62 * M ECHi 
aftronomer, who difcovered the fiucceffive propagation of 
light. It is exprefsly Hated by Leibnitz, in his letters to 
John Bernoulli!, that Roemer communicated to him the 
difcovery twenty years before the publication of De la 
Hire’s work; bat ftill we have no ground for believing 
that De la Hire was guilty of plagiarifm. Roemer’s re- 
fearches were not publifhed ; and, from the complete d'if- 
cuflion which the fubjeft has received from the French 
philofopher, it is not unlikely that he had the merit of 
being the fecond inventor. Even Camus, who about forty 
years afterwards gave a complete and accurate theory of 
the teeth of wheels, was unacquainted with the preten- 
fions of Roemer, and afcribes the difcovery to De la Hire. 
Camus was not a very profound geometrician ; but he had 
an accurate judgment, and was well verfed in the fyn- 
thetic method of the ancients, which jutlly Hood very 
high in his eHimation. In this way he folved the problem 
of placing in equilibrio, between two inclined planes, a 
rod having a weight applied to any part of its length. It 
is true this problem is very eafy in the analytical method, 
but it leads to a calculation of fome length. The fyn- 
thetic folution of Camus merits attention tor its fimplicity 
and elegance, an advantage which fynthefxs fometimes 
enjoys over analyfis, and which fhould not be neglefted 
when opportunity offers. 
The publication of Newton’s Principia contributed great¬ 
ly to the progrefs of mechanics. His difcoveries concern¬ 
ing the curvilineal motion of bodies, combined with the 
theory of univerfal gravitation, enabled philofophers to 
apply the fcience of mechanics to the phenomena of the 
heavens, to afcertain the law of the force by which the 
planets are held in their orbits, and to compute the va¬ 
rious irregularities in the folar fyHem, which arife from 
the mutual aftion of the bodies which compofe it. The 
Mecanique Celejle of La Place will be a Handing monument 
of the extenfion which mechanics has received from the 
theory of gravity. The important mechanical principle 
of the coniervation of the motion of the centre of gravity 
is alfo due to Newton. 
We have already feen that the principle of the confer- 
vation of aftive forces was difcovered by Huygens when 
he folved the problem of the centre of ofcillation. The 
principle alluded to, confifls in this, that in all theaftions 
of bodies upon each other, whether that aftion confiHs in 
the percufiion of elaltic bodies, or is communicated from 
one body to another by threads or inflexible rods, the fums 
of the mafl'es multiplied by the fquares of the abfolute ve¬ 
locities remain always the fame. This important law is 
eafdy deducible from two Ampler laws admitted in me¬ 
chanics. i. That, in the collilion of elaltic bodies, their 
refpeftive velocities remain the fame after impact as they 
were before it; and i. That the quantity of aftion, or the 
produft: of the maffes of the impinging bodies, multiplied 
by the velocity of their centre of gravity, is the fame after 
as before impaft. The principle of the confervation of 
active forces, was regarded by its inventor only as a Am¬ 
ple mechanical theorem. John Bernouilli, however, con- 
lidered it as a general law of nature, and applied it to the 
folution of feveral problems which could not be refolved 
by direct methods; but his fon Daniel deduced from it 
the law's of the motion of fluids from veffels, a fubjeft: 
which had been formerly treated in a very vague manner. 
He afterwards rendered the principle more general, and 
fltowed how it could be applied to the motion of bodies 
influenced by their mutual attractions, or folicited towards 
Axed centres by forces proportional toany function of the 
diltance. Mem. de L’Acad. Berlin, 1748. 
After the parallelogram of forces had been introduced 
into liatics by Stevinus, it was generally admitted upon 
the fame demonltration w’hich was given for the compofi- 
tion of motion. The Arrt complete demonltration was 
given by Daniel Bernouilli in the Commentaries of Peterf- 
burgh tor 1726, independent of the conAderation of com¬ 
pound motion. This demonltration, which was both 
iNICS, 
long and abflrufe, was greatly Amplified by d’Alembert i« 
the Memoirs of the Academy for 1769. Fonfeneix and 
Riccati gave a very ingenious one in the Memoirs of the 
Academy of Turin for 1761. Tins was alfo improved by 
d’Alembert, who gave another in the fame Memoirs, and 
a third in his Traite de Dynamique,, publilhed in 1743. 
Dr. Robifon has combined the demonflrations of Bernouilli 
and d’Alembert with one by Frifi, and produced one that 
is more expeditious and Ample. La Place has likewife 
given a demonflration of the parallelogram of forces in 
his Mecanique Celelte. 
All tliefe acquifitions, at firfl feparate and.in fome mea- 
fure independent of each other, having been reduced to a 
fmall number of fimple, commodious, and general, for¬ 
mulae, by means of the analyfis of infinites, mechanic-s 
took a flight, which nothing but the difficulties Hill ariftng 
from the imperfection of its inflruments could check, and 
of which we (hall endeavour to impart fome idea. The 
problems relating to motion may all be reduced to two 
clafles. The firlt comprifts the general properties of the 
motion of a Angle body, afted upon by any given powers : 
the fecond the motions which refult from the aftion and 
re-aftion that feveral bodies exert on each other in any 
given manner. In the motion of a Angle body, we ob- 
ferve, that, matter being of itfelf indifferent to reft or mo¬ 
tion, a body fet in motion mult uniformly perfevere in it.; 
and that its velocity cannot increafe or diminilb, unlefs by 
the continual aftion of a conffant or variable power. 
Hence arife two principles; that of the vis inertia:, and 
that of xtmpound motion ; on which is founded the whole 
theory of motion, reftilinear or curvilinear, conffant or 
variable, according to a given law. By virtue of the vis 
inertia, motion at every inftant is effentially reftilinear and 
uniform, all refiftance, and every kind of obftacle, being 
put out of conAderation. By the nature of compound motion, 
a body expofed to the aftion of any given number of 
forces, all tending at the fame time to change the quan¬ 
tity and direftion of its motion, takes fuch a path through 
fpace, that in the laft inffant it reaches the lame point at 
whjch it would have arrived had it fuccelTively and freely 
obeyed each of the forces propofed. On applying the firlt 
of thefe principles to reftilinear motion uniformly accele¬ 
rated, we perceive, iff, that, in this motion, the velocity 
increafing by equal degrees, or proportionally to the time, 
the accelerating force muff be conffant, or inceflantly give 
equal impulfes to the moving body ; and that, confe- 
quently, the final velocity is as the produft: of the accele¬ 
rating force multiplied by the time : 2dly, each elemen¬ 
tary portion of fpace palled through, being as the product 
of the correfponding velocity multiplied by the element 
of the time, the whole of the fpace pafied through is as 
the produfl of the accelerating force multiplied by the 
fquare of the time. Now thefe two properties equally take 
place for each elementary portion of any variable motion 
whatever ; for there is no reafon why we fliould not gene¬ 
rally confiderthe accelerating force, though varying from 
one inftant to another, as conffant during each Angle in¬ 
ftant, or as undergoing its changes only at the commence¬ 
ment of each elementary portion of the time. Thus, in 
every reftilinear motion, variable according to any given 
law, the increment of the velocity is as the produft ot the 
accelerating force multiplied by the element ot the time ; 
and the differential fecond of the fpace pafied through is as 
the produft: of the accelerating force multiplied by the 
fquare of the element of the time. Now, if to this prin¬ 
ciple v.e add that of compound motion, we fhall arrive at 
the knowledge of all curvilinear motion. In faft, what¬ 
ever be the forces applied to a body deferibing any curve 
whatever, we can at each inftant reduce thele forces to two, 
the one the tangent to the element of the curve, the other 
the perpendicular to it. The firfl produces an inftanta- 
neous reftilinear motion, to which the principle of the vis 
inertias applies : the fecond is expreffed by the fquare of 
the aftual velocity of the body divided by the radius of 
curvature. 
