Galileo Theory Tindal

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Galileo and the Theory of the Tides Author(s): E. J. Aiton and Harold L. Burstyn Source: Isis, Vol. 56, No. 1 (Spring, 1965), pp. 56-63Published by: on behalf of The University of Chicago Press The History of Science SocietyStable URL: http://www.jstor.org/stable/228458Accessed: 06-05-2015 07:05 UTC

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NOTES & CORRESPONDENCE GALILEO AND THE THEORY OF THE TIDES

The Fourth Day of Galileo's Dialogue, which called upon the tides to support the Copernican hypothesis, has long been treated - or left untreated - as a curious aberration from an otherwise well-reasoned argument. In an article published two years ago, Harold L. Burstyn 1 analyzed Galileo's theory in terms of Galilean physics and Newtonian physics. He concluded in both cases that the tides could be used as a proof of the earth's rotation and its movement about the sun.

It is refreshing when an article in these pages stimulates controversy, as Burstyn's has. And this is doubly true when the controversy focuses interest on a major subject in the history of science, thus transcending the specialized preoccupations of the participants.

In an earlier issue, E. J. Aiton questioned an incidental point in Burstyn's analysis. Galileo had postulated that there is a monthly unevenness in the motion of the earth because, while the force on the earth-moon system remains constant, the moon varies in its distance from the sun. Burstyn interpreted the force as gravitational and the unevenness as a changing earth-sun radius; he thus attributed to Galileo at least the intuition " that the point which described the earth's orbit about the sun is not the center of the earth but the center of the earth-moon system." Aiton, in reply, interpreted the force as tangential to the earth's orbit, and the unevenness as a periodic changing of the speed of the earth along the orbit. This, Aiton argued, also fits better with the context of Galileo's argument, which includes a discussion of the regulatory action of clocks' weights. For the details of this difference of opinion the reader is referred to Isis, 1963, 54: 265-266 (June) and 400-401 (September).

Now Aiton returns to question some of Burstyn's more fundamental theses. Burstyn has been asked to reply, and his remarks are printed here also. B. S. F.

COMMENTS BY E. J. AITON * Since the chief object of Galileo's theory of the tides was to prove the earth's

axial and orbital motions, it is of prime importance to decide (1) whether, within the framework of his own physics, Galileo was justified in his deduction, (2) whether, in the context of Newtonian physics, the phenomena of the tides

are capable of furnishing the proof sought by Galileo. In my view, the answers given to these questions by H. L. Burstyn in his article " Galileo's Attempt To Prove that the Earth Moves"- namely, that Galileo's theory of the tides "demands that the earth rotate on its axis and revolve in orbit around the sun," and that " these are the conditions demanded by a correct theory of the tides " 2 - are both false.

According to Galileo the principal causes of the tides are "the determinate acceleration and retardation of the earth, depending on the combination of the two motions, annual and diurnal," and " the proper gravity of the water, which being once moved by the primary cause, then seeks to reduce itself to equilibrium, with repeated reciprocations." 3 It is only Galileo's primary cause that is in question. Galileo's idea that the seas, once disturbed by the primary cause,

* Didsbury College of Education, Man- 2 Ibid., p. 181. chester, England. 3 Galileo, Le Opere di Galileo Galilei (Flor-

Harold L. Burstyn, "Galileo's Attempt To ence: Societa Editrice Fiorentina, 1842-1856), Prove that the Earth Moves," Isis, 1962, 53: Vol. 2, p. 401. 161-185.

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GALILEO AND THE THEORY OF THE TIDES

continue to oscillate with periods depending on the sizes and shapes of their natural boundaries, was a sound intuition foreshadowing modern ideas.4

Let EF (Fig. 1) represent a part of the earth's orbit. At the point A on the earth's surface, where it will be midnight, the annual and diurnal motions are in the same sense; whereas at the point B, where it will be noon, these motions are in opposite senses. Relative to axes fixed in the sun, which Galileo supposed to be at rest, the speed at A is greater than that at B. Consequently, each part of the earth's surface, Galileo argued, is alternately accelerated and retarded, thus giving rise to the tides.

First let us consider Galileo's theory within the framework of his own physics. It may be inferred from the Dialogo that Galileo regarded the earth's orbital motion and axial rotation as inertial, though this belief is nowhere stated

A

F E

B

FIGURE 1

explicitly. From this standpoint, Galileo's theory of the tides involved the belief that the combination of two inertial motions could result in a noninertial or accelerated motion. Through Simplicius, Galileo admitted that at first sight this "has the appearance of a very great paradox." 5 It is, in fact, completely false. Any force on the water arising from the combination of the two motions would be the vector sum of the forces arising from the separate motions, and since these are inertial, they cannot give rise to any forces.6 It follows that, assuming the earth's orbital motion and axial rotation to be inertial, the double motion of the earth claimed by Galileo to be demonstrated by the tides was unable to move the water relative to the earth in the slightest degree.

Once it is realized that the earth's orbital motion and axial rotation are accelerated, the paradox disappears. That Galileo had some understanding of centrifugal force may be inferred from his discussion of the propulsion of a stone by slings and similar devices.7 For Galileo, however, the motion of a stone in a

4 For a discussion of this aspect of Galileo's Santillana (Chicago: University of Chicago theory, see D. Burger, "Galilei's theorie van eb Press, 1953), p. 434. en vloed," Hemel en Dampkring, 1954, 52: 6 Cf. Santillana's explanation, ibid., p. 434, 27-36 and Burstyn, op. cit., p. 174. footnote 6 5 Galileo, Dialogue on the Great World Sys- tems, revised and annotated by Giorgio de 7Ibid., pp. 201 ff.

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E. J. AITON

sling and the motion of bodies on a rotating earth were not comparable. The discussion of the propulsion of stones from slings and spinning wheels occurs in the course of a demonstration that bodies on the earth cannot be thrown off by the earth's axial rotation. Whatever the velocity of a stone when it leaves the rim of a spinning wheel to which it was attached, Galileo argues, " in the beginning of the separation, the recession being so small by reason of the infinite acuteness of the angle of contact, every smallest inclination that draws it back toward the centre of the wheel would be sufficient to retain it upon the rim or circumference." 8 Since the stone has no inclination toward the center of the wheel, it would be thrown off; but bodies on the earth, having a natural inclination toward the center, Galileo argues, can never be thrown off. It is not simply that the velocity of rotation of the earth is too slow. According to Galileo's argument, the lightest conceivable body would not be thrown off however great the velocity of rotation. For Galileo, therefore, the circular motion of bodies moving with the earth was inertial. If, as we have seen, Galileo regarded the motion of the stone in the sling as inappropriate to the case of the earth's axial rotation, we may reasonably infer that he would also have regarded it as inappropriate to the case of the earth's orbital motion. Contrary to the opinion of Burstyn,9 Galileo's discussion of slings and spinning wheels, considered in its context, does not provide any evidence that Galileo understood intuitively that the earth's orbital motion is accelerated.

Galileo's theory of the tides was inspired by the behavior of water in moving containers, as is evident from the earliest extant statement of the theory, recorded in the notebooks of Paolo Sarpi.10 In the Dialogo Galileo mentions that he had a design for a mechanical model to illustrate his theory of the tides, but no details are given.11 Both Burstyn 12 and Drake 13 have attempted to design a model such as Galileo had in mind. Analyzed according to the principles of Newtonian mechanics, such models would give rise to oscillations of the water with a diurnal period, and this has led some commentators, of whom Strauss appears to be the first, to the belief that Galileo's theory does in fact predict a tide. Within the framework of Galileo's physics, however, the models are not proper analogues of the tides. For in the models, the water has no inclination toward the center of the wheel on which it turns; whereas the inclination of the water toward the center of the earth makes its circular motion inertial. It is possible that a sound physical intuition of the results to be expected from such thought-experiments gave Galileo the confidence to persevere with his theory of the tides, even when reason would seem to demand that he should have recognized such models to be inappropriate for the same reason that the stone and spinning wheel were inappropriate to represent the motion of a body on a rotating earth.

Although, according to the interpretation of Galileo's theory outlined above, Burstyn's model is not a true analogue of Galileo's theory of the tides, it may not be amiss to analyze the results to be expected from it, according to the principles of Newtonian mechanics, using less sophisticated mathematics than its inventor. Let the earth, radius a (Fig. 2), rotate about its center A, while the center describes a circle, radius R, about the sun (D. If the angular velocity in the orbit is Q and the angular velocity of the earth's axial rotation is o, the

8 Ibid., p. 207. 11 Santillana (Galileo, Dialogue . . .), op. cit., 9 Burstyn, op. cit., p. 167. p. 438. 10 See Stillman Drake, "Galileo Gleanings- 12 Burstyn, op. cit., p. 172.

X. Origin and Fate of Galileo's Theory of the 13 Drake, op. cit., p. 191. Tides," Physis, 1961, 3: 187.

58



acceleration of the point P has components RQ2 parallel to A and aw2 along PA. Resolving RQ2 into horizontal and vertical components (i.e., perpendicular to PA and along PA), we find that the acceleration of P consists of a horizontal component RQ2 sin 0 in the direction of 0 increasing and a downward vertical component aw2 + RQ2 cos 0. Assuming that inertial motion is rectinlinear, the water does not share this acceleration. Relative to the earth, therefore, the water experiences a force in the opposite direction. The vertical component, insignificant compared to terrestrial gravity, is unable to produce any motion relative to the earth and its effect is simply a slight variation in the apparent density

OFR R

FIGURE 2

of the water. Measuring the time t from an instant when (AP is a straight line, 0 = (o -- ;) t, so that the point P of the earth's surface experiences a periodic horizontal acceleration with a diurnal period. A unit mass of water experiences, relative to the earth, a horizontal force of magnitude RQ2 sin (w - Q) t acting in the opposite direction. This force would give rise to the diurnal tide, with high water at midnight, described by Burstyn 14 as a "tide of reaction." Since the force RQ2 sin ( - Q) t vanishes when Q = 0, the double motion of the earth is necessary to produce a diurnal tide in Burstyn's model.

From the standpoint of Newtonian mechanics, the cause of the tides is the attraction of the sun and the moon. For a comparison with Galileo's theory only the solar tide need be considered. Let the attraction of the sun on unit mass at P (Fig. 2) be F. Then F = ym/r2, where y is the gravitation constant, m the mass of the sun, and r the distance of P from the sun. To resolve F into components FAQ and FPA parallel to A and along PA respectively, PA C may be taken as a triangle of forces, so that F/r = FAO/R = FpA/a. It follows that

14 Burstyn, op. cit., p. 173.

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E. J. AITON

FAC = RF/r and Fp -= aF/r. Now r2 = R2 + 2aR cos 0 + a2, so that l/r3 (1 - 3a cos 0/R) /R3, neglecting higher powers of (1/R). It follows that, neglecting powers of (1/R) higher than the third,

ym ( - 3a cos 0\ and F yam FO --

1- _R and FA- R3

The force ym/R2 is independent of the position of P. Acting equally on the earth and the water, this force cannot cause any motion of the water relative to the earth and consequently plays no part in the production of a tide.15 Abstracting this term, the force on the water, relative to the earth, in the direction parallel to A ( is - (3aym cos 0) /R3. This may be resolved into a horizontal component - (3atym cos 0 sin 0) /R3 in the direction of 0 increasing and an upward vertical component (3aym cos2 0) /R3. Relative to the earth, a unit mass of water at P therefore experiences a horizontal force - (3aym sin 20) /2R3 in the direction of 0 increasing and an upward vertical force aym (3 cos2 0 1) /R3, where 0- (w -- ) t. These results were first obtained by Euler.16 While the vertical force, insignificant compared to the earth's gravity, simply causes a slight variation in the apparent density of the water, the horizontal force gives rise to a semidiurnal tide.

In the correct theory the maximum horizontal force is (3a-ym) /2R3; whereas in Burstyn's model the corresponding force is RQ2. Since ym/R2 - RQ2, the tide-generating force in Burstyn's model is (2R) / (3a) times the correct tide- generating force. It follows that the tide predicted by Galileo's theory, as interpreted by Burstyn and Strauss, is about 104 times greater than the actual solar tide. Although Burstyn recognized that Strauss was mistaken in believing that the tide predicted by his interpretation of Galileo's theory was insignificant compared to the actual tide,17 Burstyn is himself mistaken in supposing that the tide called for by his model has any connection with the tide predicted by the equilibrium theory. If there were any connection, which a priori seems unlikely since the causes of the two tides are different, it would have to be sought in the relation RQ2 -ym/R2. In Burstyn's model the tide results from the centripetal acceleration RQf2 but in the equilibrium theory the term ym/R2 in the expression for the attraction of the sun has no effect on the solar tide.

Finally let us consider Burstyn's claim that the double motion of the earth is demanded by a correct theory of the tides. No problem arises in the case of the axial rotation. Although this rotation cannot of itself produce tides, the rotation of the earth beneath the tidal bulge is needed to explain the semidiurnal oscillation at particular points of the earth's surface. Also the earth's axial rotation is needed to explain the modification of the tidal currents attributed to Coriolis acceleration. If, however, we take the orbital angular velocity 0 0 in the expression - [3aym sin 2 (w - -) t]/2R3 for the effective tide-generating force, it is clear that a semidiurnal tide of the same amplitude would still remain.18 It follows that the earth's orbital motion has no influence on the tides.

15 The force 'ym/R2 equals R92. In Burstyn's point on the earth. This term causes an model this force acts on the earth but not on acceleration of the earth toward the sun, equal the water. to RQ2 if the earth is revolving in a circular

16 See E. J. Aiton, "The Contributions of orbit, but equal to - d2R/dt2 if the earth is Newton, Euler and Bernoulli to the Theory moving in a straight line toward the sun. of the Tides," Annals of Science, 1955, 11: Since this term, in both cases, is common to 221. the attraction of every point of the earth and

17 Burstyn, op. cit., p. 183. the surrounding oceans, it cannot give rise to s1 The force ym/R2 is the largest term in the any relative motion of different points in the

expansion of the attraction of the sun at any oceans. Such relative motions are caused effec-

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Daniel Bernoulli,19 using a different approach, first established this result. If the earth were to revolve in its orbit without axial rotation, the different points of the earth would describe equal ellipses and at any instant the centrifugal forces on the different points would be equal in magnitude and parallel in direction. Acting equally on every part of the earth and the ocean, such forces, Bernoulli concluded, cannot produce any motion of the water relative to the earth.20 Burstyn 21 has misunderstood no less than three commentators - Harris,22 Groen,23 and Aiton,24 who have quoted Bernoulli's argument- attributing to the three only a statement (which none of them makes) of the rather obvious fact that the earth's axial rotation gives rise to equal centrifugal forces, so that the earth's axial rotation cannot give rise to tides.

Since the earth's orbital motion has no effect on the tides, it follows conversely that this motion cannot be deduced from the tides. If the earth-sun system were not in rotation, the two bodies would approach. By taking 0 = 0 in the expression for the effective tide-generating force, we have seen that if the earth were to cease its orbital motion, the solar tide would remain unchanged until a significant change in the distance between the two bodies had taken place. The earth-sun system is clearly in rotation; but whether dynamics required a motion of the earth about the sun or a motion of the sun about the earth, the tides would be the same. Consequently, a correct theory of the tides demands the earth's axial rotation but not its orbital motion; so that, in the light of Newtonian mechanics, Galileo's belief that the tides prove the earth's orbital motion is seen to be unfounded. In Newtonian mechanics the earth's orbital motion is demanded not by any terrestrial phenomenon but by the principle that the motion of the center of mass of the earth-sun system, considered in isolation from other gravitating bodies, is inertial.

REPLY BY HAROLD L. BURSTYN **

Although I am grateful to Dr. Aiton for the opportunity once more to clarify my views on the Fourth Day of Galileo's Dialogo, I fear that in the more serious of the two criticisms he offers above, his eagerness to discredit my position has led him into error. The more serious criticism of my paper is that, in Aiton's view, my statement that the earth's orbital motion is responsible for the semi-

tively by the second term in the expansion of the attraction, and this term remains sub- stantially the same on taking Q = 0. It should be noted that Mach's well-known discussion concerns a different system, in which the earth and the sun, instead of gravitating freely, are both fixed.

19 Daniel Bernoulli, "Traite sur le flux et reflux de la mer," Recueil des pieces qui ont remporte les prix de l'Academie royale des sciences (Paris, 1752), Vol. 4, p. 79. 20 Bernoulli's argument may be extended to show Burstyn's error (op. cit., p. 166) in attributing a "Coriolis" effect to the earth's orbital motion. Abstracting the earth's axial rotation, so that the earth maintains a constant orientation with respect to the fixed stars, the different points of the earth describe equal ellipses in parallel planes with the same angular velocity. Consequently, the motion of a particle of water in latitude transfers it to an

equal ellipse so that the angular velocity is unchanged. It follows that no motion in longi- tude relative to the earth is produced. 21 Burstyn, op. cit., pp. 171, 183.

22 Rollin A. Harris, "Manual of Tides," Part 4, Appendix, Report of the Superin- tendent of the United States Coast and Geo- detic Survey (Washington, 1898-1904), p. 404. 23 P. Groen, Hemel en Dampkring, 1954, 52: 80. Groen's argument was also misunderstood by Burger (ibid., p. 81) who accepted Groen's conclusion that the earth's orbital motion could not affect the tides, but who believed this to follow from the fact that, over a short distance, the earth's orbit could be regarded as recti- linear.

24 E. J. Aiton, " Galileo's Theory of the Tides," Annals of Science, 1954, 10: 56.

** Brandeis University. This note is Con- tribution No. 1524 from the Woods Hole Oceanographic Institution.

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HAROLD L. BURSTYN

diurnal character of the equilibrium tide is false. Aiton's position here is absurd, as the reader may see by examining the expression which he derives for the tide-generating force: 25

- [3aym sin 2 (o - Q) t]/2R3. (1)

Aiton claims to stop the earth's orbital motion merely by setting == 0 in (1). Such a step does not, however, accomplish his aim; it merely changes the period of the expression, so that the tidal year becomes solar rather than sidereal. Aiton's error here is his facile application of (1) to the case of an earth fixed in space, to which it does not apply. For (1) is derived on the assumption that the earth and the disturbing body (in this case, the sun) are freely gravitating. From this assumption it follows that the earth and the sun move about their common center of mass, which is another way of saying that the earth is in orbit around the sun. An earth which does not describe an orbit about the center of mass of itself and the disturbing body is not freely gravitating; hence, (1) cannot apply.

Another way of seeing the fallacy in Aiton's argument is to note that ym/R2 RQ2, in the case of the earth and the sun.26 Hence, (1) contains t2 elsewhere than in the argument of the sine function, so that setting f2 0 requires either that the entire expression vanish or that some other force exist which can provide a coefficient for the sine function. Since the assumption that the earth is fixed in space is incompatible with the existence of such a force, (1) is clearly inapplic- able to the case of the fixed earth.27

My original statement that " in the simple equilibrium theory, the semidiurnal character of the tide is a proof of the earth's double motion" 28 is thus untouched by Aiton's strictures. He himself agrees that " the axial rotation ... of the earth beneath the tidal bulge is needed to explain the semidiurnal oscillation at particular points of the earth's surface." 29 His criticism of the necessity of the earth's orbital revolution to the creation of the second " tidal bulge " has been shown to be incorrect in the preceding paragraphs, and the reader who wishes a demonstration of this necessity is again referred to the discussion of Ernst Mach.30 The problem of the equilibrium tide on an earth fixed in space is also treated by Thomson and Tait.31

25 This expression is given above by Aiton in the sentence which ends with footnote 18.

26 See Aiton's text above in the paragraph containing reference to footnote 17.

27 Aiton makes another error in footnote 20 above. Contrary to his notion, the earth's orbital motion produces a Coriolis effect of a magnitude 1/365 that of the Coriolis effect produced by the diurnal motion. Therefore, in geophysical calculations one uses the sidereal angular velocity of the earth. 28 Burstyn, op. cit., p. 167. 29 Aiton's text above, the paragraph containing reference to footnote 18. 30 Ernst Mach, Die Mechanik in ihrer Ent- wichelung, 9th ed. (Leipzig: F. A. Brockhaus, 1933), pp. 206-208, cited in Burstyn, op. cit., p. 167, footnote 23. None of the commentators whom Aiton accuses me of misunderstanding deals with this point.

31 William Thomson and Peter Guthrie Tait, Treatise on Natural Philosophy (Cambridge,

1883), Art. 803. Let me indicate here my agree- ment with Aiton that the tide called for by my phonograph and merry-go-round model is not the same kind of phenomenon as the New- tonian equilibrium tide. Like the tide on an earth fixed in space, the tide in my model is first order (a function of 1/R2); whereas the true tide is second order (a function of 1/R3). But the sole purpose for which I use the model is to demonstrate that the earth's double motion in and of itself gives rise to a tide, and Aiton has misunderstood my use of the model if he thinks that I find in it an exact analogy to the Newtonian tide-generating force. The model shows clearly that the inertia of the orbiting earth is just as necessary to the semidiurnal equilibrium tide as is the gravitational attraction of the earth and the disturbing body. The latter force is Kepler's contribution to tidal theory; I have suggested that the former is implicit in Galileo's theory of the tides.

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WILLIAM PETTY'S MECHANICAL PHILOSOPHY WILLIAM PETTY'S MECHANICAL PHILOSOPHY

Aiton's second criticism of my paper is based on my crediting Galileo with a belief that the earth's orbital motion is noninertial. My case for such a belief has been made as clearly as I know how in the original paper.32 I do not see how Galileo's use of the expression " the force which moves . . . the earth around the sun" 33 can be reconciled with a denial that he believed the earth's orbit to be accelerated.

If my argument has a weakness, it is that a case can also be made for Galileo's belief that the earth's orbital motion is inertial, and Aiton has made such a case above.34 As in our previous disagreement, there is evidence in the Dialogo to support both positions. It may be possible to reconcile these two apparently contradictory descriptions of the earth's orbit, each supported by Galileo's own writings.35 I think that such a reconciliation, if accomplished, would show, not that one view is decisively vindicated and the other refuted, but that Galileo had in mind something very different from a clear position on whether or not the earth's orbit is inertial. A more likely outcome of the present controversy is the recognition by historians of science that Galileo's physics is not completely consistent, so that Galileo's inconsistencies and not our misinterpretations can be blamed for the disagreement between Dr. Aiton and myself.

Aiton's second criticism of my paper is based on my crediting Galileo with a belief that the earth's orbital motion is noninertial. My case for such a belief has been made as clearly as I know how in the original paper.32 I do not see how Galileo's use of the expression " the force which moves . . . the earth around the sun" 33 can be reconciled with a denial that he believed the earth's orbit to be accelerated.

If my argument has a weakness, it is that a case can also be made for Galileo's belief that the earth's orbital motion is inertial, and Aiton has made such a case above.34 As in our previous disagreement, there is evidence in the Dialogo to support both positions. It may be possible to reconcile these two apparently contradictory descriptions of the earth's orbit, each supported by Galileo's own writings.35 I think that such a reconciliation, if accomplished, would show, not that one view is decisively vindicated and the other refuted, but that Galileo had in mind something very different from a clear position on whether or not the earth's orbit is inertial. A more likely outcome of the present controversy is the recognition by historians of science that Galileo's physics is not completely consistent, so that Galileo's inconsistencies and not our misinterpretations can be blamed for the disagreement between Dr. Aiton and myself.

32 Burstyn, op. cit., pp. 167, 178-179.

33 Galileo, Dialogo, in Le Opere di Galileo Galilei. Edizione nazionale .. . (Florence: Tipo- grafia Barbera, 1890-1909), p. 478, quoted in Burstyn, op. cit., p. 178.

32 Burstyn, op. cit., pp. 167, 178-179.

33 Galileo, Dialogo, in Le Opere di Galileo Galilei. Edizione nazionale .. . (Florence: Tipo- grafia Barbera, 1890-1909), p. 478, quoted in Burstyn, op. cit., p. 178.

34 See Aiton's above text, fourth and fifth paragraphs.

35 Such a reconciliation has been attempted by my student Donald Koch, " Galileo's Theory of Fall in hypothesi terrae motae," unpublished MS, 1963-1964.

34 See Aiton's above text, fourth and fifth paragraphs.

35 Such a reconciliation has been attempted by my student Donald Koch, " Galileo's Theory of Fall in hypothesi terrae motae," unpublished MS, 1963-1964.

WILLIAM PETTY'S MECHANICAL PHILOSOPHY

By Robert Kargon *

WILLIAM PETTY'S MECHANICAL PHILOSOPHY

By Robert Kargon *

Seventeenth-century England was the scene of a remarkable quickening in the pace of scientific activity. Beginning in the early years of the century with the work of William Gilbert and of Thomas Hariot,1 and culminating in Newton's momentous accomplishments in mathematics, dynamics, and optics, this " scientific revolution " was not to see its equal until our own century. Accompanying and reinforcing the surge of experimental and mathemati- cal activity was the rise of a new world view: the mechanical philosophy. The major contributors to this view were Pierre Gassendi, Rene Descartes, and Thomas Hobbes. The comprehensive systems of Gassendi and Descartes were

*University of Illinois. I should like to thank Professor Henry Guerlac for his kind advice.

Seventeenth-century England was the scene of a remarkable quickening in the pace of scientific activity. Beginning in the early years of the century with the work of William Gilbert and of Thomas Hariot,1 and culminating in Newton's momentous accomplishments in mathematics, dynamics, and optics, this " scientific revolution " was not to see its equal until our own century. Accompanying and reinforcing the surge of experimental and mathemati- cal activity was the rise of a new world view: the mechanical philosophy. The major contributors to this view were Pierre Gassendi, Rene Descartes, and Thomas Hobbes. The comprehensive systems of Gassendi and Descartes were

*University of Illinois. I should like to thank Professor Henry Guerlac for his kind advice.

doubtlessly the most influential. The full story of the introduction and estab- lishment of the mechanical philosophy in England still remains to be told. The purpose of this note is to make a small contribution toward that end by presenting in its historical context the mechanical view of nature of the emi- nent virtuoso of the Royal Society, Sir William Petty.

In 1674, William Petty appeared before the Royal Society and delivered a discourse which was published at the request of Lord Brouncker later in the year as A Discourse Made before the Royal Society . . . Concerning the Use of Duplicate Proportion . . . Together with a new Hypothesis of Springy or

1 See Johannes Lohne, "Thomas Harriott (1560-1621): The Tycho Brahe of Optics," Centaurus, 1959, 6: 113-121.

doubtlessly the most influential. The full story of the introduction and estab- lishment of the mechanical philosophy in England still remains to be told. The purpose of this note is to make a small contribution toward that end by presenting in its historical context the mechanical view of nature of the emi- nent virtuoso of the Royal Society, Sir William Petty.

In 1674, William Petty appeared before the Royal Society and delivered a discourse which was published at the request of Lord Brouncker later in the year as A Discourse Made before the Royal Society . . . Concerning the Use of Duplicate Proportion . . . Together with a new Hypothesis of Springy or

1 See Johannes Lohne, "Thomas Harriott (1560-1621): The Tycho Brahe of Optics," Centaurus, 1959, 6: 113-121.

63 63


Article Contentsp.56p.57p.58p.59p.60p.61p.62p.63

Issue Table of ContentsIsis, Vol. 56, No. 1, Spring, 1965Front Matter [pp.1-3]The Atomic Debates: "Memorable and Interesting Evenings in the Life of the Chemical Society" [pp.5-25]The Principle Omne quod movetur ab alio movetur in Medieval Physics [pp.26-45]How Was the Tunnel of Eupalinus Aligned? [pp.46-55]Notes & CorrespondenceGalileo and the Theory of the Tides [pp.56-63]William Petty's Mechanical Philosophy [pp.63-66]A Speculation on the Origin of Fahrenheit's Temperature Scale [pp.66-69]Lunar Visibilities in Ancient Babylon [p.69]

Documents and TranslationsThe Boscovich Archives at Berkeley [pp.70-78]

News [pp.79-82]Book ReviewsQuantum Comments [pp.83-84]

History of Scienceuntitled [pp.84-86]

Philosophy of Scienceuntitled [pp.86-87]untitled [p.88]

Biological Sciencesuntitled [pp.88-90]

Technologyuntitled [pp.90-92]

Classical Antiquityuntitled [pp.92-93]

Middle Agesuntitled [pp.93-95]untitled [pp.96-99]untitled [pp.99-100]

Seventeenth & Eighteenth Centuriesuntitled [pp.100-101]untitled [pp.101-103]

Nineteenth & Twentieth Centuriesuntitled [pp.103-105]untitled [pp.105-107]untitled [pp.107-108]untitled [pp.108-110]untitled [p.110]

Contemporary Scienceuntitled [pp.110-111]untitled [pp.111-113]untitled [pp.113-114]

Back Matter [pp.115-116]