Let us suppose that a planet is revolving outside Uranus, at a distance which is suggested by the several distances at which the other planets are dispersed around the sun.  Let us assume that this outer planet has started on its course, in a prescribed path, and that it has a certain mass.  It will, of course, disturb the motion of Uranus, and in consequence of that disturbance Uranus will follow a path the nature of which can be determined by calculation.  It will, however, generally be found that the path so ascertained does not tally with the actual path which observations have indicated for Uranus.  This demonstrates that the assumed circumstances of the unknown planet must be in some respects erroneous, and the astronomer commences afresh with an amended orbit.  At last after many trials, Le Verrier ascertained that, by assuming a certain size, shape, and position for the unknown Planet’s orbit, and a certain value for the mass of the hypothetical body, it would be possible to account for the observed disturbances of Uranus.  Gradually it became clear to the perception of this consummate mathematician, not only that the difficulties in the movements of Uranus could be thus explained, but that no other explanation need be sought for.  It accordingly appeared that a planet possessing the mass which he had assigned, and moving in the orbit which his calculations had indicated, must indeed exist, though no eye had ever beheld any such body.  Here was, indeed, an astonishing result.  The mathematician sitting at his desk, by studying the observations which had been supplied to him of one planet, is able to discover the existence of another planet, and even to assign the very position which it must occupy, ere ever the telescope is invoked for its discovery.

Thus it was that the calculations of Le Verrier narrowed greatly the area to be scrutinised in the telescopic search which was presently to be instituted.  It was already known, as we have just pointed out, that the planet must lie somewhere on the ecliptic.  The French mathematician had now further indicated the spot on the ecliptic at which, according to his calculations, the planet must actually be found.  And now for an episode in this history which will be celebrated so long as science shall endure.  It is nothing less than the telescopic confirmation of the existence of this new planet, which had previously been indicated only by mathematical calculation.  Le Verrier had not himself the instruments necessary for studying the heavens, nor did he possess the skill of the practical astronomer.  He, therefore, wrote to Dr. Galle, of the Observatory at Berlin, requesting him to undertake a telescopic search for the new planet in the vicinity which the mathematical calculation had indicated for the whereabouts of the planet at that particular time.  Le Verrier added that he thought the planet ought to admit of being recognised by the possession of a disc sufficiently definite to mark the distinction between it and the surrounding stars.