522 
[221 
221. 
ON THE SECULAR ACCELERATION OF THE MOON’S MEAN 
MOTION. 
[From the Monthly Notices of the Royal Astronomical Society, vol. xxn. (1862), 
pp. 171—231.] 
The present Memoir exhibits a new method of taking account, in the Lunar Theory, 
of the variation of the eccentricity of the Sun’s orbit. The approximation is carried 
to the same extent as in Prof. Adams’ Memoir “ On the Secular Variation of the 
Moon’s Mean Motion ” {Phil. Trans., vol. cxliii. (1853), pp. 397—406) ; and I obtain 
results agreeing precisely with his, viz., besides his new periodic terms in the longitude 
and radius vector, I obtain in the longitude the secular term 
and in the quotient radius, or radius vector divided by the mean distance, the secular 
term 
(f to 2 — ifp to 4 ) (e' I 2 — E'-), 
which is, in fact, as will be shown, included implicitly in the results given in Professor 
Adams’ Memoir. In quoting the foregoing results, I have written e' 2 — E' 2 in the place 
of {e' + ft) 2 — e 2 = 2eft, which in the notation of the present Memoir it should have 
been; and I purposely refrain from here explaining the precise signification of the 
symbols: this is carefully done in the sequel. The method appears to me a very simple 
one in principle; and it possesses the advantage that it is not incorporated step by 
step with a lunar theory in which the eccentricity of the Sun’s orbit is treated as 
constant; but it is added on to such a lunar theory, giving in the Moon’s coordinates 
the supplementary terms which arise from the variation of the solar eccentricity, and 
thus serving as a verification of any process. employed for taking account of such 
variation. 
I have given the details of the work in a series of Annexes, 1 to 23 : this appears 
to me the best course for presenting the investigation in a readable form.