J. N. Stockwell—Inequalities in the Moon’s Motion. 3 
the earth’s equator ; F# denotes the disturbing function; and 
d placed before a quantity denotes the variation of that quan- 
tity arising from the oblateness of the earth. I also put for 
revity 
= {p—4p}a5 sine cose, (1) 
I now give the equations which express the variations of 
the elements and coordinates of the moon, and which are inde- 
pendent of the sun’s action. In the first ‘place I find that the 
position of the node and inclination of the orbit are affected by 
the following inequalities : 
62 = 12 sin (2né¢ — &) =+ 07'185 sin (2nt — Q), (2) 
= + cos (2nt — 8) = = + 07:0165 cos (2nt— 9). (3) 
Rhea two apis a give rise to the following inequality 
in the moon's latitude 
66 = — 48 sin nt = — 0"°0165 sin né. (4) 
But I find that the direct action of the earth on the moon 
produces the following inequality : 
60 = + $ Asin nt, (5) 
The sum of these two inequalities gives 00 =0; whence it 
follows that there is no equation of the above form in the 
moon’s latitude arising from the oblateness a the earth. In 
other words, the figure of the earth does not cause the moon to 
depart from the plane of the great circle in which its orbit is 
situated. 
The above values of dQ and he also give the following ine- 
quality in the moon’s longitu 
dvu=+tfy sin Q= a 0”:00074 sin Q). (6) 
The direct action of the earth on the moon produces the 
following inequalities in the paige 
Ovu= 2 A tan esin 2nt — +, igrmin: (2nt — — 8) oe (7) 
=+ 0” 0012 sin 2nt = — 0”°00025 sin eset Q). 
exceeding fourteen feet if ceaauren 6 on the moon’s orbit, Pron 
this atealition it follows that, if the moon were entirely free 
from solar disturbance, the effect of the oblateness of the earth 
on its motions would be so small that it would never be detected 
by observation. 
Let us now examine into the effect of a “hin ae of solar 
disturbance with that arising from the earth’s oblateness. 
Since we have supposed the moon’s orbit to be circular, it is 
