DUE TO THE WEIGHT OF CONTINENTS. 
1 89 
P=(g> — v )8+2i;- 
(da dry 
T=V \di + iv 
and the other four stresses are expressed from these by cyclic changes of P, Q, It; 
S, T, U ; a, (3, y ; x, y, z. 
The first task is to find p. 
Now by adding P, Q, II together we have, 
rpz= — ( 0 } — \v)h 
We must now find 3 from (1). 
By differentiation 
da. (P W- d W- 
tvJb 
dx* 
dx 
dsd' 
and similar expressions for d/3/dy, dyjdz. 
Now W;, WiV~ 2i ~ l are spherical harmonics of degrees i, — i —1, and are also homo¬ 
geneous functions of the same degrees. If therefore we add the three expressions 
together, and note the properties of harmonics and of homogeneous functions, we have 
3= - 2 iFi Wi+ (2i+ 3)(i+1) G { W s 
Omitting for brevity that part of the divisors in the expressions for F and G which 
is common to both, 
— 2^+(2|f 3)(i+l)^=—l)(2i+3)o)+i(2t+l)v+(2jH-3)(i+l)icu 
= i(2t+l)v 
and we have, on introducing the omitted denominator, 
And 
3= 
p= 
[2 (i +l) 3 + l]co — (2 i + l)v 
-i(co-±v) 
[2(i + lf+l]co-(2i + l)v 
W; 
m 
Throughout the rest of this paper (excepting in § 10) the elastic sphere will be 
treated as incompressible, so that co is to be considered as infinitely large compared 
with v. 
Henceforth I write 
I=2(i+iy+i .(2) 
and when m is infinite compared with v, we have, 
Also we may put 
