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.

CALCULATED ON 0 ASSIMED DATA. 211
putting c for c, we have the value of r (c). Hence
B ( n - qc3'. cos qc+ q'c2. sin qc
2 -q3c3. Ccosqc q2c' sin qc +6qc. cos qc-6 sinqc
(_/_m\ qc
s_ e --.-, where z = 1 -
a2 y6zr tanqc
2+z
q" c
If we suppose q to have the value used in Art. 66, of the
5 r
Figure of the Earth, namely, -, and take the value of
6e
e —, found in Art. 66, we get for the value of B,,0031677.
44. The solar annual precession, which is found by
supposing I to be increased by 2 7 in the expression of
(30), is
6-r2. B. cos I
T~w
Now To,- = the angle described by the diurnal revolution
of the Earth in 1 year = 2r. 366,26; I = 23, 28': hence,
the solar annual precession
B. 3. cos 23~. 28'
366,26
This is in parts of the radius: to reduce it to seconds we
i. 80.60.60
must multiply it by. Thus the solar annual
7r
precession in seconds
B. 9. (60)'. cos 230. 28'
366,26
which, putting for B the value above, = 15",42.
45. From (so) it appears that the coefficient of sina2,
in the Solar Equation of the equinoxes in longitude, is
14-2