170 



ANIMAL MECHANICS. 



shall be exactly the same as that of a given penniform muscle. 

 In order that the action of the two muscles shall be, in all 

 respects, the same, it is necessary that they shall contract 

 through the same space and with the same force, the product 

 of the space and force being the work done by the muscle in 

 a single contraction. If I denote the length of the penniform 

 fibres ab (Fig. 24), and 0 the angle abV; then the contrac- 

 tion due to the penniform muscle will be equal to that of a 

 prismatic muscle whose length is 



L = / sec 0. (27) 



Let aAa bBb (Fig. 26) represent a penniform muscle, whose 

 length AB is A, the angle ABC being 0. If perpendiculars 

 AC and AD be drawn from A to the fibres Bb and Bb pro- 

 duced, it is plain that the lines AC and AD will represent 

 the total number of fibres employed in the muscle ; hence, if 

 / be the force of each fibre, the total force employed at each 

 side will be 



F=nf = fx AD = /A sin 0; 



but R - 2F cos (p. 



Hence It = 2/A sin 0 cos 0 = /A sin 2<p (28) 



This is equivalent to the force of a prismatic muscle, whose 

 cross section is A sin 20, or equal to the line CD. 

 For, 



A =AB. 



A sin <j> = AB sin 0 = AD. 

 A sin 0 cos $ = AD cos 0 = DE. 

 2A sin (j) cos (p = 2DE = CD. 



the actual width of the penniform muscle is 

 w - 2I sin (p. 



