288 Theorems and Problems 
Cor. 2. If C=c, in the prob. or C=c in 
cor. l, weshall have, as A F:a f:: BD* :bd’. 
Cor. 3. Hence if A F=a f, then BD*= 
b d*; that is, the vires vive of Band b are 
equal, and B:b::d*: D*::v* su’. 
Cor. 4. Consequently when A F=a/fy if 
Band b be so placed, as to receive equal 
angular velocities from the forces F and /; 
they also acquire equal quantities of vis viva 
at the same time. ! 
Pros. IY. Let it be required to find the 
centre of gyration of a system of material 
particles b, 1, k, (plate 4, fig. 5,) revolving 
about a given point 0, in consequence of a 
force f, acting at a, perpendicular to the arm 
ao, of the compound lever ob kia? 
SoxuTion. Assume O as a centre of 
rotation ; and let OB represent the radius of 
wyration to the system bh1; make AO=a 0; 
and let the force F=f, act at A, perpendicu- 
lar to AO; then F.AO is in constant pro- 
portion to O Br. (6+4+/), by cor. 1, prob. 3, 
and the definition of the centre of gyration. 
Now f, acting at a is, divided into as many 
parts as there are particles 6, k and J; let p, 
gandr, be these parts; p.a0o, g.a0 and 
r.ao, are as bXbo', kXko* and bx/o*, by 
cor. 2, prob. 3; therefore asp.a0:b.bo0*:: 
f.ao:b.botk.k ot]. 10°; but p.ao: 
