50 DETERMINATION OF THE ORBIT [2 



The first position on which the above results depend, that of August 4, 

 was obtained 16 clays before the planet was in opposition, and the last 

 position, that of January 15, 32 days before it was in conjunction. The 

 great variation of the planet's elongation from the Sun in this interval 

 is favourable to the correctness of the above determinations, which, although 

 they cannot pretend to extreme accuracy on account of the short period 

 over which the observations extend, are yet entitled to considerable weight. 

 Mr Adams has in fact calculated the probable errors of the above results 

 by supposing each observation of Right Ascension or of North Polar Distance 

 to be liable to an error of 3", and he finds that there is little probability 

 of their receiving any great amount of correction by taking account of 

 future observations. It may be remarked that the first and second approxi- 

 mations do not differ by any large quantities. Hence it may be inferred 

 that the places of August are deserving of confidence, and that, on account 

 of the extension given to the period of observation by including those 

 places, this second approximation to the elements is more accurate than 

 it would have been if it depended solely on observations made since the 

 discovery of the planet. 



The calculations give 59' 8" for the planet's heliocentric motion from 

 August 4 to January 15. This is so small an arc that it is not possible to 

 deduce with any degree of certainty those elements the determination of 

 which depends on change of the heliocentric distance. Mr Adams has, how- 

 ever, discussed the observations with this object in view, and has obtained 

 certain limiting results, which, as possessing considerable interest, I here 

 subjoin. 



The eccentricity of the orbit cannot exceed 0'18. The most probable 

 value is 0'06, which differs but little from the eccentricities of the orbits of 

 Jupiter, Saturn, and Uranus. 



The most probable longitude of perihelion is 49 58', and the probable 

 true anomaly 276 43', according to which the planet is near the extremity 

 of the latus rectum and is descending towards perihelion. These results 

 are extremely uncertain. 



The mean distance is 30'35, with a probable error of 0'25 ; and the 

 corresponding sidereal period is 167 years, with a probable error of about 

 2 years. It is remarkable that the periodic time is very nearly double 

 that of Uranus ; so that these two bodies will offer an instance of mutual 



