FORCE. 
part of the © equation, and if 4 exprefs the height due to the 
velocity y ; 
N = v ea 2 gh» 
N ‘then becomes what is called the aay iehy ae $ it is 
that part of eo Rae which arifes from the velocity 
alone: in ge this force varies at every rine » but 
becomes co Len wher the body defcribes ie circumference 
of .a circ cle, ‘fince v and R are in 1 that cafe conftant 
On _ oe of @ point reftrained to on a curve fur- 
jae t the — ecailion to die: file be 
=pdx+qdy, 
pand g being the ee of ce partial differences of z 
men “refpedtively relative to x and y, (fee Analytic 
Ne) 
(Let ves ae + P+ g’)» Now the — which the 
yiormal to a curve furtace ee with the axes of x 
oy Ww (fee Analytic Grometry.) Conceive a 
force N to be added in the dire&tion of the normal, equal 
.and contrary to the preffure, its producing forces in the 
q 
—_—— 
direction of the axes will be — M 
By pe ae 
and MS the 
peat 
may now be confidered as free, and folicited se i three 
N g 
accelerating forces X — Wr? Y— WT’ and Z ae 
Inftead of ‘the former equations (A‘) (B’) of curvi- 
M’ 
Jinear motion, we have (fuppofing d¢# conitant, ) 
dx _ Np 
dt M 
ay - Ng 
ge ae 
ae . N 
rr mae mM 
wow, the sar fa of. Force.— 
overly w 
ith the ca 
of true piloieuy. w that al] difference of opinion has 
nearly or entirely ceafed, we are Saale i take an impar- 
tial review of the fubje&, and it appears that the queftion 
turn 
the; ame me nd obtaining the fame refult. Newton 
had .detined the _ sme of force to be the mafs bod 
multiplied into i city, and for the ie an of ae 
philofophical i flea bearers in which New engaged 
this definition was both convenient, and at the ame time aa 
mentioned ju the preceding pages. Bernouilli and Leibnitz 
confidered the vis: shee as the true and aia meafure of 
force, in oppofitio the Newtonian definitio - t is now 
enerally. aaciitted: re thefe great mathematicians were led 
into.a miftake, by not fufficiently camer into confideration 
call the circumftances .of the .queftion of d fj But it 
auf be admitted that the meafure adopted — ok and 
ul 5 and does not raphy the leaft contradiétion to 
the New tonian definition, only the force 
fhould be siting by fom 
ual in every refpet, be infer 
oppofite fides; let there be allo two ot 
of oa 
ct 
= 
3 
oO 
itantFagainft the pegs oppofite to them, the ball a clay 
would not be moved from its place to either fide ; neverthe- 
lefs the peg impelled by the {maller body B, which oe the 
aieee aerate aE be found to have pénetrated twice as 
far as the peg in 
i is ae ee make the experiment precifely as 
here ftated, fince the refults are admitted as fa&s by both 
n 
of a body in mo ia n is juftly efti- 
mated by its seer and the {quare of its a res 
The ae ee of a quantity dependent on ps 
ee vis motrix for a certain time, may 
have its ufe, ee corr ety applied, in certain philofophical 
ee esas but the latter idea of a quantity refulting 
m ad fame force, exerted through a ee minate /pace, 
eater practical utility, as it occurs daily in the 
ufual occupations 0 men; fince any soul of ere per- 
formed is alw se appreciated, by the extent of effet refult- 
ing from their ex well oven that the raif- 
e four times as 
continuing the motion of any kind of machine. Moreover, 
if the weights fo raifed were fuffered fal Feely through 
the heights that have been afcended, by m and 
of one minutes’ labour, the ade pre would be j in 
the ratio of two to one; _an e {quares . the oe 
in proportion to the quantities ‘of labour ey 
originated, as four to one; and if the eee cand by 
their defcent were employed in driving piles, t their more fad. 
den effects produced would be found to be in that fame ratio, 
This 
