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calculation of the disturbing effects of the various other planetsupon the path of Uranus (or rather of those of Saturn andJupiter , which woxdd he by far the most important), andthen to say, that any outstanding irregularity must be causedby an exterior planet.
If this could have been done, it might have been a compara-tively easy matter to calculate at any given moment, from theextent of that irregularity, where, and how large, such a planetmust he. But the only way in which mathematical processesat present enable us to investigate the positions and movementsof the planets, is by a method of successive approximation,which involves the effect of any one upon all the rest, and ofall the rest upon it, in a sort of inextricable intimacy, suchthat it is impossible to separate any one of these effects fromthe remainder. The planets must all he supposed in our cal-culations to be acting and reacting upon the movements ofeach and all, at one and the same time, and even to bemutually acting and reacting upon one another’s disturbingeffects.
It was, however, only natural that both Le Yerrier andAdams should imagine, from the analogy of the known planets,that, if another large one existed still more remote from theSun, the size of its orbit would approximately follow Bode’slaw, and that it would, like the rest, most probably movenearly in the plane of the ecliptic. Having made these sup-positions, they next determined, by very complicated calcula-tions, the probable position of such a planet at the time at whichtheir investigations were made, i.e., in the year 1846. And sonearly did their results indicate its true place, that it was found,by Dr. dalle, of Berlin, the first night that he looked for it, inthe locality assigned by Le, Yerrier; while it was afterwardsshown, that the calculations of Adams were amply sufficient tohave detected it with almost equal facility. In fact, evenbefore Dr. dalle’s announcement of Le Verrier ’s discovery, ithad been twice seen at the Observatory at Cambridge, in theneighbourhood in which Mr. Adams had requested that searchmight be made for it. For want, however, of sufficientlyaccurate charts, it was for the time being recorded as a star