18 



We shall also put 



THE ORBIT or NEPTUNE. 



' 1 3 2 



a ^ 



Hi — —^ — — j-j 

 a (T 



r, B cB 



a fi 



c being a constant, equal to unity if we neglect the change of mean distance pro- 

 duced by the action of other planets. We then have 



hv zz mac2 F sin N, 

 h log T :=. mac2,Ri cos N, 

 5/3 = mac^By sin N. 



Substituting the above developments for the v's in V, B, and B, we have 



• FiW =(1 — it^— ie")(— 1— ^2 — 6^-'' — 19^*) 

 + ^=(1 — 2^2—30^^0 



■I7'(2) ^/ n 3 ,,2 2i ,,3\ 



T7'(3) p ( 1 _(_ 1 ,,2 _(_ 3 ,,3 I 19 ..■t\ 



Fi'^) := e' (— -t + (t^^ + 9 ^« + 25 f^*) 



F/^) =(f (— I— 3^i-— 27 ^•' — 135^") 



F/^)zre^ ( f+J^f^=+ A/.«) 



Fr^ = 6= (- 1- 1^2+ 1^3) 



F^zree'C- i+ 1^2+ ^^«) 



(21) 



(22) 



i^/i) - (1_ le^ _ 1 e2) (1 _ 2 ^2 — 6 ^-^ — 14 ft* 

 + e^-(_l_4^t2_24^3) 



i2/^)=ee'( f_ lf.2- V>^) 



i2« =e' (— i— 2^2— 6^^— 17(1^*) 



R^''^ =d ( f— 6^2— 30(«=' — 116^*) 



i?/^)=e^ ( f-,1^^2- ^V/^-^) 



i?r^ = e2( i- if.^+ f^^) 



A™ = 6e'(- i- 1^2- |^«) 



i2/i^) = e«( y_aj^2_4|5^3) 

 R^^'> = u^{ 1— 2^=+ 14fi«) 



5/"'= w(2 + 2iti2+ 2^*) 

 5/*'=:e'«(l+4;u^— 6iu-') 

 5W=:e''w(l+4^2— 6^^) 

 B,^^z:zeu{l+\li' + i^^') 



^Oy.') 



(23) 



(24) 



