THE ORBIT OF URANUS. 5 



but without any details v/hatcvcr of the investigation, or any statement of the 

 methods employed. The minuteness of the residuals in the last column of the 

 preceding table shows that employing these perturbations by Neptune, and those 

 of Le Verrier by Jupiter and Saturn, we had a theory of Uranus from Avhich quite 

 accurate tables might have bqpn constructed. But this never seems to have been 

 done. The ephemeris of Uranus in the American Nautical Almanac was intended 

 to be founded on this theory, but the proper definitive elements do not seem to 

 have been adopted in the computations, as the ephemeris does not correspond with 

 the theory. 



Although twenty-five years have elapsed since the epoch of these researches, I 

 am not aware of any published work of importance on the theory of Uranus during 

 the interval. Mr. T. H. Safi'ord has, however, made a very extended investigation 

 of tlie subject, but has published nothing more than a brief general description of 

 his work, which may be found in the Monthly Notices of the Royal Astronomical 

 Society, Vol. 22. Like Professor Peirce, he took Le Verrier's perturbations by 

 Jupiter and Saturn, but, instead of using general perturbations by Neptune, he 

 computed the efi"ect of the action of this planet by mechanical quadratures for the 

 whole period of the observations of Uranus, and thus corrected the elements and 

 the mass of Neptune from modern observations alone. The mass in question 

 deduced was 



1 

 20039 

 Mr. Safford docs not give the representation of the modern observations, but pre- 

 sents the following comparison of the ancient ones, alongside Avhich we place for 

 comparison the corresponding numbers of Peirce's theory and those of the present 

 investigation. 



Excess of Observation over Theory. 



Date. No. of obs. Saffoni. Peirce. Newcomb. 



1090 1 + 5".0 — 0".8 —11" 



1715 3 —4.2 —8-7. — 8 



1150 2 —12 ) ^,9 



1T53 1 —0.2 i ^ "' 



175G 1 —0.9 —4.0 



1704 1 + 0.4 



1769 8 -f 4.5 +6.0 —1.4 



