579] GOLD MEDAL OF THE SOCIETY TO PROFESSOR SIMON NEWCOMB. 
183 
to be founded on the theory, but the proper definitive elements do not seem to have 
been adopted: and in the Nautical Almanac for the years up to 1876, Bouvard’s Tables 
of TJranus were still employed; for the year 1877 the ephemeris is derived from 
heliocentric places communicated by Prof. Newcomb. 
An extended investigation of the subject was made by Safford, but only a brief 
general description of his results is published, Monthly Notices, R.A.S., vol. xxii. (1862). 
The effect of Neptune was here computed by mechanical quadratures; and corrections 
were obtained for the mass of Neptune and elements of Uranus. 
Professor Newcomb’s Tables of Uranus have only recently appeared. They are 
published in the Smithsonian Contributions under the title “ An Investigation of the 
Orbit of Uranus, with General Tables of its Motion,” (accepted for publication February, 
1873), forming a volume of about 300 pages. The work was undertaken as far back 
as 1859, but the labour devoted to it at first amounted to little more than tentative 
efforts to obtain numerical data of sufficient accuracy to serve as a basis of the theory, 
and to decide on a satisfactory way of computing the general perturbations. First, the 
elements of Neptune had to be corrected, and this led to the foregoing investigation 
of that planet: it then appeared that the received elements of Uranus also differed 
too widely from the truth to serve as the basis of the work, and they were provisionally 
corrected by a series of heliocentric longitudes, derived from observations extending from 
1781 to 1861. Finally, it was found that the adopted method of computing the 
perturbations, that of the “ variation of the elements,” was practically inapplicable to 
the computation of the more difficult terms, viz. those of the second order in regard 
to the disturbing force. While entertaining a high opinion of Hansen’s method as at 
once general, practicable, and fully developed, the author conceived that it was on the 
whole preferable to express the perturbations directly in terms of the time, owing to 
the ease with which the results of different investigations could be compared, and 
corrections to the theory introduced; and under these circumstances he worked out the 
method described in the first chapter of his treatise, not closely examining how much 
it contained that was essentially new. With 'these improved elements and methods the 
work was recommenced in 1868; the investigation has occupied him during the sub 
sequent five years: and, though aided by computers, every part of the work has been 
done under his immediate direction, and as nearly as possible in the same way as if 
he had done it himself: a result in some cases obtained only by an amount of labour 
approximating to that saved by the employment of the computer. 
The leading steps of the investigation correspond to those for Neptune: there is, 
first, the theoretical investigation already referred to; secondly, the formation of the 
provisional theory with assumed elements; thirdly, the comparison with observation; 
and here the observations are the accidental ones previous to the discovery of Uranus 
as a planet by Herschel in 1781, and the subsequent systematic ones of twelve 
Observatories, extending over intervals during periods from 1781 to 1872; all which 
have to be freed from systematic differences, and reduced to a concordant system as 
before: the operation is facilitated by the existence, since 1830, of ephemerides com 
puted from Bouvard’s Tables serving as an intermediate term for the comparison of