PROFESSOR ADAMS' RECENT DISCOVERIES IN

ASTRONOMY.

BY an old rule of the Editors, the technicalities of science are excluded from the pages of the Eagle: and if this article should appear to any of our readers to trench on this rule, we must make the importance of the subject, the interest it will have to many resident and non-resident subscribers, and our peculiar pleasure in the success of our eminent fellow-collegian, our apologies, if such indeed be needed. Many, we hope, of the scattered members of our college, as they read this paper, will be pleasantly reminded of the hours they have spent on Godfray's Lunar Theory, or Herschel's Astronomy, or Laplace's Exposition du Système du Monde; and many more, to whom these pleasant recollections are denied, will read with interest an account of one of the most remarkable and pregnant discoveries of modern times.

Professor Adams, director of our Cambridge Observatory, at the beginning of the present year, received from the hands of the President of the Royal Astronomical Society the Gold Medal for his valuable contributions to the Developement of the Lunar Theory. I propose in the present paper to give a short sketch of the nature of these contributions, and to point out their importance, and their position in the splendid History of Astronomical Discovery. It will be possible, I trust, to present this subject in a manner that shall be intelligible to an attentive reader, even if he is unversed in the mysteries of mathematical representation.

If a careless person were to note the position of the moon among the stars on a succession of fine evenings, he might suppose that, during the intervals of twenty-four hours between his observations, the moon moved over equal distances. A more careful observer would see that this is

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not quite the case; but that sometimes it moved faster, and at other times slower. If now his attention were arrested by this irregular motion, and he were accurately to observe what the motion of the moon really is at all times, and express it in such a manner as to enable him to predict its motions and position for the future, and assign it for the past, he would be constructing by observation a Lunar Theory. The astronomers before Newton, by means of observation alone, made progress in this direction which will always strike the student of the subject with admiration and astonishment. They discovered that the position and motion of the moon depended upon the relative position of the sun; and found means of expressing this dependence. To show how they discovered this, and how they expressed it, would be to write an historical account of the Lunar Theory, which is not my purpose; it will suffice here if it is understood that they discovered that the distance of the moon in front of, or behind the position which it would have occupied had it moved uniformly in a circle round the earth, could be represented by adding to and subtracting from that position a long series of small distances, each of which depended ultimately in a simple manner on the relative position and distances of the three bodies, the sun, the earth and the moon. These small distances are called terms, equations, variations, &c. In the discovery of the existence, and accurate establishment of the magnitude of more and more of these small terms, and thereby predicting more accurately the moon's position, resides the development of the Lunar Theory.

Newton's hypothesis of the law of gravitation, that all bodies attracted all others with a force proportional to the mass and inversely proportional to the square of the distance, altered the aspect of the Lunar Theory. If the law were true, (and the evidence for it was overwhelming,) the motion of the moon might be deduced from this law, by tracing its consequences when applied to the mutual action of the three bodies and, conversely, the truth of the law might here be submitted to the most rigorous test. Newton began this great work with unrivalled sagacity, and the great mathematicians of the age succeeding his, applying the powerful instrument of analysis to the problem, raised the theory by successive approximation to an extraordinary pitch of perfection. The highest stimulus was given to the observers and to the mathematicians; any deviation of the observed place of the moon from the place predicted for her by the mathematicians, sent them to their work again: the inexorable moon

travels on in her orbit regardless of the efforts that are being made to account for her eccentric motions; and if she is not where the mathematicians say she ought to be, either their calculations or the law of gravitation must be wrong. Lunam quis dicere falsam audeat.

Now discrepancies of this kind have several times occurred; and the importance of Adams's discoveries is well illustrated by some of them. In any single revolution, it may be well to observe, of the moon round the earth, her path will be nearly an ellipse; cutting the plane in which the earth moves round the sun, in a line which is called the line of nodes; and the axis major of which is called the line of perigee and apogee, from its passing through the points at which the moon is respectively nearest to and furthest from the earth."* But the path is not quite an ellipse; it is distorted by the action of the sun on the moon, and at the end of the month the moon has not exactly returned to the spot where she was at the beginning. Hence she sets out for the next month in a new ellipse differing slightly from the previous one; and the new line of nodes or line of perigee will be in a different position from the old one; and this is expressed by stating that the line of nodes advances or is retrograde. Now it will be understood that such motions as these admit both of being observed, and of being calculated, on Newton's hypothesis; and Newton's hypothesis is tested by its results agreeing with observation. The most famous discrepancy was in the motion of the line of perigee. The theory of Newton, in his own hands, gave only half the motion actually observed. And moreover when the higher calculus was applied by the skilful hands of Clairaut, it gave the same result. Clairaut did not hesitate to suggest that Newton's law might be an incomplete and approximative representation of the law of nature; but he was fortunate enough to discover afterwards that it was his own calculations which were incomplete and approximative; they were soon advanced to a level with observation; the agreement was complete, and Newton's law established more securely than

ever.

Once more, the smaller planets Juno and Pallas and Vesta were affected with perturbations of unaccountable magnitude. They seemed from their character to be due to Jupiter, but Jupiter's mass was inadequate to produce them. Bessel suggested that the attraction which Jupiter exercised on them might be not in proportion to his mass, but be elective, like magnetic attraction: an extraordinary solution,

which has been happily rendered unnecessary by Airy's discovery that the mass of Jupiter had previously been wrongly determined, and that when the right mass was used the disturbances of the little planets were all en règle.

So when a discrepancy is found to exist between calculation and observation, it has been always the herald of fresh discoveries.

Now when the solution of the great problem about the moon's motion was first effected, and was awaiting the verdict of the future to test its powers of accurate prediction, it was an obvious thought to verify it by an appeal to the past. If the shortness of life forbade these early mathematicians to verify their calculations in future ages, they could at least shew that the position of the moon at any past epoch could be accurately ascertained. And the accuracy of these predictions respecting the past, if I may be allowed the expression, could be examined by means of the records of eclipses. Would or would not their theory assign such a position to the moon on June 21, B.C. 399, that her shadow should be thrown on Rome just before sun-set, and on January 23, A.D. 883, that her shadow should be thrown on Antioch?

Halley seems to have been the first who considered this question. With astonishing clearness he seized the conditions of this question, saw that the knowledge of the elements, on which the solution was to be founded, was as yet incomplete, and saw also the probability that, when the accurate knowledge was obtained, it would appear that there was a peculiarity in the moon's motion entirely unforeseen by others, that it was now moving faster, and performing its revolution in a shorter time than it did in past time. If the longitudes of Bagdad, Antioch, and other places were accurately known, "I could then," he says, "pronounce in what proportion the moon's motion does accelerate; which that it does, I think I can demonstrate, and shall (God willing) one day make it appear to the public." Newton adds to his second edition of the Principia, the words, "Halleius noster motum medium Lunæ cum motu diurno terræ collatum paulatim accelerari primus omnium quod sciam deprehendit.”

This is the first chapter in the History of the discovery by observation of the amount of secular acceleration of the moon's mean motion. The next chapter should contain an account of the detailed examination of all the ancient eclipses, and the inferences as to the acceleration finally deduced. The details are however too complicated for introduction here: I can only observe that in order that an ancient eclipse

should be valuable for this purpose, its date, its hour and the place of observation are required: and to ascertain these requires often a minute historical and geographical investigation, besides elaborate mathematical work.

If the place and date are given, and the tables in which the moon's motion is minutely described, are used to calculate the path of the eclipse of that date, if the tables are in error ever so little they will make the path of the eclipse pass not over the given place, and it may thence be calculated what change must be made in the moon's mean motion as given by the tables, to bring its shadow at that particular date to that particular place. Such are the two eclipses observed by Ibn Junis at Cairo in A.D. 977, and 978, 66 quæ in astronomia lunari," says Mayer, "auro argentoque omni pretiosiores, meo quidem judicio sunt habendæ.

And again, if the place is given, the date is not given exactly but is known to be within certain limits, even this record can be made use of. For it must be recollected that total eclipses of the sun are not common at any assigned spot. In London, for example, only one has been seen since A.D. 1400. If then a calculation from the tables of the moon's motion, assuming a certain amount of secular acceleration, is made about the eclipses which have been visible at that spot, it may happen that none took place within the assigned limit of time which was total at that spot, but that there was one eclipse which would have been total at that spot if we make a slight change in the assumed acceleration. And thus the amount of the acceleration and the date are simultaneously fixed with a certain degree of probability. The degree of this probability depends of course on the previous accuracy of the tables and on the tolerable correctness of the amount of acceleration first assumed; for if they were far wrong more than one eclipse might be forced into identity with the historical eclipse, by making suitable hypothetical corrections in the moon's mean motion. And thus the eclipse which Thales is said to have predicted was identified by Bailey and Oltmann, with the one which took place on September 30, B.C. 610; but by Airy with that of May 28, B.C. 585. Hence it will be understood:

(1) That observation indicates a secular acceleration of the moon's mean motion.

(2) That eclipses furnish the means of ascertaining the amount of the acceleration with a considerable degree of accuracy.

(3) That the amount of the secular acceleration deduced