Royal Astronomical Society. 131 



nomer Royal the results of the general reduction of the Greenwich 

 Planetary Observations. 



In the meantime the Gottingen Academy had proposed for the 

 subject of a prize the theory of Uranus, and though the author had 

 no hope of being able to complete an essay in time to compete for 

 the prize, he was stimulated by the publication of this proposal again 

 to enter on the investigation. He now took into account the pos- 

 sible eccentricity of the disturbing planet to the first order, retaining 

 the same assumption for mean distance. For the modern observa- 

 tions, the tabular errors used, as far as 1830, were exclusively those 

 of the Greenwich Observations, except one by Bessel in 1823 ; after 

 1830 the Cambridge and Greenwich determinations and those in 

 the Astronomische Nachrichten were used. Those for the obser- 

 vations anterior to the discovery of the planet were taken from 

 Bouvard. 



Results for the elements of the disturbing planet were obtained, 

 which were communicated in September 1845 to Prof. Challis, and 

 in October 1 845 (slightly altered) to the Astronomer Royal. After- 

 wards the investigation was repeated, supposing tlie mean distance 

 diminished by about -^^ part. The results were communicated to 

 the Astronomer Royal in September 1 846. They seemed to show that 

 the mean distance ought to be still further diminished. 



The author, after adverting to the dates of M. Le Verrier's papers, 

 and showing that his own calculations were earlier in date, says, " I 

 mention these dates merely to show that my results were arrived at 

 independently and previously to the publication of M. Le Verrier, 

 and not with the intention of interfering with his just claims to the 

 honours of the discovery ; for there is no doubt that his researches 

 were first published to the world, and led to the actual discovery of 

 the planet by Dr. Galle, so that the facts stated above cannot de- 

 tract, in the slightest degree, from the credit due to A'l. Le Verrier. 

 The investigations proceeded as follows : — First, to diminish the 

 number of equations, the results were collected in groups of three 

 years each ; and these were so arranged as to present results nearly 

 independent of the error of radius vector. Thus twenty-one equations 

 were obtained ; and these, without extension for the two or three 

 last years (which might subsequently have been included, but which 

 would have disturbed the similarity of the calculations) were also 

 used in the subsequent calculations for a different assumed mean di- 

 stance. Then all the principal inequalities in the recognised theory 

 of Uranus were verified, and corrections for an error pointed out by 

 Bessel, and for the altered mass of Jupiter, were applied, as well as 

 for some terms of the second order of masses pointed out by Hansen. 

 Other inequalities of higher orders were neglected ; as their effects 

 may be represented, either by a very slow alteration of the epoch 

 and mean motion, or by a very slow alteration of the perihelion and 

 eccentricity ; both which may, without sensible error, be assumed 

 as constant, during the comparatively short period through which 

 Uranus has been observed. I'hc author then gives a table of the 

 differences between tlie theoretical longitudes (thus corrected), and 

 the observed longitudes : the maximum values arc as follows : — 



