212] A MEMOIR ON THE PROBLEM OF DISTURBED ELLIPTIC MOTION. 
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sun’s orbit from a departure-point, defined as above, in that orbit), and the position 
of the planet would then be determined by means of the longitude, latitude, and 
radius vector. The term sidereal longitude is, I think, used in Physical Astronomy 
rather loosely to denote the longitude in the mean ecliptic from the mean equinox, 
less the precession; so defined it is not practically different from, and may I think 
in all cases be replaced by the longitude as measured from a departure-point in the 
mean ecliptic. 
Returning from this digression, the assumed equation, da = cos <f)d6, gives the 
expression for the variation da of the departure of the node, and we now have in 
the place of the former six equations the seven equations 
dr = 0, 
d\> = 0, 
^ nae sin f 
d no? Vl — e' 
where as before = il (r, z, 0, <£). 
But the value of z is z = ]? — a, and il can be expressed, and that in a single 
way only, viz. by means of the substitution of |? - a in the place of z, in the form 
O = fl (r, ]>, a, 6, (/>), and if on the right-hand side fl = il (r, z, 6, <$>) as before, then we 
have 
dfl _ dfl 
d}> dz ’ 
dQ _ dfl 
da dz ’ 
dfl _ dfL 
d<p d(f) ’ 
dQ 
dd 
dfl 
dd’