On the Vis viva. 287 
and a, so as to disturb the:angular velocities of 
B and 6, denoted by C and c; it is required to 
find, by the doctrine of the vis viva, what ratio 
the fluxion of C has to the fluxion of ¢? 
Sorution. Let Band 6 move through the 
arcs B E and be, with the absolute velocities 
uand v, while the forces F and f are acting 
at the points A:anda; let P and p be two 
forces which would produce the same changes 
of motion in the material points B and b, by 
ing at the distances OB and ob, which are 
produced by F and f at the distances O A and 
a; put d4=OA; D=OB; a=oa; d=ob. 
By the laws of circular motion, we have as 
D*. C* :.d*. c* >: u*:v?; and by fluxions, 
as D*.Co:d?.ce::ua: vy; but by theor. 3. 
as PiBE :.p.be:: B.D*C Cb. d* ec ; 
now as BE:be::D.C:d.c;._ hence 
as P.D:p.d::B.D’*c:6.d*c; but as 
ere d::A.F:a.f; therefore as 
a 
CVesee tr. VET. 
Cor. 1. If Fand/ be constant forces acting 
at A and aon B and 8, it will be as C:c: 
AI od ' 
Cs. go} : pe +} : also, if and f be va- 
riable, but have the constant ratio of om to 2, 
it will be as @: @:' 744, &. 
, a Bip ora 
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