66 THEORBITOFURANUS. 



I have submitted these perturbations to such duplicate computations and other 

 checks as lead me to believe that none of the terms can be in error by more than 

 a small fraction of a second, but, as they are not intended to form the basis of a 

 definitive theory of Saturn, I do not vouch for their absolute precision. 



In this provisional correction of tlic orbit of Saturn only heliocentric longitudes 

 have been employed. These were derived for a series of dates from Airy's reduc- 

 tion of the Greenwich observations, the modern Greenwich observations, and the 

 Washington observations. 



For these dates the value of n^z for Saturn was computed from the formulae 

 found on pages 189 and 190 of the work of Hansen, already quoted, omitting all 

 terms less than 1", and including only tenths of seconds in the results. The dates, 

 the resulting values of nh, of the factor ei cos {g -\- \ niz) -\- 2e.. cos 2 (^ -]- | ntz), 

 and of the concluded h' are as follows. The formula? for Iv is 



lv = \.02lG nz \\ +e,cos(r/ + |M'2) + 2e,cos2(i/ + lnc'z)(. 



The perturbations by Uranus and Neptune were computed from the values of 

 their terms just given. The principal terms, the sum of which make up the helio- 

 centric longitude resulting from the adopted elements, are shown in the first of the 

 following tables. 



In the next table we have after the date the heliocentric longitude from Bouvard's 

 Tables, as deduced from the longitudes given in Airy's reductions of the Grceit- 

 wich Observations, from the Astronoyiuficheft JaJiibnch for 1831, and from the 

 Nautical Almanac. Then follow the corrections, roughly deduced from observa- 

 tions made near the opposition. Adding these columns, we have the longitude 



