58 



PROCEEDINGS OF THE AMERICAN ACADEMY 



" The most plausible value of r from this table is that in which 

 {n — n'f -)- (?i — i\!')^ is a minimum. This value by the table is 30 

 nearly, and for this value we have very nearly n z= n' zr: n" = fi. 

 Hence the orbit comes out nearly a circle, unless we suppose the plan- 

 et now to present the possible, but still improbable, case of a great ec- 

 centricity and true anomaly nearly 90°. 



" Accordingly, he selected for the next trial the circular hypothesis, 

 for which two places of thd planet sufficed, those of the 26th of Sep- 

 tember, from the mean of nine European observations, and the 26th of 

 December, from the mean of 33 transits and 11 measures in declina- 

 tion of Neptune (compared with the same two stars used in Septem- 

 ber) by himself with the Washington equatorial. All the small cor- 

 rections were taken into account. In this manner he obtained Elements 

 I. in the table below. These elements enabled him to compute an 

 ephemeris of Neptune for the six months following August 1st, 1846, 

 with which he compared one hundred and sixteen nights' works, 

 seventy of the European and forty-six of the Washington Observa- 

 tory, and derived from them sixteen normal places, which indicated 

 the following corrections of the geocentric longitude computed from 

 Elements I. 



Normal Places of Neptune. 



