque l’air enfermé est alors chargé du poids de l’atmosphère qui est égal au poids de vingt-huit pouces de mercure, et encore de celui de quatorze pouces, dont la somme 42 pouces est à 28 pouces premier poids qui tenait l’air à douze pouces dans la petite branche, réciproquement comme cette étendue de douze pouces est à l’étendue restante de huit pouces. Si l’on verse du nouveau mercure jusqu’à ce qu’il soit monté à 6 pouces dans la petite branche, et qu’il n’y reste que 6 pouces d’air, le mercure sera dans l’autre branche plus haut de 28 pouces que le haut de ces six pouces; ce qui doit arriver suivant la même hypothese: car alors l’air enfermé sera chargé de 28 pouces de mercure, & de la pesanteur de l’atmosphére qui en vaut aussi 28, dont la somme 56 est double de 28, comme la première étenduë de 12 pouces d’air est double des 6 pouces qui restent; & lorsqu’en continuant de verser du mercure dans la grande branche, il sera dans la petite a 8 pouces de hauteur, il y aura 56 pouces de mercure au-dessus, dans la grande branche; ce qui fait encore la même proportion,” Mariotte 1679, 25–30. De Volder did not own, according to his Bibliotheca, these works. He owned Mariotte’s De la nature des couleurs (1681), namely the fourth of his Essays, the Traité de la percussion ou choc des corps (1673), and the Traité du mouvement des eaux et des autres corps fluides (1686), wrongly attributed to Philippe de La Hire, who edited it: see Bibliotheca Volderina, 10 and 12.
- 347.
See part 2, discourse 2, De l’équilibre des corps fluides par le ressort: “[o]n verra donc manifestement dans cette expérience, que l’air EC aura suivi en sa condensation la proportion des poids. On trouvera la même proportion dans les autres expériences en faisant le calcul en cette sorte. Il faut prendre pour premier terme la somme du poids de l’Atmosphére & du mercure qui sera monté plus haut que le bas de l’air dans la branche EC; pour second terme, del’Atmosphére, c’est-à-dire 28 pouces de mercure; pour troisiéme, la distance EC; & le quatriéme proportionne sera l’espace ou hauteur où se réduira l’air enfermé dans le tuyau EC: comme si l’air étoit seulement reduit à l’espace IC de 8 pouces, on trouveroit que le mercure seroit en l’autre tuyau seulement 14 pouces plus haut que la ligne horizontale IL. Or ces 14 pouces avec les 28 del’Atmosphére sont 42: il faut donc dire suivant cette régle, comme 42 pouces est à 28 pouces, ainsi l’étenduë de l’air EC est à l’étenduë IC. Que. si on vouloit reduire ce même air en l’espace MC de 3 pouces, qui est le quart de EC; il faudroit mettre 84 pouces de mercure dans la branche DA au dessus de la ligne horizontale MN, & on trouveroit cette proportion par le calcul suivant: Comme MC 3 pouces est à ME 9 pouces, ainsi 28 pouces poids de l’Atmosphére, est à 84: car en changeant, 84 sera à 28 comme 9 à 3; & en composant, 84 plus 28, c’est-à-dire112, sera à 28 comme 9 plus 3, c’est-à-dire EC 12, à 3. Et si l’on veut savoir quelle hauteur de tuyau il faudroit pour reduire cet air en l’espace OC d’un pouce, il faut dire, comme OC un pouce, est à OE 11 pouces, ainsi 28 pouces de mercure poids de l’Atmosphére, à 308; & 308 sera la hauteur verticale qu’il faut donner au mercure au dessus du point O ou P: par où l’on connoîtra que pour faire cette expérience il faut que la branche DA soit plus haute que 308 pouces, c’est-à-dire qu’il faut qu’elle soit d’environ 320 pouces afin qu’il reste un espace au dessus du mercure pour empêcher qu’il ne verse,” Mariotte 1686, 142–143.
- 348.
De Volder 1676–1677, 89v.
- 349.
“[T]he aether or m[ate]r[i]a caelestis, which at the exuction of the common air, penetrating, et piercing through both the glass, and the bladder, did in the bladde[r] comminuere in minutas partas [sic] aërem coe[unte]m, insinuate itself into the pores of said common air and so dilate it and make it occupy more room than it did before […]. [H]e inferred […] that the air which was within the glass beforehand had hindered by its pression the bladder from expanding and the ingress of the aether, which was the efficient cause of said expansion,” De Volder 1676–1677, 88v–89v.
- 350.
See book 5: “[t]hose who try to show that the void does not exist do not disprove what people really mean by it, but only their erroneous way of speaking; this is true of Anaxagoras and of those who refute the existence of the void in this way. They merely give an ingenious demonstration that air is something by straining wine-skins and showing the resistance of the air, and by cutting it off in clepsydras. But people really mean that there is an empty interval in which there is no sensible body. They hold that everything which is in body is body and say that what has nothing in it at all is void (so what is full of air is void). It is not then the existence of air that needs to be proved, but the non-existence of an interval, different from the bodies, either separable or actual – an interval which divides the whole body so as to break its continuity, as Democritus and Leucippus hold, and many other physicists-or even perhaps as something which is outside the whole body, which remains continuous,” Aristotle 2014, volume 1, 362–363; cf. Physica, 213a22–213b3.
- 351.
“Ut autem nunc porro ad alterum obiectionis caput accedamus, quo si vel maxime aër premat, eam tamen pressionem gravitatem male dici: quia scilicet omnis pressio non est a gravitate. Quis negat? Sed tamen hanc pressionem, gravitatem dicendam esse existimavi semper, quae oritur ex descensu corporum sublunarium versus centrum Telluris,” De Volder 1676–1678, disputation 3, thesis 9. Cf. thesis 7: “[q]uae demonstratio non tantum in aquis locum habet, sed in fluidis quibuscunque corporibus aqua sive levioribus sive gravioribus, sive minus sive magis compressis. Non enim nititur ea peculiari aquae natura, sed universali lege gravitatis et natura fluidorum corporum.”
- 352.
“Neque obstat parvula illa aëris quantitas, quae in sphaera est, quae vix videtur tanta vi premere posse internam quanta immensa aëris externi moles externam premit sphaerae superficiem. Etenim si rem rite consideremus, nulla pars aëris agit in sphaeram, nisi ea quae eam tangit proxime, quae tamen eo agit efficacius, quo a mole superioris aëris validius comprimitur. Unde si artificio quopiam fieri posset ut aër externe sphaeram ambiens aequaliter ac nunc comprimatur, etsi nullus aër superior eum comprimeret, nonne manifestum erit hunc aërem licet in minori copia, quia tamen aeque compressus supponitur ac si omne pondus totius athmosphaerae sustineret, aequali vi acturum in ipsam sphaeram. Ex quo sane conficitur non tam aëris quantitatem quam eiusdem compressionem magis minusque validam spectandam esse,” De Volder 1676–1678, disputation 2, thesis 8.
- 353.
“Ponamus […] suspendi duo haec sibi invicem cera coniuncta hemisphaeria, aëre adhuc dum referta. Manifestum est, utramque tam internam quam externam huius Sphaerae superficiem aequaliter ab aëre premi, eo quod internus ille aër aeque ac externus condensatu sit. […] Verum educto iam aëre, quid quaeso fiet? Externa sphaerae superficies eandem habebit, quam antea, ab aëre pressionem, pauxillum enim illud educti aëris hic in censum suam ob exiguitatem non venit. Verum interna superficies educto aëre nihil habet quo resistat. Unde quid sequitur evidentius, quam cum aër immediate subiacens inferiori hemisphaerio a gravitate aëris lateralis superiora versus feratur, nec quidquam in Sphaera sit quod huic pressioni resistere valeat, oportere sane hoc hemisphaerium ad alterum, quod eadem aëris superioris vi et gravitate deorsum premitur, comprimi tota vi et pressione subiacentis aëris, quae cum tota dependeat ab ea qua aër lateralis deorsum ruit gravitate, quid est certius quam omni huius gravitatis vi et impetu, haec hemisphaeria ad se invicem compelli,” De Volder 1676–1678, disputation 2, theses 7 and 9.
- 354.
“Air, moreover, has the characteristic that it can be more and more condensed through violent compression as well as expanded by being given greater space, as will be seen in our experiments. […] The air surrounding the earth presses upon itself because it is corporeal and has a certain weight. Indeed, the upper air presses down increasingly heavily on the lower. Thus it follows that the lower air here, which surrounds us, is much denser than the upper air. And whatever is denser, has more mass, and whatever has more mass, is heavier. Therefore we have more and heavier air here on the earth’s surface than that found in towers and mountains; to be sure, the higher the air is, the lighter and more rarefied it is,” Von Guericke 1993, 112–113.
- 355.
“Because of its own weight, air presses not only upon itself but upon all things beneath it with an essentially constant pressure. We do not feel this because we live in this air which surrounds us with equal pressure on all sides and at the same time penetrates us. For as fish have no perception of pressure in the water, so animals perceive it even less in the air. The weight of air on the earth’s surface is as great as the weight of water about 20 Magdeburg cubits deep. In other words if water should rise 20 cubits above the earth’s surface, the pressure it would exert on all things beneath is the same as the pressure of air,” Von Guericke 1993, 113.
- 356.
See chapter 1: “si on prenoit un balon à demy plein d’air seulement, et non pas tout enflé, comme ils le sont d’ordinaire, et qu’on le portât sur une montagne, il devroit arriver qu’il seroit plus enflé au haut de la montagne, et qu’il devroit s’élargir à proportion de ce qu’il seroit moins chargé,” Pascal 1663, 50.
- 357.
“La mesme chose doit s’entendre de toute autre liqueur; et par consequent si deux corps sont polis et appliquez l’un contre l’autre, en tenant celuy d’en haut avec la main, et en abandonnant celuy qui est appliqué, il doit arriver que celuy d’en bas demeure suspendu, parce que l’Air le touche par dessous, et non pas par dessus; car il n’a point d’accés entre deux: et partant il ne peut point arriver à la face par où ils se touchent; d’où il s’ensuit par un effet necessaire du poids de toutes les liqueurs en general, que le poids de l’Air doit pousser ce corps en haut, et le presser contre l’autre; en sorte que si on essaye de les separer, on y sente une extréme resistance: ce qui est tout conforme à l’effet du poids de l’eau,” Pascal 1663, 67.
- 358.
See Rohault 1671, volume 1, 86–87.
- 359.
See Rohault 1671, volume 2, 150–153.
- 360.
Mariotte devotes considerations only to the resistance of bodies to being broken, rather than to the cohesion of different bodies: see Mariotte 1686, 370–388.
- 361.
“Circulo, enim et successioni hunc effectum attribuendum esse, non vero gravitati, aut pressioni aëris, sequentia evincunt experimenta. 1. Quod eo facilior est hemisphaeriorum separatio, quo facilius circulus dari, aut successio perfici potest; hinc minima admissa apertura, per quam successio perfici potest, facili negotio separantur. 2. Quia quo difficilior est successio, eo difficilior eorundem est separatio; et eo arctius cohaerent hemisphaeria, quo materia eorum minus porosa extiterit; hinc hemisphaeria, eandem habentia latitudinem, e marmore si confecta fuerint, triplo plus ponderis sustinent, quam si ex ebore; et si eburnea fuerint, duplo plus ponderis, ut a se invicem avellantur, requirunt, quam si ex aëre facta sint. 3. Quia hemisphaeria saepe multo plus ponderis sustinent, quam gravitas, vel pressio aëris, illis incumbentis, est; cum tamen ab aëre arctior non possit resultare connectio, quem quae aequivalet gravitati cylindri aërei, eandem latitudinem habentis cum hemisphaeriis connexis. Confirmat dicta cohaesio hemisphaeriorum e solido marmore confectorum, diametrum duorum digitorum cum dimidio habentium, quae tanta est, ut sibi imposita, interiecta pinguedine, ne quid inter illa se insinuet, septigentae et ultra requirantur librae ad eorum separationem efficiendam; cum aëris cylindrus, eandem cum hemisphaeriis latitudinem habens, a terra ad extremos athmosphaerae terminos protensus, ducentarum librarum gravitatem non superet,” Senguerd 1681, 45–46. See also Senguerd 1715, 173. On the elasticity of air, see Senguerd 1681, part 3, chapter 2, and Senguerd 1715, chapters 4–8, explaining the elasticity of air by the features (as their being branched and flexible) of its particles.
- 362.
Boyle 1669a, 213.
- 363.
See experiment 2 of Boyle 1660. For an extensive discussion, see Chalmers 2017, chapter 8.
- 364.
- 365.
- 366.
See Sect. 2.4.2, De Volder’s retirement, death and legacy.
- 367.
“Ex illo ergo Gallico itinere domum redux, suasu amicorum Cel. Malebranchii Scrutinium veritatis et Cartesii scripta tum primum coepit evolvere, cuius scriptoris methodum potius quam principia approbabat. Haec ei lectio ad id profuit, ut iam in philosophia ultra consueta compendia sapere inciperet. Dum in his est, cometae, qui per id tempus in caelo formidandae magnitudinis effulsit, occasione, quendam ingenii lusum de futura eius nova apparitione in publicum edidit: pauloque post A. CIƆIƆCIXXXI m. Aprili secundo Rheno alteram in Belgium et Angliam profectionem instituit, certus, id quod priori itinere a se peccatum fuerat, in hoc emendare. Et in Belgio quidem Amstelodami aliquanti temporis moram traxit, ibique Alexandrum de Bie, Matheseos Professorem, res mathematicas in gratiam nautarum vernacula lingua explicantem aliquoties audiit: ac per otium in vicinas urbes et provincias excursionem fecit. Inprimis autem Lugduno-Batava Universitati penitius lustrandae aliquod tempus dedit, in qua Celeberrimis Viris, Wittichio, le Moine, Theologis: Bockelmanno JC. et Woldero philosopho innotuit. Et huic certe Belgicae commorationi illud se debere sepe praedicabat, quod excussis quibus hactenus immersus erat, tenebris atque praeiudiciis, sanioris Philosophia: et demonstrationum mathematicarum, quas a praestantissimis eius scientiae magistris publice videbat exhiberi, dulcedine inescatus, ipse quoque ad illorum exemplum ad altiorem aliquem doctrinae gradum viam affectare coepit. […] Postquam autem in literario illo Batavicarum Academiarum mercatu animum mathematica eruditione egregie instruxerat, et gravissima scorbuti aegritudine fuerat defunctus, discendi aviditate provectus per praecipuas Brabantiae, Zeelandiae, Flandriaeque civitates, Caletum usque continuato itinere in Angliam traiecit, in qua insula Ill. Boylium, Isaacum Vossium, Robertum Hookium, Justellum, Stillingfleetum, Baxterum, Galium, aliosque Celeberrimos Viros, salutare non intermisit. Inter alios compellavit Adrianum quoque Beverlandium, Virum ab impiis, quas etiam scriptis publice editis Orbi manifestas esse voluit, sententiis quam eruditione sua celebriorem: qui tunc ex Belgio relegatus in Isaaci Vossii familia degebat. Non quod malae frugis hominem vel tanti aestimaret, sed ut ex perspecta bonorum malorumque, et eorum qui vere, quique ad speciem tantum eruditi edent, indole, qua nativa esset eruditionis facies, pollet internoscere: secutus in ea re exemplum prudentium familiae patrum, qui, dicente Plinio, pluribus saepe veris denariis adulterinum emunt, ut verus agnoscatur. Ex Anglia Hamburgum est transvectus, unde brevi per Germaniam transitu in patriam A. CIƆIƆCIXXXII rediit. Quanquam ne tum quidem prius sibi certandum existimavit, quam bimestri itinere Helvetia pagos omnes in duorum amicorum, et inter eos dilectissimi Fratris mei, comitatu esset emensus. Ex eo tempore stabilem in patria pedem posuit, et mathematica studia, cum principia tam pulchre ipsi se dedissent, maiori etiam latiore urgenda sumsit: ad quorum amorem et diligentem tractationem ut popularium animos, hactenus in ea re segniores, excitaret, Collegium, quod vocant, experimentale Physico-Mechanicum publice aperuit, primusque rerum harum pulcherrimarum in urbe nostra vel autor vel evulgator extitit,” Bernoulli 1744, volume 1, Vita, 14–17. Cf. Album studiosorum Academiae Lugduno-Batavae MDLXXV–MDCCCLXXV, column 352. On Jakob Bernoulli, see Fleckenstein 1977; Bell 1986, chapter 8; Dunham 1987; Sierksma 1992.
- 368.
“Occasio scripti. Quia vero maximi momenti esse et ad maiorem intelligentiam quamplurimum conducere iudico, si qua primum occasione quave via in cogitationes tuas incideris, enarres, quod alias per modum praefationis fieri solet; non abs re erit, si tribus id verbis hic innuam. Incidi nuper in Scriptum aliquod de Gravitate aëris, Auctore Cl. Voldero, Professore in Academia Lugduno-Batava Celeberrimo. Id cum secunda vice evolverem, coepi attentius ruminare, quae sect. 37. seqq. de receptis duobus motus generibus [i.e., thrust and attraction], docte et solide scripsit. Quae quia sequenti tractatui ortum dedere, non posum, quin totidem pene Auctoris verbis, quantum ad propositum meum faciunt, huc transferam; quod citra plagii notam interpretabitur benignus lector,” Bernoulli 1683, 7.
- 369.
“Quid sit elaterium aëris? Haec dicta sunt de motu gravitatis. Postquam autem Naturae Consulti vidissent, hunc solum motum non sufficere explicandis omnibus circa suspensionem liquorum phaenomenis; quippe qui non explicat, quare suspensus haereat in tubo liquor, obturato vasculo, ubi totius tamen atmosphaerae gravitatio intercepta: hinc alium adhuc acri peculiarem, atque a motu graviatis independentem, ascripsere motum, quo aëris particulae conatum quendam (non communem aquae, fluidisque aliis crassioribus) habeant sese expandendi, dilatandi, remotoque obstaculo maius occupandi spatium; quique conatus, in aëre incluso, par fit sustentando tanto ponderi liquoris alicuius, quantum sustinere valeat gravitate sua tota atmosphaerae moles; non nunquam minori, aliquando etiam maiori, pro re rata. Illud mirari subit, quod cum omnes hydrostaticorum Scriptores hanc aeris vim elasticam unanimi fere fateantur ore, plerique eam ostendisse sint contenti; pauci vero in naturam et causam illius penitius inquirere sustinuerint, aut solliciti fuerint, ut certas illi regulas praescriberent, atque omnes evolvendo casus aëris liberi, inclusi, condensati, rarefacti, exponerent, quantum in singulis horum casuum effectum sortiri aër debeat. Eius causa Obscura. Enimvero unde istud elaterium sive conatus sese dilatandi in aëris particulis proficiscatur; an ex eo, quod singulae illarum circa proprios axiculos rotentur, vel plures aliquot in unum motum circularem conspirantes, infinitos parvos vortices constituant; dumque ab horum centris recedere conantur, ambientes particulas loco pellendi ac se dilatandi vim acquirant: an vero procedat ex peculiari harum particularum figura vel textura; quod forsan sint graciles, flexiles, intortae ac conglomeratae spirae, instar taeniae, funis, aut elaterii horologii portatilis: an quod, ab agitatione materiae primi et secundi Elementi inter corpuscula aëria rapidissime discurrentis, illis hic elaterii motus communicetur, quo in continua quasi conserventur bullitione, ut qua licet sese diffundant: an denique quod ista sese dilatandi virtus, absque adminiculo causae externae, immediate a Primo Motore in creatione illis indita olima fuerit: hoc, inquam, negotium est tam arduum, coniecturis ubique aequali difficultatum numero laborantibus; ut inter abstrusissima naturae mysteria iure merito referatur. Quocirca, hac de re quicquam determinare non sustineo; praesertim cum unusquisque, salvis forte phaenomenis, hic suo sensu abundare possit,” Bernoulli 1683, 81–82.
- 370.
“Quid sit aëris resistentia passiva? Quod vero effectum spectat huius Elaterii; illi paulo distinctius excutiendo inhaerebimus; et quia multis id videtur comprehensu valde difficile, qua ratione pauxillum aëris etiam non compressi, ingentis atmosphaerae pressionem, aequivalente pressione et actione efficaci (talem enim activam efficaciam significatio vocis in illis rebus, quibus tribui solet, requirit) repellere irritamque reddere valeat: hinc ad captum illorum nos accommodaturi, atque elaterium hocce mitigaturi, aliud quiddam praeterea in aëre considerabimus, quod resistentiam vocabimus passivam, atque ita effectum soli hactenus elaterio tributum bipertiemur, partem relinquendo actioni elaterii, partem vero asserendo resistentiae illi passivae, monstrabimusque, quo pacto idem sequi debeat effectus, omniaque allata experimenta non minus, sed forte intelligibilius, solvi possint, etiamsi aër longe minori, quam vulgo creditur, elatere foret praeditus, caetera vero mere passive se haberet, resistentia supplente elateris vicem. Notandum vero ante omnia, per hanc aëris resistentiam passivam me non tam intelligere qualitatem aliquam in ipso aëre latitantem, et a nostra cognitione remotam, quam vero defectum virtutis in liquore aërem premente, ut non satis habet virium ad aërem loco movendum vel condensandum,” Bernoulli 1683, 82–83.
- 371.
“[…] aëri competit resistentia quae passiva dicitur. Haec non consistit in virtute, impetu, efficacia, aut conatu aëri impresso, quo eiusdem particulae in se mutuo, vel in vicina irruendo corpora, suamve in illa exercendo vim, actuosus foret, eorumve operationes promoveret, aut contraria virtute easdem irritas redderet: sed passive se habendo, sola sui substantia, ac mole corporea, indeque impenetrabili, excipiendo vim, et actuositatem corporum in se incidentium, efficaciae ac motui eorum, proportionaliter molis suae magnitudini, ac convenienter naturae legibus, quantum in se est, resistit, illorum introitum in spatium a se occupatum avertit, et tamdiu impedit, donec devita aëris resistentia, iis, utpote potentioribus, cedere cogatur; quod tamen fieri nunquam poterit, nisi alia ipsi cedant corpora, eorumque loca occupare aëri concedatur,” Senguerd 1715, 90–91.
- 372.
“Ut vero distinctius cognoscamus, quae possint esse partes huius Resistentiae passivae, consideremus duo corpora se invicem prementia, (puta duos luctatores, vel duas pilas) sitque primo utrumque libero aëri, (id est, loco ubi nihil vel adiuvat, vel impedit illorum motum) expositum, nullique innixum sustentaculo occurratque corpus A corpori B; quo si fortius est, illud propellet; si debilius, pelletur ab ipso in contrariam partem; si aequali denique vi premat et renitatur utrumque, sublatis ex aequo viribus eodem loco tanquam quiescentia spectabuntur ambo. Hoc unico proinde in casu, non constabit ex sola loci consideratione, utrum alterum in alterum aequali pressionis conatu agat, an vero ambo inertia et otiosa iuxta se quiescant; quod postmodum demum cognoscere datur, cum alterum loco moveris; si pone enim sequatur alterum, concludes sese pressisse antea: si immotum maneat, indicio est, antea quievisse utrumque; quamvis interim utrobique praestet illa considerare, ut omnibus viribus destituta, cum si quas habent, tantundem iis efficiant, ac si non haberent. Sit vero etiam porro corpus B (luctator vel pila) innixum solido alicui fulcro, puta luctator parieti cuidam, vel pila lateri mensae tudiculariae; faciatque corpus A impetum in corpus B sussultum, quid fiet? hoc quidem illud in contrariam adhuc partem repellet, ubi plus illo impendit virium: sed sive vires utriusque sint aequales, sive vires corporis B. sint debiliores, sive plane nullae; in omnibus his tribus casibus neutrum corpus loco suo expellet alterum, sed iuxta se quiescent, adeo ut hactenus nulla pateat ratio, quae nos cogat ad credendum, corpus B. ad impetum corporis A infringendum et sufflaminandum, aequalem potius conatum adhibere, quam vel debilius vel plane non reniti. Sed ubi porro consideraverimus, etiamsi mille praeterea homines aut pilae in directum positae essent, quae omnes vires suas iungerent cum luctatore vel pila A, ad pellendum corpus B, illas tamen omnes non plus effecturas, quam antea fecerat solum corpus A iustam habebimus suspicandi ansam, obstaculum, quo impediebatur paulo ante corpus A, ne propellere posset corpus B non provenisse a renitentia et repulsione aequivalente facta a corpore B id est ab aliquo eius elaterio (quale praecipue in pila eburnea concipere absurdum foret), cum non sit verosimile, eandem hanc vim corporis B, postea parem esse potuisse repellendo impetui millies maiori: sed a mera interpositione corporis B. quae sola sufficiens esse possit sistendo impetui corporis A totiusque seriei corporum istud iuvantium. Pergat enim, si possit, corpus A moveri in directum post contactum corporis B; aut penetret necesse est dimensiones huius, quod omnino impossibile; aut faciat, ut hoc permeet solidum fulcimentum, cui innixum esse supponimus: sed sic vel integrum corpus B deberet traiicere, quod idem involvit absurdum, vel deberet prius in minutissimas partes conteri, eaeque dein per poros muri adigis quod cum non fiat, concludendum, corpus B esse talis texturae, cui dissolvenda impar sit conatus quantumvis maximus corporis A. Omnium quae reliquorum vires suas, huic adiungentium, atque in hoc illud ipsum consistere puto, quod vocare soleo resistentiam passivam,” Bernoulli 1683, 83–87.
- 373.
“[S]i corpora aequalia in motu constituta in se mutuo impingant, utrumque versus oppositum terminum reflectetur,” Senguerd 1681, 35. Senguerd’s theory of motion requires a little digression. He conceived motion in quasi-Cartesian terms, namely, he still intended quantity of motion as something which is conserved through impact, but he 1) criticized the idea that movement is respective, or reciprocal, for the reason that it is a real mode of bodies, so that one cannot arbitrarily attribute it to this or that body. On this basis, he criticizes Descartes’s characterization of motion as given in Principia II.25 because it is contradictory to his idea of motion (given in II.24) as relative (Senguerd 1681, 25, §§ 4–5). Being an absolute mode of bodies, a body can be said to be in motion even without considering all the other bodies (Senguerd 1681, 28, § 11), and intends it as a ‘translation from space to space’, rather than a ‘translation from place to place’, because place is defined as the space occupied by a body already present in it (Senguerd 1681, 29, § 13). Accordingly, he distinguishes between space and body. For him, the quantity of motion is only probably conserved (because God is free in the conservation of such quantity) – (Senguerd 1681, 31, § 19), and motion is distinguished from the vis or force to motion (which pertains to God only), from the impetus impressed by divine force in bodies: so that by ‘motion’ only the translation of bodies has to be intended, which is the effect of the impetus (Senguerd 1681, 32–33, § 21). The quantity of motion, in turn, can be quantified as m·s (i.e. it depends on the size and speed of a body) – (Senguerd 1681, 35, § 26), and is conserved through collisions. These are the rules of impact of Senguerd, which he conceived as between perfectly hard bodies (Senguerd 1681, 39, § 32): 1) the same situation as in Descartes’s rule 1 (two equal bodies moving against each other at equal speed), which is valid for Senguerd as well. 2) The situation of Descartes’s rule 6 – namely the same case considered in De Volder’s 1684 De motu (two equal bodies, one of which is at rest) – which Senguerd resolved in another way, namely, by reducing it to Descartes’s rule 4. For Senguerd, the body at motion cannot move the resting body, and is rebounded by it, because there is a condition of equilibrium between the force of motion of the moving body, and the force to resist the motion of the resting one (Senguerd 1681, 35, § 27). 3) The case of Descartes’s rule 5 (i.e. a bigger body impacting on a smaller body, which is at rest). In this case, the outcome is as it was for Descartes (i.e. the two bodies form a new body, in which m·s is conserved) – (Senguerd 1681, 37, § 30). 4) The case of Descartes’s rule 3 (i.e. two equal bodies move against each other, but one of them has more speed): also in this case the outcome is ‘Cartesian’ (i.e. the move in the same direction, with m·s conserved) – (Senguerd 1681, 38, § 31). 5) The case, not expressly considered by Descartes’s rule 7, in which two equal bodies move in the same direction at different speeds: in this case, the faster one ‘carries’ the preceding, slower one, with m·s conserved (Senguerd 1681, 38–39, § 31). Such rules presuppose that motion is not reciprocal: for instance, if we consider Senguerd’s third case by assuming that the smaller body is moving, and the bigger one is at rest, the outcome does not follow the rule he sets for this case, as the smaller body would be rebounded in the opposite direction.
- 374.
“Fluxum liquoris per siphonem in loco clauso explicatur per resistentiam aëris passivam. […] Hanc in rem autem opportune incidit experimentum, a Cl. Voldero pro ultimo superioris anni specimine in Theatro Physico Academiae huius publice ostensum, quo elateristae admodum gloriantur,” Bernoulli 1683, 107–108.
- 375.
“Sumsit vitrum cylindricum a. aqua subrubido colore tincta impletum, eique immisit crus brevius siphonis bcd atque ore admoto longiori adsuxit per siphonem aquam, qua fluente protinus vitrum cum siphone demisit in recipiens efg quod pariter mox aqua subrubida ad summam usque oram adimplevit, ne quid in illo remaneret aëris, atque tandem operculo admoto clausit, et cera undiquaque probe munivit. Quo facto coeptum est, agitatione emboli evacuari recipiens, extracto per eius collum e liquore, usque ad superficiem circiter il quo subsidente sensim, subsidit pariter liquor in cavitate siphonis contentus, mansitque subinde in eodem plano cum superficie liquoris extra siphonem, descendens in breviori quidem crure ad summam usque oram vitri cylindrici; in longiori vero, quousque subsederat reliquus in recipienti liquor; propterea quod, praeter materiam subtilem, nihil aderat quod ponderare super liquore in recipienti, eumque in siphonem impellere, vel in eo suspensum tenere potuisset. Evacuato sic maximam partem recipienti, intromisit per apertum obstructorium aërem, qui irruens in liquorem vitri cylindrici, eum pondere suo impellebat in crus siphonis brevius, et exinde porro in longius; nec cessabat liquoris per siphonem fluxus, quantumvis postea obstructorium loco suo iterum intrusum fuisset. Cuius rei quidam ratio, supposito aëris elaterio, reddi potest facile; cum enim per obstructorium intromissus aër, virtute sua elastica, premat cum super liquore in vitro cylindrico contento, tum super reliquo extra cylindrum; fit ut liquor in utroque crure sursum impellatur, usque ad mutuum occursum in flexura siphonis c ubi quia in contrarias tendit partes, species quaedam luctae oritur inter liquores utriusque cruris, adeo ut neuter alteri praevaleret, sed immoti haererent, si aequalibus ambo viribus fuissent impulsi: Verum, quia elaterio columnas aëris qr a pondere liquoris in longiori crure magis resistitur, quam elaterio columnae op resistitur a minori pondere cruris brevioris; fit ut liquor fortius adactus in crus brevius, alterum debilius impulsum repellat, et ita in continuo fluxu perduret, ex vitro cylindrico ascendendo in crus brevius, ex breviori descendendo in longius, et ex longiori in recipiens. Atque sic quidem elaterio res conficitur: idem vero absque elaterio demonstrari quoque posse, forsan videbitur nonnullis prima fronte impossibile; cum facile quidem intelligi possit, qua ratione aëris inclusi resistentia passiva suspensum teneat in cruribus siphonis liquorem, eiusque descensum impediat; non vero identidem, quo pacto fluxu continuo novus subinde liquor in crus brevius assurgat, nisi supponatur aliquid supra liquorem vitri cylindrici, quod eum efficaci pressione in crus illud intrudat, quae pressio aliunde procedere posse non videtur, quam ab aëris elaterio,” Bernoulli 1683, 108–111.
- 376.
“Atque sic quidem Elaterio res conficitur: idem vero absque elaterio demonstrari quoque posse, forsan videbitur nonnullis prima fronte impossibile: cum facile quidem intelligi possit, qua ratione aëris inclusi Resistentia passiva suspensum teneat in cruribus siphonis liquorem, eiusque descensum impediat; non vero identidem […] Consideremus vero nunc recipiens iterum obstructum, et liquorem in utroque siphonis crure suspensum; quid fiet? cessabit atmosphaerae gravitatio, nec aëris inclusi pondus ullius erit momenti; et siquidem elaterio nullum quoque locum hic tribuimus, cessabit omnis premendi in illo conatus: sed non cessat pariter gravitatio liquoris in cruribus suspensi, qui naturali suo pondere subinde descensum moliens, liquorem in recipiente et vitro cylindrico sublevare, et cum liquore aërem imminentem versus supremam recipientis cavitatem attollere conabitur, longioris quidem cruris liquor columnam qr; brevioris columnam op; ille nisu maiori, quia ponderosior, hic minori, quia ut brevior, ita minus gravis. Cedet ergo fortiori pressioni columna po unaque deprimet liquorem sibi subiectum, eumque in crus brevius ascendere faciet, non vi propriae elasticitatis, sed vi adventitia, communicata sibi a pressione praevalente liquoris in crure longiori: adeo ut, quemadmodum prius ex Elateristarum mente considerabamus pugnam duorum liquorum ab elaterio aëris impulsorum in flexura siphonis c factam, fortioremque ex parte posita vice versa eandem nunc contemplari conveniat, tanquam inter duas columnas aërias a pondere liquorum impulsas, in superficie concava operculi g gestam, fortioremque ex altera parte qr,” Bernoulli 1683, 111–113. Not surprisingly, as Senguerd came to explain respiration in his Connubium by the idea of the passive resistance of air, he relied on the idea of circumpulsion as well: see Senguerd 1715, 155–161. Bernoulli’s solution, besides to Senguerd’s, is particularly similar to Schott’s explanation of the functioning of Hero’s fountain, which he attributed to a rebounding of air caused by the resistance to penetration by water: see Schott 1657, 46–48.
- 377.
“Si tubus satis angustus fuerit, saepe videbis descensum gravissimi illius liquoris impediri ab incluso aëre; utpote qui nonnihil quidem comprimi potest, sed mox tamen ob vim interfluentis materiae subtilis, quae singulas eius particulas seorsim movendo, eas omnino coire non sinit, durissimi corporis instar renititur ac resistit, et vel in tubi fundo universam mercurii quantitatem sustinet, vel in locis intermediis eundem in duas pluresve portiones divulsum ostendit,” De Raey 1654, 193–194.
- 378.
“Si quis enim me iuberet divinare numerum, quem quis mente concepit, neque adiiceret conditiones, quibus vestitus esse debeat, quibusque ceu characteribus ipse mihi se prodat, is αδύνατον profecto mihi perciperet. Pariter quoque, antequam quis perspectam habeat naturam aëris, reliquaque Principia hydrostatica ad praesentem quaestionem necessaria, is illius solutioni frustra insudabit; et si paulo sit morosior, usu fere illi veniet, quod antehac celebri cuidam Professori Amstelodamensi, primo Cartesii Discipulo, iuxtaque Defensori acerrimo Clave Philosophica claro, cuius tanto libentius, quanto opportunius mentionem hic iniicio. Cum ante quadriennium scribendae modo dictae dissertationi in Belgio vacarem, atque inter peregrinandum, experiundi destitutus ipse copia, haererem circa eventum huius ipsius, quod nunc prae manibus habemus, Phaenomeni; Amstelodamum concessi, consulturus ibidem hac de re celebre illud Oraculum. Ille, intellecta mei adventus causa, subticuit primo, sed ne quid nescire videretur, argentum in tubo non descensurum, sed in eadem, qua prius, haesurum altitudine, magistraliter asseveravit, Ego, qui descensurum certo praenoveram, et scire saltem efflagitabam, utrum maior minorve aëris copia in tubo relicta illud humilius detrusura esset, modeste Philosopho regessi; ad quae ille torvo me statim intueri vultu, dehinc percontari quis essem, postea indignari, stomachari, in Philosophiam Experimentalem invehi, eamque histrionicam nuncupare, et me tantum non vi ex aedibus suis expellere. Haec erat tum solutio celebris istius Cartesiani. Nos vero ut minus militariter, ac magis philosophice rem aggrediamur, stabiliemus ante omnia principia quaedam,” Bernoulli 1686a, 257–258.
- 379.
See Sect. 2.3.1, The correspondence with Thévenot.
- 380.
“Unius adhuc superest phaenomeni ut evolvamus causam (quod intellectis nostris de elaterio et resistentia passiva regulis non erit arduum) quare viz. si in tubi mercurio impleti summitate relictum fuerit pauxillum aëris, argentum vivum nec omne effluere, nec omne in tubo suspensum haerere, sed notabiliter tamen descendere debeat, etiamsi argentum ad longe minorem altitudinem 29 digitis infusum fuerit. Notandum autem, duo hic distincte quaeri posse, semel cur argentum, quamvis ad minorem altitudinem infusum, non ascendat; columna enim atmosphaerica vasculo imminens illud altius impulsura esset in tubum, sine interventu aëris in summitate relicti: dein, cur praeterea etiam notabiliter descendat. Prioris causam reiiciemus non in elaterium, sed passivam tantum resistentiam inclusi aëris, qui cum naturalem habeat consistentiam, et a summa base tubi suffultus sit, iuxta reg. 2 toti atmosphaerae ponderi, argentum altius subinde impellere conanti, obicem ponere potis est. Quod vero argentum non tantum non ascendat, sed et descendat, exinde est, quoniam aër inclusus non premitur a tota cylindri atmosphaerici mole, sed a tanta duntaxat illius portione, quae correspondet excessui, quo totum eius pondus superat pondus cylindri mercurialis inclusi: ex. gr. si altitudo mercurii infusi fuerit 20 digitorum; aër, inter tubi summitatem et mercurium interceptus, sentiet tantum pondus 9½ digitorum mercurialium; quanta videlicet est differentia inter pondus atmosphaericum, aequivalens 29½ digitis mercurialibus, et pondus mercurii inclusi: quoniam enim atmosphaera ab una parte, tota sua mole sursum impellere conatur argentum, ab alter vero argentum naturali sua gravitate, contra nititur; fit ut aequalibus, illinc pellendi sursum, hinc descendendi, viribus sublatis, aër inclusus ea tantum pressione afficiatur, qua pondus cylindri mercurialis inclusi superatur a simili cylindro atmosphaerico,” Bernoulli 1683, 115–117.
- 381.
“Et quoniam per reg. 4 […] volumen aëris inclusi debet esse ad volumen aëris rarefacti, ut vicissim Pondus sustentandum ab hoc, ad Pondus totum atmosphaericum sustentabile ab illo. […] Certum autem est, a parte nostri nullam posse esse hallucinationem, eo quod suppositio haec, Densitates aëris esse ad invicem, ut pondera sustentata, e qua calculus noster immediate fluxit, non alia est quam ipsissima Clar. Boylii hypothesis, egregiis insuper experimentis, gemina tabula in Tractatu eius contra Linum exhibitis, stabilita: quodque in toto hoc negotio nullum aliud inter nos discrimen est, quam quod ille Elaterio tribuit, quae sola nonnunquam aëris resistentia passiva explicari posse autumo; caetera vero iidem omnino utrinque effectus expectandi,” Bernoulli 1683, 118, 121–122.
- 382.
“Phaenomenum […] nunc […] ut methodus ususque utriusque logicae eo clarius patesceret, prolixius enodandum mihi proposui, istud est. Si fistula cylindrica 29 pollicum longitudinem non excedens, una extremitate clausa, altera patula, repleta sit ex parte mercurio seu argento vivo, reliquo spatio aëri concesso, eaque postmodum obstructo digiti pulpa orificio invertatur, atque erecta perpendiculariter immergatur cum obstruente digito in stagnantem alicubi mercurium; explorandum est, an et quousque remoto digito mercurius in fistula descensurus sit?” Bernoulli 1686a, 256.
- 383.
“Principia autem sunt sequentia: I. omnes partes cuiuscunque liquoris aequaliter a centro Terrae remota, a pondere perpendiculariter sibi incumbente premi debent aequaliter: et si premuntur aequaliter, eo situ quiescunt, sin minus, non prius componuntur ad quietem, quam res ad aequipondium reducta fuerit, assurgentibus hinc partibus quibusdam, subsidentibus inde aliis. Celebratissimum hoc principium hydrostaticum fluit ex ipsa natura liquidi. […] II. Atmosphaericus noster, quem spiramus, aër, non minus atque argentum vivum, pondere seu gravitate aliqua instructus est. […] III. Aër, secus quam alia fluida, praeter gravitatem insigni quoque praeditus est elaterio, seu virtute sese expandendi et contrahendi. […] IV. Neque vero […] natura incerto hic agit motu, sed certam observat Legem et Proportionem in aëris magis minusve densati pressionibus. Deprehendit enim Illustris Boylius eleganti Experimento, nobis etiam feliciter tentato, quod Pressiones aëris sint in ratione directa densitatum, vel reciproca raritatum illius,” Bernoulli 1686a, 258–261.
- 384.
Bernoulli follows a syllogistic reasoning, by which he excludes all these alternative, and infers his conclusion: see Bernoulli 1686a, 261–267.
- 385.
See Bibliotheca Volderina, 95.
- 386.
Cf. the text quoted supra, n. 333.
- 387.
“Ita quoque mihi retulit Cl. Volderus, sibi observatum aliquando fuisse circa duo thermoscopia, quorum unum utrinque sigillatum erat, alterum infima sua extremitate cum aëre externo correspondebat, quod videlicet eodem die aestivo liquor in utroque thermoscopio ascenderet; notum autem est, solius thermoscopii utrinque sigillati genium esse, ut liquor in eo aestate ascendat, reliqui vero naturam esse, ut liquor in eo aestate deprimatur. Causam ergo anomaliae istius adiecit hanc fuisse, quod gravitas aëris externi solito fuerit maior, adeoque aëri superius incluso impedimento fuerit, ne per calorem sese dilatando, liquorem deprimeret,” Bernoulli 1683, 214.
- 388.
Both defended or possibly authored by Antonius van Houten, who also acted as respondens of the 28th of De Volder’s Exercitationes against Pierre-Daniel Huet’s Censura philosophiae Cartesianae (1689): namely, Burchard de Volder (praeses), Disputatio philosophica de causis variationum thermometrorum, Leiden, Elsevier, 1693; Disputatio philosophica de thermometris, Leiden, Elsevier. Mentioned in Bierens de Haan 1960, 131.
- 389.
In the disputation the two kinds of thermoscopes are presented: the thermoscope whose lower part is opened and inserted in a vessel of water or aqua fortis (theses 3–4), and whose level increases when it is cold, and the thermometer of Florence, where the liquid dilates when it is hot (thesis 15). However, since Rattrey enrolled at Leiden just few days before his graduation (see Album studiosorum Academiae Lugduno-Batavae MDLXXV–MDCCCLXXV, column 628), it seems that behind this disputation there was, rather, the hand of Petrus Hoffwenius, professor at Uppsala, who is positively mentioned in the disputation and who had studied under De Raey at Leiden. De Raey’s Clavis, in turn, is cited by Rattrey in his account of rarefaction (theses 9 and 22).
- 390.
“Iam enim ostendi, quod, quo aër magis sit compressus et condensatus, eo vis eius elastica sit maior, rarefactione vero minuatur, ita ut, modo eiusdem maneat condensationis, eandem etiam vim elasticam retinere debeat. Cum ergo infimus aër a vi totius athmosphaerae sit compressus, eiusdemque maneat condensationis, sive in recipiente, sive extra ipsum constitutus, patet evidenter, quod aër, sive in recipiente contineatur undique clauso, sive totam habeat incumbentem athmosphaeram, easdem vires, eandemque pressionem necessario habere debeat. Unde simul patet, quod causa omnium illorum effectuum, qui a pressione aëris dependent, ut sunt: duorum haemisphaeriorum firmissima cohaesio, adscensus mercurii alteriusve liquoris in baroscopii, et antliis, et c. non gravitati aëris, sed vi eius elasticae sit adscribenda,” Schuyl 1688a, chapter 2, 7–8 (unnumbered); cf. Serrurier 1690, theses 9–10: “IX. Diximus antea aërem altitudine sua premere cui refragari videtur experientia, in recipiente scilicet undique aëri impervio mercurius aeque suspenditur ac in aëre aperto. Ex quo videtur sequi aëris gravitatem hic nihil facere, tantillulum enim quod est inclusi aëris pondus ne millesimam quandoque mercurii suspensi partem aequat. Huic autem difficultati ut obviam eamus, cum doctissimis viris aëri vim elasticam tribuimus, talem videlicet qua postquam a vi externa compressus est sese elateris instar dilatat. […] X. Considerari velim aërem qui circa nos est premi ab incumbente atmosphaera, et sic impediri in motu suo vorticoso, aetherem autem qui interfluit aëris interstitia sollicitare continuo ad liberiorem motum quod ipsum in posterum dicetur vis elastica. Haec autem dupliciter considerari debet, vel quatenus remoto pondere atmosphaerae aërem dilatat, vel quatenus compressioni aëris resistit. Notetur insuper aërem qui nobis est contiguus tanta vi elastica praeditum quanta aequivalet comprimenti atmosphaerae; ideoque quamdiu manet idem pondus tandiu idem vigebit elaterium. Quid autem evidentius quam quod liceret atmosphaerae intercipiatur a corpore satis firmo aër mansurus sit eiusdem compressionis ac si cum incluso aëre externus communicaret; illud enim ponitur ita firmum ut dilatationi aëris queat resistere, manebit itaque eiusdem condensationis et simul elaterii quod […] habebat; sed illud valebat atmosphaerae pondus, huius autem pondus aequivalet mercurio 29 digitos alto, ergo et aër inclusus, quem per consequens sustinebit in eadem altitudine qua potest gravitas totius atmosphaerae. Respondemus itaque ad propositam difficultatem mercurium ideo suspendi a pauco illo aëre quoniam si descenderet deberet aërem […] comprimere in angustius spatium sed coarctationi huic resistit aequali vi, qua mercurius eam molitur, conatus itaque descendendi et lapsum impediendi in mercurio et aëre aequalis est, et idcirco primus effectum non sortietur i.e. mercurius manebit suspensus.” Cf. also thesis 13.
- 391.
“Cuius causa ut detegatur, considerari velim, quod corpora sphaerica, sive quiescant, sive moveantur circa suum axem, quicunque demum ille sit, aequale semper sua circumferentia describant spatium. E contrario vero, quod corpora angulosa, et praecipue oblonga in orbem moveri nequeant, quin multo plus spatii motu suo describant, quam, cum quiescunt, occupant. Adeoque cum eadem pars aëris modo maius, modo minus spatium occupare queat, patet evidenter, aëris particulas non sphaericam, sed oblongam habere figuram. Figura autem oblonga ad duas hasce primarias species reduci potest, quod nimirum sit, vel cylindrica, vel conica. Quantum ad priorem, non videtur illa ad hanc rem accomodata, non potest enim talis figura in orbem moveri, nisi una eius extremitas, altera vel immota, vel saltem fortius impellatur, si enim utraque eadem vi versus eandem partem impellatur, secundum lineam rectam progredietur, cum sint eiusdem […] ubique crassitiei. Contra vero posterior eo ipso, quod utraque eius extremitas aequali vi impellatur, necessario in orbem moveri debet; alter enim eius extremitas […] altera est tenuior, quae propterea […] altera celerius moveri debet, quod fieri non potest, cum partes maius sint continuae, nisi moveatur in orbem. Quare, cum nulla hic appareat ratio, cur una particularum extremitas, altera fortius impelleretur, sed contra, partim propria gravitate, partim actione materiae caelestis, per ipsarum intervalla dispersae, aequaliter premantur, […] aëris particulas non cylindricam, sed conicam figuram haere concludo. Quo positis omnia, quae circa vim hanc aëris elasticam observantur phaenomena, facillimo negotio explicari possunt. Cum enim figura haec conica apice suo circa basim, tanquam centrum sui motus diversae amplitudinis gyros describere possit, patet evidenter, cur aër varios per gradus condensari, et rarefieri queat. Docet enim experientia, quod machinarum ope multo plus aëris intra idem spatium, quam naturaliter in ipso continetur, cogi possit, vel contra multum aëris ex ipso educi queat, ita ut multo minor quantitas idem spatium, vel eadem multo maius occupet. Hac autem aëris condensatione, vis eius elastica intenditur, rarefactione vero minuitur, ut innumera probant experimenta, quae, quia hodierno tempore sunt vulgatissima, ipsorum relatione chartas hasce meas implere, supervacaneum existimo. Ratio autem huius rei non potest iam esse obscura. Hac enim condensatione, intervalla inter aëris particulas interiecta, redduntur minora, quo fit, ut non tantum singulae minores apicibus suis gyros describere debeant, sed et materia caelestis multum in suo per eadem tranfluxu impediatur, quo mutua ipsarum pressio non parum augetur, et ut, simul ac detur exitus, cum praevaleat aëri externo, ex recipiente expellatur, tamdiu, donec cum eodem ad aequilibrium sit redactus,” Schuyl 1688a, chapter 2, 5–6 (unnumbered). Notably, in Serrurier’s disputation this idea is defended after having presented Boyle’s corpuscular theory of the elasticity of air, including Boyle’s own judgment on Descartes’s theory (described above): see Serrurier 1690, thesis 9: “Illustris Boyle experimentis suis Physico-mechanicis vim hanc aëris elasticam ita manifestavit, ut nullus doctior ulterius dubitet. Elaterium hocce nullo alio in fluido observarunt curiosissimi quique, quocirca hoc aërearum particularum speciali figurae adscribendum censuerunt physici. Nobiliss. Boyle duplicem huius elaterii proponit caussam. Primam constituit in figura aëri ramosa et flexili instar velleris seu spongiae, haec enim manu compressa, simulac desinis premere in priorem statum sese expandit; pili velleris similiter compressi ubi dimittuntur sponte sua, vel per caussam sensus latentem sese restituunt. Eodem ritu concipit flexiles inferiori aëris particulas comprimi ab incumbente atmosphaera; quod pondus atmosphaerae si artificio tollatur aër antea compressus nunc autem pondere aëris liberatus instar spongiae sese explicat. Tandem Nobilis Author cum Cartesio concipit particulas aëris vi aetheris circumrotatas gyris suis parvulam quandam circa se sphaeram constituentes, hae autem particulae circa Tellurem ab incumbentis in motu suo impediuntur, quod impedimentum continuo amovere nituntur, donec eo sublato, aether subtilior qui aëris permeat poros ita circumrotet partes aëris ut maiorem describentes circulum ex sphaera suae activitatis expellant obvias quasvis particulas. Posterior caussa maxime mihi arridet, interim illum conatum maiorem describendi circulum pono in figura conica quam aëris particulis adscribo. Si enim cylindraceam ponamus quoniam in his centrum magnitudinis cum centro gravitatis coincidit, cum moventur circa axem uniformi gyrant motu, neque plus spatii quam quod sua mole dimetiuntur requirunt pro circulo suo motus absolvendo.” It is worth mentioning that De Volder is mentioned in two other disputations concerning the elasticity of air: namely the Dissertatio de vi elastica corporum solidorum et fluidorum (May 1704), presided over by Johann Georg von Bergen and authored by Daniel Fremaut (who was to enrol at Leiden in September 1704, but who apparently had already attended lectures there), defended at the Viadrina University (Frankfurt (Oder)) in which De Volder appears as a dedicatee together with Frederik Ruysch, both labelled as Fremaut’s ‘preceptors’. In the disputation, the positions of a large bulk of sources, including Boyle and Huygens, are discussed. Moreover, De Volder’s discussion of the elasticity of the air is mentioned (but not detailed) in the Disputatio medica inauguralis de functione pulmonis of Georgius Remus, held at Leiden in September 1711.
- 392.
De Volder probably read this book in its second edition (Leiden, 1686), which he owed: see Bibliotheca Volderina, 3.
- 393.
“Hanc ad rem perspiciamus, quanam via insistant geometrae, quos unicos habemus certi inveniendi magistros, ubi circa res physicas occupantur, inquisituri, num et illa medicis inserviat. Quod eo propono confidentius, quia mathematicorum more rem medicam novo exemplo tractare iam coeperunt illustres omnium suffragiis viri Borellus, Bellinus. Quorum libros a tam paucis etiam inter eos, qui mechanicam philosophiam sectantur, medicis evolvi, et a paucioribus intelligi, dolendum est summopere,” De Volder 1698, 25. De Volder probably referred to Borelli’s De motu animalium (1680–1681), and Bellini’s De urinis et pulsibus (1685), Opuscula aliquot ad Archibaldum Pitcarnium (1695) (which he owned: see Bibliotheca Volderina, 3, 58).
- 394.
See proposition 265 of his De motionibus naturalibus a gravitate pendentibus (1670): Borelli 1670, 535–537.
- 395.
Borelli 2015, 125–128. See especially proposition 125: “[t]he properties of air are better explained if its minute particles are hard, flexible and resilient like springs and if they have the shape of tubes or hollow cylinders made of smooth or multiple sheets or threads obliquely coiled,” Borelli 2015, 127. Cf. Borelli 1670, 257–261. Alternative hypotheses Borelli conceives are more Boylean: namely, air can be composed by sub-particles, entangled as flexible tubes, which can assume, if compressed, an elliptic shapes. According to the third, they have a spring-like shape, i.e. a spiral shape, and made by a flexible, but elastic matter: Borelli 1670, 261–262.
- 396.
See supra, n. 391.
- 397.
See Horstmanshoff et al. 2012.
- 398.
See the bibliography for more details.
- 399.
De Beaumont later graduated in medicine at Utrecht, with a Disputatio medico-physica inauguralis de natura sanguinis, 1699. No traces of his magisterial graduation are extant. Other disputations dedicated to or presided over by De Volder, touching upon the functioning of human body, such as Bernard de Mandeville’s Disputatio philosophica de brutorum operationibus (1689), Hermann Oosterdijk Schacht’s Disputatio philosophica inauguralis de sensibus internis memoria et imaginatione (1693), Johannes Robberghtsten’s Disputatio philosophica de sensu brutorum (1694) and Elias Petrus de Beaumont’s Dissertatio physica de carentia sensuum et cognitionis in brutis (1698) were in fact concerning the theory of knowledge rather than physiology.
- 400.
In part 3, chapter 16 of his Experimenta, Von Guericke claims that “[o]ne could very clearly see from this that all bodily movement ceased in the animal with the loss of air and that its life-force, residing in the heart, had been extinguished (like a flame of wine spirits),” Von Guericke 1993, 143. See Sturm 1676, 106–107.
- 401.
See the Racconto degli accidenti vari di diversi animali messi nel voto, in Magalotti 1666, 113–125.
- 402.
For instance, as to the cause of the convulsions observed in such animals, or the colour of their dissected lungs (which De Volder, on the other hand, was to address): “I forgot to mention, that having caus’d these three Creatures to be open’d, I could, in such small Bodies, discover little of what we sought for, and what we might possibly have found in larger Animals; for though the Lungs of the Birds appear’d very red, and as it were inflam’d, yet that colour being usual enough in the Lungs of such winged Creatures, deserves not so much our notice, as it does, That in almost all the destructive Experiments made in our Engine, the Animals appear’d to die with violently Convulsive Motions: From which, whether Physicians can gather any thing towards the Discovery of the Nature of Convulsive Distempers, I leave to them to consider,” Boyle 1660, 332.
- 403.
Boyle 1660, 336–337.
- 404.
“But that it may appear what kinde of service it is that may be expected from it on this occasion, we must premise a few Words to shew wherein the strength of the Objection we are to answer, lies: In favor then of those that would have the Lungs rather passive then active in the business of Respiration, it may against the common opinion be alledg’d, That as the Lungs being destitute of Muscles and of Fibres, are unfit to dilate themselves, so it appears, that without the motion of the Thorax they would not be fill’d with Air,” Boyle 1660, 337.
- 405.
Boyle 1660, 342–345.
- 406.
Boyle 1660, 348, 350–353.
- 407.
“That (on the other side) an Air too much dilated is not serviceable for the ends of Respiration, the hasty death of the Animal we kill’d in our exhausted Receiver, seems sufficiently to manifest. And it may not irrationally be doubted, whether or no, if a Man were rais’d to the very top of the Atmosphere, he would be able to live many minutes, and would not quickly dye for want of such Air as we are wont to breath here below. And that this Conjecture may not appear extravagant, I shall on this occasion subjoyn a memorable Relation that I have met with in the Learned Josephus Acosta, who tells us, That when he himself past the high Mountains of Peru, (which they call Pariacaca) to which, he says, That the Alps themselves seem’d to them but as ordinary Houses, in regard of high Towers, he and his Companions were surprised with such extreme Pangs of Straining and Vomiting, (not without casting up Blood too) and with so violent a Distemper, that he concludes he should undoubtedly have died, but that this lasted not above three or four hours, before they came into a more convenient and natural temperature of Air,” Boyle 1660, 355–357; cf. Acosta 1589, book 3, chapter 9.
- 408.
“That, which some of those that treat of the height of Mountains, relate out of Aristotle, namely, That those that ascend to the top of the Mountain Olympus, could not keep themselves alive, without carrying with them wet Spunges, by whose assistance they could respire in that Air, otherwise too thin for Respiration: (That Relation (I say) concerning this Mountain) would much confirm what hath been newly recited out of Acosta, if we had sufficient reason to believe it: But I confess, I am very diffident of the truth of it; partly because cause when I pass’d the Alps, I took notice of no notable change betwixt the consistence of the Air at the top and the bottom of the Mountain; partly because in a punctual Relation made by an English Gentleman, of his ascension to the top of the Pike of Tenariff (which is by great odds higher than Olympus) I find no mention of any such difficulty of breathing,” Boyle 1660, 357–358. One cannot find such a statement in Aristotles’s works: however, it was attributed to Aristotle, among others, by Kepler: for a discussion, see West 1998, 3–4.
- 409.
Sprat 1667, 201.
- 410.
See the text quoted supra, n. 402.
- 411.
De Volder 1676–1677, 95r.
- 412.
“Even just as we had seen in the last experiment of the bladder, and the weight, wherein the air being taken out of the great bottle glass (which did compress bladder, et constipate the air within the bladder) that which was within did presently dilate itself, and so much even to the lifting up of such a weight: and the said air being let in again did condense and constipate the air in the bladder whereby it de-swelled, et crumpled and let down the weight to its place where it was before: and this was also the reason of several other experiments before-seen, and rehearsed in this bask,” De Volder 1676–1677, 93v.
- 413.
“The dog being cut up he took one the lungs and showed unto us: the which were found to be of two colours: the one was of a darkish red colour which he called color fuscus. The other part were of a whitish colour such as we see in the lungs of other animals that are sound. […] [H]ence might easily be examined, if an infant was born dead or alive: for if born dead the lungs will certainly sink: if it was born alive, and breathed never so little while, they will never sink do what you can,” De Volder 1676–1677, 91v–94r. See Craanen 1689, 254–255.
- 414.
“Of these convulsive fits he said it was very remarkable that all animals that […] ever he had put into the vacuum did die all alike by convulsions whereof he said the cause was not easy to be rendered, convulsions being caused by contraction of the muscles which is performed by the affluxion unto them of the animal spirits: {now} why the extraction of the air should cause the animal spirits to conflux unto the muscles after such a {nattra} and there to convell the muscles he said again it was not easy to explicate. Let he thought in some manner it might be explicated thus: viz. that these spirits are of the nature of liquid things as being of engendered of the subtlest, and purest part of our blood even as spirit of wine is the purest, and subtlest part of the wine, although the liquidity thereof seemeth to be only the vehicle of said spirit of wine, and not so properly the spirit itself,” De Volder 1676–1677, 96v–97r.
- 415.
“Of the frog he told us afterwards that he had left him in that posture for a whole hour, and at 12 o’ clock he found the glass, as it should be without air but the frog still alive: at 2 he found him not with any motion at all, and the glass without air: yet he dared not let in the air fearing he would come to himself again: at five he come again and found the frog again without the least motion, and then he let in the air, and presently his sides, which were much swelled, did fall down flat, yea more flat then they were before he put the frog into the glass: yea in his side appeared some small rupture either with too much swelling, or else with the force of the air <g>rarified which in his body, or of the air when it was let in,” De Volder 1676–1677, 103r–v.
- 416.
“[W]hen men ascend unto some very high mountains as el pico de Tenerife they experiment squeamishness of stomach and vomits and other symptoms whereby they are feign to make use of several preparatives the air, there, by reason of its thinness, subtility, and too much rarefaction, being scarce sufficient for life, and some ascending too high have died for want of breathing for although there \is/ much and open air enough, yet it is not of such a consistency as is requisite for human breathing, and life,” De Volder 1676–1677, 93r.
- 417.
De Volder 1676–1677, 95r–v.
- 418.
“[T]horax plus vel minus dilatatur, prout plus vel minus aëris attrahendum est. Sed non fit eius dilatatio, quia thorax extenditur; verum sua virtute pulmo dilatatur, et impletur tantum, quantum par est, ut vacuum evitetur. […] [L]icet per se solus pulmo hunc motum non absolvat, sed etiam thoracis motus necessarius sit: tamen quia totus motus hic in eum finem dirigitur, ut aër attrahatur, atque a pulmone fiat haec eius attractio: merito pulmo praecipuum respirationis organum statuitur: cui etiam peculiaris vis, eodem modo ut cordi, a facultate animali diversa, indita est. […] Pulmo non dilatatur, quia impletur. Sed impletur, quia dilatatur. […] si dilataretur ob repletionem, sicut vesica, quae inflatur: aliunde aërem in pulmonem immitti, et quasi inflari necessum esset: sed repletur, quia dilatatur suapte natura, ad modum follis scilicet,” Sennert 1667, 102–103. According to the Bibliotheca Volderina, 55, Sennert’s Opera omnia (in the edition of 1656) was extensively annotated by De Volder. Sennert’s medical theories were taught by De Raey: a copy of his dictata on Sennert’s Epitome institutionum medicinae (1644) is extant at the British Library, ms. Sloane 1733.
- 419.
See Harvey 1651, 4–5.
- 420.
“Hactenus a musculorum respirationi ancillantium inaequalitate, atque a diaphragmate antagonista carente, (ad quae porro et alia illa, quae iam enumeravimus, accedunt) thoracis motum perpetuum, alternatum, atque infinitis quoque modis mutatum, deduximus. […] Sed quoniam in pennatis, serpentibus, et c. diaphragma desideratur, iure quaerat aliquis, quo modo in iisdem respiratio peragatur? Respondemus, quod in pennatis aër vesiculas aliquas, in abdomine absconditas, intret, idque mediantibus pulmonibus, quos tamen ob arctam connexionem haud expandi videmus. Quae forsan ratio est, cur in aquatilibus, imo in aliis etiam avibus, meatus in venis arteriisque, etiam foetui humano peculiares et c. haud claudantur, attamen in ipsis totum pecus, secus ac in aliis animalibus, a validioribus musculis, eos, qui exspirationi ancillantur longe superantibus, valde movetur, et sonum atque stridorem in costulis, cum pectore per peculiarem articulationem unitis, (nam cartilagines non habent), in vehementi inspiratione excitari notamus,” Swammerdam 1667, 83–84. Cf. supra, n. 93. Also Van Helmont maintained that the lungs of bird do not dilate in respiration: see Van Helmont 1652, 355.
- 421.
“[…] ranae recipienti cuidam impositae, licet ex ipsa educatur aër, non tamen, nisi admodum difficulter extinguuntur, cuius contrarium obtinet in aliis animalculis, quae in solo degunt aëre,” Schuyl 1688b, chapter 4, 7–8 (unnumbered); cf. “[o]f the frog he told us afterwards that he had left him in that posture for a whole hour, and at 12 o’ clock he found the glass, as it should be without air but the frog still alive,” De Volder 1676–1677, 103r.
- 422.
“[A]nte respiratione, compressis adhuc pulmonibus a vi incumbentis aëris hae partes introrsum deprimuntur, quocirca, si aër in pulmones irruens, eosque ita distendens, ut quaquaversum costas, et diaphragma premant, vel aequalem duntaxat cum externo haberet vim, ad eam certe altitudinem elevari deberent, in qua naturaliter, priusquam foetus aëri exponeretur, constitutae erant. Quare, cum aër hac sua in pulmones invasione maiores acquirat vires […], patet evidenter, quod thorax et abdomen in inspiratione elevari, et possint, et debeant. Adeo ut haec thoracis dilatatio mihi non causa, sed effectus sit inspirationis, et pulmones in tantum active se habere dici possint, in quantum thoracem, diaphragma, hinc et abdomen distendunt, passive vero, quatenus ipsi ab irruente aëre expanduntur. Eodem ferme modo se res habet, ac si ex vesica recipienti cuidam inclusa per tubulum ipsi insertum omnis quantum pote educatur aër, concidet enim hoc in casu et comprimetur vesica a pressione aëris in recipiente contenti, et deinde, clauso istius tubuli orificio, ne quid aëris vesicam ingredi queat, omnis ex recipiente aër educatur. Si enim hoc in casu orificium tubuli vesicae inserti aperiatur, hoc solo aër externus omni sua vi in vesicam irruet, ipsamque quaquaversum distendet. Cum autem totum hoc sit, quod in inspiratione contigit, nihilque assumpserim, nisi quod necessario ex vi aëris elastica sequi debet, nullum potest remanere dubium, quin revera hoc pacto in respiratione automatica peragatur inspiratio,” Schuyl 1688b, chapter 2, 2–3 (unnumbered).
- 423.
“Restat igitur altera duntaxat respirationis pars, quae consistit in eiusdem aëris exspiratione. Certum est, quod, quamdiu aër in pulmonibus iam contentus eadem vi partes illas, quas dilatavit, et expandit, premat, non possint nisi a fortiori quadam vi comprimantur, in pristinum reduci statum, eodem modo, ac arcus vi quadam incurvatus, resilire non potest, quamdiu eadem illa causa perseverat, a qua incurvatus est […]. Videamus ergo, num ipsas ab aëris illa pressione liberare queamus. Hunc in finem in memoriam revocanda sunt ea, quae in praeced. disp. […] dicta sunt [i.e. in Schuyl’s De vi corporum elastica], nimirum quod aëris vis elastica calore augeatur, quo fit ut ex corporibus, qua data via, expellatur. Magnum autem in thorace adesse calorem nemo dubitat, nemo est, qui negat. Debet igitur aëris in pulmonibus contenti vis elastica augeri, quo cum praevaleat aëri externo, ex iisdem per os, et nares, cum hic, nec ullibi alias pateat exitus, expelli debet. Quo fit, ut exigui illi ramuli, qui in pulmonum cellulas terminantur, quique ratione trunci in quem omnes coeunt, admodum sunt exiles, et quo trunco sunt propiores, eo ampliores sunt, omni destituantur aëre, vel saltem ita rarefiat aër, qui in ipsis remanet, ut omni sua privetur vi elastica, ita ut hac expulsione aëris pulmones ab eiusdem pressione non parum liberentur. Debent ergo pulmones vi propria elastica, interim dum hoc pacto aër ex iisdem expellitur, denuo subsidere, eandemque ob causam et thorax, et diaphragma, et hinc abdomen in pristinum statum reduci debent, in quo tamen non parum a pressione aëris externi adiuvari debent, ita ut in exspiratione hae partes ultra elaterem introrsum nonnihil comprimantur,” Schuyl 1688b, chapter 3, 3–4 (unnumbered). As to the relation between temperature and pressure, see Schuyl 1688a, chapter 2.
- 424.
“Omnia ergo in eundem statum reduci debent, in quo fuere ante primam inspirationem, hac sola cum differentia, quod non omnis, ut iam vidimus, ex pulmonibus expellatur aër, postquam enim ad aequilibrium perventum est, nihil amplius ex iisdem expelli potest. Hoc autem aequilibrium ne per momentum quidem subsistere potest. Simul ac enim eo perventum est, ut nihil amplius ex pulmonibus expellatur aëris, statim vis eius elastica, quae, quamdiu expellebatur, maxima ex parte eo versus erat determinata, cessante iam illa expulsione, quaquaversum aequaliter vires suas exercere incipit. Quare cum pulmones eodem sint in statu, in quo erant ante primam inspirationem, et vis aëris elastica sit eadem (haeret enim cum externo in aequilibrio, quod certe nunquam contingere posset, nisi eandem cum ipso haberet vim elasticam) hinc necessario pulmones, partesque reliquae circumiacentes, eodem modo, ac contigit in prima inspiratione, dilateri, et expandi debent,” Schuyl 1688b, chapter 3, 4–5 (unnumbered).
- 425.
“[…] etsi in respiratione automatica omnis, quantum pote, aër sit expulsus, ita ut iam iam in pulmones denuo sit illapsurus, voluntaria tamen pectoris constrictione multum insuper aëris ex iisdem expellere possum,” Schuyl 1688b, chapter 3, 4 (unnumbered).
- 426.
See Quaestio 82: “Pulmones an ad respirationem sint necessari?” Craanen 1685, 206–207.
- 427.
“Aëris absentiam occasionem suppeditare pororum isti dispositioni, quam […] affirmavimus. Cuius asserti veritatem experimentis ab ingeniosissimo viro […] B. De Volder in theatro physico publice coram frequenti studiosorum corona factis, confirmare est animo. Coepit igitur vir Cl. phialam aqua forti dimidia fere parte plenam; dein et alteram oleum tartari continentem: quas vitro ad id adaptato imposuit. Omnibus rimis bene clausis (ne aër externus irrepere posset) extrahendum per antliam pneumaticam (cuius iconem si quis desiderat, adeat Boylaei Tractatum de vi aëris elastica, ubi parum diversam reperturus est figuram) curavit aërem. Quo extracto quantum fieri potest, oleum tartari aquae forti commiscuit, quid fit? Continuo ebulliunt liquores, usque adeo ut vix intra vitri limites contineri possent. Eosdem liquores in aëre libero commiscuit, sed diverso cum successu. Etenim effervescentiae excitata multo minor, nec tam efferata, liquores qui ante ad supremam, nunc vix ad mediam fecit ascendere partem. Idem tentavit cum oleo tartari et spiritus vitrioli, eadem φαινόμενα, quae in praecedenti comparuere,” Lufneu 1679, thesis 12. Cf. Craanen 1689, 263.
- 428.
“Quantum ad usum, quem respiratio praestat oeconomiae animali, nemo certe est, quin fateri, ipsum esse permagnum, necesse habeat, cum sola hac cohibita, moriatur homo, et quodvis aliud animal, quod respirat; sed in quonam praecise usus ille consistat, et quidnam ad conservationem vitae conferat, in eo dissentiunt ab invicem authores. Non autem varias illorum opiniones hic recensere, multo minus refutare est animus, sed meam solummodo hac de re sententiam proferam. Dico ergo, quod per respirationem promoveatur sanguinis circulatio, ita ut, cohibita respiratione, sensim retardetur et tandem cesset,” Schuyl 1688b, chapter 4, 6 (unnumbered).
- 429.
- 430.
“Respirationis plane aliud est negotium, sed cum hic de ea ex professo agere non possumus, quia nervos nondum vidimus, attendemus ad illa solummodo, quae experientia nos docet; videmus enim hic, ventrem intumescere, quod dicimus fieri ab aëre: sed quomodo ille hoc facit? Quia aër, primo a ventre et thorace inflatis, propellitur, et cum vacuum dari repugnet, debet ille aër ingredi pulmones, eosque inflare, qui inflati propellunt diaphragma deorsum, hoc viscera id abdomine contenta, quae, cum cedere non possint multum, ventrem extendunt, ac proinde prima causa intumescentiae ventris et inspirationis est aëris motus circularis. Altera causa potest esse ipsa gravitas aëris, quam multis experimentis in physica probatam vidimus: sic enim aër propter pulsionem sui ruit cum vi in pulmones, eosque inflat et deprimit sua gravitate, hi diaphragma, hoc viscera abdominis, illa ventrem, et sic porro. Alias causas respirationis videbimus, cum ad nervos respirationi inservientes pervenerimus: tunc videbimus, quod pulmones sint tantum passiva respirationis instrumenta, qui aërem propulsum solummodo excipiunt, eique repulso exitum concedunt. Activa vero instrumenta respirationis, dicemus esse musculos, tam abdominis, quam diaphragmatis,” Craanen 1689, 264–265.
- 431.
Senguerd’s theory of respiration is given in his Philosophia naturalis and then in his Inquisitiones experimentales (first edition 1690, second edition 1699), reporting experiments from 1687 onwards. According to Senguerd’s Philosophia naturalis, respiration – which has a cooling function – takes place as follows: (1) air enters in the lungs of the newborn, and dilates them for the first time – (as shown by the fact that the lungs of a fetus who was born dead do not float); (2) once in lungs, air is expelled by the contraction of thorax, ribs, and lungs themselves (not explained by Senguerd) and by its own rarefaction, which is caused by the subtle matter in the body. (3) The air left in the lungs cannot resist to the pressure of external air, so that lungs are filled once again: see Senguerd 1681, 289–290. In turn, in the third experiment described in his Inquisitiones, and taking place in December 1687, Senguerd argued that the air is propelled into the lungs by the expansion of thorax, thus still relying on the idea of circumpulsion: see Senguerd 1690, 27 and 31.
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Strazzoni, A. (2019). The Theory of Hydrostatics and Pneumatics. In: Burchard de Volder and the Age of the Scientific Revolution. Studies in History and Philosophy of Science, vol 51. Springer, Cham. https://doi.org/10.1007/978-3-030-19878-7_5
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