346 «=Quinby on the maximum effect of Machines. 
ree that there is a loss of “‘ more than one third of the 
wer.” Let us examine how he derives this result. In the 
cei @R=Pr, he has two variable quantities ; and he 
a one of them to be equal to a constant quantity ; 
and then finds the value of the other by the rule for a simple 
eins This method of solving an apes: requires ne 
comment. The equation, however, which he has given, will 
solve the problem ; and gives the same result as that which I 
gave im my demonstration ;—for since @R=Pr, and this 
for any position whatever of the crank, it is plain that there 
can be no loss of power ; for if there be a loss of power, there 
must be a loss at some point; but there = not a less at any 
point, and therefore there is no loss of pow 
t now only remains to be pest oa thet in the three 
things which the writer of this ‘‘ Examination’’ has attempted 
to demonstrate, he has failed in all. 
A. B. Quinsy. 
March 28, 1827. 
Arr. XXIV.—Examination of the doctrine of Mare 
Effect of Machines. By Mr. A. B. QUIN 
Most of the works on- Mechanics, contain a chapter o# 
the “ Maximum effect of Machin The doctrine contain- 
ed in this chapter has been long recive by mathematicians ; 
and now forms a part of the course in every mathematica 
school. I propose. im the paper I am about to offer, to ex- 
amine this doctrine 
Asi it would be impracticable to refer to all the works which 
¢ the doctrine in question, [ shall confine my examina- 
per the chapters given by three authors, viz. Dr. Grego- 
ry, Mr. Whewell, and Prof. Farrar. 
In Dr. Gregory’ s Mechanics, vol. i. p. 320, we have. the 
following proposition 
If Rand r be thedistances of hb pomee Ps and the weight OB 
resistance W from the fulerum F of a straight lever, (fig. 1. pl. 
3) then will the velocity of the power and of the weight at 
end of any ‘ala ae Beet ag BrP oe - St 
— ReP+rW cee ” R?-P+rew 
