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.”

The conclusion that Pluto’s mass is small is confirmed by its brightness. Its visual magnitude is 14.9—just equal to that which Neptune’s satellite Triton would have if brought to the same distance. (Since Pluto’s perihelion distance is less than that of Neptune, this experiment is one which Nature actually performs at times.) Now Nicholson’s observations show that the mass of Triton is between 0.06 and 0.09 times the Earth’s. It is highly probable that Pluto’s mass is about the same—in which case the perturbations which it produces, even on Neptune, will be barely perceptible, so long as observations have their present degree of accuracy.

The value of seven times the Earth’s mass, derived in Percival Lowell’s earlier calculations, must have been influenced by some error. His mathematical methods were completely sound—on Professor Brown’s excellent authority—and the orbit of Planet X which he computed resembled so closely that of the actual Pluto that no serious discordance could arise from the difference. But, in this case also, the result obtained for the mass of the perturbing planet depended essentially on the few early observations of Uranus as a star, made before its discovery as a planet, and long before the introduction of modern methods of precise observation. Errors in these are solely responsible for the inaccuracy in the results of the analytical solution.

The question arises, if Percival Lowell’s results were vitiated in this way by errors made by others more than a century before his birth, why is there an actual planet moving in an orbit which is so uncannily like the one he predicted?

There seems no escape from the conclusion that this is a matter of chance. That so close a set of chance coincidences should occur is almost incredible; but the evidence assembled by Brown permits of no other conclusion. Other equally remarkable coincidences have occurred in scientific experience. A cipher cable-gram transmitting to the Lick Observatory the place of a comet discovered in Europe was garbled in transmission, and when decoded gave an erroneous position in the heavens. Close to this position that evening another undiscovered comet was found. More recently a slight discrepancy between determinations of the atomic weight of hydrogen by the mass-spectrograph and by chemical means led to a successful search for a heavy isotype of hydrogen. Later and more precise work with the mass-spectrograph showed that the discrepancy had at first been much over-estimated. Had this error not been made, heavy hydrogen might not yet have been discovered.

Like this later error, the inaccuracy in the ancient observations, which led to an over-estimate of the mass and brightness of Pluto, was a fortunate one for science.

In any event, the initial credit for the discovery of Pluto justly belongs to Percival Lowell. His analytical methods were sound; his profound enthusiasm stimulated the search, and, even after his death, was the inspiration of the campaign which resulted in its discovery at the Observatory which he had founded.