MECH 
to his beautiful theory of central forces in the circle. 
This theory may be applied to the motion of a body in 
any curve, by confidering all curves as compofed of an 
infinite number of frnall arcs of circles of different radii, 
which Huygens had already done in his theory of evolutes. 
The theorems of Huygens concerning the centrifugal 
force and circular motions, were publiffied without de- 
monftrations. They were firft demonffrated by Dr. Keill, 
at the end of his Introduction to Natural Philofophy, 1700. 
The demonftrations of Huygens, however, which were 
more prolix than thofe of the Englilh philofopher, were 
afterwards given in his pofthumous works. 
About this time the true laws of collifion or percuffion 
were feparately difcovered by Wallis, Huygens, and fir 
Chriftopher Wren, in 1661, without having the leatt com¬ 
munication with each other. They were tranfmitted to 
the Royal Society of London in 1668, and appeared in 
the 43d and 46th numbers of their Tranfaclions. The 
foundation of all their folutions is, that, in the mutual 
collifion of bodies, the abfolute quantity of motion of the 
centre of gravity is the fame after impact as before it; 
and that, when the bodies are elaftic, the refpeftive velo¬ 
city is the fame after as before the Ihock. We are in¬ 
debted like wife to fir Chriftopher Wren for an ingenious 
method of demonftrating the laws of impulfion by expe¬ 
riment. He fufpended the impinging bodies by threads 
of equal length, fo that they might touch each other 
when at reft. When the two bodies were feparated from 
one another, and then allowed to approach by their own 
gravity, they impinged againft each other when they ar¬ 
rived at the pofitions which they had when at reft, and 
their velocities were proportional to the chords of the 
arches through which they had fallen. Their velocities 
after impaft were alfo meafured by the chords of the 
arches through which the ftroke had forced them to afcend, 
and the refults of the experiments coincided exactly with 
the deduflions of theory. The laws of percuffion were 
afterwards more fully inveftigated by Huygens, in his 
pofthumous work De Motu Corporum ex Percnjfione, and by 
Wallis, in his Mechanica, publiffied in 1670. 
The attention of philofophers was at this time directed 
to the two mechanical problems propofed by Merfennus 
in 1635. The firft of thefe problems was to determine 
the centre of ofcillation in a compound pendulum, and 
the fecond to find the centre of percuffion of a fingle 
body, or a fyftem of bodies turning round a fixed axis. 
The centre of ofcillation is that point in a compound 
pendulum, or a fyftem of bodies moving round a centre, 
in which, if a final 1 body were placed and made to move 
round the fame centre, it would perform its ofcillations 
in the fame time as the fyftem of bodies. The centre of 
percuffion, which is fituated in the fame point of the fyf¬ 
tem as the centre of ofcillation, is that point of a body 
revolving or vibrating about an axis, which being (truck 
by an immoveable obftacle, the whole of its motion is 
deftroyed. Thefe two problems were at firft difcuffed by 
Defcartes and Roberval; but the methods which they 
employed were far from being correct. The firft folution 
of the problem on the centre of ofcillation was given by 
Huygens. He aflumed as a principle, that, if feveral 
weights attached to a pendulum defcended hy the force 
of gravity, and if at any inftant the bodies were detached 
from one another, and each afcended with the velocity it 
had acquired by its fall, they would rife to fuch a height, 
that the centre of gravity of the fyftem in that ftate would 
defcend to the fame height as that from which the centre 
of gravity of the pendulum had defcended. The folution 
founded on this principle, which was not derived from 
the fundamental laws of mechanics, did not at firft meet 
with the approbation of philofophers ; but it was after¬ 
wards demonftrated in the cleared manner, and now forms 
the principle of the confervation of aftive forces. The 
problem of the centre of percuflion was not attended with 
iuch difficulties. Several incomplete folutions of it were 
given by different geometers 5 but it was at la ft refolved 
Vol. XIV. No. 1000. 
A N I C S. 621 
in an accurate and general manner by James Bernoulli/ 
by the principle of the lever. 
In 1666, a treatife De Vi PercnJJIonis, was publiffied by 
J. Alphonfo Borelli; and, in 1686, another work, De Mo- 
tionibus Naturalibus a Gravitate Pendentibus; but he added 
nothing to the fcience.of mechanics. His ingenious work, 
De Motu Animalium, however, is entitled to great praife, for 
the beautiful application which it contains of the laws of 
ftatics to explain the various motions of living agents. 
The application of ftatics to the equilibrium of machines, 
was firft made by Varignon, in his Projeft of a new Syftetn 
of Mechanics, publiffied in 1687. The fubjeft was after¬ 
wards completely difcuffed in his Nouvelle Mecanique , a poft¬ 
humous work publiffied in 1725. In this work are given 
the firft notions of the celebrated principle of virtual ve¬ 
locities, from a letter of John Bernoulli's to Varignon, in 
1717. The virtual velocity of a body is the infinitely-fmall 
fpace, through which the body excited to move has a ten¬ 
dency to delcribe in one inftant of time. This principle 
has been fuccefsfully applied by Varignon to the equili¬ 
brium of all the fimple machines. The refinance of fo¬ 
lk! s, which was firft treated by Galileo, was difcuffed more 
correctly by Leibnitz, in the Afla Eruditorum for 1687. 
In the Memoirs of the Academy for 1702, Varignon has 
taken up the fubjeft, and rendered the theory much more 
univerfal. 
An important ftep in the confirmation of machinery was 
about this tiir.t made by Parent. He remarked in gene¬ 
ral, that if the parts of a machine are fo arranged, that the 
velocity of the impelling power becomes greater or lefs 
according as the weight put in motion becomes greater 
or lefs, there is a certain proportion between the velocity 
of the impelling power and that of the weight to be 
moved, which renders the effect of the machine a maximum 
or a minimum. (Mem. de l’Acad. 1704.) He then applies 
this principle to underffiot wheels, and (hows that a maxi¬ 
mum eft'eiSt will be produced when the velocity of the 
ft ream is equal to thrice the velocity of the wheel. In 
obtaining this conclufion, Parent fuppofed that the force 
of the current upon the wheel is in the duplicate ratio of 
the relative velocity, which is true only when a fingle 
floatboard is impelled by the water; but, when more 
floatboards than one are a fled upon at the fame time, it 
is obvious that the momentum of the water is directly as 
the relative velocity; and, by making this fubltitution in 
Parent’s demonftration, it will be found that a maximum 
eft’eft is produced when the velocity of the current is 
double that of the wheel. This refult was firft obtained 
by the chevalier Borda, and has been amply confirmed by 
the experiments of Smeaton. 
The Trait* de Mecanique of De la Hire, publiffied fepa- 
parately in 1695, and in the 9th volume of the Memoirs 
of the French Academy from 1666 to 1699, contains the 
general properties of the mechanical powers, and the de- . 
feription of feveral ingenious and ufeful machines. But 
it is chiefly remarkable for the Trade des Epicycloides, which 
is added to the edition publiffied in the Memoirs of the 
Academy. In his interefting treatife, De la Hire confiders 
the genefis and properties of exterior and interior epicy¬ 
cloids, and demonltrates, that, when one wheel is employed 
to drive another, the one will move fometimes with greater 
and fometimes with lefs force, and the other will move 
fometimes with greater and fometimes with lefs velocity, 
unlefs the teeth of one or both of the wheels be parts of a 
curve generated like an epicycloid. The fame truth is 
applicable to the formation of the teeth of rackwork, the 
arms of levers, the wipers of Hampers, and the lifting- 
cogs of forge-hammers ; and, as the epicycloidal teeth 
when properly formed roll upon one another without much 
friflion, the motion of the machine will be uniform and 
pleafant, its communicating parts will be prevented from 
wearing, and there will be no unneceflary wade of the 
impelling power. Although De la Hire was the firft who 
publiffied this important dilcovery, yet the honour of it 
is certainly due to Olaus Roemer, the celebrated Daniffi 
7 T i altrcnomu'j 
