ANIMAL MECHANICS. 



431 



If, from any cause, the fibre be prevented from contract- 

 ing to its full extent represented by (109), there is a loss of 

 work which might otherwise be done, and the principle of 

 least action is violated. We may, therefore, state the prin- 

 ciple of " least action," as applied to the heart, in the follow- 

 ing manner : — 



The arrangement of the fibres of the heart must be such as to 

 allow each fibre to contract to the fullest extent required by the 

 law of muscular contraction. 



Before proceeding to prove that the actual arrangement 

 of the fibres of the heart is such as will satisfy the foregoing 

 Law, it will be worth while to show by an illustration how 

 easy it would be to devise a heart that would not satisfy the 

 Law, and would, therefore, be an imperfect contrivance. 



The special work done by the heart is to contract itself 

 upon an internal cavity containing fluid at a given pressure, 

 and so to expel that fluid from the cavity. Let us imagine 

 that it is proposed to do this work by a number of concentric 

 spheres of muscular fibres placed over each other, the fibres 

 of each sphere being quite independent of those of the other 

 spheres. Let V denote the volume of the ventricles of the 

 heart distended with blood at the commencement of the 

 systole, which volume is reduced to zero at the close of the 

 contraction ; let r denote the radius of any sphere of muscular 

 fibres at the commencement, and r' the radius of the same 

 sphere at the end of the systole. It is obvious that r } r' are 

 proportional to /, l\ the lengths of the fibres of the sphere in 

 question before and after the systole. Now, as V denotes 

 the difference in volume of the sphere before and after its 

 contraction, we have 



