The conditions here are quite unlike those at the discovery of Neptune, for there the existence of the perturbations was clear, because fairly large, and the orbit predicted was wrong because of an error in the distance assumed; and the question was whether the presence of Neptune in the direction predicted, though in a different orbit, was an accident, or inevitable. Here the predicted orbit is substantially the actual one, adequate to account for the perturbations of Uranus if such really exist, and the question is whether they do or not. If not the discovery of Pluto is a mere unexplained coincidence which has no connection with the prediction. Whether among recognized uncertainties it is more rational to suppose a very high density, and very low albedo, with corresponding perturbations of Uranus and Neptune, whose orbits are still imperfectly known, or to conclude that a planet, which would account for these things if dense enough, revolves in fact in the appropriate path, a mere ghost of itself—a phantom but not a force—one who is not an astronomer must leave to the professionals.
In the case of both Neptune and Pluto the calculation was certainly a marvellous mathematical feat, and in accord with the usual practice whereby the discoverer of a new celestial body is entitled to propose its name the observers at Flagstaff selected from many suggestions that of “Pluto” with the symbol
; and henceforth astronomers will be reminded of Percival Lowell, by the planet he found but never saw.
APPENDIX I
Professor Henry Norris Russell’s later views on the size of Pluto (written to the Biographer and printed with the writer’s consent).
Later investigations have revealed a very curious situation. When once the elements of Pluto’s orbit are known, the calculation of the perturbations which it produces on another planet, such as Neptune, are greatly simplified. But the problem of finding Pluto’s mass from observations of Neptune is still none too easy, for the perturbations affect the calculated values of the elements of Neptune’s orbit, and are thus “entangled” with them in an intricate fashion.
Nicholson and Mayall, in 1930, attacked the problem, and found that the perturbations of Neptune by Pluto, throughout the interval from its discovery to the present, were almost exactly similar to the effects which would have been produced by certain small changes in the elements of Neptune’s orbit, so that, from these observations alone, it would have been quite impossible to detect Pluto’s influence. Outside this interval of time, the effects of the perturbations steadily diverge from those of the spurious changes in the orbit, but we cannot go into the future to observe them, and all we have in the past is two rather inaccurate observations made in 1795 by Lalande.[53] If the average of these two discordant observations is taken as it stands, Pluto’s mass comes out 0.9 times that of the Earth, and this determination is entitled to very little weight.
Uranus is farther from Pluto, and its perturbations are smaller; but it has been accurately observed over one and a half revolutions, as against half a revolution for Neptune, and this greatly favors the separation of the perturbations from changes in the assumed orbital elements. Professor E. W. Brown—the most distinguished living student of the subject—concludes from a careful investigation that the observations of Uranus show that Pluto’s mass cannot exceed one-half of the Earth’s and may be much less. In his latest work a great part of the complication is removed by a curiously simple device. Take the sum of the residuals of Uranus at any two dates separated by one-third of its period, and subtract from this the residual at the middle date. Brown proves—very simply—that the troublesome effect of uncertainties in the eccentricity and perihelion of the disturbed planet will be completely removed from the resulting series of numbers, leaving the perturbations much easier to detect. The curve which expresses their effects, though changed in shape, can easily be calculated. Applying this method to the longitude of Uranus, he finds, beside the casual errors of observation, certain deviations; but these change far more rapidly than perturbations due to Pluto could possibly do, and presumably arise from small errors in calculating the perturbations produced by Neptune. When these are accurately re-calculated, a minute effect of Pluto’s attraction may perhaps be revealed, but Brown concludes that “another century of accurate observations appears to be necessary for a determination which shall have a probable error less than a quarter of the Earth’s mass.”