﻿Isotropic Spheres under Uniform Surface-Pressure. 175 



the surfaces of the altered layer ; or we may take the com- 

 plete values of the displacements. In either case we arrive 

 ' at much simpler results than for tbe compound shell. 



For the increments of pressure we find in place of (1G) 

 and (17), 



P b = 4/^p^^(k l -k)n(Sk + ^n i ), (47) 



l=- 4 i / ff^(*i-*)W^+4n)6» + 3*(fi 1 --«)(a 8 -6 8 )h (48) 



where 

 I = k(U + 4/i) (3*! + 4n0 + 4 *pj^ (*,-*) { Wl (3* + 4n)£ 3 



+ 3^ 1 -n)(a 3 -^ 3 )}. . . (49) 

 If 



ki = k, 



then, however n x and n may differ, 



8p 6 =:Sp c =0, 



whence 



u = — ^rp'jk 



throughout the whole of the unaltered material. 



For the displacements in the compound sphere we find 

 in place of (38), (39), and (40), IT being given by (49), 

 in (0. a. . c) 



tt=-|^(3* + 4n)(3Ar 1 +4n 1 ); (50) 



in (c . a x . b) 



u=-£,(3/c + 4n) |>(3*+4»i) + £(*i-*)] ; • (51) 

 in (b.a.a) 



" = ~ fp[W(3* + 4n)(3A 1 + 4n 1 ) +12^- 3 (n.-n) (A,-*)} 



-^ 3 -c 3 K*i-*)(3A + 4>h)} • (52) 



One of the most noticeable phenomena in a simple sphere 

 is the vanishing * of the stress-difference S at every point. 



* See Phil. Mag. September 1891, pp. 240-42. 



