The upper curve is in each case the Sunspot Curve, the lower the Vane Curve. The break in 1882 in the Vane Curve is due to the omission of evidently accidental turns from that date.
Plate XV.
The chromosphere, from which shoot out the prominences or “red flames,” can now be observed without an eclipse if we employ the beautiful instrument above-mentioned, the spectroheliograph; and Professor Hale has succeeded in photographing spots, faculæ, and prominences all on the same plate. But although many have made the attempt (and Professor Hale, perhaps, a more determined attempt than any man living), no one has yet succeeded in obtaining any picture or evidence of the existence of the corona excepting on the occasion of a total solar eclipse.
Now these occasions are very rare. There are two or three eclipses of the sun every year, but they are generally of the kind known as partial; when the moon does indeed come between us and the sun to some extent, but only cuts off a portion of his light—a clean-cut black disc is seen to encroach more or less on the surface of the sun. Most of us have had an opportunity of seeing a partial eclipse, probably more than once; but few have seen a total eclipse. For this the moon must come with great exactness centrally between us and the sun; and the spot where this condition is fulfilled completely only covers a few hundred miles of the earth’s surface at one moment. As the earth turns round, and as the moon revolves in its orbit, this patch from which the sun is totally eclipsed travels over the earth’s surface, marking out a track some thousands of miles in length possibly, but still not more than 200 miles wide;Total eclipses rare. and in order to see the sun totally eclipsed even on the rare occasions when it is possible at all (for, as already remarked, in the majority of cases the eclipse is only partial), we must occupy some station in this narrow belt or track, which often tantalisingly passes over either the ocean or some regions not easily accessible to civilised man. Moreover, if we travel to such favoured spots the whole time during which the sun is totally eclipsed cannot exceed a few minutes, and hence observations are made under rather hurried and trying conditions. In these modern days of photography it is easier to take advantage of these precious moments than it used to be when there was only the eye and memory of an excited observer to rely upon. It is perhaps not surprising that some of the evidence collected on these earlier occasions was conflicting; but nowadays the observers, generally speaking, direct their energies in the first place to mounting accurately in position photographic apparatus of different kinds, each item of it specially designed to settle some particular problem in the most feasible way; secondly, to rehearsing very carefully the exact programme of exposures necessary during the critical few minutes; and finally, to securing these photographs with as few mistakes as possible when the precious moments actually arrive. Even then the whole of their efforts are quite likely to be rendered unavailing by a passing cloud; and bitter is the disappointment when, after travelling thousands of miles, and spending months in preparation, the whole enterprise ends in nothing owing to some caprice of the weather.
Hence it will easily be imagined that our knowledge of the corona, the part of the sun which we can still only study on occasions of a total solar eclipse, advances but slowly. During the last twenty years there has been altogether scarcely half-an-hour available for this research, though it may fairly be said that the very best possible use has been made of that half-hour. And, what is of importance for our immediate purpose, it has gradually been established by comparing the photographs of one eclipse with those of another,Corona follows spots. that the corona itself undergoes distinct changes in form in the same period which governs the changes of sun-spots. When there are many sun-spots the corona spreads out in all directions from the edge of the sun’s disc; when there are few sun-spots the corona extends very much further in the direction of the sun’s equator, so that at sun-spot minimum there is an appearance of two huge wings. Although the evidence is necessarily collected in a scrappy manner, by this time there is sufficient to remove this relationship out of the region of mere suspicion, and to give it a well-established place in our knowledge of the sun’s surroundings.
Now the corona of the sun may be compared to some rare animal which we only see by paying a visit to some distant land, and may consider ourselves even then fortunate to get a glimpse of; and it might be thought that the habits of such an animal are not likely to be of any great importance in our everyday life. But so far from this being the case in regard to the corona, it is more than possible that the knowledge of its changes may be of vital interest to us. I have already said that, as yet, we have no satisfactory account of the reason why changes in sun-spots seem to influence changes in our magnets on the earth; but one of the theories put forward in explanation, and one by no means the least plausible, is that this influence may come, not from the sun-spots themselves, but from some other solar phenomenon which varies in sympathy with them; and in particular that it may come from the corona.Corona may influence magnets. These wings which reach out at sun-spot minimum can be seen to extend a considerable distance, and there is no reason to suppose that they actually cease at the point where they become too faint for us to detect them further; they may extend quite as far as the earth itself and even beyond; and they may be of such a nature as to influence our magnets. As the earth revolves round the sun it may sometime plunge into them, to emerge later and pass above or below them; as again the wings spread themselves at sun-spot minimum and seem to shrink at maximum, so our magnets may respond by sympathetic though very small vibrations. Hence it is quite possible that the corona is directly influencing the magnetic changes on the earth.
But it may be urged that these changes are so slight as to be merely of scientific interest. That may be true to-day, but who will be bold enough to say that it will be true to-morrow? If we are thinking of practical utility alone, we may remember that two great forces of Nature which we have chained into the service of man, steam and electricity, put forth originally the most feeble manifestations, which might readily have been despised as valueless; but by careful attention to proper conditions results of overwhelming practical importance have been obtained from these forces, which might have been, and for many centuries were, neglected as too trivial to be worth attention. Recently the world has been startled by the discovery of new elements, such as radium, whose very existence was only detected by a triumph of scientific acuteness in investigation, and yet which promise to yield influences on our lives which may overwhelm in importance all that has gone before. And similarly it may be that these magnetic changes, when properly interpreted or developed, may become of an importance in the future out of all proportion to the attention which they have hitherto attracted. Hence, although perhaps sufficient has already been established to show the immense consequences which flow from Schwabe’s remarkable discovery of the periodicity in solar spots, we may be as yet only on the threshold of its real value.
From what little causes great events spring! How little can Schwabe have realised, when he began to point his modest little telescope at the sun, and to count the number of spots—the despised spots which he had been assured were of no interest and exhibited no laws, and were generally unprofitable—that he was taking the first step in the invention of the great science of Solar Physics!—a science which is, I am glad to say, occupying at the present moment so much of the attention, not only of the great Yerkes Observatory, but of many other observatories scattered over the globe.
CHAPTER VI
THE VARIATION OF LATITUDE
If we should desire to classify discoveries in order of merit, we must undoubtedly give a high place to those which are made under direct discouragements. In the last chapter we saw that Schwabe entered upon his work under conditions of this kind, it being the opinion of experienced astronomers who had looked at the facts that there was nothing of interest to be got by watching sun-spots. In the present chapter I propose to deal with a discovery made in the very teeth of the unanimous opinion of the astronomical world by an American amateur, Mr. S. C. Chandler of Cambridge (Massachusetts). It is my purpose to allow him to himself explain the steps of this discovery by giving extracts from the magnificent series of papers which he contributed to the Astronomical Journal on the subject in the years 1891-94, but it may help in the understanding of these extracts if I give a brief summary of the facts. And I will first explain what is meant by the “Variation of Latitude.”
We are all familiar with the existence of a certain star in the heavens called the Pole Star, and we know that at any particular place it is seen constantly in the north at a definite height above the horizon, which is the latitude of the place. When watched carefully with a telescope it is found to be not absolutely stationary, but to describe a small circle in the heavens day by day, or rather night by night. These simple facts are bound up with the phenomenon of the earth’s rotation in this way: the axis about which it is rotating points to the centre of that little circle, and any change in the position of the axis can therefore be determined by observing these motions of the Pole Star. Such changes may be of two kinds: firstly, we might find that the size of the circle increased or diminished, and this would mean that the earth’s axis was pointing farther away from the Pole Star or nearer to it—pointing, that is to say, in a different direction in space.Precession. This actually happens (as has been known for some thousands of years) owing to the phenomenon called “precession”; the circle described by our Pole Star is at present getting a little smaller, but it will ultimately increase in size, and after thousands of years become so large that the Pole Star will entirely lose its character as a steady guide to the North.
Secondly (and this is what more immediately concerns us), the centre of the circle may alter its position and be no longer at the same height above the horizon of any given place. This would mean that the earth’s axis was shifting in the earth itself—that the North Pole which our explorers go to seek is not remaining in the same place. That it does not change appreciably in position we know from familiar experience; our climates, for instance, would suffer considerably if there were any large changes. But astronomers are concerned with minute changes which would not have any appreciable effect on climate, and the question has long been before them whether, putting aside large movements, there were any minute variations in position of the North Pole.Twenty years ago disbelieved. Twenty years ago the answer to this question would have been given decidedly in the negative; it was considered as certain that the North Pole did not move at all within the limits of our most refined astronomical observations. Accepted theory seemed to indicate that any movements must in any case recur after a period of ten months, and careful discussion of the observations showed that there was no oscillation in such a period. Now we know that the theory itself was wrong, or rather was founded upon a mistaken assumption; and that the facts when properly examined show clearly a distinct movement of the North Pole, not a very large one, for all its movements take place within the area occupied by a moderate-sized room, but still a movement easily measurable by astronomical observations, and Mr. Chandler was the first to point out the law of these movements, and very possibly the first to suspect them.
With these few words of explanation I will let Mr. Chandler tell his own story. His first paper appeared in the Astronomical Journal in November 1891, and is courageously headed, “On the Variation of Latitude”—I say courageously, because at that time it was believed that the latitude did not vary, and Mr. Chandler himself was only in possession of a small portion of the facts. They unravelled themselves as he went forward; but he felt that he had firm hold of the end of the thread, and he faced the world confidently in that belief. He begins thus:—
“In the determination of the latitude of Cambridge[5] with the Almucantar, about six years and a half ago, it was shown that the observed values, arranged according to nights of observation, exhibited a decided and curious progression throughout the series, the earlier values being small, the later ones large, and the range from November 1884 to April 1885 being about four-tenths of a second. There was no known or imaginable instrumental or personal cause for this phenomenon, yet the only alternative seemed to be an inference that the latitude had actually changed. This seemed at the time too bold an inference to place upon record, and I therefore left the results to speak for themselves. The subsequent continuation of the series of observations to the end of June 1885 gave a maximum about May 1, while the discussion of the previous observations from May to November 1884 gave a minimum about September 1, indicating a range of 0″.7 within a half-period of about seven months.”
Mr. Chandler then gives some figures in support of these statements, presenting them with the clearness which is so well marked a feature of the whole series of papers, and concludes this introductory paper as follows:—
“It thus appears that the apparent change in the latitude of Cambridge is verified by this discussion of more abundant material. The presumption that it is real, on this determination alone, would justify further inquiry.
“Curiously enough Dr. Küstner, in his determination of the aberration from a series of observations coincident in time with those of the Almucantar, came upon similar anomalies, and his results, published in 1888, furnish a counterpart to those which I had pointed out in 1885. The verification afforded by the recent parallel determinations at Berlin, Prague, Potsdam, and Pulkowa, which show a most surprising and satisfactory accordance, as to the character of the change, in range and periodicity, with the Almucantar results, has led me to make further investigations on the subject. They seem to establish the nature of the law of those changes, and I will proceed to present them in due order.”
The second paper appeared on November 23, and opens with the following brief statement of his general results at that time:—
“Before entering upon the details of the investigations spoken of in the preceding number, it is convenient to say that the general result of a preliminary discussion is to show a revolution of the earth’s pole in a period of 427 days, from west to east, with a radius of thirty feet, measured at the earth’s surface. Assuming provisionally, for the purpose of statement, that this is a motion of the north pole of the principal axis of inertia about that of the axis of rotation, the direction of the former from the latter lay towards the Greenwich meridian about the beginning of the year 1890. This, with the period of 427 days, will serve to fix approximately the relative positions of these axes at any other time, for any given meridian. It is not possible at this stage of the investigation to be more precise, as there are facts which appear to show that the rotation is not a perfectly uniform one, but is subject to secular change, and perhaps irregularities within brief spaces of time.”
It is almost impossible, now that we have become familiar with the ideas conveyed in this paragraph, to understand, or even fully to remember, the impression produced by them at the time; the sensation caused in some quarters, and the ridicule excited in others.Contrary to received views. They were in flat contradiction to all accepted views; and it was believed that these views were not only theoretically sound, but had been matured by a thorough examination of observational evidence. The only period in which the earth’s pole could revolve was believed to be ten mouths; and here was Mr. Chandler proclaiming, apparently without any idea that he was contradicting the laws of dynamics, that it was revolving in fourteen months! The radius of its path had been found to be insensible by careful discussion of observations, and now he proclaimed a sensible radius o£ thirty feet. Finally, he had the audacity to announce a variable period, to which there was nothing at all corresponding in the mathematical possibilities. This was the bitterest pill of all. Even after Professor Newcomb had shown us how to swallow the other two, he could not recommend any attempt at the third, as we shall presently see; and Mr. Chandler was fain ultimately to gild it a little before it could be gulped.
But this is anticipating, and it is our intention to follow patiently the evidence adduced in support of the above statements, made with such splendid confidence to a totally disbelieving world. Mr. Chandler first examines the observations of Dr. Küstner of Berlin, quoted at the end of his last paper, and shows how well they are suited by the existence of a variation in the latitude of 427 days; and that this new fact is added—when the Cambridge (U.S.A.) latitudes were the smallest those of Berlin were the largest, and vice versâ, as would clearly be the case if the phenomenon was due to a motion of the earth’s pole; for if it moved nearer America it must move further from Europe.Pulkowa puzzle solved, He then examines a long series of observations made in the years 1864-1873 at Pulkowa, near St. Petersburg, and again finds satisfactory confirmation of his law of variation. Now it had long been known that there was something curious about these observations, but no one could tell what it was. The key offered by Mr. Chandler fitted the lock exactly, and the anomalies which had been a puzzle were removed. This was in itself a great triumph; but there was another to come, which we may let Mr. Chandler describe in his own words:—
“In 1862 Professor Hubbard began a series of observations of α Lyræ at the Washington Observatory with the prime vertical transit instrument, for the purpose of determining the constants of aberration and nutation and the parallax of the star. The methods of observation and reduction were conformed to those used with such success by W. Struve. After Hubbard’s death the series was continued by Professors Newcomb, Hall, and Harkness until the beginning of 1867. Professor Hall describes these observations as the most accurate determinations of declination ever made at the Naval Observatory. The probable error of a declination from a single transit was ±0″.141, and judging from the accidental errors, the series ought to give trustworthy results. Upon reducing them, however, it was found that some abnormal source of error existed, which resulted in anomalous values of the aberration-constant in the different years, and a negative parallax in all. A careful verification of the processes of reduction failed to discover the cause of the trouble, and Professor Hall says that the results must stand as printed, and that probably some annual disturbance in the observations or the instrument occurred, which will never be explained, and which renders all deductions from them uncertain. The trouble could not be connected with personal equation, the anomalies remaining when the observations of the four observers who took part were separately treated. Nor, as Professor Hall points out, will the theoretical ten-month period in the latitude furnish the explanation.
“It is manifest, however, that if the 427-day period exists, its effect ought to appear distinctly in declination-measurements of such high degree of excellence as these presumably were, and, as I hope satisfactorily to show, actually are. When this variation is taken into account the observations will unquestionably vindicate the high expectations entertained with regard to them by the accomplished and skilful astronomers who designed and carried them out.”
From this general account I am excluding technical details and figures, and unfortunately a great deal is thereby lost. We lose the sense of conviction which the long rows of accordant figures force upon us, and we lose the opportunities of admiring both the astonishing amount of work done and the beautiful way in which the material is handled by a master. But I am tempted to give one very small illustration of the numerical results from near the end of the paper.Direction of revolution of Pole. After discussing the Washington results, and amply fulfilling the promise made in the preceding extract, Mr. Chandler compares them with the Pulkowa results, and shows that the Earth’s Pole must be revolving from west to east, and not from east to west. And then he writes down a simple formula representing this motion, and compares his formula with the observations. He gives the results in seconds of arc, but for the benefit of those not familiar with astronomical measurements we may readily convert these into feet;Example of results. and in the following tables are shown the distances of the Earth’s Pole in feet from its average position,[6] as observed at Washington and at Pulkowa, and the same distances calculated according to the formula which Mr. Chandler was able to write down at this early stage. The signs + and - of course indicate opposite directions of displacement:—
Washington.
Deviation of Pole.
| Date. | Observed. | Formula. |
| 1864, Dec. 28 | - 28 feet | - 23 feet |
| 1865, Mar. 19 | - 1" | - 12" |
| "June 1 | +15" | +12" |
| "Aug. 11 | +22" | +23" |
| "Oct. 9 | +11" | +15" |
| "Dec. 13 | - 17" | - 6" |
Pulkowa.
Deviation of Pole.
| Date. | Observed. | Formula. |
| 1865, July 25 | - 18 feet | - 12 feet |
| "Sept. 9 | + 3" | + 3" |
| "Nov. 22 | +26" | +22" |
| 1866, Feb. 22 | +18" | +13" |
| "June 4 | - 11" | - 18" |
| "July 17 | - 16" | - 23" |
Of course the figures are not exact in every case, but they are never many feet wrong; and it may well be imagined that it is a difficult thing to deduce, even from the most refined observations, the position of the earth’s pole to within a foot. The difficulty is exactly the same as that of measuring the length of an object 300 miles away to within an inch!
Mr. Chandler winds up his second paper thus:—
“We thus find that the comparison of the simultaneous series at Pulkowa and Washington, 1863-1867, leads to the same conclusion as that already drawn from the simultaneous series at Berlin and Cambridge, 1884-1885. The direction of the polar motion may therefore be looked upon as established with a large degree of probability.
“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.”
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.Latitude varied in twelve months then. The facts, when analysed 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:—
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 latitude.” And he concludes this paper with the following fine passage:—
“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.
“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 pass. 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.
“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,Other puzzles explained. 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 Königsberg, 1820-24, with the Reichenbach circle, and in 1842-44 with the Repsold circle; the latitudes derived from the polar-point determinations of Struve and Mädler 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 Brünnow, 1845-46, in which I hope to show that the parallax of β Draconis derived from them is simply a record of the change of latitude; the conflicting latitude 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 space.
“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 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.”
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 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.
“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 entitled to assume 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 entitled to pronounce 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.”
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.Chandler’s reply. Mr. Chandler’s answer will speak for itself. It was delayed a little in order that he might present an immense mass 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 principally 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 XXXV.), 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 space 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 entitled to pronounce 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 rebuttal.
“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, latitudes, 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?”