ANIMAL MECHANICS. 



481 



three points on the curve to be known. Expanding (143), 

 we find 



xy + ya - xfi - k' 1 + a/3. 



If we substitute in this equation the corresponding co- 

 ordinates 



x = 5 x = 30- x = 55 



y = 25 \y = 16 y = 14 



we obtain three linear equations to determine a, j3, and k? t 

 The values of these constants are 



(5 - 10.85; 

 a ~ 9.29 

 = 202.67* 



We have now to determine the work done, when the 

 condition of dynamical equilibrium is attained, and the re- 

 freshment restores the work during each cycle. By the equa- 

 tions which lead to (127), the work done is 



whe 



Work. = u) {w fa) xt 

 0/ — I . 



id m weight held in hand. 

 a ~ weight of arm, 



sn =s distance of centre of gravity of loaded arm from 

 centre of glenoid cavity. 



In addition to the work done during the time t, which 

 denotes the time of holding the arm horizontally , we must 

 take account of the work done in lifting the loaded arms from 

 the vertical into the horizontal position, which is evidently 



(tv + a) x. 



Hence 



Total work = (w + a)x (t + 1) (144) 

 2i 



