Having computed the true elliptic anomaly and radius vector of Neptune by 

 the formulae 



tan i » = cot (45° — -I fp) ta.n ^ (jx- t -\- i — Tt -\- e" sin E) 

 r = a (1 — ■ e cos E) 



the heliocentric co-ordinates in the disturbed or instantaneous orbit are thus 

 found : 



o ; II 



X = [9.9998769] sin (137 12 52.04 -\- v -\- i v) {r -\- h r) 



y = [9.9662261] sin ( 47 46 27.35 + v -\- h v) {r -\- i r) 



z = [9.5800982] sin ( 43 53 37.36 -\- v ^ h v) {r -{- h r) 



Where, hv ^ Peirce's perturbations of the true anomaly. 



8 7-=" " " radius vector. 



In order that none of the data for this Ephemeris may be wanting, I subjoin 

 Professor Peirce's second Ephemeris of the Perturbations of Neptune, from 

 the Proceedings of the American Academy of Arts and Sciences for Decem- 

 ber, 1847. 



PROFESSOR PEIRCE'S EPHEMERIS OF THE PERTURBATIONS OF NEPTUNE'S TRUE LONGITUDE 

 AND RADIUS VECTOR, TO BE ADDED TO THE ELLIPTIC VALUES. 



Date. t> V h r 



May 



9, 1795 



-f 47.80 



+ 0.01283 



October 



1, 1846 



27.03 



0.01793 



January 



1, 1847 



27.13 



0.01728 



April 



1, 1847 



28.88 



0.01664 



July 



1, 1847 



25.75 



0.01602 



October 



1, 1847 



24.37 



0.01544 



January 



1, 1848 



22.58 



0.01491 



April 



1, 1848 



20.40 



0.01443 



July 



1, 1848 



17.89 



0.01400 



October 



1, 1848 



15.12 



0.01363 



January 



1, 1849 



12.18 



0.01332 



April 



1, 1849 



9.06 



0.01308 



July 



1, 1849 



5.84 



0.01290 



October 



1, 1849 



+ 2.59 



0.01277 



January 



1, 1850 



— 0.64 



0.01270 



April 



1, 1850 



— 3.83 



0.01270 



July 



1, 1850 



— 6.96 



0.01276 



October 



1, 1850 



— 9.96 



0.01288 



January 



1, 1851 



— 12.64 



0.01308 



