Quinby on the maximum effect of Machines. 35% 
Where, then, would be the saving of —_ and where 
would be the maximum effect of such a machin 
I shall now consider the chapter given by Prof Farrar. 
In his-Mechanics, p. 278, we have the following, art. 396. 
In proceeding to investigate general expressions for the ratie 
of the Seticsties of the im pelled and working points of ma- 
chines, when their performance is a maximum, let 
=the radius of the wheel to which the power is applied ; 
or, which is the same thing, the velocity of the impelled point 
ef the machine ; 
d =the radius of the axle to which the resistance is applied, 
er the velocity of the working point of the machine ; 
p=the moving force applied at the impelled point ; 
7 =the resistance arising solely from the work to be per- 
formed ; 
m=the inertia of the moving power p, or the quantity of 
matter to which that power must communicate the velocity of — 
the impelled point ; 
n=the inertia of the resistance, or the quantity of matter 
to be moved with the velocity of the working point before 
any work can ormed ; 
=the quantity of matter, which, if placed at the working © 
point, would create the same resistance as friction ; 
t=the quantity of matter, which, if placed at the working 
point, would oppose the same resistance as the inertia of all 
the parts of the machinery. 
Since D and d are the radii of the wheel and axle, we 
shall have pa d: tir: bs a weight aes to that Ee of the 
. ~ Seer a We 
nave ‘ betaee p-oa as an eiotant tor ss ie ned ~ aii 
of the power; and as D is the distance at which this force is 
applied, we have — 
pD—rd 
to represent the force which is employed i in giving a a rotatory 
a to the machine he resistance which friction op- 
s to this force will be fd; the moment of the inertia of the 
ae p will be as mD” ; the moment of inertia of the resist- 
ance as nd? ; and the moment of inertia of the pect 
will be asid?. Since the moving foree is diminished by the 
Fesistance of friction, we shall have pD —rd—fd for the mov- 
