352 Quinby on the maximum effect of Machines. _ ¥- 
ing force ; and since the resistance arises from the moment of 
inertia of ‘the resistance, the moment of inertia of the power, 
and that of the machinery, it will be as mD?+nd’ +id?. 
But the velocity is proportional to the moving force directly, 
and to the resistance inversely ; therefore, the rotatory velo- 
eity will be 
_ pD—rd—fa 
mb? +nd? +id? 
Now, since the velocities of the impelled and working 
points are as their distances from the center of motion, or as 
D and d, we shall obtain these velocities respectively, by 
multiplying the rotatory velocity by D and d; and as the 
work performed is equal to the Lee multiplied by the 
velocity of the working point, we shall have for the velocity 
ef the working point 
pD? —rDd—fDd 
mD)? +nd? +id* 
for the velocity of the working point 
pDd—rd* —fa* | 
mD? +nd? Pid?’ 
and for the work performed 
- rpDd—r?d? —rfd* 
mD)? +nd? +1d* 
In order to obtain absolute measures. of the velocities and 
the work we must consider, that q being the ac- 
celerating force, and gz the velocity acquired in a second, 
we shall have 1: ¢:: @g: v=qgt; and as the pepe 
forces are Soooreual to the velocity generated by them in 
equal times, the preceding sachets for the ve se ca of 
the impelled and working points, may be substitu 
accelerating force g in the equation v=qgt, and we 2 shall a 
tain, for the absolute velocities of the Sire point 
pD? —rDd—fDd 
mD? +nd?-4 id? 83 
for the absolute velocity of ite hee: point 
SD ae 
