ANIMAL MECHANICS. 



211 



In the simplest case of ellipsoidal muscles, that in which 

 the curvature at a given point coincides with that of a certain 

 sphere, let 0 be the vertex of the tangent cone, Fig. 48, 01] 

 O T being sides of the cone touching the surface at £, t. 



Let C be the centre of the circular indicatrix, txyt, and 

 join OC. This joining line pierces the surface at the point 8, 

 at which point, a tangent plane would be parallel to the plane 



Fig. 48. 



of the indicatrix ; and it can be shown, as in the case of the 

 circle p. 198, that the line OC is bisected at the point S, be- 

 cause 0 is indefinitely near the surface. 



Let the surface now be supposed to be composed of mus- 

 cular fibres, and to contain a fluid reacting perpendicularly 

 to the surface, it is required to determine the conditions of 

 equilibrium. Let P denote the force acting perpendicularly 

 on the unit surface, and let T denote the tangential strain 

 caused by the muscular contraction, acting along the side of the 

 tangent cone, upon the unit of length of the indicatrix. It is 

 necessary and sufficient for equilibrium, that the perpendicular 

 pressure upon any element xyC, of the indicatrix, shall equi- 

 librate the corresponding muscular strain acting in the element 

 P 2 



