1 PROFESSOR CHALLIS'S REPORT 



was now evident that the ancient observations had been rejected on insufficient grounds, 

 and that from some unknown cause the theory was in fault. Were the Tables cal- 

 culated inaccurately? The difference between observation and theory (amounting in 

 1841 to 96" of geocentric longitude) was too great, and Bouvard's calculations were 

 made with too much care to allow of this explanation. The effect of small terms 

 neglected in the calculation of the perturbations caused by Jupiter and Saturn, could 

 not be supposed to bear any considerable proportion to the observed amount of error. 

 This state of the theory suggested to several astronomers the idea of disturbances, 

 caused by an undiscovered planet more distant than Uranus. But there is no evidence 

 of this hypothesis having been put to the test of calculation previous to 1843. The 

 usual problem of perturbations is to find the disturbing action of one body on another, 

 by knowing the positions of both. Here an inverse problem, hitherto untried, was to 

 be solved ; viz. from known disturbances of a planet in known positions, to find the 

 place of the disturbing body at a given time. Mr Adams, Fellow of St John's College, 

 showed me a memorandum made in 1841, recording his intention of attempting to solve 

 this problem as soon as he had taken his degree of B.A. Accordingly, after graduating 

 in January 1843, he obtained an approximate solution by supposing the disturbing body 

 to move in a circle at twice the distance of Uranus from the Sun. The result so far 

 satisfied the observed anomalies in the motion of Uranus, as to induce him to enter upon 

 an exact solution. For this purpose he required reduced observations made in the years 

 1818 1826, and requested my intervention to obtain them from Greenwich. The 

 Astronomer Royal, on my application, immediately supplied (February 15, 1844) all the 

 heliocentric errors of Uranus in longitude and latitude, from 1754 to 1830, completely 

 reduced. Mr Adams was now furnished with ample data from observation, and his next 

 care was to ascertain whether Bouvard's theoretical calculations were correct enough for 

 his purpose. He tested the accuracy of the principal terms of the perturbations caused 

 by Jupiter and Saturn, and concluded that the small terms which Bouvard had not 

 taken into account would not sensibly affect the final results, the chief of them being 

 either of long period or of a period nearly equal to that of Uranus. Besides which he 

 introduced into the theory several corrections which had been derived from observation 

 and calculation by different astronomers since 1821. The calculations were completed in 

 1845. In September of that year, Mr Adams placed in my hands a paper containing 

 numerical values of the mean longitude at a given epoch, longitude of perihelion, eccentricity 

 of orbit, mass, and geocentric longitude, September 30, of the supposed disturbing planet, 

 which he calls by anticipation " The New Planet," evidently showing the conviction in 

 his own mind of the reality of its existence. Towards the end of the next month, a 

 communication of results slightly different was made to the Astronomer Royal, with the 

 addition of what was far more important, viz. a list of the residual errors of the mean 

 longitude of Uranus, for a period extending from 1690 to 1840, after taking account of 

 the disturbing effect of the supposed planet. This comparison of observation with the 

 theory implied the determination of all the unknown quantities of the problem, both the 

 corrections of the elements of Uranus and the elements of the disturbing body. The 

 smallness of the residual errors proved that the new theory was adequate to the expla- 

 nation of the observed anomalies in the motion of Uranus, and that as the error of 

 longitude was corrected for a period of at least 130 years, the error of radius vector was 



