DUE TO THE WEIGHT OF CONTINENTS. 
201 
results of tlie preceding sections are directly available for finding tire state of stress 
due to continents and mountain chains. 
We must in fact put 
m- 1 ) 
2^ + 1 
r 
a 
Now in the previous developments the factors involving g, w, See., have been 
omitted and Wi has been put equal to a zonal harmonic which had the value unity at 
the equator. 
If we write 
9 ;—sin *0— ~ sin l ~ 2 6 cos 2 #-{-&c.(30) 
i 
where 6 is the colatitude, and put h as the height above the mean sphere of the 
elevation at the equator, then h<s;=cri and 
2(»-l) 
2i + l 
as 
Wi was in (12) put equal to rfi. 
Thus in order to apply the preceding results to finding the stresses caused in a 
sphere, possessing the power of gravitation, by the weight and attraction of surface 
inequalities expressed by 
r=a+h$i .(32) 
we must multiply the preceding results for P, P, T, Q by 
2 (i — 1) gwh 
2i + l a 1 
§ 5. The state of stress due to ellipticity of figure or to tide-generating forces. 
When the effective disturbing potential W t is a solid harmonic of the second degree 
the solution found above will give the stresses caused by oblateness or prolateness of 
the spheroid. It will of course also serve for the case of a rotating spheroid with 
more or less oblateness than is appropriate for the equilibrium figure. 
When an elastic sphere is under the action of tide-generating forces the disturbing 
potential is a solid harmonic of the second degree, and therefore the present solution 
will apply to this case also. 
The formula for the stress-difference admits of reduction to a simple form when 
i= 2. 
On substituting colatitude 6 for latitude l, (22) gives 
P-P=r 3 sin 2 6[(A 0 —C 0 )f(A 2 — C 2 ) cot z 0] + a\B 0 -D Q ) 
T=r 2 sin 6 cos 0{E O ) 
2 n 
MDCCCLXXXII. 
