Mathematical tracts on the lunar and planetary theories, the figure of the earth, precession and nutation, the calculus of variations, and the undulatory theory of optics.

EXPLANATION OF THE EFFECT OF DIFFERENT TERMS. 4
or oc:u 1- 4+ -- cos(2g0 -2e y)
Taking for u the expression found in Prop. 20, parallax
oc a 1 - k - 2 + e cos(ce - a) + m2 cos(2 - 2m)0 - 213
2
15
+ - me. cos(2 - 2m - c)0 -23+ al
8
omitting the term - m2e', cos (mo + 3 - t) which is of the
third order; or, if P be the mean parallax, that is, that part
of the expression independent of cosines, the parallax
= P{ + e cos(c0 - a) + m2.cos(2 - 2m)0- 23
+ 8 me. cos(2 - m- c) - 2/3 + a}.
61. PaoP. 26. To explain the effect of the different
terms in these expressions.
The first and greatest inequality of parallax is
ecosc (0 -
This, though similar to the inequality which would exist in
an elliptic orbit, is not exactly the same, but it would be the
same if it depended on the angle 0- a instead of c 0 - -
c
Let then EA, fig. 4, be the Moon's least distance: EM
any other distance: z AEM =0 -: let AmB be an
ellipse, whose latus rectum is -, and eccentricity e: take
a
z AEm = c x / AEM (c being < 1): then, EM will = Em.
For
— = a(l + e cos AEm) = a(l + ecosc0 - a) = EMEm
If now an ellipse aMb be described similar and equal to
AmB, whose major axis ab is inclined to AB at an angle