278 
A MEMOIR ON THE PROBLEM OF DISTURBED ELLIPTIC MOTION. [212 
I write also 
8, the longitude in orbit of departure-point, or, as it may be termed, the adjustment; 
that is 
8 = 6 — o\ 
In the undisturbed motion the departure-point is simply a fixed point in the 
orbit, but when the orbit is variable, the departure-point is taken to be the point 
of intersection of the orbit with any orthogonal trajectory of the successive positions 
of the orbit, a definition which is expressed analytically b} r the equation, 
da = cos cf) dd. 
The equation, z = p — a, gives 
or, what is the same thing, 
dz = dj? — da — dp — cos <£ dO, 
dp = dz + cos cf) dd. 
But we have dz + cos <£ dd = 0, and consequently dp = 0, an equation which expresses 
that the increment of departure, in so far as such increment arises from the variation 
of the elements, is equal to zero. Or, what is the same thing, the total increment 
of departure is equal to the infinitesimal angle between two consecutive radius vectors 
of the planet. 
I propose to consider the departure-point as a point which is constantly defined 
as above, viz., when the orbit is variable, the departure-point is the point of inter 
section of the orbit with any orthogonal trajectory of the successive positions of the 
orbit; and as a particular case of the definition, when the orbit is fixed, the 
departure-point is simply a fixed point on the orbit. The orbit here considered is 
that of the planet and the position of the planet is determined by the departure and 
radius vector (the latitude being zero), and this is assumed to be the case whenever 
the departure is spoken of, and it is such departure which is denoted by the letter p. 
But we might consider a departure-point (defined as above), upon any other orbit 
whatever, and use such departure-point as an origin of longitude (for instance, in the 
lunar theory we might consider a longitude measured along the variable plane of the