2] ON THE PERTURBATIONS OF URANUS. 41 



HYPOTHESIS II. 



a s ar Y a 



- dr = --j-S4-- 7 Q'000144 



r r rfe 2 



+ 0-000073 cos {nt-n't + e-e 1 } 



+ 0-000266 cos 2 {nt - n't + e - e'} 



+ 0-000115 cos3{nt-rit + e-t'} 



+ 0-000016 cos {n't + f'-vr} 



-0-000188 cos 



+ 0-000068 cos {nt - 2n't + e - 2e' + w'} 



- 0-000053 cos {Int - 3n't + 2e - 3e' + 



+ 0-000165 cos 



75 X 



58. The values of S and , for some recent years are the following: 



HYPOTHESIS I. 



HYPOTHESIS II. 



1834 21-46 -20-85 



1840 74-40 -31-62 



1846 -145-91 -38-30 



Hence, by means of the above formulae, we find the corrections of the 

 tabular radius vector to be 



Year. Hypothesis I. Hypothesis II. 



1834 +0-00505 +0-00492 



1840 +0-00722 +0-00696 



1846 +0-00868 +0-00825 



A. 6 



