218] 
505 
218. 
A THIRD MEMOIR ON THE PROBLEM OF DISTURBED ELLIPTIC 
MOTION. 
[From the Memoirs of the Royal Astronomical Society, vol. xxxi, pp. 43—56. 
Read January 10, 1863.] 
The object of the present Memoir is to obtain the differential equations for deter 
mining 
r, the radius vector, 
v, the longitude, 
y, the latitude, 
of the disturbed body, when the last two coordinates are measured in respect to an 
arbitrarily varying plane (which however, to fix the ideas, is called the variable ecliptic) 
and the departure point or origin of longitudes therein. This is very readily effected 
by means of an expression for the Vis Viva function given in my “Supplementary 
Memoir on the Problem of Disturbed Elliptic Motion,” Mem. Roy. Ast. Soc., t. xxviir. pp. 
217—234 (1859), [215]. Neglecting the squares of the variations of the variable ecliptic, 
and also the products of the variations by sin y, or ^, then (as might be expected) 
it is found that the equations for r and v are the same as for a fixed ecliptic, and 
the equation for y is found in a simple form, which is ultimately reduced to coincide 
with that obtained for the lunar theory by Laplace in the seventh book of the 
Mécanique Celeste, and which is used by him to show that the effect of the variation 
of the ecliptic on the latitude of the Moon (as measured from the variable ecliptic) 
is insensible. And it is shown conversely how the approximate formula of the Memoir 
may be obtained by a process similar to that made use of in the Mécanique Celeste. 
C. III. 64