Quimby on the macimum effect of Machines. 358 
The expression which Prof. Farrar has given solves this - 
problem ; but it will not apply to any case in practice ; for, 
as has alread ady been shown, iu order that it may apply to any 
case in practice, it must embrace the space through which 
* has moved. ‘To make it do this we must write 
(pD—rd) D eer 
m1)? +nd?+id2 “ 
rd 
pd’ 
which, as in the prece eceding case, isa limit.. Hence we per- 
ceive by this ease, as well as by the one which was before 
considered, that there is no such thing as a maximum effect 
of machines. 
[ shall now consider one or two of the demonstrations in 
the chapter given by Mr. Whewell. 
His first problem is 
A weight P, acting at a wheel, produces rotation ina 
mass which moves about an axis passing through the center 
of gravity; it is required to determine the distance at which 
P must act, that the angular velocity, generated in a given 
time, may be the greatest possible. 
Here the accelerating force on P is 
Pa’g 
f= pa MK?’ 
P acting at a radius a. And the soe Hagen in time 
n the cireumference at which Pj is ft. And henc 
angular veloc. _ a fe max. 
a 
tg E2 Pac MK = min. 
Pa? + MK? | 
Pots = min, whieyse <p ME = ee 
a =KJ5 at: 
blem which is here 
This demonstration is true < the pro 
considered ; but there is mo such case in practice ; and it is 
