﻿THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



AUGUST 1894. 



XVII I. An Examination into the Physical Consequences of 

 the Local Alteration of tlie Material of Isotropic Spheres or 

 Spherical Shells under Uniform Surface-Pressure. By 

 C. Chree, M.A* 



Simple Shell ; Strains and Stresses. 



§ 1. r pHE equilibrium of au isotropic sphere or spherical 

 A shell under uniform surface-pressure is one of the 

 oldest problems satisfactorily treated in elastic solids. It is 

 necessary, however, to consider it briefly here, as preliminary 

 to the main object of this paper, which treats from a physical 

 standpoint of a sphere or a spherical shell composed of several 

 concentric layers of different isotropic materials. This latter 

 problem is not altogether new mathematically f, but the points 

 to which attention is principally directed here have not, I 

 believe, been previously considered. 



The displacement u is at every point along the radius 

 vector r from the centre. The principal strains are 



-=- = s along the radius, 



and two equal strains 



u/r = s' 



* Coniniunicated by the Author. 



f See ' Quarterly Journal of Pure and Applied Mathematics,' vol. xxi. 

 p. 193 (1886). 



Phil. Mag. S. 5. Vol. 38. No. 231. Aug. 1894. M 



