E.. F’. Burr on the Neptunian Theory of Uranus. 243 
theory of Uranus. This has already been done by Messrs. Le Ver- 
rier and Adams. The values which they have obtained differ 
widely from each ot and Poca as will be seen, essentially 
different final-resv ’ 
” et G = Ganskaitel longit . 
H = Heliocentric mee reduced to the ecliptic. 
ry = Radius vector reduced to the ecliptic. 
dG = Residual perturbation of true } geocentric longitude, 
R = Radius vector of the eaith. 
s°= Its op doe 
N =Nutation. © 
Then the residual tote of true heliocentric Idhginiaiess 
. cos (G 
~ r.cos (G—! me “7 
which, near ~ time of pa apap practically reduces to. 
dG.* 
Hence w we Lite 7% * 
ae Bf Verrier's. Adams’. . Le Verrier’s.| Adams’. 
(1715:17)=| 462"9 | 473"-8'| (181640)— +327 | 422-9 
95495) pie oe ‘5 | (1819-44) | 429-2 | 4120-7 
tr64038 —21-4 | —34 -9 ] (1822-47 +28 -1 | 421-0 
(1771-95). | —11*4 | — 23 1895351) +271: | 418-2 
(1783-00) | +17-7 | + 8:4 | (1828-55) | +16 -6 | +10:8 
(1789:07) | +28 -7 | +19 6 t1831 38) OT a 
(179515) | 427-4 | 121-4 | (183461) “66 | __ 90+) 
(1801-22) | +81 -6 | +22 -2 | (1837-65) | —42 -4 | —42-7 
(1807-29) | +35 -0 | 422-1] (184069) | +65 -4 | —66-6 
© —-« (1818-36) | +35 -7 | 4229 0 
From these two systems of values and an application of the 
method of least squares, are derived the following values of the 
arbitrary constants of our equations of condition. It is to be ob- 
served that these are ag strictly. the ess rasige corrections of the 
elements of Uranus for the epoch, but these corrections together 
with certain other ou -quantities to which —- ion was made 
at the commencement of the article. 
Mass of Neptutie, ° ris bey + a wae ae soit 
to Residual ~~ Due to Residual | 
Due id 
cs fags Perturbations « of Adams. . Perturbations of 1a Versio 
fy. °, i peo 4 ne a f = 6085"-0 | —s274"-2 
pans og based on the tesidual perturbations of Le Vei 
were pssst from the modern equations of conditi ion alone: the 
others were furnished “ the modern and ancient.equations united. 
The fi sults are comprised in the following table. . It ¢ ex- 
hibits the pagan of, perturbation of true heliocentric longitude, 
which, according to our theory, remains unexplained after the 
