280 Dynamics. 



j?pd rd 2 /d 2 

 m D 2 -f n d 2 -I- i d 2 ' 



and for the work performed 



r p D tf r z 32 r/d 2 

 mo 2 -J- nd 2 -f id 2 



In order to obtain absolute measures of the velocities and the 

 work performed, we must consider that, q being the accelerating 

 force, and q g the velocity acquired in a second, we shall have 

 1 : t :: qg : v = qgt; and as the accelerating forces are pro- 

 portional to the velocities generated by them in equal times, the 

 preceding expressions for the velocities of the impelled and 

 working points may be substituted for the accelerating force q 

 in the equation v = qg t, and we shall obtain, for the absolute ve- 

 locity of the impelled point 



D 2 rod /*P d 



X et: 



+ nd 2 -f i 

 for the absolute velocity of the working point, 





ID + nd 2 -fid 2 

 and for the work performed 



r p D d r 2 d 2 rfd 2 



m D 2 -f n d 2 + i d 2 "' ^ ** 



This is a maximum when the differential, d being considered 

 variable, is equal to zero, which gives 



0>D 2d(r+/)) (mo 2 4- <? 2 (n -f )) 



2* (w -f t) (^D* d (r -f /) ) 5= 0, 



or, by reducing, 



^mD 3 pv# 2 (n + i) 2^mD 2 (r -f /) =0; 



that is, 



2 ^ m D ( 



