33 ANIMAL MECHANICS. 



and as w and 0 vanish together, we have 



= v (00. 



or 



f=*9 s > (12) 



where t> denotes the velocity acquired by the centre of oscil- 

 lation in traversing a small arc, such as would be described 

 in ^nd part of a second, and s denotes the space passed 

 through by the same point. 



The equation (12) is the same as that of falling bodies, 

 and therefore for small arcs and times, the centre of oscilla- 

 tion of the arm falls through the same space as it would if 

 the arm were released from its socket, and fell freely through 

 space. 



Let us now use the following notation : — 

 I = radius of oscillation ; 



x = distance of centre of gravity from centre of glenoid 

 cavity ; 



8s = small space through which the centre of oscillation 



falls in ^nd part of one second ; 

 n = number of such falls during 

 t = whole time required to fatigue the muscles ;* 

 a = weight of arm. 



The total work done by the muscles, on the foregoing 

 supposition, in the time t, is evidently 



