AND ON THE REMOTE HISTORY OF THE EARTH. 
4G1 
Sir William Thomson’s theory of elastic tides, H 1? II,, H 3 are all zero. Those theories 
both neglect inertia but the actuality is not likely to differ materially therefrom. 
Thus every term where oj 1 and an occur may be omitted and the equations reduced to 
A— X +(C — B)w 3 tu 3 +n—+ird + -^y+wHo=IL 
B5+(A-C)» sB| +»'"-»V+f-»H 1 =i« (24) 
c^-hb-ah^ rf 5 • i ■ 
As before with the couples, so here, we are only interested in terms with the argument 
n in the small terms on the left-hand side of the first two of equations (24), and in 
non-periodic terms in the last of them. 
Now for each term in the moon’s potential, as developed in Section 1, there is (by 
hypothesis) a corresponding co-periodic flux and reflux throughout the earth’s mass, 
and .therefore the H l3 II.,, IT 3 must each have periodic terms corresponding to each 
term in the moon’s potential. Hence the only term in the moon’s potential to lie con¬ 
sidered is that with argument n, with respect to H, and Ho in the first two equations ; 
and H 3 may be omitted from the third as being periodic. 
Suppose then that II x was equal to h cos n-\-li sin n, then precisely as we found J$l 
from It by writing 1 n —y for n we have H.,=/i sin n— h' cos n. Thus 4-wH, = 0, 
J ° 2 dt " 
rZHo 
dt 
wH L 
= 0, and the H’s 
disappear from the first two equations. 
Next retaining only terms in argument n in d' and e, we have from (10) 
e' = G T ^E'pq{jr — (f) cos (n — e), d'=C -E'pq^—q 2 ) sin (n — e) 
Therefore —+nd' — 0, ——we'=0, and these terms also disappear. 
Lastly, put B=A, and our equations reduce simply to those of Euler, viz. 
Aq~-(- (C — A)ct) 3 £Wg — H 
(25) 
Now J2 is small, and therefore gj 3 remains approximately constant and equal to —n 
for long periods, and as C — A is small compared to A, we may put <u ; —• —n in the first 
