Soon after Uranus was discovered, certain irregularities in its motion were observed, which could not be explained. It is well known that the planets are all the while disturbing each other's motions, so that none of them describe perfect ellipses. These mutual disturbances are called _perturbations_. In the case of Uranus it was found, that, after making due allowance for the action of all the known planets, there were still certain perturbations in its course which had not been accounted for. This led astronomers to the suspicion that these might be caused by an unknown planet. Leverrier in France, and Adams in England, independently of each other, set themselves the difficult problem of computing the position and magnitude of a planet which would produce these perturbations. Both, by a most laborious computation, showed that the perturbations were such as would be produced by a planet revolving about the sun at about twice the distance of Uranus, and having a mass somewhat greater than that of this planet; and both pointed out the same part of the heavens as that in which the planet ought to be found at that time. Almost immediately after they had announced the conclusion to which they had arrived, the planet was found with the telescope. The astronomer who was searching for the planet at the suggestion of Leverrier was the first to recognize it: hence Leverrier has obtained the chief credit of the discovery. The observed planet is proved to be nearer than the one predicted by Leverrier and Adams, and therefore of smaller magnitude. 281. _The Observed Planet not the Predicted One._--Professor Peirce always maintained that the planet found by observation was not the one whose existence had been predicted by Leverrier and Adams, though its action would completely explain all the irregularities in the motion of Uranus. His last statement on this point is as follows: "My position is, that there were _two possible planets_, either of which might have caused the observed irregular motions of Uranus. Each planet excluded the other; so that, if one was, the other was not. They coincided in direction from the earth at certain epochs, once in six hundred and fifty years. It was at one of these epochs that the prediction was made, and at no other time for six centuries could the prediction of the one planet have revealed the other. The observed planet was not the predicted one." 282. _Bode's Law Disproved._--The following table gives the distances of the planets according to Bode's law, their actual distances, and the error of the law in each case:-- Planet. Numbers of Actual Errors. Bode. Distances. Mercury 0 + 4 = 4 3.9 0.1 Venus 3 + 4 = 7 7.2 0.2 Earth 6 + 4 = 10 10.0 0.0 Mars 12 + 4 = 16 15.2 0.8