Combined Effect 6 7 7 5 3 3 5 7 8 6 4 2 4 6 8 7 5 3 3 5 7 7 6 4 4 4 6 6 6 5 5 Great disturbance.
[Sidenote: Ill.u.s.tration from ocean travel.]
Adding the two rows together, the oscillations at first reinforce one another and we get numbers ranging from 2 to 8 instead of from 1 to 4; but one wave gains on the other, until it is rising when the other is falling, and the numbers add up to a steady series of 5's. It will be seen that there are no less than seven consecutive 5's, and all the variation seems to have disappeared. But presently the waves separate again, and the period of great disturbance recurs; it will be seen that in the "combined effect" the numbers repeat exactly after the 42nd term. Now those unfamiliar with the subject may not be prepared for the addition of one physical wave to another, as though they were numbers, but the a.n.a.logy is perfect. Travellers by some of the fast twin-screw steamers have had unpleasant occasion to notice this phenomenon, when the engineer does not run the two screws precisely at the same speed; there come times when the ship vibrates violently, separated by periods of comparative stillness.
Instances from other walks of life may recur to the memory when once attention is called to the general facts; but enough has been said to explain the point numbered (2) in the subjoined statement. To understand the rest, we must remember that if the two waves are not equal in "amplitude," _i.e._ if the backward and forward motion is not the same in both, they cannot annul one another, but the greater will always predominate. Those interested in following the matter further should have no difficulty in constructing simple examples to ill.u.s.trate such points.
We will proceed to give Mr. Chandler's statements:--
[Sidenote: Chandler's final formulae.]
"We now come upon a new line of investigation. Heretofore, as has been seen, the method has been to condense the results of each series of observations into the interval comprised by a single period, then to determine the mean epoch of minimum and the mean range for each series, and, finally, by a discussion of these quant.i.ties, to establish the general character of the law of the rotation of the pole. It is now requisite to a.n.a.lyse the observations in a different way, and discover whether the deviations from the general provisional law, in the last column of Table II., are real, and also in what manner the variation of the period is brought about. The outcome of this discussion, which is to be presented in the present paper, is extremely satisfactory. The real nature of the phenomenon is most distinctly revealed, and may be described as follows:--
"1. The observed variation of the lat.i.tude is the resultant curve arising from two periodic fluctuations superposed upon each other.
The first of these, and in general the more considerable, has a period of about 427 days, and a semi-amplitude of about 0".12. The second has an annual period with a range variable between 0".04 and 0".20 during the last half-century. During the middle portion of this interval, roughly characterised as between 1860 and 1880, the value represented by the lower limit has prevailed, but before and after those dates, the higher one. The minimum and maximum of this annual component of the variation occur at the meridian of Greenwich, about ten days before the vernal and autumnal equinoxes respectively, and it becomes zero just before the solstices.
"2. As the resultant of these two motions, the effective variation of the lat.i.tude is subject to a systematic alternation in a cycle of seven years' duration, resulting from the commensurability of the two terms. According as they conspire or interfere, the total range varies between two-thirds of a second as a maximum, to but a few hundredths of a second, generally speaking, as a minimum.
"3. In consequence of the variability of the coefficient of the annual term above mentioned, the apparent average period between 1840 and 1855 approximated to 380 or 390 days; widely fluctuated from 1855 to 1865; from 1865 to about 1885 was very nearly 427 days, with minor fluctuations; afterwards increased to near 440 days, and very recently fell to somewhat below 400 days. The general course of these fluctuations is quite faithfully represented by the law of eq. (3), (No. 267), and accurately, even down to the minor oscillations of individual periods, by the law of eq. (15), hereafter given, and verbally interpreted above. This law also gives a similarly accurate account of the corresponding oscillations in the amplitude. The closeness of the accordance between observation and the numerical theory, in both particulars, places the reality of the law beyond reasonable doubt."
Those who cannot follow the details of the above statement will nevertheless catch the general purport--that the difficulties felt by Professor Newcomb have been surmounted; and this is made clearer by a later extract:--
"A very important conclusion necessarily follows from the agreement of the values of the 427-day term, deduced from the intervals between the consecutive values of T in Table XII., namely, that there has been no discontinuity in the revolution, such as Professor Newcomb regarded as so probable that he doubted the possibility of drawing any conclusions from the comparison of observations before and after 1860 (_A. J._, 271, p. 50).
[Sidenote: Theory must go, if it will not fit observation.]
"The present investigation demonstrates that the way out of the apparently irreconcilable contradiction of theory and observation in this matter does not lie in the direction of discrediting the observations, as he is inclined to do. On the contrary, the result is a beautiful vindication of the trustworthiness of the latter, and, at the same time, of the theory that demands an invariable rate of motion; providing a perfectly fitting key to the riddle by showing that another cause has intervened to produce the variability of the period. I feel confident that Professor Newcomb will agree with the reality of the explanation here set forth, and will reconsider his view that the perturbations in the position of the Pole must be of the nature of chance acc.u.mulations of motion, a view which he then considered necessary to the maintenance of the constancy in the period of lat.i.tude-variation."
[Sidenote: The final paper.]
The paper from which these words are taken appeared on November 4, 1892.
The next paper on the main theme did not appear till a year later, though much work was being done in the meantime on the constant of aberration and other matters arising immediately after the discovery. On November 14, 1893, Mr. Chandler winds up the series of eight papers "On the Variation of Lat.i.tude," which he had commenced just two years before. His work was by no means done; rather was it only beginning, for the torch he had lit illuminated many dark corners. But he rightly regarded his discovery as now so firmly established that the series of papers dealing with it as still under consideration might be terminated. In this final paper he first devotes the most careful attention to one point of detail. He had shown earlier in the series that the North Pole must be revolving from West to East, and not from East to West; but this was when the motion was supposed to be simple and not complex, and it was necessary to re-examine the question of direction for each of the components. After establishing conclusively that the original direction holds for each of the components, he almost apologises for the trouble he has taken, thus:--
"It is therefore proved beyond reasonable doubt that the directions of the rotations is from West to East in both elements; whence the general form of the equation for the variation of lat.i.tude adopted in _A. J._, 284, p. 154, eq. (19). It may be thought that too much pains have been here bestowed upon a point which might be trusted to theory to decide. I cannot think so. One of the most salient results of these articles has been the proof of the fact that theory has been a blind guide with regard to the velocity of the Polar rotation, obscuring truth and misleading investigators for a half a century.
And even if we were certain, which we are not, that the fourteen months' term is the Eulerian period in a modified form. It would still be necessary to settle by observation the direction of the annual motion, with regard to which theory is powerless to inform us.
To save repet.i.tion of argument, I must refer to the statement in _A.
J._, 273, pp. 68, 70, of the principles adopted in beginning these inquiries in 1891."
Finally, he answers one of the few objectors of eminence who still lingered, the great French physicist Cornu:--
[Sidenote: Cornu answered.]
"The ground is now cleared for examination of the only topic remaining to be covered, to establish, upon the foundation of fact, every point in the present theory of these remarkable movements of the earth's axis. This is the question of the possibility that these movements are not real, but merely misinterpretations of the observed phenomena; being in whole or in part an illusory effect of instrumental error due to the influence of temperature. Such a possibility has been a nightmare in practical astronomy from the first, frightening us in every series of unexplained residuals, brought to light continually in nearly all attempts at delicate instrumental research. A source of danger so subtile could not fail to be ever present in the mind of every astronomer and physicist who has given even a superficial attention to the question of the lat.i.tude variations, and there is no doubt that some are even now thus deterred from accepting these variations as proved facts.
Perhaps the most explicit and forcible statement of the doubts that may arise on this subject has been given very recently by Mr. Cornu.
The views of so distinguished a physicist, and of others who are inclined to agree with him, call for careful attention, and cannot be neglected in the present closing argument upon the theory presented in these articles. It is unnecessary, for the purpose of disposing of objections of the sort raised by Cornu, to insist that it is not sufficient to show that the observed variations, attributed to the unsteadiness of the Earth's Pole, are near the limit of precision attainable in linear differential measures, and in the indication of the direction of gravity by means of the air bubble of the level; or to show that there are known variations in divided circles and in levels, dependent on temperature and seasons. Nor need we require of objectors the difficult, although essential, task--which they have not distinctly attempted--of showing that these errors are not eliminated, as they appear to be, by the modes in which astronomers use their instruments. Neither need we even urge the fact that a large portion of the data which have been utilised in the present researches on the lat.i.tude were derived by methods which dispense with levels, or with circles, a part of them indeed with both, and yet that the results of all are harmonious. On the contrary, let us admit, although merely for argument's sake, that all the known means of determining the direction of gravity--including the plumb-line, the level, and a fluid at rest, whether used for a reflecting surface or as a support for a floating instrument--are subject to a common law of periodical error which vitiates the result of astronomical observation, obtained by whatever methods, and in precisely the same manner. Now, the observed law of lat.i.tude variation includes two terms, with periods of fourteen and twelve months respectively. Since the phases of the first term are repeated at intervals of two months in successive years, and hence in a series of years come into all possible relations to conditions of temperature dependent on season, the argument against the reality of this term, on this ground, absolutely fails, and needs no further notice. As to the second, or annual term, while the phases, as observed in any given longitude, are indeed synchronical with the seasons, they are not so as regards different longitudes. If, therefore, the times of any given phase, as observed in the same lat.i.tude, but in successively increasing longitudes, occurred at the same date in all of them, there would be a fatal presumption against the existence of an annual period in the polar motion. If, on the contrary, they occur at times successively corresponding to the differences of longitude, the presumption is equally fatal to the hypothesis that they can possibly be due to temperature variation as affecting instrumental measurement. But the facts given in the foregoing section correspond most distinctly to the latter condition. Therefore, unless additional facts can be brought to disprove successively these observed results, we may dismiss for ever the bugbear which has undoubtedly led many to distrust the reality of the annual component of the lat.i.tude-variation, while they admit the existence of the 427-day term."
[Sidenote: Consequences of the discovery.]
[Sidenote: Suspected observers acquitted.]
At this point we must leave the fascinating account of the manner in which this great discovery was established, in the teeth of opposition such as might have dismayed and dissuaded a less clear-sighted or courageous man.
It is my purpose to lay more stress upon the method of making the discovery than upon its results; but we may afford a brief glance at some of the consequences which have already begun to flow from this step in advance. Some of them have indeed already come before us, especially that large cla.s.s represented by the explanation of anomalies in series of observations which had been put aside as inexplicable. We have seen how the observations made in Russia, or in Washington, or at Greenwich, in all of which there was some puzzling error, were immediately straightened out when Chandler applied his new rule to them. We in England have special cause to be grateful to Chandler; not only has he demonstrated more clearly than ever the greatness of Bradley, but he has rehabilitated Pond, the Astronomer Royal of the beginning of the nineteenth century; showing that his observations, which had been condemned as in some way erroneous, were really far more accurate than might have been expected; and further he has shown that the beautiful instrument designed by Airy, and called the Reflex Zenith Tube, which seemed to have unaccountably failed in the purpose for which it was designed, was really all the time acc.u.mulating observations of this new phenomenon, the Variation of Lat.i.tude. Instead of Airy having failed in his design, he had in Chandler's words "builded better than he knew."
[Sidenote: Constant of Aberration improved.]
Secondly, there is the modifying influence of this new phenomenon on other phenomena already known, such, for instance, as that of "aberration." We saw in the third chapter how Bradley discovered this effect of the velocity of light, and how the measure of it is obtained by comparing the velocity of light with that of the earth. This comparison can be effected in a variety of ways, and we should expect all the results to agree within certain limits; but this agreement was not obtained, and Chandler has been able to show one reason why, and to remove some of the more troublesome differences. It is impossible to give here an idea of the far-reaching consequences which such work as this may have; so long as there are differences of this kind we cannot trust any part of the chain of evidence, and there is in prospect the enormous labour of examining each separate link until the error is found. The velocity of light, for instance, may be measured by a terrestrial experiment; was there anything wrong in the apparatus? The velocity of the earth in its journey round the sun depends directly upon the distance of the sun: have we measured this distance wrongly, and if so what was the error in the observations made?
These are some of the questions which may arise so long as the values for the _Constant of Aberration_ are still conflicting; but it requires considerable knowledge of astronomy to appreciate them fully.
[Sidenote: Lat.i.tude Variation Tide.]
Another example will, perhaps, be of more general interest. If the axis of the earth is executing small oscillations of this kind, there should be an effect upon the tides; the liquid ocean should feel the wobble of the earth's axis in some way; and an examination of tidal registers showed that there was in fact a distinct effect. It may cause some amus.e.m.e.nt when I say that the rise and fall are only a few inches in any case; but they are unmistakable evidences that the earth is not spinning smoothly, but has this kind of unbalanced vibration, which I have compared to the vibrations felt by pa.s.sengers on an imperfectly engineered twin-screw steamer. A more sensational effect is that apparently earthquakes are more numerous at the time when the vibration is greatest. We remarked that the vibration waxes and wanes, much as that of the steamer waxes and wanes if the twin-screws are not running quite together. Now the pa.s.sengers on the steamer would be prepared to find that breakages would be more numerous during the times of vigorous oscillation; and it seems probable that in a similar way the little cracks of the earth's skin which we call great earthquakes are more numerous when these unbalanced vibrations are at their maximum; that is to say, about once every seven years. This result is scarcely yet worthy of complete confidence, for our observations of earthquakes have only very recently been reduced to proper order; but if it should turn out to be true, it is scarcely necessary to add any words of mine to demonstrate the importance of this rather unexpected result of the Lat.i.tude Variation.
[Sidenote: The Kimura phenomenon.]
Finally I will mention another phenomenon which seems to be at present more of a curiosity than anything else, but which may lead to some future great discovery. It is the outcome of observations which have been recently made to watch these motions of the Pole; for although there seems good reason to accept Mr. Chandler's laws of variation as accurate, it is necessary to establish their accuracy and complete the details by making observations for some time yet to come; and there could be no better proof of this necessity than the discovery recently made by Mr. Kimura, one of those engaged in this watch of the Pole in j.a.pan. Perhaps I can give the best idea of it by mentioning one possible explanation, which, however, I must caution you may not be by any means the right one. We are accustomed to think of this great earth as being sufficiently constant in shape; if asked, for instance, whether its centre of gravity remains constantly in the same place inside it, we should almost certainly answer in the affirmative, just as only twenty years ago we thought that the North Pole remained in the same place. But it seems possible that the centre of gravity moves a few feet backwards and forwards each year--this would at any rate explain certain curious features in the observations to which Mr.
Kimura has drawn attention. Whatever the explanation of them may be, or to settle whether this explanation is correct, we want more observations, especially observations in the Southern Hemisphere; and it is a project under consideration by astronomers at the present moment whether three stations can be established in the Southern Hemisphere for the further observation of this curious phenomenon. The question resolves itself chiefly into a question of money; indeed, most astronomical projects do ultimately resolve themselves into questions of money; and I fear the world looks upon scientific men as insatiable in this respect. One can only hope that on the whole the money is expended so as to give a satisfactory return. In this instance I have no hesitation in saying that an immediate return of value for a comparatively modest expenditure is practically certain, if only in some way we can get the means of making the observations.
It would be natural, at the conclusion of this brief review of some types of astronomical discovery, to summarise the lessons indicated: but there is the important difficulty that there appear to be none. It has been pointed out as we proceeded that what seemed to be a safe deduction from one piece of history has been flatly contradicted by another; no sooner have we learnt that important results may be obtained by pursuing steadily a line of work in spite of the fact that it seems to have become tedious and unprofitable (as in the search for minor planets) than we are confronted with the possibility that by such simple devotion to the day's work we may be losing a great opportunity, as Challis did. We can scarcely go wrong in following up the study of residual phenomena in the wake of Bradley; but there is the important difficulty that we may be wholly unable to find a clue for the arrangement of our residuals, as is at present largely the case in meteorology. And, in general, human expectations are likely to be quite misleading, as has been shown in the last two chapters; the discoveries we desire may lie in the direction precisely opposite to that indicated by the best opinion at present available. There is no royal road to discovery, and though this statement may meet with such ready acceptance that it seems scarcely worth making, it is hoped that there may be sufficient of interest in the ill.u.s.trations of its truth.
The one positive conclusion which we may derive from the examples studied is that discoveries are seldom made without both hard work and conspicuous ability. A new planet, even as large as Ura.n.u.s, does not reveal itself to a pa.s.sive observer: thirteen times it may appear to such a one without fear of detection, until at last it encounters an alert Herschel, who suspects, tests, and verifies, and even then announces a comet--so little did he realise the whole truth. Fifteen years of unrequited labour before Astraea was found, nineteen years of observation before the discovery of nutation could be announced: how seldom do these years of toil present themselves to our imaginations when we glibly say that "Bradley discovered nutation," or "Hencke discovered Astraea"! That the necessary labour is so often forgotten must be my excuse for recalling attention to it somewhat persistently in these examples.
But beyond the fact that he must work hard, it would seem as though there were little of value to tell the would-be discoverer. The situation has been well summarised by Jevons in his chapter on Induction in the "Principles of Science;" and his words will form a fitting conclusion to these chapters:--
"It would seem as if the mind of the great discoverer must combine contradictory attributes. He must be fertile in theories and hypotheses, and yet full of facts and precise results of experience.
He must entertain the feeblest a.n.a.logies, and the merest guesses at truth, and yet he must hold them as worthless till they are verified in experiment. When there are any grounds of probability he must hold tenaciously to an old opinion, and yet he must be prepared at any moment to relinquish it when a clearly contradictory fact is encountered."
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