LITMIR.BIZ

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between the observed planets and our earth.

      Unfortunately, it turned out that Jupiter, one of the planets from which Herschel expected most, does 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 was 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 not 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 is 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, 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. 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

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