CHAPTER V. 



TABLES OF NEPTUNE. 



§ 3G. Fundamentcd tlieory. 



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



1. Undisturbed elements of Neptune, referred to the mean. ecliptic and equinox of 

 tlie epoch. 



h =z eccentricity X ^^ine perihelion =: + 1201.69 

 Z; m eccentricity X cos perihelion :zi + 1275.57 

 p z= sine inclination X sine node rz + 4909.44 

 q ^z sine inclination X cos node rz: — 4137.87 

 n := mean motion in 365^ days zz 7864.935 

 £ =z mean longitude at epoch z= 335° 5' 3S".91 



Epoch 1850, Jan. 0, Greenwich mean noon. 



From these expressions we deduce 



7t =43° 17'30".3 



e z= 0.0084962 



log« =1.4781414 



Period =z 164.782 Julian years. 



In log a we have included the constants of log r 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 cdiove 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, 



/^,i sin I -f /^,i cos I + P,.o sin 2 I + P,, cos 2 Z -f ho- 



To the logarithm of the radius vector, 



R,i sin I -f i^ci cos I -{- hr<s- 



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



i?,,,] sin V -\- 5,1 cos V -\- h(3o. 



