218 



ANIMAL MECHANICS. 



Hence we obtain 



P x irab = nab x T ( — + — 



or 



P= T - + - 



V/O, ? 3 



which is Lagrange's theorem, already employed at page 152. 



The first example of ellipsoidal muscles that I shall dis- 

 cuss is the case of the abdominal muscles, already considered 

 in a general way in treating (p. 151) of the muscular force 

 employed in parturition. The principal curvatures of the 

 abdomen at the navel (p. 161) were shown to correspond to 

 circles of curvature of 22.7 in. and 12.6 in. diameter respec- 

 tively ; and the tensile strain in the walls of the abdomen is 

 produced by the simultaneous action of the eight abdominal 

 sheets of muscle. According to the theory just developed, 

 the tensile strains produced by all the muscles in the vertical 

 and transverse directions at the navel, should be in the pro- 

 portion of the diameters of curvature in the same directions ; 

 and the axes of the indicatrix ellipse at the navel should be in 

 the proportion of the square roots of those diameters. 



A severe test may thus be applied to the theory, and to 

 the measurements of the forces produced by the abdominal 

 muscles. For the purpose of applying this test 1 shall make 

 use of the muscles of subject No. 2 (female), p. 160, the 

 measurements of whom corresponded nearly with the mean of 

 all. 



The four muscles at each side of the central line have the 

 following mean thickness : — 



1. Rectus abdominis, . . . . 0.29 inches. 



2. Obliquus exter mis, . . . . 0.25 



3. Olrfiquus interims, . . . . 0.17 „ 



4. Tr ansver salts t . . . . . 0.15 „ 



