The British Society for the History of Science
Mechanics and the Royal Society, 1668-70
Author(s): A. Rupert Hall
Source: The British Journal for the History of Science, Vol. 3, No. 1 (Jun., 1966), pp. 24-38
Published by: Cambridge University Press on behalf of The British Society for the History
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MECHANICS
AND THE ROYAL SOCIETY,
By A. RUPERT
I668-70
HALL
APART from statics, about which I shall say nothing, there were three
chief centres of interest in mechanics in the i66o's:
(I) the motions of pendulums;
(2) the laws of motion;
(3) the free fall of heavy bodies and the motion of projectiles.
In the first the influence of Huygens was dominant; I have placed it
so because it was of very lively contemporary concern. The second area
of interest descended partly from Galileo and partly from Descartes;
the third from Galileo alone. Perhaps one should consider adding a fourth
area, the investigation of central forces, but this in fact did not attract
much attention as yet.
In its first years the Royal Society, although it included a number
of competent mathematicians, paid surprisinglylittle attention to mechanics. There are some cursory allusions to pendulum experiments, and
in May i66i "Mr. Boyle, Dr. Goddard and Dr. Petty [were instructed]
to consult concerning the nature of gravity", with no recorded result.'
The question of the use of a pendulum as a natural standard of length
came up quite early, but I shall not pursue this theme.2 More interesting
is a paper by Brounckerread on 22 January i66i/2 in which he proved
(as Huygens had done before by other reasoning) that the cycloid is
the curve of isochronous descent, and that the evolute of a cycloid is
a cycloid. Brouncker'sproof requires one explicit assumption:
"the increaseof the velocity of the same body descendingis always in
proportionto the power of the weight, that is, on planes of equal length,
proportionalto the verticalheight of the plane".
w (falling
weight)
height
varied
W
static weight
fulcrum
FIG.
See Birch, Histoy, i, 7 (ig December i66o), 22 (8 May I661), 46
November I66i).
Old style dates are used throughout this paper, as in Birch.
2 See ibid.,54 (!2o November I66I), 75 (5 February I661/2).
I
54
I.
(25
September i66ix),
(20
THE BRITISH JOURNAL FOR THE HISTORY OF SCIENCE VOL. 3 NO. 9 (t966)
Mechanicsand the Royal Society,I668-70
25
In justifying this assumption he refers to Stevin's Statics.3
It was Brouncker who suggested somewhat later that experiments
be made "on the first velocity of bodies", that is to find out, for example,
what force would be required to raise one pound weight one yard high
in one second. (He did not further define his sense of the word "force",
nor in what units it should be expressed.) Hooke made a machine to
measure the force of impact of falling bodies, which failed at first but
which later gave some results.4
I reproduce one of Hooke's two tables, the figures in parentheses
being my own: s is the height through which the weight w fell, raising
minimally the counterpoise W (expressed as n times w); V is the velocity
of w on impact, which I have calculated.
TABLEI
W
s (inches)
(
21()4
3
(3-5)
Id
(9.2)
2-3
31
3
5
61
(I 2 . 25)
(18.4)
(20 I)
(26-25)
(35.0)
I)(I
8 (2)
i6
32
48
64
(4)
(8)
(I2)
(i6)
96 (24)
I28 (32)
V (as a ratio)
( .87)
(3.03)
(3 5)
(4-3)
(4.48)
(5- I2)
(5 9)
It appears that, as might be expected, W increases in proportion to
s, i.e. roughly in proportion to V2. Such was not Hooke's opinion,
however; he remarks of his experiments, "though they do not answer
our expectations as to the accurate exhibiting the strength of a moved
body, yet seem to prove, that a body moved with twice the celerity
acquires twice the strength, and is able to move a body as big again".
It seems that Hooke is here taking the velocity to be directlyproportional
to the distance fallen. However, Hooke also discusses Descartes's belief
that a body could not by impact move another larger than itself,5 which
on the basis of these experiments he tends to reject.
Hooke was also responsible for experiments on falling bodies carried
out in the summer of i664, which gave one bad value for g at 40 feet
per sec.2 and one good one at 3I, and performed other experiments on
the oscillation of long pendulums.6 It was at this point that a fresh
impetus came from Huygens, who announced to Moray the success
of his work on the determination of centres of oscillation: the Society
tested Huygens's rules.7
3
4
5
6
7
Ibid., 70-74.
Ibid., I24 (I2 November I662), I92 (4 February I662/3), I95-7 (I8 February 1662/3).
Descartes's fourth rule of impact (Principiaphilosophiae,2e Partie, xlix).
Birch, History,i, 449, 455-456, 46i, 464, 466-467.
Ibid., 480, 508.
26
A. RUPERT HALL
In i 666, after the dispersal of the Society during the Plague, discussion
moved to a more theoretical level. Wallis's paper on the mechanical
theory of tides, though it proposed only a modified form of Galileo's
incorrect theory, is notable if only for its plain-spoken preamble:
"How much the world, and the great bodies therein, are managed
according to the laws of motion and static principles, and with how much
more of clearness and satisfaction many of the more abstruse phenomena
have been salved on such Principles within this last century of years than
formerly they had been, I need not discourse to you, who are well versed
in it [that is Boyle, to whom the paper was addressed]. For since that Galileo
and Torricellio and others have applied mechanic principles to the salving
of philosophical difficulties, natural philosophy is well known to have been
rendered more intelligible, and to have made a much greater progress in
less than an hundred years, than before for many ages."8
As a starting-point for his argument, Wallis says,
"We shall first take for granted what is nowadays pretty commonly
entertained by those who treat of the laws of motion and mechanical principles:
'That a bodyin motionis apt to continueits motion,andthatin thesamedegreeof celerity,
unlesshinderedby somecontraryimpediment'."
This is a very loose definition. More novel is Wallis's assertion that the
centre of gravity of the earth-moon system describes an orbit about
the sun, while about this revolve both the centre of the earth and the
centre of the moon: this is his basic modification to Galileo. Against
the objection that "It appears not, how two bodies that have no tie
can have one common centre of gravity" Wallis rejoins that
"it is harder to see how they have, than that they have it. That the loadstone and iron have somewhat equivalent to a tie, though we see it not, yet
by the effects we know. And it would be easy to show that two loadstones
at once applied in different positions to the same needle, at some convenient
distance, will draw it not to point directly at either of them, but to some
point between both; which point is, as to those two, the common centre of
attraction".
Wallis is quite clear that there is a tie that makes "satellites attend their
lords, and move in a body".9
Since Wallis's tidal theory was read and discussed on i6 May, when
Hooke ventured the remark that the motion of the celestial bodies might
be represented by pendulums, I think there is little doubt that it was
Wallis's theory which occasioned Hooke at the next meeting (on the 23rd)
to present his well-known paper on "the inflection of a direct motion
into a curve by a supervening attractive principle" which he illustrated
by pendulum motions.'0 To enter in detail into these physical theories of
Wallis and Hooke would draw me too far aside from my line, but I
8 Phil. Trans., No. i6 (6 August i666), 264.
9 Ibid., 268, 282.
lo Birch, History, ii, 90-92. Oldenburg's attention was caught by this paper, about which
he wrote at length to Boyle. Is it possible that Hooke discouraged its printing in Phil. Trans.?
And what effect would it have had if printed?
Mechanics and the Royal Society, I668-70
27
would observe that Hooke here gives a proof that the "conatus to the
centre" or restoring force towards the neutral vertical position on a
pendulum bob is for small angles proportional to the angle of displacement
which is correct (I think) in its result though not in the way it is set out.
After this prefatory summary of the earlier activity of the Royal
Society, it will be convenient now if I discuss first the investigation of
the laws of impact, and then some other matters. There can be no doubt
that when the "laws of motion" were spoken of at this time the words
were used in a wholly Cartesian sense to signify the law of inertia as
the foundation of all, then the laws of the distribution of motion among
colliding bodies. I shall return to the law of inertia: as to the latter,
it is well known that Christiaan Huygens, dissatisfied with Descartes's
treatment in the Principia Philosophiae, had worked out fresh rules in
the mid i650's." These were made known to some members of the
Royal Society during Huygens's visit to England in i66i; Huygens was
given certain cases, of which he privately calculated the results, results
fully conforming to the trials already made by Wren and Rooke. In
correspondence, attention was drawn to these experiments by Spinoza
in October i 665; upon which Moray wrote to Oldenburg:
"The story of what Mr. Huygens says was thus, as both Dr. Wallis and
I do well remember. When Mr. Huygens first came over we were with him
at his lodging at the end of New Street in Covent Garden, where he told us
amongst other things of what he had done in the business of motion . . . At
that time Dr. Rooke and Dr. Wren had made diverse experiments with balls
of wood and other stuff hanging by threads whereof you may remember to
have seen some; upon Mr. Huygens undertaking to solve some questions of
motion according to this rule Dr. Wren did propose some which he had tried
by experiments, and Mr. Huygens did in a very short space solve them so
as was concluded by all the solution did agree with the experiments that had
been made.""2
Sprat (i667) also speaks in some detail of Wren's experiments with a
specially devised apparatus (pp. 3 1I-3I 2).
A year later (October i666) the Society devoted a little time to
such experiments on colliding balls (without any mention of comparison
with a theory), and as examples of continuing interest in the laws of
motion, on the i6 January I666/7 Oldenburg announced that the
Council "had thought fit, that the experiments for making out a theory
of the laws of motion begun by Dr. Wren, Dr. Croone and Mr. Hooke, . . .
should be prosecuted", and that Wren should report his experiments.
But nothing was done, and the next event of any note was the fact that
Wallis, on 30 April i668, was asked to hasten his Mechanica. That is
the first mention of this book.'3
See e.g. Rend Dugas, La Mecaniqueau XVIIe Siecle (Neufchatel, 1954), 284-287.
of Henry Oldenburg(hereafter
A. Rupert Hall and Marie Boas Hall, The Correspondence
of Oldenburg)Madison, Wisconsin, I966, ii, 541, 550, 56I-562, 575.
cited as Correspondence
'3 Birch, History, ii, i i6, 117, 140, 275.
II
I2
28
A.
RUPERT
HALL
Meanwhile, the De vi percussionis of Giovanni Alphonso Borelli
reached London, which dealt with the laws of impact as well as many
other questions in mechanics. This book had not yet reached Paris in
November I667, and was never reviewed in Phil. Trans., but there was
discussion of it by the Royal Society in July i668.
It may have been Borelli, at least indirectly, who inspired Hooke
on 22 October-the first meeting after the Society's summer recess-to
propose "that the experiments of motion might be prosecuted, thereby
to state at last the nature and laws of motion". Now it might be thought
that experiment (if it were really the best means of attack on this problem)
had been given a pretty good run already; accordingly Brouncker from
the Chair suggested that Huygens and Wren "had already taken great
pains to examine that subject, and were thought to have also found out
a theory to explicate all the phenomena of motion". Oldenburg was
thereupon instructed to solicit Huygens and Wren to communicate
their results.'4 Oldenburg speaks of a "theorie" or "hypothese"; "hypothesis" is used in this connection by both Huygens and Wren, though
the former also referred to the "regles et theoremes que j'ai trouve".
Huygens did not at first understand that only the laws of impact were
in question; Wren required time not because he doubted his "hypothesis"
-he did not-but to check his experiments.
Now Hooke was able to renew his pressure for more experiments,
and on I2 November:
"The experiment of the communication of motion was tried by a contrivance, whereby three balls of the same wood, and of near equal bigness,
were so suspended that either of the two extremes being let fall from a certain
height against the intermediate ball, the other extreme was impelled upwards
to the same height, from whence the first was let fall, that in the middle moving
but little. Of which the President conceived this to be the reason, that the
intermediate ball when struck by one of the lateral ones found the resistance
of the other lateral ball, but this other lateral ball met with no other resistance
than that of the air."'5I
Hooke was thereupon ordered to think on further experiments which
might show that motion is neither created nor destroyed, a thoroughly
one-sided and thoroughly Cartesian directive. The meeting further agreed
to ask John Collins to make a study of all the authors who had written
on the "nature, principles, and laws of motion", especially Descartes,
Borelli and Marcus Marci; Wallis was also to be asked to take part in
this business.
Wallis, the last invoked, was the first to reply, in a letter of
15 November i668.16 In several ways this is a curious paper. In the
14 Ibid., 315. Oldenburg to Huygens, 26 October, Oldenburg to Wren, 29 October,
Huygens to Oldenburg, 3 November and Wren to Oldenburg of the same date will be found
in Correspondence
of Oldenburg,v.
I5 Birch, History,ii, 320.
z6 Correspondence
of Oldenburg,v. It was printed in Phil. Trans., no. 43 (i i January i668/9),
864-866.
Mechanicsand the Royal Society,I668-70
29
first place Wallis states that he has already given his views on the laws
of motion, not only in his earlier communication to the Royal Society
already mentioned (p. 27), but in "two papers shown to the Royal Society
several years ago, which are still in your [Oldenburg's] possession".
He describes these papers further, but they do not seem to be recorded.
Secondly, Wallis appears to assume, yet never in this paper explicitly
formulates, the correct law of inertia. Thirdly, although Wallis treats
of the collision of "weights" or heavy bodies (pondera) without specifying
the characteristics of such a body other than its weight (that is, propriedictu,
its mass), towards the end of the paper he makes it explicitly clear that
the pondera are supposed to be inelastic, equating elasticity with less
than perfect hardness, and hardness with lack of elasticity; for, he says,
"If the bodies that thus collide are taken to be not absolutely hard (as
we have so far supposed) but as yielding to the shock although able to restore
themselves by an elastic force, it will come about that such bodies may rebound
from each other when otherwise [that is, if perfectly hard] they would move
along together."
I shall return to this point in a moment. My fourth observation is
that Wallis's relationship of force and velocity is perfectly Aristotelian:
"if a force V moves a weight P, a force mV will move mP, all things being
equal, that is, through the same distance in the same time, or with the same
speed".
Wallis has no idea that a force produces an acceleration; rather his
model is the lever, where the product of forces and velocities is the same
at either end. This is (as Wallis says himself) a force law for machines.
One should not imagine that he was alone in his error: for example,
on 2I November I666 Hooke had laid it down quite categorically that
"wherever the proportion of strength is greater to the proportion of the
bulk, there the motion is swifter, and where less, there slower"."7 However,
this misconception does not vitiate Wallis's study of collision in inelastic
bodies, where he is chiefly concerned with a quantity he calls "impetus",
the product of "weight" and "celerity". Consider now the case (in
Wallis's manner) of two bodies moving in opposite directions which
collide directly: his procedure is to calculate the impetus for each body
on the assumption that the other was at rest, and then sum algebraically
the two impetus thus derived for each body. From these the velocities
and directions follow. Thus if the impetus of the first body be PIC, and
that of the second be -P2C2, the resultant impetus after collision will be
( I)
(P2C2
pP,
PICI)
P+
(2'1?x
x7
Birch,History,ii,
I26.
+
: (P2C2-PIC1)
30
A.
RUPERT
HALL
From this it is obvious that if the initial impetus (P1CE, P2C2) are equal,
there is no motion of either body after collision. This was the case considered by Newton to support his argument that "Motion is much more
apt to be lost than got, and is always upon the Decay." The point of
Newton's argument is, of course, that in so far as bodies are less than
perfectly elastic they will in collision lose motion. Since Newton is not
here considering the transformation of energy this motion is, in his view,
lost to the universe.'8 In terms of the seventeenth-century mechanical
philosophy it could very well have been argued that in the deformation
of matter by percussion macroscopic motion was translated into microscopic, manifested as heat; but even this would hardly have saved
Descartes's principle of the conservation of motion, without making it
much more sophisticated.
Wallis's paper was produced-not
apparently read-on 26 November. By this time, inspired by Hooke, the Society's interest seems to have
shifted to elasticity, Hooke seeking to prove by experiments that only
elastic bodies are capable of rebounding. Hence Wallis's treatment of
inelastic bodies might have lacked interest, though Wallis himself was
of the view that only springy bodies rebound.'9 Wren brought in his
own study of collision on I7 December, claiming that he had had this
"hypothesis" several years before when experiments illustrating it had
been made by himself and Rooke, in the presence of Lord Brouncker,
Sir Paul Neile, William Balle and others.20
Wren's paper on "The Natural Law concerning the Collision of
Bodies"-like
Wallis's, it is in Latin-was
printed immediately after
Wallis's in the Philosophical Transactions for January I668/9. As it is
brief I will give the whole of it in English:
"The proper and most truly natural velocities of bodies are reciprocally
proportional to the bodies.
Hence bodies (R, S) having their proper velocities retain
The
them even after collision; and bodies (R, S) having imJ proper velocities are returned to equilibrium by collision;
Law
of
that is to say, what in R exceeded its proper velocity and
Nature
was lacking from S before the collision, is by the collision
taken from R and added to S, and vice-versa.
"For this reason the collision of bodies having their proper velocities is
equivalent to a balance swinging about its centre of gravity.
"And the collision of bodies which have improper velocities is equivalent
to a balance on two centres equidistant from the centre of gravity; for the
i8 Newton, Opticks,Query 31 (5th edn., London, 1931, 398).
I9 Birch, History,ii, 328; Wallis to Oldenburg, 3 December I668. Wallis declared himself
at this stage undecided about the conservation of motion.
20 Ibid., ii, 335. As is well known, Wren's scientific work is shrouded
in mystery, and many
assertions about it unfortunately cannot now be verified. For example, even his plan for the
projected College of the Royal Society in the Strand is only conjecturally identifiable now.
Such associates of Wren as Sir Paul Neile (c. I613-86), his son William (I637-70) and Lawrence
Rooke (I622-62) are even less well known at present.
Mechanicsand the Royal Society,i668-70
3'
balance may be extended into a yoke when the need arises.
"Thus there are three ways in which equal bodies may move improperly,
and ten ways in which unequal bodies may move improperly (either in the
same direction or in opposite directions), five of which arise by conversion
from the other five."
Then Wren gives a rather awkward symbolic calculus representing
these eight cases.
EQUAL
UN EQUAL
R
R
+
a
aS
o a e
S
R
6
9
o
4
7_
e
R
a
......... R
..
a
e
R
o
5~~~~~~
a
Se
4
R
S
8
S
e
a
_
R
s
o a e
R
0
R
R
o;
2
aS
_
_
a
_
_
Se
9
the
oR, oS, eR, eS, etc.,represent
of thesymbolism
is omitted;themagnitudes
Fig. 2. Wren'sexplanation
variousvelocities
of thebodiesR andS. a is thecentreof gravity.
I hope it may not be superfluous to interpret this communication
a little farther. Wren is clearly concerned with perfectly elastic bodies,
so that no motion is lost and the sum of the two products of "body" and
velocity is constant. (It will be observed that Wren has no term for mass,
not defining what he means by "equal" and "unequal" bodies.) Consider
"equal" bodies (that is, bodies of equal mass), then if they move at equal
speeds in opposed directions they must rebound with the same equal
speeds; nothing else is logically possible. In the three non-symmetrical
cases (one body at rest, one moving; two bodies moving in the same
direction at different speeds; two moving in opposed directions at different
speeds) it is again logically essential that any gain in velocity by one
body must be made up by an equal loss in the other. Did Wren solve the
question of the distribution of this gain and loss by experiment alone,
or did he at a fairly early stage see into the theory? We do not know;
but it would appear natural for Wren to have recognized that the total
distributable motion must be shared equally between equal bodies; or
(between unequal bodies) in proportion to their magnitude. With these
3
A.
32
RUPERT
HALL
principles it is not very difficult to solve the various cases. However this
may be, we can now understand Wren's terminology somewhat better:
two bodies collide with "proper" velocities when their products of mass
and velocity are equal (this is the "balance"); but the correction of
imbalance by collision (as Wren calls it) is elliptically expressed in his
rule, since there is not an equalization of velocity as his words might
suggest, but a transfer of the imbalance. Thus in the three cases of the
improper motion of equal bodies, the numerical velocities are exchanged
by collision. This is what Wren means by the "yoke":
BEFORE
WI
t
V-v
F
~~~V
W2
V
V IV
I
V-vI
-
AFTER
WI
W2
FIG. 3.
Before collision the products WI (V-v) and -W2 (V+v) are out of
balance; after collision the products -WI (V+V) and W2 (V-v) are
symmetrically unbalanced. I feel sure that this symmetry appealed to
Wren, since it is so clearly evident from his rather odd formulation.
For what it is worth, it seems to me highly unlikely that this formulation could have been derived from experiment alone, though it may have
been facilitated by some experiments (e.g. the exchange of velocities
when one of the colliding balls is at rest). At least the title of the paper in
Phil. Trans. speaking of "Dr. Wren's theory ... verified by many Experiments . . ." is unambiguous. It is clear that Huygens, also, adopted a
highly theoretical approach to the problem of collision.
In a letter whose obscurity was, I suppose, unintentional Oldenburg
wrote to Huygens on i8 November I668 suggesting that he approach
the subject of motion in the most logical way, that is putting first things
first. He did not make it clear that the Society was at that very moment
intent on the subject of collision. Thus it was by sheer coincidence or
Cartesian precedent that Huygens decided to begin his communication
on motion to the Royal Society with collision, adding that
"the reason why I have chosen to begin with this topic in motion rather
than with another, is my eagerness to know the judgement of your distinguished
members of my way of demonstrating, for although this seems plain to myself
and some of us [in the Academie des Sciences] it has not satisfied others,
less experienced in such speculations, or prejudiced by other false principles".
And Huygens goes on to say that in the course of the discussions
in Paris his theorems were confirmed by repeated experiments.2" Un2I
Christiaan Huygens, OeuvresCompletes,vi, 295, 335.
Mechanics and the Royal Society, I668-70
33
fortunately the preparation of his paper on his Hypothesison the Motion of
Bodies arisingfrom Mutual Impact was delayed some weeks, and it reached
London only on 4 January i668/9.22 In summary form this paper will
doubtless be familiar to everyone: Huygens opens with a group of axioms
or assumptions (they are not titled) of which the first is a partial statement
of the law of inertia:
"Any body when once it is moved will continue to move, if nothing
hinders it, with the same velocity and following the same straight line."
The second defines direct collision, and states that two equal hard bodies,
colliding with equal velocities, rebound with the same velocities as before,
but "hard" and "equal" are not defined; the third axiom is Huygens's
relativity principle, which is, all events in a collision are the same with
respect to any given frame of reference whether that frame is itself
moving, or at rest; and the fourth and last is a further example of the
same. Then Propositions i and 2 deal with what Wren called the three
cases of improper motion in equal bodies, where collision occasions an
exchange of velocities between the two bodies. Now, before going on
to unequal bodies, Huygens adds the further "hypothesis": "If a greater
body strikes a less, it gives some motion to it, and hence loses some of its
own." Equivalence of gain and loss is not asserted, however. Then
there follow two more propositions: the first states that "Any body
however large is moved by any other body, however small, moving with
any velocity"; the second deals with the general case of impact between
unequal bodies; but this last was not completely proved, the whole
proof being presented later in the Treatise on Percussionwhich remained
unpublished at the time of Huygens's death.
Everyone agreed that Huygens's theorems and Wren's were identical,
and that both originated quite independently from a considerably
anterior epoch. No priority dispute sprung up. Huygens, to whom Oldenburg had posted a copy of Wren's paper as soon as he received Huygens's
own, and who had written to Sluse many years before in this connection:
"Do not believe that I follow experience, for I know how deceitful that
is,23 inquired whether Wren had found demonstrations "or whether he
had only based his proposed law of nature on experiments."24 So far as
I know this question was never answered.
Through an excess of scruple, and not through any ill-intent, Huygens's
paper was not published in the Philosophical Transactionsalong with those
of Wallis and Wren. Huygens accordingly, without saying anything,
produced his rules in a briefer and superior form in the Journal des Sfavans
on 8 March i668/9.25 Subsequently Oldenburg published in the Philo22
23
24
25
Ibid., vi, 336-343, 345.
Ibid., ii, II5, quoted by Dugas, 286.
OeuvresCompletes,vi, 354.
It is reprinted in ibid., vi, 383-385.
34
A. RUPERT HALL
sophical Transactions,no. 46 (I2 April I669), 925-928, a judicious account
of the whole business together with a Latin translation of the Journal
des Sfavans paper. This differs in some significant ways from the original
document; it omits the axioms or hypotheses, but adds four general
mechanical principles:
" (i) The quantity of motion which two hard bodies have may be increased
or diminished by their collision, but when the quantity of motion in the opposite
direction has been subtracted there remains always the same quantity in
the same direction.
" (2) The sum of the products made by multiplying the magnitude
(grandeur)of each hard body into the square of its velocity is always the same
before and after collision.
"(3) A hard body at rest will receive more motion from another larger
or smaller than itself if a third intermediately sized body is interposed, than
it would if struck directly, and most of all if this is a mean proportional [between
the two extremes]. In all this [adds Huygens] I am thinking of bodies of the
same material, or else I mean that their magnitude can be measured by their
weight.
"(4) A wonderful law of nature (which I can verify for spherical bodies,
and which seems to be general for all whether the collision be direct or oblique
and whether the bodies be hard or soft) is that the common centre of gravity
of two, three or more bodies always moves uniformly in the same direction
in the same straight line, before and after their collision."
Huygens does not explain how the apparent discrepancies between
the first of these principles and the second and fourth which both insist
upon the conservation of motion, are to be accounted for.
After this rather heavy concentration of interest on the theoretical
treatment of collision, the Royal Society's experimental tastes began to
revive and there was some effort to test the equivalent theorems of Wren
and Huygens. Hooke was instructed to do so, but apparently did not;
instead he talked of air-resistance, and made experiments to prove that
"the strength of a body moved is in a duplicate proportion to its velocity".
One of these experiments I do not understand; the other showed that
when the height of a reservoir of water was quadrupled, it ran out twice
as fast from a hole. This indeed confirms Voc Vs or V/h, but it does not
tell us explicitly about the relation between force and velocity.26 Not
surprisingly, attempts to verify the theorems for perfectly elastic bodies
did not succeed well in practice; after a time, on 8 April I669, the conduct
of these experiments was made the responsibility of William Croone,
who had long been associated with the question of collision, and had
brought in his own hypothesis of motion on 2 I January. He also produced
no conclusive experimental results. Croone of course was an anatomist
and physician; curiously enough it was a biologist, Francis Willughby,
26 Birch, History, ii, 335, 337, 338-339. It is well known that Newton had difficulties with
this question of the flow of water from a reservoir (cf. Prin4ipa, ist. eda. Book II, Prop. 37,
and 3rd edn. Book II, Prop. 36. See also A. Rupert Hall, "Correcting the Pr icipia", Osiris,
xiii (I958),
291-326).
Mechanics and the Royal Society, I668-70
35
who protested most forcefully against the acceptance of the Wren-Huygens
theorems on the ground that they violated commonsense. His Animadversionswere presented to the Royal Society early in June I 669:
"As it seemed to me absurd that motion should be destroyed or created
from nothing" (he began) "and more than that, incredible, I suspected that
there was some other sense concealed in Dr. Wren's words, which I long sought
to discover, in vain. At length Huygens by publishing the same hypothesis
as also discovered by himself quite freed me from that suspicion, for he expressly
allowed that the quantity of motion of two bodies might be increased or
diminished by their collision."
After (in effect) defining mv as the quantity of motion, Willughby
went on to examine six cases of collision in which, on Wren's principles,
the quantity of motion varied. He concluded that "The hypothesis from
which these paradoxes follow should by no means be admitted unless
it is confirmed by store of experiments."27 Or, as he put it in his letter
to Oldenburg: "no man ought to thinke his fame strong enough to
impose an improbable thing upon this inquisitive world nakedly without
either reasons or experiments".2" To this Wren answered "that what the
Author of this Animadversions esteemed for Paradox, he judged to be a
Truth, and had before this considered as a Corollary naturally following from his Rules"; and he pointed out that confirmatory experiments
had been made by himself and others. After a fresh protest from
Willughby, Oldenburg was ordered to communicate to him the experiments formerly made by Wren and Rooke.29
Croone, whom I have already mentioned, was another dissentient
from the Wren-Huygens theorems. The argument in his long paper is hard
to follow in detail; but Croone began with a number of essentially sound
first principles: he states that "all motion once produced always continues
with the same speed, unless impeded by something"; he defines motive
force or quantity of motion as the product of the mass ("moles") and the
degree of motion; and holds that motion is infinitely divisible. At the
same time he maintains some unusual ideas, such as that motion is
never transferredby impact (a rather metaphysical issue!) and that when
a body impedes another the motion of the second is destroyed. Thus,
he says, the first body can acquire motion from the second oiily to the
extent that it yields to it. I feel that although Croone limits his treatment
to hard bodies in a non-resisting medium, he is in fact confused by introducing the behaviour of non-elastic bodies ilnto his conception. However,
there is an interesting touch at the end of his paper. It is quite obvious
that within the terms of seventeenth-century mechanical philosophy
collision between particles was the basic phenomenon of physics-at least
Royal Society Classified Papers, vol. iii (I), no. 54.
Royal Society MS. W3, no. 30.
29 Oldenburg's annotation on the document noted in note 27; see also Birch, History, ii,
27
28
38I, 392.
A.
36
RUPERT
HALL
until Newton began to speak of qualities, virtues and forces acting on
particles. This is explicitly put by Thomas Sprat in I667: "Generation,
Corruption, Alteration, and all the Vicissitudes of Nature, are nothing
else but the effects arising from the meeting of little Bodies of differing
Figures, Magnitudes, and Velocities" (p. 3I2). Croone is one writer on
collision who makes the same point:
"Hence [he concludes his paper] the cause of fluidity, springyness, the
acceleration of falling bodies and projectiles, and of the resistance of the air
and of the cessation of motion in projectiles is to be sought. Which I think may
be done without difficulty."30
Another clinging firmly to aberrant ideas quite similar to Croone's,
and anticipating him in point of time, was William Neile, author of the
first rectification of the cycloid (I657). His "hypothesis in philosophy" is
first mentioned in March I666/7, although it is not heard of again until
December i 668 when discussion of the laws of motion was in full swing.3'
Neile's ideas on motion, like those of everyone else, are clearly greatly
influenced by Descartes; for example one document begins thus:
"We have no knowledge of anything but by our own conceptions. For
though a man may have a wrong conception of a thing, yet knowledge, if
it be never so right, is but a conception.
"The conception we have of Body, is, that it is extended through space...
"Suppose ye Body A to be in motion in a straight line; it will move in
yt streight line eternally with the same velocity, without an external cause
to hinder it. But it moves on not out of any repugnancy to being stopped,
but because there is nothing to give it a cause to stopp.
"In like manner a quiescent Body rests not out of any repugnancy to
motion, but because there is nothing to give it a cause of motion."32
Obviously Neile here asserts the indifference of matter to motion or rest;
but he seems to conclude from this indifference that there is no force
required to move a resting body or stop a moving one. Only a body in
contrary motion actually impedes a moving body; another at rest does
not do so. Yet at the same time Neile asserted (against Wren) that while
phenomena may be described as in accord with the laws of nature, the
laws of nature are not to be invoked as sufficient cause of their appearance.
Unlike Hooke and others he does not regard hardness as opposed to
elasticity; rather he thinks that the hardest bodies are most elastic.
He thinks that all secondary bodies are like fire only a mass of particles
variously moving and sometimes resting, making a distinction accordingly
between rest secundumtotum and rest secundumpartes. Neile admitted no
such entity as force in the modern sense; hence he also denied (against
Wallis) that there is any such thing as a compound or resultant motion
Royal Society Classified Papers, vol. iii (i), no. 44.
Wallis to Oldenburg, 2I March s666/7, Neile to Oldenburg, i8 December [I668];
see Correspondence
of Oldenburg,iii, 373, and v (in press). It is difficult to dispute the date of the
former letter.
32 Royal Society Classified Papers, vol. iii (i),
no. 48. This paper is in Oldenburg's hand,
and endorsed (without date) "Mr. Neile's Principles of Philosophy".
30
3I
Mechanics and the Royal Society, I668-70
37
such as may be represented vectorially in a parallelogram of forces;
a body at A may be struck by another moving in the line AB or by a
third moving in the line AC but it would be impossible for it to be struck
simultaneously by two such bodies.33
A
C
FIG.
4.
Neile's thoughts were communicated through Oldenburg to Wallis
and other Fellows in the autumn of I668 and winter of I668/9; a long
controversy between Wallis and Neile developed which I shall not pursue
now; the letters will be found in our Correspondence
of Oldenburgand are,
indeed, of considerable interest. The heart of the matter was the question
of the destruction of motion. At first Wallis was in doubt on the question:
"Whether any motion perish, I am not yet resolved what to say. I have
thought much of it; & see somewhat pro, & somewhat contra.But if wee say
none perisheth; I doubt wee must say yt none begins."
Only a few weeks later, however, he is prepared to state categorically
that there are cases in which "two bodies in motion do mutually stop each
other, so yt ye motion of both is thereby extinguished & both remain at
rest", in which case in the ordinary sense of words the motion is lost.34
And Wallis is at pains to show, later, that by no manner of collision
between particles can the sum total of motion be increased.
Although there is much else that could be discussed in detail, I
have shortened this last discussion in order to save space for a few conclusions. The first point one notices is that at this time the two major
traditions in mechanics and the metaphysics of science (if I may so term
them, and the two were closely related), stemming on the one hand from
Galileo and on the other from Descartes, were as yet imperfectly assimilated despite the work of Huygens, which would by the way have been
far more constructive if only he had made his reasoningplain, and not
merely stated some scattered results. As a result there were intellectual
confusions such as one does not find in Newton's Principia concerning
even definitions and terminology (force, mass, quantity of motion,
momentum), as well as the basic principles of mechanics. None of the
discussions of the laws of motion presented to the Royal Society is logically
adequate and complete.
There were three outstanding issues, each of them transcending the
33
34
Neile to Oldenburg, i8 December i668 and
Wallis to Oldenburg, 3 December I668 and
2 January i668/9.
2I December i668.
38
A.
RUPERT
HALL
particular problem of the laws of motion. The first was one of method;
are the foundations of mechanics to be laid down by induction from
experiments, or by applying mathematical reasoning to self-evident
principles? It is clear enough that marked empiricism, as in Hooke and
Willughby, yielded little in the way of constructive results, whereas
theoretical analysis produced, by different methods, a set of principles
and a method of predicting the behaviour of colliding bodies fulfilling
certain rathei narrow conditions. By I669 the various theoreticians
were all agreed. But they did not stand on theorems alone; both Huygens
and Wren asserted roundly that if the theorems were not the fruit of
induction, still they had been decisively confirmed by experiments,
while their critics had failed to produce counter-evidence.
Secondly, there was the question of the measure of the quantity of
motion. As everyone knows, the critical discussion of vis viva was inaugurated considerably later by Leibniz's criticisms of Descartes, but one can
see that the issue is latent here. And in particular the third question,
that of the conservation of motion, is meaningless unless there is a definition of the measure of what is to be conserved, or not conserved. Perhaps
this was the most interesting question of all, since (as Newton was to
argue later) it seemed that the universe could only be perfectly mechanical
and enduring if the quantity of motion were conserved; if Descartes's
conservation principle were rejected on grounds of reason, as it was
by the students of collision on the ground that bodies are less than perfectly
elastic, then either the universe must run down, or fresh motion must come
into it from some non-mechanical source. Accordingly the whole fate of the
mechanical philosophy-at least in its Cartesian expression-turned upon
this issue. It is easy to understand that those who felt deeply committed
to this modern scientific world-view should feel deeply disturbed at the
suggestion that the source of activity in nature is not conserved, but must
in time diminish. On the whole science has always been reluctant to
embrace the idea that the collapse or destruction of the universe is
relatively imminent. It would be interesting to make a study of the
successive conservation-principles and other proposals that have been
made, from time to time, in order to postpone the dissolution of the
status quo as long as possible; the constant tendency has been (of course)
to prolong the age of the universe backwards and extend its prospective
duration forwards. But it is not surprising (if I may hazard this final
remark) that Newton, for all his anxiety to render the universe isotropic
in space and time, should have found difficulty in rendering it so without
appeal to non-mechanical sources of energy and stability.*
* This paper was originally read to the seminar on the history and philosophy of
mathematics organized by Dr. J. G. Whitrow and Dr. C. Tanner at the Imperial College of Science
and Technology, London. In discussion, Dr. D. T. Whiteside called attention to Newton's
unpublished early work on percussion; however, I have not attempted to explore this as it
had no effect upon the public discussion described above.