213] 
293 
213 
ON THE DEVELOPMENT OF THE DISTURBING FUNCTION IN 
THE LUNAR THEORY. 
[From the Memoirs of the Royal Astronomical Society, vol. xxvil, (1859), pp. 69—95. 
Read November 12, 1858.] 
The development of the disturbing function for the lunar theory is effected in 
a very elegant manner in Hansen’s Fundamenta Nova, and it requires only a single 
easy step to exhibit the result in a perfectly explicit form, and to compare it with 
those of other geometers. To do this is the immediate object of the present memoir, 
and the mode of development is a mere reproduction of that made use of by Hansen. 
But the memoir is written with a view to the development of and application to the 
lunar theory, of the theory contained in my “ Memoir on the Problem of Disturbed 
Elliptic Motion,” ante pp. 1—29, [212], and the notation adopted (differing from Hansen’s 
very slightly) is consequently that of the memoir just referred to. 
Taking, as usual, il to denote the disturbing function with the sign employed 
by Lagrange (il = — R, if R be the disturbing function of the Mécanique Céleste), then 
where we have 
m!, the mass of the sun, 
r , the radius vector of the moon, 
r' , the radius vector of the sun, 
H, the angular distance of the sun and moon, 
the earth being, of course, taken as the centre of motion; (Hansen’s il is the above 
value divided by M + m, where M and m are the masses of the earth and moon 
respectively; that is, the disturbing function here represented by il is Hansen’s il 
multiplied into M + m).