CHAPTER V. 



TABLES OF NEPTUNE. 



30. F/II/I/IIHH i/ttt/ theory. 



The fundamental theory on which these tables are founded is as follows : 



1. Undisturbed elements of Neptime, referred to the mut <t-/!j>/!i- <ni<! Kji/i/id.r <>/ 

 the epocli. 



h zz eccentricity X * mc perihelion zz -f- 1201.69 

 k eccentricity X cos perihelion zz -f- 1275.57 

 p =. sine inclination X g i ne node zz -j- 4909.44 

 q zz sine inclination X cos node zz 4137.87 

 n zzmean motion in 365^ days zz 7864.935 

 E zz mean longitude at epoch zz 335 5' 38".91 

 Epoch 1850, Jan. 0, Greemvich mean noon. 



From these expressions we deduce 



n zz4317'30".3 



e - 0.0084962 



log a zz 1.4781414 



Period zz 164.782 Julian years. 



In log a we have included the constants of log ? introduced by the action of 

 the planets, and also the effect of the secular variation of the longitude of the 

 epoch, both of which are computed on p. 31. 



2. Secular and long-period, perturbations of the above elements. 

 These are taken without change from the table p. 39. 



The elements being corrected by the addition of these perturbations for the 

 epoch of computation, we thence deduce the elliptic place of the planet. 



3. Perturbations of the co-ordinates. 



To the elliptic place of the planet we apply corrections for- periodic perturb- 

 ations of the co-ordinates, as follows : 

 To the longitude in orbit, 



P tl sin I + P c .j cos I + P s , 2 sin 2 / -f P c . 2 cos 2 1 + &v 

 To the logarithm of the radius vector, 



R sl sin I + R c j cos I + 5r . 



To the north latitude, computed with the true longitude in orbit, 



B, , sin v -\- J3 cl cos v -f fy?o- 



70 



