OF UEANUS AND NEPTUNE. XXXIX 



and aC= --(&,<»- a), 



2 

 and R[ = mC'cosxJ/, 



where o'C = - - (V*> - -,) . 



Then the more important parts of the disturbance of mean longitude depending on R t 



and R' are 



„ 3rrin 2 aC . , y . 8mri*a'Cf . 



and ^=^r+^r 



de s de s 

 x (D x e sin <£ + Z> 2 e'sin <£'), 



x {D x e sin (<£ - \J/) + D 2 e sin (<£' - \J/)}, 

 neglecting the terms involving <p + \j/, and (£' + \|/-. 



J i J i 



d$R) 

 de 



(]8m'V I n \ % mmmn* ( ri \ 2 , 1 



x a \D v e sin (X + ■sr) + D 2 e'sin (X + •nr')}. 

 Again, let &S, - -£* £ + -rV ^, 



de de' 



where £ and £' depend on i2 and i?', 



„ 6m'n 2 a . _ . _ , . , .. 



and .-. C = 7 775 (Aesin0+Z> 2 esin0), 



(2rc - 3n y 



9mn' 2 d , . .^ 



^ = - ( aw - 8B O' (A< " in0+ ' ° 0); 



d $R) 



then as before, 3w 2 a if 



de 



= + l^sinl" \»n - 8»'J ° + 2w 2 sinl" U» - S»7 ° J 

 x a{D,e sin (X + ■&) + D % e sin (X + T«r')}. 



Now n = 2n nearly, .-. T = 2 = —7 nearly, 



17 n -n 2ra - 3n 



r I 



and ; = 1 = —7 nearly ; 



» - n 2n -3n 



