154- On the maximum of mechanic powers, axd 



Prob. 18. Let ABD be a solid wheel, whose 

 weight is W, and CC be an axle, but whose weight 

 is so small, compared with that of the wheel, as not 

 to be regarded. Then if P, as a power, be suspended 

 to a line passing round the circumference of the 

 wheel, whose radius call b ; and .v a weight to be 

 raised suspended to a line passing round the axle, 

 whose radius let be a: it is required to determine a\ 

 so that its eifect may be a maximum. 



Since W is the weight of the wheel, f \Y is the 

 p' of thfe whole, acting at B, 

 when in motion by Problem 8 ; 



and ~ is the value of .v re- 

 duced to B. Therefore P+ i W 

 + ^ is the mass to be moved, A 

 after a- is overcome by P : and 

 P— ^- vv'ill be the moving pcw- 



P ^ 



cr. Hence 



isthcac- 



celerative force of P= 

 Then as Z> ; a : 



vh — t 



ib-\-ax 



n: the accelerative 



force of a\ and therefore 



tb'^-\-bax 

 ah?x — (7^x 



its motive force 



when suspended at C, which by making its fluxio n 

 equal to nothing, we shall obtain <v—~ v ^* + ^P~" 



a and b become equal the same as in Problem 15. 



Prob. I9. Let the wheel and axle be as in the 



last, with \\\\s difference, that the weight (zv) of 

 the axle projecting on each side the wheel, be con- 

 sidered. 



Then 



