58 



THE ORBIT OF TJRAXUS. 



perturbations of the longitude deduced from all the remaining terms of the per- 

 turbations of the elements. The sum of the columns o^ 2 and &v s shows the entire 

 perturbations computed by the method of variation of elements. Thus, in 6^ 

 and &v 2 -j- 33 we have two complete sets of perturbations computed by methods 

 entirely independent. The differences of the results, expressed in thousandths of 

 a second, are given in the last two columns of the table. 



This comparison gives rise to remarks similar to those suggested by the per- 

 turbations of Saturn computed by the same methods. The only terms in which 

 the difference of results amounts to as much as one-tenth of a second are those of 

 very long period, and those very nearly the period of Uranus, where a more accu- 

 rate value is not at present of great importance, because the error will be com- 

 pensated by the corrections of the element during several centuries. 



