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 rotating 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 the 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 of 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.
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 ways—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 earth’s errors? Suppose, for a moment,