"In the next paper I will present the results derived from PETERS, STRUVE, BRADLEY, and various other series of observations, after which the results of all will be brought to bear upon the determination of the best numerical values of the constants involved."
[Sidenote: Bradley's observations.]
[Sidenote: Lat.i.tude varied in twelve months then.]
The results were not, however, presented in this order. In the next paper, which appeared on December 23, 1891, Mr. Chandler begins, with the work of Bradley, the very series of observations at Kew and Wansted which led to the discoveries of aberration and nutation, and which we considered in the third chapter. He first shows that, notwithstanding the obvious accuracy of the observations, there is some unexplained discordance. The very constant of aberration which Bradley discovered from them differs by half-a-second of arc from our best modern determinations. Attempts have been made to ascribe the discordance to changes in the instrument, but Mr.
Chandler shows that such changes, setting aside the fact that Bradley would almost certainly have discovered them, will not fit in with the facts. The facts, when a.n.a.lysed with the skill to which we have become accustomed, are that there is a periodic swing in the results _with a period of about a year_, and not fourteen months, as before, "a result so curious," as he admits, that "if we found no further support, it might lead us to distrust the above reasoning, and throw us back to the possibility that, after all, BRADLEY'S observations may have been vitiated by some kind of annual instrumental error. But it will abundantly appear, when I have had the opportunity to print the deductions from all the other series of observations down to the present time, that the inference of an increase in the period of polar revolution is firmly established by their concurrent testimony." We shall presently return to this curious result, which might well have dismayed a less determined researcher than Mr.
Chandler, but which only led him on to renewed exertions.
The results obtained from Bradley's observations may be put in the form of a diagram thus:--
[Ill.u.s.tration: FIG. 7.]
It will be seen that the maxima and minima fall in the spring and autumn, and this fact alone seemed to show that the effect could not be due to temperature, for we should expect the greatest effect in that case in winter and summer. It could not be due to the parallax of the stars for which Bradley began his search, for stars in different quarters of the heavens would then be differently affected, and this was not the case.
"There remains," concluded Mr. Chandler after full discussion, "the only natural conclusion of an actual displacement of the zenith, in other words, a change of lat.i.tude." And he concludes this paper with the following fine pa.s.sage:--
"So far, then, as the results of this incomparable series of observations at Kew and Wansted, considered by themselves alone, can now be stated, the period of the polar rotation at that epoch appears to have been probably somewhat over a year, and certainly shorter by about two months than it is at the present time. The range of the variation was apparently in the neighbourhood of a second of arc, or considerably larger than that shown by the best modern observations.
[Sidenote: Bradley's greatness.]
"Before taking leave of these observations for the present I cannot forbear to speak of the profound impression which a study of them leaves upon the mind, and the satisfaction which all astronomers must feel in recognising that, besides its first fruits of the phenomena of aberration and nutation, we now owe also our first knowledge of the polar motion to this same immortal work of Bradley. Its excellence, highly appreciated as it has been, has still been hitherto obscured by the presence of this unsuspected phenomenon.
When divested of its effects, the wonderful accuracy of this work must appear in a finer light, and our admiration must be raised to higher pitch. Going back to it after one hundred and sixty years seems indeed like advancing into an era of practical astronomy more refined than that from which we pa.s.s. And this leads to a suggestion worthy of serious practical consideration--whether we can do better in the future study of the polar rotation, than again to avail ourselves of Bradley's method, without endangering its elegant simplicity and effectiveness by attempts at improvement, other than supplying certain means of instrumental control which would without doubt commend themselves to his sagacious mind.
[Sidenote: Other puzzles explained.]
"In the next article Bradley's later observations at Greenwich, the results of which are not so distinct, will be discussed; and also those of Brinkley at Dublin, 1808-13 and 1818-22. This will bring again to the surface one of the most interesting episodes in astronomical history, the spirited and almost acrimonious dispute between Brinkley and Pond with regard to stellar parallaxes. I hope to show that the hitherto unsolved enigma of Brinkley's singular results finds its easy solution in the fact of the polar motion. The period of his epoch appears to have been about a year, and its range more than a second. Afterwards will follow various discussions already more or less advanced towards completion. These include Bessel's observations at Konigsberg, 1820-24, with the Reichenbach circle, and in 1842-44 with the Repsold circle; the lat.i.tudes derived from the polar-point determinations of Struve and Madler with the Dorpat circle, 1822-38; Struve's observations for the determination of the aberration; Peters' observations of _Polaris_, 1841-43, with the vertical-circle; the results obtained from the reflex zenith-tube at Greenwich, 1837-75, whose singular anomalies can be referred in large part to our present phenomenon, complicated with instrumental error, to which until now they have been exclusively attributed; the Greenwich transit-circle results, 1851-65, in which case, however, a similar complication and the large accidental errors of observation seem to frustrate efforts to get any pertinent results; the Berlin prime-vertical observations of Weyer and Brunnow, 1845-46, in which I hope to show that the parallax of [beta] _Draconis_ derived from them is simply a record of the change of lat.i.tude; the conflicting lat.i.tude determinations at Cambridge, England; the Washington observation of _Polaris_ and other close Polars, 1866-87, with the transit-circle; also those at Melbourne, 1863-84, a portion of which have already been drawn upon in the last number of the _Journal_, and some others. While the list is a considerable one, I shall be able to compress the statement of results for many of the series into a short s.p.a.ce.
[Sidenote: Provisional nature of results.]
"In connection with this synopsis of the scope of the investigations, one or two particulars may be of interest, which at the present writing seem to foreshadow the probable outcome. I beg, however, that the statement will be regarded merely as a provisional one. First, while the period is manifestly subject to change, as has already once or twice been intimated, I have hitherto failed in tracing the variations to any regular law, expressible in a numerical formula.
Indeed, the general impression produced by a study of these changes in the length of the period is that the cause which produces them operates capriciously to a certain degree, although the average effect for a century has been to diminish the velocity of the revolution of the pole. How far this impression is due to the uncertainty of the observations, and to the complication of the phenomenon with other periodical changes of a purely instrumental kind, I cannot say. Almost all of the series of any extent which have been examined, have the peculiarity that they manifest the periodicity quite uniformly and distinctly for a number of years, then for a while obscurely. In some cases, however, what at first appears to be an objective irregularity proves not to be so by comparison with overlapping series at other observatories.
"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 a.s.sociated 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."
[Sidenote: 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.
[Sidenote: Newcomb's explanation.]
"Mr. Chandler's remarkable discovery, that the apparent variations in terrestrial lat.i.tudes 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. 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 princ.i.p.al axis to the mean of the other two princ.i.p.al 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 h.o.m.ogeneous 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 a.s.signed 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 [alpha] 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.
[Sidenote: The forgotten a.s.sumption.]
"The question now arises whether Mr. Chandler's result can be reconciled with dynamic theory. I answer that it can, because the theory which a.s.signs 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."
[Sidenote: But Chandler's work still mistrusted.]
This was very satisfactory. Professor Newcomb put his finger on the a.s.sumption 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 a.s.sumption: and we must be ever ready to cast our eyes backward over all our a.s.sumptions, 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 consequence 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 lat.i.tudes, 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 quant.i.ty.
"2. That the amplitude of the inequality has remained constant for the last half century."
Professor Newcomb proceeds to give his reasons for scepticism, which are too technical in character to reproduce here. But I will quote the following further sentence from his paper:--
"The question now arises how far we are ent.i.tled to a.s.sume that the period must be invariable. I reply that, perturbations aside, any variation of the period is in such direct conflict with the laws of dynamics that we are ent.i.tled to p.r.o.nounce it impossible. But we know that there are perturbations, and I do not see how one can doubt that they have so acted as to increase the amplitude of the variation since 1840."
[Sidenote: Chandler's reply.]
In other words, while recognising that there may be a way of reconciling one of the "minor" conclusions with theory, Professor Newcomb considers that in this case the other must go. Mr. Chandler's answer will speak for itself. It was delayed a little in order that he might present an immense ma.s.s of evidence in support of his conclusions, and was ultimately printed on August 23, 1892.
"The material utilised in the foregoing forty-five series aggregates more than thirty-three thousand observations. Of these more than one-third were made in the southern hemisphere, a fact which we owe princ.i.p.ally to Cordoba. It comprises the work of seventeen observatories (four of them in the southern hemisphere) with twenty-one different instruments, and by nine distinct methods of observation. Only three of the series (XXI., XXV., and x.x.xV.), and these among the least precise intrinsically, give results contradictory of the general law developed in No. 267. This degree of general harmony is indeed surprising when the evanescent character of the phenomenon under investigation is considered.
"The reader has now before him the means for independent scrutiny of the material on which the conclusions already drawn, and those which are to follow, are based. The s.p.a.ce taken in the printing may seem unconscionable, but I hope this will be charged to the extent of the evidence collected, and not to diffuseness or the presentation of needless detail; for I have studiously sought to compress the form of statement without omitting anything essential for searching criticism. That it was important to do this is manifest, since the conclusions, if established, overthrow the existing theory of the earth's rotation, as I have pointed out on p. 21. I am neither surprised nor disconcerted, therefore, that Professor Newcomb should hesitate to accept some of these conclusions on the ground (_A. J._, No. 271) that they are in such conflict with the laws of dynamics that we are ent.i.tled to p.r.o.nounce them impossible. He has been so considerate and courteous in his treatment of my work thus far, that I am sure he will not deem presumptuous the following argument in reb.u.t.tal.
[Sidenote: He "put aside all teachings of theory," and "is not dismayed."]
"It should be said, first, that in beginning these investigations last year, I deliberately put aside all teachings of theory, because it seemed to me high time that the facts should be examined by a purely inductive process; that the nugatory results of all attempts to detect the existence of the Eulerian period probably arose from a defect of the theory itself; and that the entangled condition of the whole subject required that it should be examined afresh by processes unfettered by any preconceived notions whatever. The problem which I therefore proposed to myself was to see whether it would not be possible to lay the numerous ghosts--in the shape of numerous discordant residual phenomena pertaining to determinations of aberration, parallaxes, lat.i.tudes, and the like--which had heretofore flitted elusively about the astronomy of precision during the century; or to reduce them to tangible form by some simple consistent hypothesis. It was thought that if this could be done, a study of the nature of the forces, as thus indicated, by which the earth's rotation is influenced, might lead to a physical explanation of them.
"Naturally, then, I am not much dismayed by the argument of conflict with dynamic laws, since all that such a phrase means must refer merely to the existent state of the theory at any given time. When the 427-day period was propounded, it was as inconsistent with known dynamic law as the variation of it now appears to be. Professor Newcomb's own happy explanation has already set aside the first difficulty, as it would appear, and advanced the theory by an important step. Are we so sure yet of a complete knowledge of all the forces at work as to exclude the chance of a _vera causa_ for the second?"
[Sidenote: Faraday's words.]
There is a splendid ring of resolution about these words. Let us compare them with a notable utterance of Faraday:--
"The philosopher should be a man willing to listen to every suggestion, but determined to judge for himself. He should not be bia.s.sed by appearances; have no favourite hypothesis; be of no school; and in doctrine have no master. He should not be a respecter of persons, but of things. Truth should be his primary object. If to these qualities be added industry, he may indeed hope to walk within the veil of the temple of Nature."
[Sidenote: Chandler's other work at this time.]
[Sidenote: His ultimate satisfactory solution.]
[Sidenote: Interference of two waves.]
Tested by this severe standard, Mr. Chandler fails in no particular, least of all in that of industry. The amount of work he got through about this time was enormous, for besides the main line of investigation, of which we have only had after all a mere glimpse, he had been able to turn aside to discuss a subsidiary question with Professor Comstock; he had examined with great care some puzzling characteristics in the variability of stars; he computed some comet ephemerides; and he was preparing a new catalogue of variable stars--a piece of work involving the collection and arrangement of great ma.s.ses of miscellaneous material. Yet within a few months after replying as above to Professor Newcomb's criticism, he was able to announce that he had found the key to the new puzzle, and that "theory and observation were again brought into complete accord." We will as before listen to the account of this new step in his own words, but a slight preliminary explanation may help those unaccustomed to the terminology. The polar motion was found to be compounded of _two_ independent motions, both periodic, but having different periods. Now, the general results of such a composition are well known in several different branches of physics, especially in the theory of sound. If two notes of nearly the same pitch be struck at the same time, we hear the resultant sound alternately swell and die away, because the vibrations caused by the two notes are sometimes going in the same direction, and after an interval are going exactly in opposite directions. Diagrammatically we should represent the vibrations by two waves, as below; the upper wave goes through its period seven and a half times between A and D, the lower only six times; and it is easily seen that at A and C the waves are sympathetic, at B and D antipathetic. At A and C the compound vibration would be doubled; at B and D reduced to insensibility. The point is so important that perhaps a numerical ill.u.s.tration of it will not be superfluous. The waves are now represented by rows of figures as below.
The first series recurs after every 6, the second after every 7.
[Ill.u.s.tration: FIG. 8.]
First Wave 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 Second Wave 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 ------------------------------------------------------------- Combined Effect 2 4 6 8 7 5 3 3 5 7 7 6 4 4 4 6 6 6 5 5 5 5 5 5 5 6 6 6 4 4 4 Great disturbance. Calm.
First Wave 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 Second Wave 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 -------------------------------------------------------------
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