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. 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 moon’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 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
