1872.] Elementary Principles in Animal Mechanics. 329 



secting in a line P Q. If we suppose one bone A B to be fixed and the 

 other bone A' B' to be movable, and that the contraction of the muscle 

 compels the bone A' B' to revolve round P Q as an axis of rotation, it is 

 required to find the conditions necessary in order that the work done by 

 the contraction of the muscle shall be a maximum. I shall in this note 

 discuss only the case in which the bones A B, A' B' lie in the same plane. 

 In this case I have succeeded in demonstrating the following propositions 

 in the case of maximum work : — 



1. The axis of rotation PQ must be formed by the intersection of 

 rectangular planes passing through A B and A' B\ 



2. The quadrilateral muscle A B A' B' must be inscribable in a circle. 

 If it be true (as I believe it is) that the muscles, bones, and joints of all 



vertebrate animals are so related to each other as to produce in all cases 

 the maximum amount of work possible with a given weight of muscle, then 

 the second proposition affords us a severe test of the truth or falsehood of 

 my postulate. If the muscle be circumscribable by a circle, it follows, from 

 Ptolemy's theorem, that its sides and diagonals must fulfil the following 

 condition : — 



ah + cd=ef } 



where a, b are one pair of opposite sides and c } d the other pair, and e, f 

 are the diagonals of the quadrilateral. 



The pectineus muscle of many animals forms a plane quadrilateral when 

 in its position of maximum extension of fibres, and therefore furnishes us 

 with a favourable test. In the freshly dissected animal it is easy to mea- 

 sure with accuracy the lengths of the six lines in question, and so test the 

 truth of the postulate. 



I have thus obtained the following results : — 



1. Adult Male Lion. Pectineus Muscle. 



in. 



a. Length of pubic origin 1-/0 



b. „ femoral insertion 2*95 



c. „ anterior fibre 4*52 



d. ,, posterior fibre 7*61 



e. First diagonal 5*77 



/. Second diagonal 6* 76 



Hence we have 



ab=l'70x 2-95= 5-01 

 cd =4-52x 7-61=34-39 



ab + cd =39-40 



of =5-77 x 6-76 = 39-00 

 Difference =~0 T 40 



This difference amounts to - y J., part of the whole. 



