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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
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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.
56
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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 inclina- tion 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
inappro- priate 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
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GALILEO AND THE THEORY OF THE TIDES
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, insignifi- cant 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, neglect- ing 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 semi-
diurnal 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 semi- diurnal
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-
60
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GALILEO AND THE THEORY OF THE TIDES
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 de- manded 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 angu- lar 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 pro- duced 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 con- taining 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 mo- tion 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 semi-
diurnal 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 be- fore 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 be- fore 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
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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]