ne 
me NE, 
Quinby on the maximum effect of Machines. 357 
_ make this expression apply to any case in practice, we must 
write 
(Pa— qb) gb 
+ SRS C3 ae eee 2 
1X part gb? 
Ft ge. SEES 
Pa? + qb? + MK? 
pda ag 
Pa’ 
which, as before, isa limit. Hence we see that im these 
three cases, when the expression is reduced to a form that 
will render it applicable to any case in practice, the Prob. 
does not admit of a maximum. 
It may now be remarked that the expression for either case 
will solve the other two ; but I thought it best to exhibit the 
expression as it is derived by each author ; and, in doing this, 
I hope that the space I have occupied is not unnecessary. 
It remains only to remark that all the demonstrations and 
formulz given by these three authors, and contained in the 
chapters which have been referred to, are founded on the same 
false principle that has been pointed out ; and that not one 
_ of the demonstrations which these chapters contain, and not 
one of the formulz which the authors have derived from them, 
will apply to any case in practice, or that can be conceived 
and put into practice. 
Hating now concluded my examination, I shall offer a few 
remarks on the detriment and mischief which the doctrine of 
‘*‘ Maximum Effect of Machines” has produced. 
ill suppose that some individual has constructed a 
machine precisely similar to that described by Prof. Farrar, 
in his chapter, p, 263, His words are, “ Let us suppose that 
we wish to raise two cubic feet of water ina second, [ Query. 
How high does Prof. Farrar mean that these two cubic feet of 
water shall be raised in the given second?] by means of the 
wer of astream which a five cubic feet of water ina 
second, applied to a wheel and axle, the diameter of the 
wheel being seven feet. It is required, therefore, to find the 
diameter which we must give to the axle, in order to obtain 
a maximum effect. We have obviously p=5, and r=2, and 
since p 1 r225:2, we have p=3t ; but in the above table, 
r=10; hence p=$10=25. Now it appears from the table, 
that when p=25, the diameter of the axle, or d, is 0 .38708, 
