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Rh was strikingly confirmed by Mauvais' discovering that Lalande had observed the star on the 8th of May as well as on the 10th, but because the two places did not agree, he had rejected the first observation, and marked the second as doubtful, thus carefully avoiding a discovery that actually knocked at his door.

Meanwhile Peirce had made a remarkable contribution to the whole subject. In a series of profound papers presented to the American Academy, he went into the matter more generally than either of the discoverers, to the startling conclusion "that the planet Neptune is not the planet to which geometrical analysis had directed the telescope, and that its discovery by Galle must be regarded as a happy accident." He proved this first by showing that Leverrier's two fundamental propositions,—

1. That the disturber's mean distance must be between 35 and 37.9 astronomical units;

2. That its mean longitude for January 1, 1800, must have been between 243° and 252°,—

were incompatible with Neptune. Either alone might be reconciled with the observations, but not both.

In justification of his assertion that the discovery was a happy accident, he showed that three solutions of the problem Leverrier had set himself were possible, all equally complete and decidedly different from