150 On the maximum of mechanic powers, and 

 Hence P + ^^r^ — : — ■ —• will be the motive 



2n %n,n — I n — I 



force or moving power. Then again, when the bo- 

 dies are in motion, g^ is the/ of the Avhole beam 

 acting at B: and ^^3^, the value of x when reduced 



to B, it follows that V-\-g'w-\ — ^is the whole mass 

 compared at B with respect to angular velocity. 



n — I. w ■^^^ X 



Hence -—^ "•:!LJ: — l_l jg the accelerative force 



X 



pxifw+7z:7 

 at B ; — or the accelerative force of P; — or of 00 re- 



n — I. w 

 P + 



duced to B. Then 2.^n^\ :\ : : _ ^ 



p+<?^^ + ;i-i 



X n — I. w ^^ X 



Hl'lZ^lZ^^ELIiEI the accelerative force of 



n — 1.P+/1 — i.^w + x 



X suspended at A : which, by putting q for 



n — I. w 



a« Itt.n — I 



, and t for n-\, P + ?^- 1. ^ W, will 

 be expressed by -"~ ^"^"~^ =z:r : and therefore the mo- 



n — \.t ■\-n — I. X 



tive force, or momentum of x will be '^'^■'J''^ , ^ 



whose fluxion being equal to nothing, we have 



n- 1. qx-Q, XX X Ji-l. t -\-n- 1. x-n- 1. xXn - 1. 



qx — x^ =: 0, and x =: v//''+ 7t — I. q - t, a general 

 expression, when the shorter end is unity, and the 

 Avhole length of the beam, any whole number. 

 When n is 2, so that the arms are equal, then cr~ 



Prob. 14. If the two arms be of any given length 

 Avhatever, the shorter being expounded by a, and 

 the longer by /5»; aiid their weights by c and d re- 

 spectively : then if P as in the former case be ap- 

 plied to act as a power at B ; it is required to deter- 

 mine the value ot\r in terms oi' a and b, in case of 

 a maximum. 



Now 



