236 
MR. LUBBOCK’S RESEARCHES IN PHYSICAL ASTRONOMY. 
The term b 3>2 e e { cos (nr — nr,) in the development of R gives 
d nr — — 't-OL b* o e, cos (nr — nr.) 
4a,°~ 3.. I ,/ 
a-n 
V 
h = e sin nr 
, a-n , . , x 
(le = — -t), 3e,sin (nr — nr.) 
4a a 3,2 i v y/ 
Jf Zi = e sin nr Z = e cos nr 
d Zi = e cos nr d nr + sin nr d e 
e, sin nr^ 
Z ; = e y cos nr / 
d Z = — e sin nr d nr + cos nr d e = - 
The integrals of which equations are 
li = IVsin (g t + C) 1= N cos (g t + C) 
Zi ; = IV ( sin (g t + C) 1 = N t cos (g t + C) 
a 2 re , „ „ a 2 re , , 
• 4^5 03,2 e / c °s CT /— — 4-^5 ^3,2 ^ 
a 2 re , . a-n , , 
—— Oo q 61 sin — —- o-l n /ii 
4 a* 3,2 ' 1 4 a/ 2 3,2 ' 
ATg= - 
a-re 
4a7 2 
e cos (71Z + g — nr) = IV cos (re — g) Z + s — C) 
which will agree with the previous solution, p. 233, if 
N = e i/> £ — C = e — nr ( , nk,= — g. 
This theory of the secular inequalities appears to require to be extended to 
the terms depending on higher powers of the eccentricities ; but I may remark 
that the coefficient of the term e 2 e 2 cos (2 nr — 2 st,) in the development of R 
vanishes in the theory of the moon, or at least such part of it as is multiplied 
