ANIMAL MECHANICS 



439 



respective lengths of the two groups of fibres. This relation 

 may be investigated as follows: — 



Let L denote the length of the common fibres passing 

 round both ventricles, and let the volumes of the left and 

 right ventricle be denoted by A and p. 



Let / denote the length of the proper fibres that pass round 

 the left ventricle only. 



Let the fibres L and /, become L' and V when contracted ; 

 then it is plain that we have 



(112) 



/ 3 -/ /3 A ' 



If n denote the coefficient of muscular contraction, and i 

 it be supposed to be the same for both groups of fibres, then 

 equation ( 1 12) becomes 



L>(i-n*) _ A + p t 

 / 3 (i - O " A ' 



or 



IJ A + o 



y = — ■ 0*3) 



As the left-hand side of this equation depends on measure- 

 ments of the lengths of the two systems of fibres, while the 

 right-hand side depends on measurements of the volumes of 

 the two ventricles, it is plain that it affords us a test, within 

 limits of errors of observation, of whether the principle of 

 least action applies in all its force to the theory of the action 

 of the heart. 



As the lengths of the fibres and sizes of the hearts 

 examined differed considerably, 1 selected a large and small 

 heart for measurement, with the following results : — 



No. 1. No. 2. 



Length of common fibres, . 13 25 in. . 8.5 in. 

 Length of proper fibres, . . 10.75 . 6.5 ,, 



