ANIMAL MECHANICS. 



187 



of cue blending of the fibres with each other. Thus, in a tri- 

 angular muscle formed from a uniform sheet of muscle of equal 

 thickness throughout, the strength of the section near the 

 vertex would be much less than of that near the base, and the 

 muscle might be torn by the application of external violence ; 

 whereas, in a muscle whose fibres are arranged in a fan- 

 shaped form, the cross section being the same everywhere, 

 the muscle is of equal strength, and the tendency to tear 

 across is lessened. 



The following measurements, made on a male human sub- 

 ject, confirm the results obtained from the pectoral muscle in 

 Birds :— 



Pectoral Muscle in Man. 



Length of Section. 



Mean Thickness. 



Cross Section. 



2. 20 inches. 

 4-25 „ 

 ii.5° » 



0.31 inches. 

 0.16 



0.06 ,, 



0.682 sq. in. 



. 0.680 „ 

 0.690 ,, 



There is always a loss of Work done in a triangular muscle, 

 which is due to the peculiar arrangement of its fibres in a fan- 

 like form ; and, in this respect, muscles with radiating fibres 

 differ remarkably from the penniform muscles, in which, as I 

 have shown, the Work done is always equal to the inherent 

 Work. This may be proved as follows : let P, P', P'\ &c., 

 be any forces, and let p, p, p", &c, be the displacements 

 (estimated in the directions of the forces) undergone by their 

 points of application ; and let B, r, be the resultant of the 

 forces, and the displacement of its point of application, esti- 

 mated in the direction of the resultant itself ; — then we have, 

 by Lagrange's principle of virtual velocities, 



Rr = Pp + P'p + P"p" + &c. (32) 



