Isotropic Elastic Solid Ellipsoids 



39 



" The Stresses and Strains in Isotropic Elastic Solid Ellipsoids 

 in Equilibrium under Bodily Forces derivable from a 

 Potential of the Second Degree." By C. CHREE, M.A., 

 Fellow of King's College, Cambridge, Superintendent of 

 Kew Observatory. Communicated by Professor W. G. 

 ADAMS, F.R.S. Received March 2, Read May 10, 1894. 

 Abridged February 20, 1895. 



General Formulas. 

 1. Let the isotropic elastic solid ellipsoid, 



t/ 2 + c~V = 1 . 



(1), 



of uniform density />, be acted on by bodily forces whose components 

 P^J Qy> Rz ar e derivable from a potential 



. (2). 



Let II denote the determinant 



3 6 + 2 6V + 3 c 4 , c 4 - / (6V + c 2 a 2 + 3 a 2 6 2 ) , 6 4 - r, (6V + 3 cV + a 2 6 2 ) 



c 4 -? (6V + c 2 a 2 +3a 2 6 2 ), 3c 4 +2c 2 a 2 +3a 4 , a 4 -*/ (36V + c 2 a 2 + a 2 6 2 ) 



(3) 



and let its minors be ITn, Tlu, &c., where I1 12 = IT 2 ,. 



Then with the notation of Todhunter and Pearson's "History," 

 rj denoting Poisson's ratio, the stresses are given by 



yz = 

 VOL. LVIIJ. 



xij = 2 



