OX PHYSICAL LIXES OF FORCE. 



Let p. be the coefficient of cubic elasticity, so that if 



493 



Let m be the coefficient of rigidity, so that 



dr)\ , 



_- I j &(. 



Then we have the following equations of elasticity in an isotropic medium, 



, x (dj; d-n d\ d% 



ff\ f ii ^ .A.-jyi I I I L -- .. I J Vfli ' * 



f xx \i o / \ /V'/* fill ft 7. I Ci 'IT 



with similar equations in y and z, and also 



ft .-^f^ + ^) f &c (83). 



z \az ay I 



In the case of the sphere, let us assume the radius = a, and 



=exz, rj = ezy, t,=f(x' + 'i/ f )-\-gz 1 + d (84). 



Then p a = 2(fj. m) 



(e+g)z + 2mgz 



(85). 



The equation of internal equilibrium with respect to z is 



d d d 



dx dy "* dz \ )> 



which is satisfied in this case if 



m (e + 2f+2g) + 2 (/A -Jm) (e+g) = (87)- 



The tangential stress on the surface of the sphere, whose radius is a at 

 an angular distance from the axis in plane xz, 



.(88) r: , 



.(89). 



