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.

MOON'S MASS AND EARTHIS ELLIPTICITY DETERMINED. 215
50. The ellipticity of the Earth cannot be determined
at once from these data, but an equation can be found depending on the law of density of its strata, such that if a
law be assumed with one indeterminate coefficient, that coefficient can be found by approximation, and the ellipticity
of the Earth can then be determined. The solar annual
precession we have found = a - b. C: but the expression for
it in seconds, by (44), is
9..603. cos 23~. 28'=
B. — ^ -- = 6`B. 4869;
366,26
making these equal, and putting for C its value,
B = a x,0002054 - b x,0007675.
This gives the value of
e —.c
3 (e - 2 ). c.Co-(c)
If, as in Art. 65 of the Figure of the Earth, we assume
for the form of the expression for p, A si q, we have this
c
equation,
5 3zm
2 hqce 6Z i
+ Z-3 2+ ---
cZ
where z = 1
tan qc
finding the value of qc by approximation, the ellipticity of
the surface will be found by substituting it in the equation
-e ---- - I
5 m q c:_3
2 q2c'C'
+ -3