Quinby on the maximum effect of Machines. 349 
in subsequent parts of - chapter, he has committed the error 
which I wish to point 
In cor. 4. he oi "The work done in the time ¢ is= 
RrP—r?W 
R?P+r2W ~ 
metitum of W. The expression for the work done is W- 
x by the space threngh which it has been moved=W x 
gtx W ; but this is the expression for the mo- 
But it is in his 5th cor. that he commits the error which I 
wish particularly to point out, He states that, When the 
work done is to a maximum, we wish to know the 
weight W when P is Suen, * must make the fluxion of the 
last expression=o, This he does, and obtains 
(+e) 
This ur is true for the case which Dr. Cees has 
been considering 5 but it is plainly = true for any case in 
practice ; for t expression from w it is deriv: not 
embrace the space through which P ree moved; but in all 
cases in practice, the space through which P has ‘moved must 
be embraced, or the formule derived will not be true. 
There appears to have been a strange misconception, or 
want of information, in the minds of those mathematicians who 
have written on this subject. They have all taken P for the 
measure of the power applied to a machine; but it is plain 
that the measure of abe: power Sous Bs to every machine in 
prockoer is Pxby th seein it ioe. ia 
ai 
qeecin in which the foree ag a 
ence, if we wish to obtain the iss of w (in selation si S 
hen the effect of the power applied to any machine 
P) o practice i is a maximum, we must make the product of the 
remade (W) and the space through w which it moved - 
* It is true that the expression ates sd 2xw is aa — ‘a 
; and in cousernt* ita maximum, the result is the same as if 
lg i fect ; for the 
i we is nec ie to make this definition per 
aia of sis power e) of water acting upon a wheel, is not P mult tiplied 
meron se of the circumference through w which it acts, - Pe Prof, Pasay by 
hi vertical height through which it a As so Spay shown that Prof. 
@id not consider this difference in one of fis pr 
