a 
; ' - ee 
238 E.F. Burr on the Neptunian Theory of Uranus. 
corrections of the longitudes of the epoch and perihelion. ‘There 
it always oscillates beneath the tenth of a second. The other 
elements were taken from Bouvard’s tables of Uranus, and are 
the same with those employed by Mr. Adams. He assumed the 
ancient residual perturbations of Bouvard, and obtained those of 
modern date by a comparison of his ephemeris, corrected by the 
‘equatioys of Bessel and Hansen, with English and German ob- 
servations. + 
We have taken the time of Uranus’s mean opposition in 1810 
as the epoch of the formule. This diminishes the effect of some 
By comparing the planetary eccentricities. for 1750 with those 
for 1800, it will be seen that,no one changes its value in the half- 
century by more than 0:00022; while the variation of most of 
them is much less. Assume the eccentricity of Neptune to be 
in error to this amount., The general effect of this error on ine- 
qualities of the first order in longitude is, 
Lie 0-00022M sin. a, | soln 
Assigning to the general factors their greatest values in the present 
eory, : 
M=m/’ 1915-65 
sin r= .7946 
4 
constant term. Similarly it may be found that the change in the 
longitudes of the perihelia. of ‘Se planets during the fifty years 
the subsequent variation of which is 0-1. The terms of higher 
orders depending on these errors, as well as those depending on 
corresponding errors in inclination and longitude of the node, are 
onsiderable with respeet. to the preceding. Hence each of 
them is either less than the error to which we are probably liable 
