NOTE ON THE LUNAR THEORY. 
[From the Monthly Notices of the Royal Astronomical Society, vol. LH. (1892), pp. 2—5.] 
In the Lunar Theory, in whatever way worked out, the values ultimately obtained 
for the coordinates r, v, y should of course satisfy identically the equations of 
motion; and that they do so, is the ultimate verification of the correctness of the 
results obtained. It can hardly be hoped for that such a verification will ever be 
made for Delaunay’s results; and yet it would seem generally that the labour of 
such a verification of the results to any extent, while exceeding (and possibly greatly 
exceeding) that of obtaining these results by any method employed for that purpose, 
ought still to be, so to speak, a labour of the same order. And one can, moreover, 
imagine the process of verification so arranged as to be a process of mere routine 
which could be carried out by ordinary computers. But, however this may be, I 
think it is not without interest to exhibit the verification to a very small extent, 
viz. to e, to 4 . 
I think there is an advantage in using capital letters for the arguments, and I 
accordingly write G (instead of Delaunay’s g), to denote the mean anomaly. 
The equations of motion are : 
or say 
D = —(I cos 2 H — U> where cos H = cos y cos (v — v'), 
il = m%ri T ^ r 2 (I cos 2 y cos 2 (v — v) — R ; 
TO 2 ?i 2 a' 3