THE ORBIT OF NEPTUNE. 49 



Taking the means of the separate results for equatorial ponat, we have, for the 

 apparent declinations of Neptune — 



May 8. May 10. 



O I II O I II 



Observed circle reading, 60 8 17 60 7 19 



Refraction, 1 39.0 1 39.0 



Corrected circle reading, 60 9 56.0 60 8 58.0 



Equatorial point, 48 49 18.4 48 49 19.6 



Apparent declination, —11 20 37.6 —11 19 38.4 



§ 23. Probable errors of thesd positions. 



So far as we can judge from the discordance of the clock errors, and equatorial 

 points derived from the several stars, the probable error of a single observation 

 over a single wire in right ascension would appear to be about 0\27, and the pro- 

 bable error of a single observed zenith distance about 2".2. The agreement of 

 the difference of the two observations with the computed motion of the planet 

 shows that neither observation is affected with any abnormal error. We conclude, 

 therefore, that the probable error of the normal place derived from the two obser- 

 vations is about 2".8 in R. A. and 1".5 in declination. 



Notwithstanding the magnitude of these probable errors, the observations will 

 be very valuable during the remainder of the present century, owing to the weight 

 with which they enter into the expressions of the elements. But in the twentieth 

 century the observations made after 1846 will enable astronomers to compute the 

 position of the planet in 1795 with a much higher degree of accuracy than La- 

 lande could observe it. 



A similar remark applies to Lamont's accidental zone observations in 1845. 

 Valuable during the first two or three years, they afterward ceased to be so, 

 because the theory soon became more accurate than the observation for an epoch 

 so near the time of optical discovery. Had they been made in 1820, they would 

 still have been valuable. 



Reduction of the modern observations. 



§ 24. The modern observations will be treated in the following manner. The 

 observations of each year will be divided into four groups, according to the time 

 of culmination of the planet. The first group will include all observations made 

 after 



h. m. h. m. 



13 30 m. t. 

 Second, between 10 30 and 13 30. 



Third, " 7 30 and 10 30. 



Fourth, all made before 7 30. 



The mean correction derived from each group will at first be regarded as the 

 true correction applicable to the mean of the times of observation. This involves 

 the supposition that the error of the ephemeris is changing uniformly during each 

 series of obsei'vations. If we could compare with an ephemeris of the heliocentric 



7 May, 1865. 



