A distinguished French astronomer, author of one of the most fascinating works on popular astronomy that has hitherto appeared, remarks that a man would be looked upon as a maniac who should speak of the influence of Jupiter’s moons upon the cotton trade. Yet, as he proceeds to show, there is an easily traced connection between the ideas which appear at first sight so incongruous. The link is found in the determination of celestial longitude.

Similarly, we should be disposed to wonder at an astronomer who, regarding thoughtfully the stately motion of the sidereal system, as exhibited on a magnified, and, therefore, appreciable scale by a powerful telescope, should speak of the connection between this movement and the intrinsic worth of a sovereign. The natural thought with most men would be that ‘too much learning’ had made the astronomer mad. Yet, when we come to inquire closely into the question of a sovereign’s intrinsic value, we find ourselves led to the diurnal motion of the stars, and that by no very intricate path. For, What is a sovereign? A coin containing so many grains of gold mixed with so many grains of alloy. A grain, we know, is the weight of such and such a volume of a certain standard substance—that is, so many cubic inches, or parts of a cubic inch, of that substance. But what is an inch?31 It is determined, we find, as a certain fraction of the length of a pendulum vibrating seconds in the latitude of London. A second, we know, is a certain portion of a mean solar day, and is practically determined by a reference to what is called a sidereal day—the interval, namely, between the successive passages by the same star of the celestial meridian of any fixed place. This interval is assumed to be constant, and it has, indeed, been described as the ‘one constant element’ known to astronomers.

We find, then, that there is a connection, and a very important connection, between the motion of the stars and our measures, not merely of value, but of weight, length, volume, and time. In fact, our whole system of weights and measures is founded on the apparent diurnal motion of the sidereal system, that is, on the real diurnal rotation of the earth. We may look on the meridian-plane in which the great transit-telescope of the Greenwich Observatory is made to swing, as the gigantic hand of a mighty dial, a hand which, extending outwards among the stars, traces out for us, by its motion among them, the exact progress of time, and so gives us the means of weighing, measuring, and valuing terrestrial objects with an exactitude which is at present beyond our wants.

The earth, then, is our ‘chief time-piece,’ and it is of the correctness of this giant clock that I am now to speak.

But how can we test a time-piece whose motions32 we select to regulate every other time-piece? If a man sets his watch every morning by the clock at Westminster, it is clearly impossible for him to test the accuracy of that clock by the motions of his watch. It would, indeed, be possible to detect any gross change of rate; but for the purpose of illustration I assume, what is indeed the case, that the clock is very accurate, and therefore that minute errors only are to be looked for even in long intervals of time. And just as the watch set by a clock cannot be made use of to test the clock for small errors, so our best time-pieces cannot be employed to detect slow variations, if any such exist, in the earth’s rotation-period.

Sir William Herschel, who early saw the importance of the subject, suggested another method. Some of the planets rotate in such a manner, and bear such distinct marks upon their surface, that it is possible, by a series of observations extending over a long interval of time, to determine the length of their rotation-period within a second or two. Supposing their rotation uniform, we at once obtain an accurate measure of time. Supposing their rotation not uniform, we obtain—(1) a hint of the kind of change we are looking for; and (2), by the comparison of two or more planets, the means of guessing how the variation is to be distributed between the observed planets and our earth.

Unfortunately, it turned out that Jupiter, one of the planets from which Herschel expected most, does33 not afford us exact information-his real surface being always veiled by his dense and vapour-laden atmosphere. Saturn, Venus, and Mercury are similarly circumstanced, and are in other respects unfavourable objects for this sort of observation. Mars only, of all the planets, is really available. Distinctly marked (in telescopes of sufficient power) with continents and oceans, which are rarely concealed by vapours, this planet is in other respects fortunately situated. For it is certain that whatever variations may be taking place in planetary rotations must be due to external agencies. Now, Saturn and Jupiter have their satellites to influence (perhaps appreciably in long intervals of time) their rotation-movements. Venus and Mercury are near the sun, and are therefore in this respect worse off than the earth, whose rotation is in question. Mars, on the other hand, farther removed than we are from the sun, having also no moon, and being of small dimensions (a very important point, be it observed, since the tidal action of the sun depends on the dimensions of a planet), is likely to have a rotation-period all but absolutely constant.

Herschel was rather unfortunate in his observations of Mars. Having obtained a rough approximation from Mars’ rotation in an interval of two days—this rough approximation being, as it chanced, only thirty-seven seconds in excess of the true period, he proceeded to take three intervals of one month each. This should have given a much better value; but, as it happened, the mean of the values he obtained was34 forty-six seconds too great. He then took a period of two years, and being misled by the erroneous values he had already obtained, he missed one rotation, getting a value two minutes too great. Thirty years ago, two German astronomers, Beer and Madler, tried the same problem, and taking a period of seven years, obtained a value which exceeds the true value by only one second. Another German, Kaiser, by combining more observations, obtained a value which is within one-fifteenth of a second of the true value. But a comparison of observations extending over 200 years has enabled me to obtain a value which I consider to lie within one-hundredth part of a second of the truth. This value for Mars’ rotation-period is 24 hours 37 minutes 22·73 seconds.

Here, then, we have a result so accurate, that at some future time it may serve to test the earth’s rotation-period. We have compared the rotation-rate of our test-planet with the earth’s rate during the past 200 years; and therefore, if the earth’s rate vary by more than one-hundredth of a second in the next two or three hundred years, we shall—or rather our descendants will—begin to have some notion of the change at the end of that time.

But in the meantime, mankind being impatient, and not willing to leave to a distant posterity any question which can possibly be answered now, astronomers have looked around them for information available at once on this interesting point. The search has not35 been in vain. In fact, we are able to announce, with an approach to positiveness, that our great terrestrial time-piece is actually losing time.

In our moon we have a neighbour which has long been in the habit of answering truthfully questions addressed to her by astronomers. Of old, she told Newton about gravitation, and when he doubted, and urged opposing evidence offered—as men in his time supposed—by the earth, she set him on the right track, so that when in due time the evidence offered by the earth was corrected, Newton was prepared at once to accept and propound the noble theory which rendered his name illustrious. Again, men wished to learn the true shape of the earth, and went hither and thither measuring its globe; but the moon, meanwhile, told the astronomer who remained at home a truer tale. They sought to learn the earth’s distance from the sun, and from this and that point they turned their telescopes on Venus in transit; but the moon set them nearer the truth, and that not by a few miles, but by 2,000,000 miles or more. We shall see that she has had something to say about our great terrestrial time-piece.

One of the great charms of the science of astronomy is, that it enables men to predict. At such and such an hour, the astronomer is able to say, a celestial body will occupy such and such a point on the celestial sphere. You direct a telescope towards the point named, and lo! at the given instant, the promised orb sweeps across the field of view. Each year there is36 issued a thick octavo volume crowded with such predictions, three or four years in advance of the events predicted; and these predictions are accepted with as little doubt by astronomers as if they were the records of past events.

But astronomers are not only able to predict—they can also trace back the paths of the celestial bodies, and say: ‘At such and such a long-past epoch, a given star or planet occupied such and such a position upon the celestial sphere.’ But how are they to verify such a statement? It is clear that, in general, they cannot do so. Those who are able to appreciate (or better, to make use of) the predictions of astronomy, will, indeed, very readily accord a full measure of confidence to calculations of past events. They know that astronomy is justly named the most exact of the sciences, and they can see that there is nothing, in the nature of things, to render retrospection more difficult than prevision. But there are hundreds who have no such experience of the exactness of modern astronomical methods—who have, on the contrary, a vague notion that modern astronomy is merely the successor of systems now exploded; perhaps even that it may one day have to make way in its turn for new methods. And if all other men were willing to accept the calculations of astronomers respecting long-past events, astronomers themselves would be less easily satisfied. Long experience has taught them that the detection of error is the most fruitful source of knowledge; therefore, wherever such a course is possible,37 they always gladly submit their calculations to the test of observation.

Now, looking backward into the far past, it is only here and there that we see records which afford means of comparison with modern calculations. The planets had swept on in their courses for ages with none to note them. Gradually, observant men began to notice and record the more remarkable phenomena. But such records, made with very insufficient instrumental means, had in general but little actual value: it has been found easy to confirm them without any special regard to accuracy of calculation.

There is one class of phenomena, however, which no inaccuracy of observation can very greatly affect. A total eclipse of the sun is an occurrence so remarkable, that (1) it can hardly take place without being recorded, and (2) a very rough record will suffice to determine the particular eclipse referred to. Long intervals elapse between successive total eclipses visible at the same place on the earth’s surface, and even partial eclipses of noteworthy extent occur but seldom at any assigned place. Very early, therefore, in the history of modern astronomy, the suggestion was made, that eclipses recorded by ancient historians should be calculated retrospectively. An unexpected result rewarded the undertaking. It was found that ancient eclipses could not be fairly accounted for without assigning a slower motion to the moon in long-past ages than she has at present!

Here was a difficulty which long puzzled mathematicians.38 One after another was foiled by it. Halley, an English mathematician, had detected the difficulty, but no English mathematician was able to grapple with it. Contented with Newton’s fame, they had suffered their Continental rivals to shoot far ahead in the course he had pointed out. But the best Continental mathematicians were defeated. In papers of acknowledged merit, adorned by a variety of new processes, and showing a deep insight into the question at issue, they yet arrived, one and all, at the same conclusion—failure.

Ninety years elapsed before the true explanation was offered by the great mathematician Laplace. A full exposition of his views would be out of place in such a paper as the present, but, briefly, they amount to this:—

The moon travels in her orbit, swayed chiefly by the earth’s attraction. But the sun, though greatly more distant, yet, owing to the immensity of his mass, plays an important part in guiding our satellite. His influence tends to relieve the moon, in part, from the earth’s sway. Thus she travels in a wider orbit, and with a slower motion, than she would have but for the sun’s influence. Now the earth is not at all times equally distant from the sun, and his influence upon the moon is accordingly variable. In winter, when the earth is nearest to the sun, his influence is greatest. The lunar month, accordingly (though the difference is very slight), is longer in winter than in summer. This variation had long been recognised as the moo39n’s ‘annual equation;’ but Laplace was the first to point out that the variation is itself slowly varying. The earth’s orbit is slowly changing in shape—becoming more and more nearly circular year by year. As the greater axis of her orbit is unchanging, it is clear that the actual extent of the orbit is slowly increasing. Thus, the moon is slightly released from the sun’s influence year by year, and so brought more and more under the earth’s influence. She travels, therefore, continually faster and faster, though the change is indeed but a very minute one;—only to be detected in long intervals of time. Also the moon’s acceleration, as the change is termed, is only temporary, and will in due time be replaced by an equally gradual retardation.

When Laplace had calculated the extent of the change due to the cause he had detected, and when it was found that ancient eclipses were now satisfactorily accounted for, it may well be believed that there was triumph in the mathematical camp. But this was not all. Other mathematicians attacked the same problem, and their results agreed so closely that all were convinced that the difficulty was thoroughly vanquished.

A very noteworthy result followed from Laplace’s calculations. Amongst other solutions which had been suggested, was the supposition (supported by no less an authority than Sir Isaac Newton, who lived to see the commencement of the long conflict maintained by mathematicians with this difficulty), that it is not the moon travelling more quickly, but our earth rotating40 more slowly, which causes the observed discrepancy. Now it resulted from Laplace’s labours—as he was the first to announce—that the period of the earth’s rotation has not varied by one-tenth of a second per century in the last two thousand years.

The question thus satisfactorily settled, as was supposed, was shelved for more than a quarter of a century. The result, also, which seemed to flow from the discussion—the constancy of the earth’s rotation-movement—was accepted; and, as we have seen, our national system of measures was founded upon the assumed constancy of the day’s duration.

But mathematicians were premature in their rejoicings. The question has been brought, by the labours of Professor Adams—co-discoverer with Leverrier of the distant Neptune—almost exactly to the point which it occupied a century ago. We are face to face with the very difficulties—somewhat modified in extent, but not in character—which puzzled Halley, Euler, and Lagrange. It would be an injustice to the memory of Laplace to say that his labours were thrown away. The explanation offered by him is indeed a just one. But it is insufficient. Properly estimated it removes only half the difficulty which had perplexed mathematicians. It would be quite impossible to present in brief space, and in form suited to these pages, the views propounded by Adams. What, for instance, would most of our readers learn if we were to tell them that, ‘when the variability of the eccentricity is taken into account, in integrating the41 differential equations involved in the problem of the lunar motions—that is, when the eccentricity is made a function of the time—non-periodic or secular terms appear in the expression for the moon’s mean motion’—and so on? Let it suffice to say that Laplace had considered only the work of the sun in diminishing the earth’s pull on the moon, supposing that the slow variation in the sun’s direct influence on the moon’s motion in her orbit must be self-compensatory in long intervals of time. Adams has shown, on the contrary, that when this variation is closely examined, no such compensation is found to take place; and that the effect of this want of compensation is to diminish by more than one-half the effects due to the slow variation examined by Laplace.

These views gave rise at first to considerable controversy. Pontécoulant characterised Adams’s processes as ‘analytical conjuring-tricks,’ and Leverrier stood up gallantly in defence of Laplace. The contest swayed hither and thither for a while, but gradually the press of new arrivals on Adams’s side began to prevail. One by one his antagonists gave way; new processes have confirmed his results, figure for figure; and no doubt now exists, in the mind of any astronomer competent to judge, of the correctness of Adams’s views.

But, side by side with this inquiry, another had been in progress. A crowd of diligent labourers had been searching with close and rigid scrutiny into the circumstances attending ancient eclipses. A new light had been thrown upon this subject by the labours of42 modern travellers and historians. One remarkable instance of this may be cited. Mr. Layard has identified the site of Larissa with the modern Nimroud. Now, Xenophon relates that when Larissa was besieged by the Persians, an eclipse of the sun took place, so remarkable in its effects (and therefore undoubtedly total), that the Median defenders of the town threw down their arms, and the city was accordingly captured. And Hansen has shown that a certain estimate of the moon’s motion makes the eclipse which occurred on August 15, 310 B.C., not only total, but central at Nimroud. Some other remarkable eclipses—as the celebrated sunset eclipse (total) at Rome, 399 B.C.; the eclipse which enveloped the fleet of Agathocles as he escaped from Syracuse; the famous eclipse of Thales, which interrupted a battle between the Medes and Lydians; and even the partial eclipse which (possibly) caused the ‘going back of the shadow upon the dial of Ahaz’—have all been accounted for satisfactorily by Hansen’s estimate of the moon’s motion: so also have nineteen lunar eclipses recorded in the Almagest.

This estimate of Hansen’s, which accounts so satisfactorily for solar and lunar eclipses, makes the moon’s rate of motion increase more than twice as fast as it should do according to the calculations of Adams. But before our readers run away with the notion that astronomers have here gone quite astray, it will be well to present, in a simple manner, the extreme minuteness of the discrepancy about which all the coil has been made.

43

Suppose that, just in front of our moon, a false moon exactly equal to ours in size and appearance (see note at the end of this paper) were to set off with a motion corresponding to the present motion of the moon, save only in one respect—namely, that the false moon’s motion should not be subject to the change we are considering, termed the acceleration. Then one hundred years would elapse before our moon would fairly begin to show in advance. She would, in that time, have brought only one one-hundred-and-fiftieth part of her breadth from behind the false moon. At the end of another century she would have gained four times as much; at the end of a third, nine times as much: and so on. She would not fairly have cleared her own breadth in less than twelve hundred years. But the whole of this gain, minute as it is, is not left unaccounted for by our modern astronomical theories. Half the gain is explained, the other half remains to be interpreted; in other words, the moon travels further by about half her own breadth in twelve centuries than she should do according to the lunar theory.

But in this difficulty, small as it seems, we are not left wholly without resource. We are not only able to say that the discrepancy is probably due to a gradual retardation of the earth’s rotation-movement, but we are able to place our finger on a very sufficient cause for such a retardation. One of the most firmly established principles of modern science is this—that where work is done, force is, in some way or other, expended. The doing of work may show itself in a variety of ways44— in the generation of heat, in the production of light, in the raising of weights, and so on; but in every case an equivalent force must be expended. If the brakes are applied to a train in motion, intense heat is generated in the substance of the brake. Now, the force employed by the brakesman is not equivalent to the heat generated. Where, then, is the balance of force expended? We all know that the train’s motion is retarded, and this loss of motion represents the requisite expenditure of force. Now, is there any process in nature resembling, in however remote a degree, the application of a brake to check the earth’s rotation? There is. The tidal wave, which sweeps, twice a day, round the earth, travels in a direction contrary to the earth’s motion of rotation. That this wave ‘does work,’ no one can doubt who has watched its effects. The mere rise and fall in open ocean may not be strikingly indicative of ‘work done;’ but when we see the behaviour of the tidal wave in narrow channels, when we see heavily-laden ships swept steadily up our tidal rivers, we cannot but recognise the expenditure of force. Now, where does this force come from? Motion being the great ‘force-measurer,’ what motion suffers that the tides may work? We may securely reply, that the only motion which can supply the requisite force is the earth’s motion of rotation. Therefore, it is no mere fancy, but a matter of absolute certainty, that, though slowly, still very surely, our terrestrial globe is losing its rotation-movement.

Considered as a time-piece, what are the eart45h’s errors? Suppose, for a moment, that the earth was timed and rated two thousand years ago, how much has she lost, and what is her ‘rate-error?’ She has lost in that interval nearly one hour and a quarter, and she is losing now at the rate of one second in twelve weeks. In other words, the length of a day is now more by about one eighty-fourth part of a second than it was two thousand years ago. At this rate of change, our day would merge into a lunar month in the course of thirty-six thousand millions of years. But after a while, the change will take place more slowly, and some trillion or so of years will elapse before the full change is effected.

Distant, however, as is the epoch at which the changes we have been considering will become effective, the subject appears to us to have an interest apart from the mere speculative consideration of the future physical condition of our globe. Instead of the recurrence of ever-varying, closely intermingled cycles of fluctuation, we see, now for the first time, the evidence of cosmical decay—a decay which, in its slow progress, may be but the preparation for renewed genesis—but still, a decay which, so far as the races at present subsisting upon the earth are concerned, must be looked upon as finally and completely destructive.2

(From Chambers’s Journal, October 12, 1867.)