Abstract
In October 1640, Pierre Gassendi left the port of Marseilles on a trireme with the intention of carrying out on the open sea an experiment that Galileo had described in the Dialogo sopra i due massimi sistemi (1632), but of which he had claimed that he had never performed it.1 In the presence of Louis de Valois, Governor of the Provence, Gassendi confirmed Galileo’s prediction that a ball dropped from the head of a mast of a moving ship landed exactly at the foot of the mast irrespective of whether the ship was at rest or was instead moving at high speed.2 This observation was fraught with important implications, for it falsified one of the principal arguments against the diurnal motion of the Earth. Partisans of the Ptolemaic and the Tychonian theories had argued that just as a ball dropped from the masthead of a moving ship struck the deck at some distance behind the foot of the mast, so on a rotating Earth an object dropped from a high tower would not touch the ground next to the tower. Having verified that a falling body behaved exactly in the same way on a ship in motion and on a ship at rest, Gassendi felt entitled to conclude, following Galileo, that the behavior of objects on the surface of the Earth did not allow for any conclusion as to whether the Earth rotated or not.
Research for this article was made possible through the financial support of the Netherlands Organization for Scientific Research (Nwo), grant 200–22–95 and of the “Borsa Ruberti per ricerche su metocli moclalitâ e strumenti cdi diffusione della cuitora scientifica ”
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References
Galilei, Dialogue [Drake], p. 145. However, in his Lettera a Francesco Ingoli in risposta alla “Disputatio de situ et quiete Terrae” (1624), Galileo claimed to have personally carried out this experiment (see Galilei, Le Opere [Favaro], vI, p. 545). For a discussion of this claim, see i. a. Ariotti, “From the Top to the Foot;” esp. pp. 201–202; Conti, “La dimensione sperimentale., According to Conti, the “experimental baptism” of Galileo’s relativity principle took place on the Lake of Piediluco in April 1624, during Galileo’s stay at Prince Cesi’s residence at Acquasparta.
On Gassendi’s experiment, cf. Debus, “Pierre Gassendi and his Scientific Expedition”; Ariotti, “From the Top to the Foot”
Westfall, Force, pp. 102–103.
“Puisque l’atome gassendien possède un mouvement et une vitesse qui lui sont propres, et que si on le lâchait librement dans l’espace, il se mettrait immédiatement à se mouvoir avec une vitesse donnée, Gassendi est obligé, comme d’autres avant et en même temps que lui, de nier la continuité du mouvement et de concevoir tout mouvement moins rapide que le mouvement propre de l’atome, comme composé d’une série de mouvements et de repos, d’une série de petits sauts, ce qui est évidemment incompatible avec les principes qu’il a lui–même développés;’ Koyré, “Pierre Gassendi;” p. 109. Cf. also Westfall, Force, p. 103.
Galluzzi, “Gassendi e l’affaire Galilée:’
“Et causa quidem generalis est, quia, quicquid movetur, motum suum imprimit rebus omnibus, quas sustentat; resque perinde emittuntur, sive emittens motum a se, sive ab alio impressum habeat. Experimentum vero facillimum est, ut dum per prolixiorem illam nobilissimae Bibliothecae deambulabis pergulam, pilam lusoriam, aliumve globum manu teneas, remque explores;’ Gassendi, Opera omnia, III, p. 478b.
“Habe interea pilam ad manum, quam sine ulla contentione manus, brachiive dimittas; ac tum, si dimiseris quidem, dum manus anterius contendet, non anterius modo movebitur, sed duplo etiam celerius movebitur, quam corporis truncus. Sin dum manus posterius fiet, neutram in partem movebitur, sed ad perpendiculum semper cadet;’ ibid., p. 479b.
“Verum res iam pene intelligitur ex its quae paulo ante sunt dicta; et observare solum est opus, quomodo bracchij extensio inter ducendum rectam fiat, motis ex ordine digitis, manu, cubito, bracchio super propriis, ac specialibus centris. Considera quoque ut inter expedite ambulandum, spontaneus ille bracchiorum motus, cuius centrum scapulae sunt, non perinde sit defatigationi obnoxius, ac motus crurum, cuius centrum coxendices, quod non perinde inhibeatur, et multiplicari cogatur;’ ibid., p. 488b.
Ibid.
Galilei, Dialogue [Drake], p. 259.
“Discrimen est solum, quod corpus, cui cohaeret manus, intra pergulam moveatur per se; in via moveatur a curru;’ Gassendi, Opera omnia, III, p. 481a–b.
Galilei, Dialogue [Drake], p. 142.
Maurice Clavelin has observed that Salviati’s “purely dialectical answer would have brought the mechanical solution of the problem not a whit nearer [ ... ]. Galileo’s merit was precisely to have trascended this simple ad hominem argument and to have offered a solution in strict keeping with the idea of mechanical relativity,” Clavelin, The Natural Philosophy of Galileo, pp. 229–23o.
Galilei, Dialogue [Drake], p.156.
Koyré, Galileo Studies, p. 170.
“Unum; corpus suopte decidens motu ea ratione accelerari, ut temporibus aequalibus maiora semper spatia pervadat, iuxta proportionem, quam habent numeri impares inter se, initio sumpto ab unitate. [ . . . ] Heinc fieri, ut spatia quibuscumque temporibus peracta, sint inter se in duplicata ratione suorum temporum (nempe ut eorundem temporum quadrata) veluti Geometrae loquuntur. Alterum; viam sive lineam, quam imaginamur describi in aëre a corpore oblique proiecto [ . . . ], non esse circularem [ . . . ] sed parabolicam,” Gassendi, Opera omnia, III, p. 483a–b.
Galilei, Dialogue [Drake], p. 165. For an analysis of Galileo’s demonstration see i.a. Mansion, “Sur une opinion de Galilée”; Feinberg, “Fall of Bodies”; Drake, “Galileo Gleanings xvI”; Koyré, “A Documentary History”; Galluzzi, “Galileo contro Copernico;’ esp. pp. 87–92; Barcaro, “Un’analisi della `bizzarria: ”
Galilei, Two New Sciences [Drake], p. 217.
“Il est à remarquer qu’il prend la converse de sa proposition, sans la prouver, ni l’expliquer; à sçavoir que, si le coup tiré horizontalement de B vers E suit la parabole BD, le coup tiré obliquement suivant la ligne DE doit suivre la mesme parabole DB; ce qui suit bien de ses suppositions. Mais il semble n’avoir osé l’expliquer, de peur que leur fausseté parust trop evidemment. Et toutefois il ne se sert que de cette converse en tout le reste de son quatriesme discours, lequel il semble n’avoir escrit que pour expliquer la force des coups de canon tirez selon diverses elevations;’ letter to Mersenne, 11 October 1638, Descartes, Oeuvres [Adam e.a.], II, p. 387. For Descartes’ critique of Galileo, cf. Dugas, La Mécanique, Shea, “Descartes as Critic;’ pp. 150–151; Damerow e.a., Exploring the Limits, pp. 129, 264–269.
Note that Galileo too, had not managed to provide an autonomous justification for the principle of the composition of motions. See Wohlwill, “Über die Entdeckung;’ pp. 111—116; Damerow e.a., Exploring the Limits, pp. 241–242; Prudovsky, “The Confirmation.,
“Quia videmus motum deorsum eadem proportione velocitatis increscere, qua motus sursum decrescit; eapropter videri omnino duo esse principia externa, quae mutuo quasi colluctentur, certatimque exserant vireis circa idem mobile. Et principium quidem externum motus sursum constat esse manum aliudve corpus proiiciens; at cum principium externum motus deorsum non perinde appareat, ideo–ne nullum est dicendum? Non sane; nisi forte cum vides ferrum, alias immotum iacens, ad magnetem pellici, nullam causam externam censeas, quae pellectionem faciat,” Gassendi, Opera omnia, III, p. 489b.
Galilei, Dialogue [Drake], p. 235.
“Il n’est pas difficile de combattre l’opinion de Gassendi touchant la pesanteur, puisqu’après avoir dit plusieurs fois que la pesanteur consiste en ce qu’il sort perpetuellement de la terre des corpuscules crochus semblables à des petits hameçons, lesquels attirent en bas tous les corps qu’ils rencontrent, [... ] il avoue luy mesme [ ... ] qu’il ne voit point comment est–ce que ces corpuscules pourraient obliger les corps [ ... ] de descendre [ ... ] . En effet [ ... ] il faut encore qu’il y ait quelque chose qui retire ces petites chaînes, ou qui repousse fortement en bas les mesmes corpuscules, après qu’ils se sont attachés aux corps pesants;’ La Grange, Les principes de la philosophie, p. 192. In recent years, the non–mechanical character of Gassendi’s explanation of electric and magnetic phenomena has been stressed by Freudenthal, “Clandestine Stoic Concepts;’ p. 163 and by Osler, “How Mechanical was the Mechanical Philosophy?;’ pp. 433–437.
“Quaeres obiter, quid–nam eveniret illi lapidi, quem assumpsi concipi posse in spatiis illis inanibus, si a quiete exturbatus aliqua vi impelletur? Respondeo probabile esse, fore, ut aequabiliter, indefinenterque moveretur; et lente quidem, celeriterve, prout semel parvus, aut magnus impressus foret impetus. Argumentum vero desumo ex aequabilitate illa motus horizontalis iam exposita; cum ille videatur aliunde non desinere, nisi ex admistione motus perpendicularis; adeo, ut quia in illis spatiis nulla esset perpendicularis admistio, in quacumque partem foret motus inceptus, horizontalis instar esset, et neque acceleraretur, retardereturve, neque proinde unquam desineret;’ Gassendi, Opera omnia, III, p. 495 b.
“ [ ... ] si ex duobus his motibus, perpendiculari nempe, et horizontali, qui obliquum illum componunt, alter habendus naturalis sit, ilium horizontalem potius, quam perpendicularem esse. [ ... ] quia cum proiectum pars fuerit aliqua totius, quod secundum horizontem, seu circulariter movebatur, ideo ad eius imitationem movetur circulariter, ac naturaliter proinde, et prorsus aequabiliter; adeo ut quantumcumque motus perpendicularis increscat semper, aut decrescat; ipse tarnen horizontalis uno semper tenore fluat, invariabiliter procedat,” ibid., p. 489a.
Galilei, Dialogue [Drake], pp. 162–163. See also ibid., p. 149, where Salviati explains to Simplicio that the trajectory of a ball falling from the mast of a moving ship is the result of the composition of two motions, namely “the circular around the center and the straight motion toward the center:’ For an analysis of Galileo’s argument, see i.a. Clavelin, The Natural Philosophy, pp. 261 ff.; Drake, “Galileo Gleanings xvI”; Drake, “Galileo Gleanings xvII”; Coffa, “Galileo’s Concept of Inertia,” esp. pp. 270 sgg.; Chalmers e.a., “Galileo on the Dissipative Effect.”
“Ex quo par est existimare, motum horizontalem, a quacumque causa is fiat, ex sua natura perpetuum fore, nisi causa aliqua intervenerit, quae mobile abducat, motumque exturbet,” Gassendi, Opera omnia, III, p. 489a.
“Tametsi ipsis partibus Terrae nihil subest periculi, quae, quod cohaerant omnes inter se, motuque semper naturali, aequabilique ferantur, perinde se habent, ac si quiescerent; solusque foret casus timendus, si Terra impingeretur in corpus obsistens, aut alias quiete repentina consisteret; quod magis tarnen timendum non est;’ ibid., p. 507a.
Galilei, Dialogue [Drake], pp. 212–217.
This point is made by Drake, “Galileo Gleanings xvII”; Coffa, “Galileo’s Concept of Inertia;’ and Gaukroger, Explanatory Structures, p. 196. More nuanced is the position of Chalmers and Nicholas: “Our own view is that the case against there being a general principle of circular inertia in Galileo’s writings capable of being applied to terrestrial and celestial phenomena is decisive [ ... ] . There is no general principle of inertia in Galileo’s work, but there are some specific cases of inertial motion that persists indefinitely without the aid of a force, impetus or any active cause,” Chalmers e.a., “Galileo on the Dissipative Effect;’ p. 329.
Clavelin, The Natural Philosophy, p. 237.
Galilei, Dialogue [Drake], pp. 212–213.
“Nam fac unicam esse causam, exempli gratia attractionem; concipies quidem ex dictis sequi, ut quia radij magnetici, quasi stringentes chordulae, contin<g>entem motum, sive impetum lapidi imprimunt, talem imprimant in primo momento, qui non deleatur, sed perseveret in secundo, in quo alius similis imprimitur, qui in priori iunctus perseveret una cum illo in tertio; in quo alius similis adiungitur, atque ita consequenter; adeo ut impetus ex continua illa adiectione continuo increscat, motusque semper velocior fiat. Verum facile erit pervidere consequi ex hac adiectione incrementuum celeritas secundum unitatum seriem; nempe ita ut in primo momento sit unus velocitatis gradus, in secundo sint duo, in tertio tres, in quarto quatuor,” Gassendi, Opera omnia, III, p. 497a.
Ibid., p. 498a.
Westfall, Force, p. Io8.
For an analysis of Descartes’ arguments against the Galilean theory of fall and of their impact on Mersenne, see Palmerino, “Infinite Degrees of Speed.”
Gassendi, Opera omnia, in, pp. 448–452. On Cazre’s polemic with Gassendi, see Galluzzi, “Gassendi e l’affaire Galilée,’ pp. 90–97; Palmerino, “Two Jesuit Responses;’ pp. 204–214.
Gassendi, Opera omnia, in, p. 626. Gassendi’s experiment is clearly an adaptation of the inclined plane experiment which Galileo had described in the Third Day of the Discorsi (Galilei, Two New Sciences [Drake], pp. 169–170).
“Pervellem proinde ipsum ostendisses, atque adeo subindicasses, qua ergo alia proportione accelerationem decidentium fieri, aut experiundo notaveris, aut deduxeris demonstrando. Gerte non satis intelligo quamobrem censueris, sive haec proportio, sive alia sit, earn nihil referre ad meum institutum: quippe si alia fuerit, quam quae supposita a me est, frustra est tota ratiocinatio,” Gassendi, Opera omnia, in, p. 626a.
Le Cazre, Physica demonstratio. For an analysis of Cazre’s theory of acceleration, see Palmerino, “Two Jesuit Responses,” pp. 206–208.
“Nihil est opus, ut desudem ad ostendendum non increvisse velocitatem aequabiliter, eodemve tenore ex c in D, quo incoeperat, perrexeratque usque in D; ut fecisset enim, oporteret descriptum esse non quadrangulum LD constans ex duobus triangulis; sed trapezion CN constitutum ex tribus. Eadem autem ratione manifestum est, si ad DE aptentur tria triangula, defutura duo; si ad EF quatuor, defutura tria, et ita deinceps [ ... ] ut proinde intelligamus totidem deesse ad accelerationis aequabilitatem velocitatis gradus, quot numerare licet triangulos ad laevam e regione cuiusque partis, complendo summam traingulorum APB. Constare ergo videtur Motum aequabiliter acceleratum definiri non posse ilium Qui aequabilibus spatiis aequalia celeritatis augmenta acquirat; sed potius ilium, Qui acquirat aequalia aequalibus temporibus,” Gassendi, Opera omnia, III, p. 567b.
Ibid., pp. 567b–568a.
Ibid., p. 621b.
“ [ . . . ] ut primum tempus AE non est individuum, sed in tot instantia, seu temporula potest dividi, quot sunt puncta particulaeve in ipsa AE (aut AD) ita neque gradus velocitatis individuus est, seu uno instanti, acquisitus totus; sed ab usque initio per totum primum tempus increscit, ac repraesentari potest per tot lineas, quot possunt parallelae duci ipsi DE inter puncta linearum AD, et AE,” ibid., p. 566a.
Galilei, Two New Sciences [Drake], p. 157.
“Declaratum certe est quoque iam ante et infinitatem illam partium in continuo, et insectilitatem mathematicam in rerum natura non esse, sed mathematicorum hypothesin esse, atque idcirco non oportere argumentari in physica ex iis quae natura non novit;’ Gassendi, Opera omnia, I, P. 341b.
In the Syntagma, Gassendi explains that the only really continuous movement found in nature is the rectilinear uniform motion of the atoms which move all at a speed of one minimum of space per minimum of time. The motions of the res concretae, which are slower than those of the atoms, are in fact all discontinuous: “Ita licere videtur concipere motum, quo Atomi per inane ferri dicuntur [ ... ] esse velocissimum; omneis vero gradus, qui ex illo, ad meram usque quietem sunt, ex intermistis paucioribus, pluribusve quietis particulis esse;’ Gassendi, Opera omnia, I, p. 341b. Since according to Gassendi’s theory, the atoms possess an innate principle of motion, the res concretae can be encountered only in a state of rest if the speeds of their constituent atoms cancel each other out. The first to observe the radical inconsistency between the principle of inertia stated by Gassendi in his Epistolae and the theory of discontinuous motion set forth in the Syntagma philosophicum was Koyré, “Pierre Gassendi;’ esp.109. Koyré’s argument has been further developed by Pay, “Gassendi’s Statement”; Carré, “Pierre Gassendi and the New Philosophy”; Detel, “War Gassendi ein Empirist?”; Brundell, Pierre Gassendi, p. 79. Disagreement with Koyré’s criticism has been voiced by Bloch, La philosophie de Gassendi, pp. 226–227, who claims that the theory of the discontinuity of motion plays only a passing role in the Syntagma, being nothing more than an ad hoc hypothesis introduced so as to account for the paradoxes of motion. Bloch’s interpretation has been convincingly refuted by Messeri, Causa e spiegazione, pp. 86–93.
“Il semble que la méfiance de Gassendi envers les mathématiques l’empêche d’accorder entre elles ses propres conceptions; et c’est pourquoi sa physique semble faite de pièces et de morceaux. Les hypothèses qu’il propose sont, chaque fois, appropriées et adptées au chapitre qu’il traite; il ne cherche pas à savoir comment ces différentes hypothèses s’accorderont. C’est là, je crois, une des raisons de l’infériorité de la science et aussi de la philosophie gassendiste;’ Koyré, “Pierre Gassendi;’ p. 1o8.
Westfall, Force, p. 47.
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Palmerino, C.R. (2004). Galileo’s Theories of Free Fall and Projectile Motion as Interpreted by Pierre Gassendi. In: Palmerino, C.R., Thijssen, J.M.M.H. (eds) The Reception of the Galilean Science of Motion in Seventeenth-Century Europe. Boston Studies in the Philosophy of Science, vol 239. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2455-9_8
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