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.

210 PRECESSION AND NUTATION,
sibly differ from those found by the formulae above. And,
since the latter differ from the true ones only by quantities
which are insensible, it follows that the values found by
using the true longitude of the node, are sensibly erroneous.
In calculating Nutation, therefore, the mean longitude of the
node must be used, not the true.
43. PROP. 16. Assurring the law of density of the
Earth, and the mass of the Moon, to calculate numerically the annual precession and the coefficients of solar and
lunar nutation.
It is first necessary to calculate the value of B, or — (,
o- (c)
which enters into all the expressions. Suppose, then, as in
Prop. 29, of the Figure of the Earth, p A. i q. By
Art. 61, of the same,
(c) (e —) - p (c),... B= e-~ c.
3 2j (J (c)
d, G3
Now ( (c) = fp d = 3sfA. c.sin qc
de
=A ( c. cos qe sin qc
=-3A _ -+- S A;
q q /
which, taken from c = o to c = c, gives
)(c) 3a ( c.cos qc sinqc\
d. c5
And a (c) = fIp. -- by (26) = 5Ac3' sin qc
f- c. cos qc 3 c2. sin qc 6c. cos qc 6 sin qc
5A \+ - q,, + _
q q2 q: 4 '