2] ON THE PERTURBATIONS OF URANUS. 



Theory of Uranus, as disturbed by the action of Jupiter and Saturn, in 

 which he pointed out several small inequalities which had previously been 

 neglected ; and in June, of the present year, he followed up this investi- 

 gation by a memoir, in which he attributed the residual disturbances to 

 the action of another planet at a distance from the sun equal to twice 

 that of Uranus, and found a longitude for the new planet agreeing very 

 nearly with the result which I had obtained on the same hypothesis. On 

 the 31st of August, he presented to the Academy a more complete investi- 

 gation, in which he determined the mass and the elements of the orbit 

 of the new planet, and also obtained limiting values of the mean distance 

 and heliocentric longitude. I mention these dates merely to shew that 

 my results were arrived at independently, and previously to the publication 

 of those 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 

 detract, in the slightest degree, from the credit due to M. Le Verrier. 



6. In order not to have an inconvenient number of equations of 

 condition, I divided the modern observations into groups, each including a 

 period of three years, and as Mr Airy had shewn that the error of the 

 tabular radius vector was sometimes considerable, I either selected those 

 observations which were made near opposition, or combined the others in 

 such a manner that the results should be nearly free from the effects of 

 this error. From the observations of each group, the error of the tables 

 in heliocentric longitude was found, corresponding to the time of mean 

 opposition in the middle year of the group. Thus were formed 21 normal 

 errors of the tables, corresponding to as many equidistant periods between 

 1780 and 1840. The error for 1780 was found by interpolating between 

 the errors of 1781, 1782, and 1783, and those given by the ancient 

 observations of 1769 and 1771; and though not entitled to the same 

 weight as the others, cannot, I think, be liable to much uncertainty. In 

 my last calculations I might have used more recent observations, but in 

 order to obtain the effect due to the change of mean distance, it was 

 necessary that the investigation should be founded on the same elements 

 as before, and the later observations might be used as a test of the theory. 



7. In order to satisfy myself that there was no important error in 

 Bouvard's tables, I re-computed all the principal inequalities produced by the 

 action of Jupiter and Saturn, and found no difference of any consequence, 



