358  Quinby on the maximum effect of Machines: 
D being 1 ; but as D=7, the diameter of the axle must. be 
7x 0.8708 —6.0956.* 
Now let us obtain the rativ of the effect of this ma- 
chine to the power expended. e measure of the powe 
expended is 25x 7=175; and the measure of the effect is 
6.0956 x -—— a wo" x 2=19.1539. Hence the ratio of the 
effect to the power is 19.1539+175=.115. Consequently 
100 cubic feet of water applied to such a machine, would 
raise 114 cubic feet covotigh the same vertical height—and 
this is a maximum ! 
Thus it appears that if a machine were constructed for 
raising water according to the best principles given by Prof. 
rrar ; i.e. according to the doctrine of maximum effect of 
machines, the greatest eflect of 100 cubic feet of water ap- 
plied to such a machine would be=114 cubic feet raised 
through the same vertical height ! But there are many ma- 
chines in practice in which the effect of 100 cubic feet of wa- 
ter is equa! to 85 cubic feet raised through the same vertic 
height. The loss therefore in applying such a machine in 
practice, wenkd be about i of the whole power ! 
I shall now only add that for the reputation of the gentle- 
men whose works I have criticised, I have the Biebeth res- 
pect. For Prof. Farrar I have a personal estee 
A. 
7 B. Quinn 
April 2, 1827. 
* To this Prob. Prof. Farrar has committed an _——— for the formula 
d=Dx,/P+ [rab 
he not apply to the case here taken ; fo in the case of water acting upe 
wheel, the distance from the center, at which the force (P) acts, (estimat- 
ol for the direction in which it acts,) is not constant ; but in the case from 
which the formula is ‘aiived the distance from the center, at which the 
force y 
and to make this formula apply to the case of water acting upon a wheel, 
oo the error it coutains,) we must write 
a=(Dx J241-p) x 6365; 
the quantity 6365 being the distance of the ce mney < = eer ity of a semi-cit- 
¥, $s een: Oe radius being 1; and like Fe ratio of the di- 
; its sem’ mi-cireumte erence. From ‘this will be perceived 
result w ‘of. Farrar given in t estereel ree 286 af : 
e that al mbers in the tables at age 289 and pa are no 
ewe Cat Se need bes” “ils 
