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126 each other, the positions of the supposed planet being 120° apart. Had Leverrier and Adams fallen upon either of the other two, Neptune would not have been discovered.

He next showed that at 35.3 astronomical units, an important change takes place in the character of the perturbations because of the commensurability of period of a planet revolving there with that of Uranus. In consequence of which, a planet inside of this limit might equally account for the observed perturbations with the one outside of it supposed by Leverrier. This Neptune actually did. From not considering wide enough limits, Leverrier had found one solution, Neptune fulfilled the other. And Bode's law was responsible for this. Had Bode's law not been taken originally as basis for the disturber's distance, those two great geometers, Leverrier and Adams, might have looked inside.

This more general solution, as Peirce was careful to state, does not detract from the honor due either to Leverrier or to Adams. Their masterly calculations, the difficulty of which no one who has not had some experience of the subject can appreciate, remain as an imperishable monument to both, as does also Peirce's to him.