44 



ANIMAL MECHANICS. 



This equation shows that the tangent to the curve does 

 not become horizontal for any value of w, except infinity. 



An interesting consequence may be drawn from equation 

 (12c) by seeking the relation between the useful work done 

 and the weight w. The useful work may be represented by the 

 product of w and t ; hence if u denote the useful work, we find 

 u = wt, 



but 



Hence u - ^ w (120) 



From this equation, which denotes a cuspidal cubic, 1 shall 

 hereafter show that the useful work is a maximum when the 

 weight held in the hand is half the weight of the arm. 



4. On the Dynamical Work done by Muscles alternately 

 contracted and relaxed. — In the preceding section, I have dis- 

 cussed the work done by muscles kept in a state of continued 

 contraction until tired out; and I have called this work 

 "Statical," because the muscles appear to be at rest, and 

 really do undergo no movement of translation in space, al- 

 though a very rapid and active molecular movement takes 

 place within their substance, to which the work done is al- 

 together due. 



In the present section, I shall consider the more usual 

 kind of work done by muscles, to which the name "Dyna- 

 mical" is given, the amount of which is measured by external 

 movements of various parts of the body, and by the removal of 

 external resistances through spaces easily measured. 



In most kinds of labour which are recognised as effective, 

 and which are usually employed, almost all the muscles of the 

 upper and lower extremity are employed, together with the 



