432 



ANIMAL MECHANICS. 



From these equations, it is easy to see, after a few reduc- 

 tions, that 



= Ji + ( IIO > 



4rrr 



This equation establishes a relation between n and r ; that 

 is, between the coefficient of muscular contraction and the 

 radius of the muscular sphere, and shows that if n be taken 

 for the fullest amount of contraction possible to the fibre, the 

 value of r becomes fixed, and there is only one sphere of 

 muscular fibres that does the whole of the work possible 

 for it. 



Solving equation (no) for r, we find 



(in) 



4 47r ( I - n z ) 



As an example of the foregoing we may take the human 

 heart, in which the united volumes of the two ventricles is 

 10 cubic inches; and assuming that each fibre contracts 

 through one-ninth of its length, we have 



r= io, 



8 



n = —. 

 9 



Introducing these values into (in), we find 

 r = 2.002 in. 



Hence, in the case supposed, the muscular sphere whose 

 radius is 2 inches, does its full work; the spheres of greater 

 radius do less than their full work, and the spheres of lesser 

 radius are called upon to do more than their full work. In 

 fact, in order to make a heart of the structure supposed a 

 perfect mechanism, it would be necessary to have a different 

 law of muscular contraction for each sphere of fibres; the 



