AND on the remote history of the earth. 
517 
[It will however appear, I believe, that this secular change of elli pticity of the 
earth’s figure will exercise an important influence on the plane of the lunar orbit and 
thereby will affect the secular change in the obliquity of the ecliptic. The investiga¬ 
tion of this point is however as yet incomplete.]'* 
The other small term which I shall consider arises out of the ordinary precession, 
together with the fact that the tide-generating force diminishes with the time on 
account of the tidal reaction on the moon. 
The differential equations which give the ordinary precession are in effect (compare 
equations (26)) 
dco-, C—A . . 
— = T— - - Sill '% COS l Sill U 
dt (J 
dco 2 C — A 
—f = — r—r,— sm i cos 1 cos n 
at L/ 
and they give rise to no change of obliquity if r be constant, but 
when t is small. 
. . C—A 5 -.rd 
Also —— =£=—— = i~- 
C hj 3 Q 
equations may be written 
T o 
Hence as far as regards the change of obliquity the 
1 
Jl 
3*1 AJ 
^ 1 ^ 
3r 0 n 2 , 
5 ' 
'dj\ 
\dt) 
| sin i cos i t sin n 
dco 2 _ 
3r 0 n*i 
1 sin i cos i t cos n 
dt 
9 ' 
\dt) 
Then if we regard all the quantities, except t, on the right-hand sides of these 
equations as constants and integrate, we have 
3 T o/d£\ . . ., . . 
aq = — I -- J sm 1 cos i{nt cos n— sm n\ 
5 t o fd£\ • ., , 
Wn = — — sm i cos i\ nt sm cos n \ 
3 a \dt) 
And if these be substituted in the geometrical equations (1) we have 
cl% 3t 0 . . . dt 
- =— sm 1 cos ^ — 
dt t( \dt 
* Added July 3, 1879. 
