ANIMAL MECHANICS. 



469 



the work of holding out the loaded arms horizontally. In 

 other words, the arm and weight must be not only lifted but 

 sustained during the time t. 



Using the same notation as before, we have 



Dynamical work = (w -f a) sen; (135) 



n y\ ■ ^ 1 {w +a)x 

 Kate of Dynamical work j-?—. 



If the arm were held in the horizontal position during the 

 time t, the statical work would be represented by 



10 (iv -f a) xt, 



and the total statical work would be 



h) (w + a) xnt. 



But the arm is not held horizontally, but sustained for equal 

 times in every position of the quadrant from vertical to hori- 

 zontal, while the arm and weight are passing from the vertical 

 to the horizontal position. 



Hence, the statical work done bears a certain fixed pro- 

 portion to the statical work of holding the arm and weight 

 horizontally, and 



Statical work = w (to + a) xnt x K • 



Kate of statical work = w (w -t a) x x R. ^ * ' 



The coefficient K is thus found : let 0 denote the angle 

 between the vertical and the axis of the arm in any position ; 

 and let the whole time t be divided into m parts ; and let the 

 loaded arm rest at the angle 9 during the rath part of the 

 time t. The work done in the position 0 is (resolving the 

 weight along the tangent to the circle), 



to (w + a) xn x sin 0 * — . 



ra 



Let us now divide the quadrant into ra equal parts, and 



