350 Quinby on the maximum effect of Machines. 
by the product of the power (P) and the space through which 
it has moved, a maximum.* 
And to do this, if we take the case of the wheel and axle, 
we shall have 
— = 
REPT? et 
7 x. 
— — . 
? 
which is obviously a /imit, and not a maximum.? 
And this result is true for all possible cases in practice, or 
that can be conceived and put into practice. We therefore 
have the conclusion that there is no such thing as a maximum 
effect of machines ; and all the doctrine which has been giv- 
en and pene on this subject, is inapplicable to every ma- 
chine in 
will now recur to the problem which Dr. Gregory has 
demonstrated. It is this: 
wheel and axle being given, and a power P suspended 
by a cord over the circumference of a wheel being given, it 
is required to find the weight W suspended by a cord over 
the axle, so that the power P, in descending by its own grav- 
ity, shall generate in the weight W the greatest momentum in 
a given time. 
~ Lhave already a ~ Dr. fare ory’s demonstra- 
tion of this problem is true; but = will ask, could 
such a case ever be put 28g practice i iy And if such a case 
could be put into practice, where, I would ask, would be the 
saving of power? To put such a case into practice, it would 
be required to have an indefinite space for the machine to work 
in; for both P and W would have to move on continuously ; ; 
and neither ever be detached. And, again, in the ex- 
treme case of the wheel and axle, in which r=R, the maxi- 
mum effect of such a machine would be Px. 4142 3 but in 
all well tag Se machines in practice the effect of P is 
Px 1, very near 
an Tent 4 ratio of = effect to the power that must be a maximum. 
to P equals pe of rto 
he ratio of r to R, then will the 
ion must be considered as representing the product 
through which it I 
