2] ON THE PERTURBATIONS OF URANUS. 7 



vations, especially since, with the exception of Flamsteed's first observation, 

 which is more than twenty years anterior to any of the others, they are 

 mutually confirmatory of each other. 



2. Now that the discovery of another planet has confirmed in the 

 most brilliant manner the conclusions of analysis, and enabled us with 

 certainty to refer these irregularities to their true cause, it is unnecessary 

 for me to enter at length upon the reasons which led me to reject the 

 various other hypotheses which had been formed to account for them. It 

 is sufficient to say, that they all appeared to be very improbable in them- 

 selves, and incapable of being tested by any exact calculation. Some had 

 even supposed that, at the great distance of Uranus from the sun, the 

 law of attraction becomes different from that of the inverse square of the 

 distance. But the law of gravitation was too firmly established for this 

 to be admitted till every other hypothesis had failed, and I felt convinced 

 that in this, as in every previous instance of the kind, the discrepancies 

 which had for a time thrown doubts on the truth of the law, would 

 eventually afford the most striking confirmation of it. 



3. My attention was first directed to this subject several years since, 

 by reading Mr Airy's valuable Report on the recent progress of Astronomy. 

 I find among my papers the following memorandum, dated July 3, 1841 : 

 " Formed a design, in the beginning of this week, of investigating, as 

 soon as possible after taking my degree, the irregularities in the motion 

 of Uranus, which are yet unaccounted for, in order to find whether they 

 may be attributed to the action of an undiscovered planet beyond it, and, 

 if possible, thence to determine approximately the elements of its orbit, &c., 

 which would probably lead to its discovery." Accordingly, in 1843, I at- 

 tempted a first solution of the problem, assuming the orbit to be a circle, 

 with a radius equal to twice the mean distance of Uranus from the sun. 

 Some assumption as to the mean distance was clearly necessary in the 

 first instance, and Bode's law appeared to render it probable that the above 

 would not be far from the truth. This investigation was founded exclusively 

 on the modern observations, and the errors of the tables were taken from 

 those given in the equations of condition of Bouvard's tables as far as 

 the year 1821, and subsequently from the observations given in the Astrono- 

 mische Nachrichten, and from the Cambridge and Greenwich Observations. 

 The result shewed that a good general agreement between theory and obser- 

 vation might be obtained ; but the larger differences occurring in years where 

 the observations used were deficient in number, and the Greenwich Planetary 



