21G 



ANIMAL MECHANICS. 



upon the indicatrix. Tt follows from the foregoing, that the 

 tension of the surface in any azimuth CR, varies directly as 

 the square of CP. 



Hence the greatest and least tensions will be at the ex- 

 tremities of the major and minor axes of the ellipse, and will 

 be proportional to the squares of those axes. 



The preceding problem, as is evident, contains the so- 

 lution of the conditions necessary in architecture to construct 

 an ellipsoidal dome. 



It is sometimes convenient in problems in Animal 

 Mechanics to use the mean tension of the muscular wall, 

 without regard to its variation as the azimuth varies ; and for 

 this purpose, we must take the mean of all the tensions in 

 every possible azimuth. 



The tensile strain at each point of the indicatrix is Tds, 

 acting parallel to the line Oz, Fig. 49, and perpendicular to 

 xy. The component of this tension, in the direction OC, is 



Tds cos (zOC) = Tds x P ; 



9 



but, by equation (37) 



p 2C 



and hence, the tensile force acting on the element xy, in the 

 vertical direction 0(7, becomes 



Ids x — 



P 



We must now regard Tas a constant, having the mean 

 value of the tensions taken in every azimuth, and integrate 

 the foregoing expression all round the ellipse. 



