ae 
370, A. Hall on the Secular Perturbations of the Planets, 
Art. XXXIX.—On the Secular Perturbations of the Planets 4 
by AsaPH HALL. 
In view of the recent consideration in geological speculations 
of the secular inequalities of the excentricity of the earth’s 
orbit, it may be worth while to state briefly the method of 
treating secular perturbations, and our present knowledge of the 
su 
Denoting by ¢, 7, 9, and § the excentricity, the longitude of 
the perihelion, the inclination of the orbit and the longitude of 
its ascending node, it has been found easier in the discussion of 
the problem to substitute for these quantities four others which 
are simple functions of them; and thus are assumed 
A=e sin 2, ==tang ¢ sin 4, 
l=e cos 2, q=tang ¢ cos 6. 
A=N sin t 1=—N cos t : 
V=N' oat teh l'=N' cos 4 ay &e. 
Differentiating these equations and substituting the value of 
dh dh’ al ; : : Se 
at’ dt? dt’ &c., in the differential equations and then eliminating 
the ratios of the coefficients N, N’, N”, &c., a numerical equa- 
tion is obtained for the determination of g. This equation will 
