“To determine the inclination of the orbit of the unknown from the residuals in latitude of Uranus has proved as inconclusive as Leverrier found the like attempt in the case of Neptune.
“The cause of failure lies, it would seem, in the fact that the elements of X enter into the observational equations for the latitude. Not only e and ῶ are thus initially affected but ε as well. Hence as these are doubtful from the longitude results, we can get from the latitude ones only doubtfulness to the second power.” Nevertheless he makes some calculations on the subject which, however, prove unsatisfactory.
Such in outline was his method of calculating the probable orbit and position in the sky of the trans-Neptunian planet; an herculean labor carried out with infinite pains, and attaining, not absolute definiteness, but results from the varying solutions sufficiently alike to warrant the belief in a close approximation. In dealing with what he calls the credentials for the acceptance of his results, he points out that one of his solutions for X in which he has much confidence, reduces the squares of the residuals to be accounted for by ninety per cent., and in the case of some of the others almost to nothing. Yet he had no illusions about the uncertainty of the result, for in the conclusions of the Memoir he says:
“But that the investigation opens our eyes to the pitfalls of the past does not on that account render us blind to those of the present. To begin with, the curves of the solutions show that a proper change in the errors of observation would quite alter the minimum point for either the different mean distances or the mean longitudes. A slight increase of the actual errors over the most probable ones, such as it by no means strains human capacity for error to suppose, would suffice entirely to change the most probable distance of the disturber and its longitude at the epoch. Indeed the imposing ‘probable error’ of a set of observations imposes on no one familiar with observation, the actual errors committed, due to systematic causes, always far exceeding it.
“In the next place the solutions themselves tell us of alternatives between which they leave us in doubt to decide. If we go by residuals alone, we should choose those solutions which have their mean longitudes at the epoch in the neighborhood of 0°, since the residuals are there the smallest. But on the other hand this would place the unknown now and for many decades back in a part of the sky which has been most assiduously scanned, while the solutions with ε around 180° lead us to one nearly inaccessible to most observatories, and, therefore, preferable for planetary hiding. Between the elements of the two, there is not much to choose, all agreeing pretty well with one another.
“Owing to the inexactitude of our data, then, we cannot regard our results with the complacency of completeness we should like.”
The bulk of the computations for the trans-Neptunian planet were finished by the spring of 1914, and in April he sent to Flagstaff from Boston, where the work had been done, two of the assistant computers. The final Memoir he read to the American Academy of Arts and Sciences on January 13, 1915; and printed in the spring as a publication of the Observatory. Naturally he was deeply anxious to see the fruit from such colossal labor. In July, 1913, he had written to Mr. Lampland: “Generally speaking what fields have you taken? Is there nothing suspicious?” and in May, 1914, “Don’t hesitate to startle me with a telegram ‘FOUND.’” Again, in August, he writes to Dr. Slipher: “I feel sadly of course that nothing has been reported about X, but I suppose the bad weather and Mrs. Lampland’s condition may somewhat explain it”; and to Mr. Lampland in December: “I am giving my work before the Academy on January 13. It would be thoughtful of you to announce the actual discovery at the same time.” Through the banter one can see the craving to find the long-sought planet, and the grief at the baffling of his hopes. That X was not found was the sharpest disappointment of his life.
If so much labor without tangible result gave little satisfaction, there was still less glory won by a vast calculation that did not prove itself correct. Curiously enough, he always enjoyed more recognition among astronomers in Europe than in America; for here, as a highly distinguished member of the craft recently remarked, he did not belong to the guild. He was fond of calling himself an amateur—by which he meant one who worked without remuneration—and of noting how many of the great contributors to science were in that category. The guild here was not readily hospitable to those who had not been trained in the regular treadmill; and it had been shocked by his audacity in proclaiming a discovery of intelligent handiwork on Mars. So for the most part he remained to the end of his life an amateur in this country; though what would have been said had he succeeded in producing, by rigorous calculation, an unknown planet far beyond the orbit of Neptune, it is interesting to conjecture, but difficult to know, for the younger generation of astronomers had not then come upon the stage nor the older ones outlived their prejudice.
The last eighteen months of his life were spent as usual partly at Flagstaff, where he was adding to the buildings, partly in Boston, and in lecturing. In May, 1916, he writes to Sig. Rigano of “Scientia” that he has not time to write an article for his Review, and adds: “Eventually I hope to publish a work on each planet—the whole connected together—but the end not yet.” Fortunately he did not know how near it was.
In May he lectured at Toronto; and in the autumn in the Northwest on Mars and other planets, at Washington State and Reed Colleges, and the universities of Idaho, Washington, Oregon and California. These set forth his latest views, often including much that had been discovered at Flagstaff and elsewhere since his earlier books were published; for his mind was far from closed to change of opinion on newly discovered evidence. It was something of a triumphal procession at these institutions; but it was too much.