ANIMAL MECHANICS. 



213 



plane parallel to the tangent plane at S ; and let Otxyt be the 

 tangent cone drawn to the surface along the indicatrix. It 



Fig. 49. 



can be shown as before, that OS is equal to C. Let the 

 following notation be used. 



P = perpendicular pressure acting on the unit of surface. 

 T = tangential strain acting on the unit of length. 

 a = Ct = semiaxis major of indicatrix. 

 b = 6V= semiaxis minor of indicatrix. 

 c = CS= SO. 



r = Cm, Cy, = radius vector of indicatrix at any point. 



Let xy be any element of the indicatrix, and produce the 

 tangent xyz to meet a perpendicular Oz, let fall upon it from 

 the vertex of the cone ; and draw Cz. The lines Oz and Cz 

 are both perpendicular to the tangent to the indicatrix, and 

 are to be considered equal to each other, because the point 0 

 is very near the surface. Let the element xy be called ds, 

 and let Oz or Cz be called p. It is necessary and sufficient 

 for equilibrium that the pressure P acting upon the elemen- 

 tary triangle Cxy, shall be equilibrated by the vertical com- 

 ponent of the tangential strain acting on the element xy. 



