“Another characteristic which has struck my attention, although somewhat vaguely, is that the variations in the length of the period seem to go hand in hand with simultaneous alterations in the amplitude of the rotation; the shorter periods being apparently associated with the larger coefficients for the latter. The verification of these surmises awaits a closer comparative scrutiny, the opportunity for which will come when the computations are in a more forward state. If confirmed, these observations will afford a valuable touchstone, in seeking for the cause of a phenomenon which now seems to be at variance with the accepted laws of terrestrial rotation.”
Reception of discovery.
Let us now for a few moments turn aside from the actual research to see how the announcement was received. It would be ungracious to reprint here any of the early statements of incredulity which found their way into print, especially in Germany. But the first note of welcome came from Simon Newcomb, in the same number of the Astronomical Journal as the paper just dealt with, and the following extract will indicate both the difficulties felt in receiving Mr. Chandler’s results and the way in which Newcomb struck at the root of them.
“Mr. Chandler’s remarkable discovery, that the apparent variations in terrestrial latitudes may be accounted for by supposing a revolution of the axis of rotation of the earth around that of figure, in a period of 427 days, is in such disaccord with the received theory of the earth’s rotation that at first I was disposed to doubt its possibility. But I am now able to point out a vera causa which affords a complete explanation of this period.Newcomb’s explanation. Up to the present time the treatment of this subject has been this: The ratio of the moment of inertia of the earth around its principal axis to the mean of the other two principal moments, admits of very accurate determination from the amount of precession and nutation. This ratio involves what we might call, in a general way, the solid ellipticity of the earth, or the ellipticity of a homogeneous spheroid having the same moments of inertia as the earth.
“When the differential equations of the earth’s rotation are integrated, there appear two arbitrary constants, representing the position of any assigned epoch of the axis of rotation relative to that of figure. Theory then shows that the axis of rotation will revolve round that of figure, in a period of 306 days, and in a direction from west toward east. The attempts to determine the value of these constants have seemed to show that both are zero, or that the axes of rotation and figure are coincident. Several years since, Sir William Thomson published the result of a brief computation from the Washington Prime-Vertical observations of α Lyrae which I made at his request and which showed a coefficient 0″.05. This coefficient did not exceed the possible error of the result; I therefore regarded it as unreal.
The forgotten assumption.
“The question now arises whether Mr. Chandler’s result can be reconciled with dynamic theory. I answer that it can, because the theory which assigns 306 days as the time of revolution is based on the hypothesis that the earth is an absolutely rigid body. But, as a matter of fact, the fluidity of the ocean plays an important part in the phenomenon, as does also the elasticity of the earth. The combined effect of this fluidity and elasticity is that if the axis of rotation is displaced by a certain amount, the axis of figure will, by the changed action of the centrifugal force, be moved toward coincidence with the new axis of rotation. The result is, that the motion of the latter will be diminished in a corresponding ratio, and thus the time of revolution will be lengthened. An exact computation of the effect is not possible without a knowledge of the earth’s modulus of elasticity. But I think the result of investigation will be that the rigidity derived from Mr. Chandler’s period is as great as that claimed by Sir William Thomson from the phenomena of the tides.”
This was very satisfactory. Professor Newcomb put his finger on the assumption which had been made so long ago that it had been forgotten: and the lesson is well worth taking to heart, for it is not the first time that mistaken confidence in a supposed fact has been traced to some forgotten preliminary assumption: and we must be ever ready to cast our eyes backward over all our assumptions, when some new fact seems to challenge our conclusions. It might further be expected that this discovery of the way in which theory had been defective would as a secondary consequenceBut Chandler’s work still mistrusted. inspire confidence in the other conclusions which Mr. Chandler had arrived at in apparent contradiction to theory; or at least suggest the suspension of judgment. But Professor Newcomb did not feel that this was possible in respect of the change of period, from about twelve months in Bradley’s time to fourteen months in ours. We have seen that Mr. Chandler himself regarded this as a “curious result” requiring confirmation: but since the confirmation was forthcoming, he stated it with full confidence, and drew the following remarks from Professor Newcomb in July 22, 1892:—
“The fact of a periodic variation of terrestrial latitudes, and the general law of that variation, have been established beyond reasonable doubt by the observations collected by Mr. Chandler. But two of his minor conclusions, as enumerated in No. 3 of this volume, do not seem to me well founded. They are—
“1. That the period of the inequality is a variable quantity.