Quinby on the maximum effect af Machines: 85S 
This is a maxiinum when the eeeenaial d, being consid- 
ered as variable, is om to zero, which gives 
r+f)) (mD? +d"(n+i)) 
— 2d(n+7) a a(r+f)) =; 
or, by reducing 
mD* — pDd? (n+7)—2dmD? (r +f) =0 
“ee 
that is 
Fiera 2mD(r+f)d mv” ; 
~ p(n+i) n+ 
Resolving this nine the manner of an equation of the se- 
cond Gegrees we obta 
=D» VaCETP Tara. 
— p(r+i) 
When r=o, we have - 
d=Dx Vm fi +p" +p? n(n) — 1) —mf. 
p(n+i) 
This case takes place when the resistance to be overcome 
mill-stone, a fly, or in pushing a body along a horizonial 
plane. 
When I=s, 
d=D x Vm?r? +p? m(n +i) —mr 
pn+i) 
This case takes place when the friction i is so a —_= ee 
may be disregarded, w 
When r=o and f=o, we have 
d=Dx YPMM+9_p x. jes =: =D oe. 
pP(n+?) p (nti)? . m+ 
This case takes place when the circumstances 5 of thet two 
preceding cases are combined. 
When n=0, we have 
d=Dx dares) vim mmr). 
s — = inding of corn, the sawing 
of ea ae aE co wooden Srrie pitaders, &e. where the 
‘quantity of motion communicated to the flour, the saw dust, 
-or the iron > is too es to be taken into the account, 
VOL. XI1.—NO. 
