286 The Laws of Motion of Y Cylinder, &c. 
fore when c—v = nothing, the fyflem is reduced to 
2 
5 fx? 
b re 
a ftate of reff, &/- 
} 
which gives x — are: cso ea Q; 
ET. 
Cor. I. If x and g be determined by experi- 
ment, f may be found ; for by fubftituting, for 4 in the 
fx’ bc? 2a0° 
equation, P sehr aa a we get 
f= pooh ; and, by two expe- 
riments, g may be determined; for let A, P, 
X and F exprefs the fame quantities in the latter 
as a, p, xand f do in the former cafe: then F = 
2PAo*? 2bPgX +2b° PX 
is we) 3 but, by hypothefis, as 
a o- 2b ee 4 20°27 *"* 
prPropaF; therefores-——— 
b22 + 20 p x 
2AozobgX+ 2b X eh Ping X+2PxXx4 2p 
bXy2bPX © * 2xxt2p—X+P 
2 Aor 2b? X 2a04,2b« 
X GX, 2bPX  bxt2bpx 
Cor. II. Hence the truth of the hypothefis, af- 
fumed in this Problem, may be eftablifhed o1 re- 
futed : for, if three experiments be made, two values 
of g may be determined from them; and, as g is” 
fuppofed to be a conflant quantity, thefe values will 
be 
