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# but at that moment he was deep in experiments on his new

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[PLATE: CAMBRIDGE OBSERVATORY.]

It has been pointed out that, in consequence of the solar disturbance, the orbit of the moon must be some what enlarged. As it now appears that the solar disturbance is on the whole declining, it follows that the orbit of the moon, which has to be adjusted relatively to the average value of the solar disturbance, must also be gradually declining. In other words, the moon must be approaching nearer to the earth in consequence of the alterations in the eccentricity of the earth's orbit produced by the attraction of the other planets. It is true that the change in the moon's position thus arising is an extremely small one, and the consequent effect in accelerating the moon's motion is but very slight. It is in fact almost imperceptible, except when great periods of time are involved. Laplace undertook a calculation on this subject. He knew what the efficiency of the planets in altering the dimensions of the earth's orbit amounted to; from this he was able to determine the changes that would be propagated into the motion of the moon. Thus he ascertained, or at all events thought he had ascertained, that the acceleration of the moon's motion, as it had been inferred from the observations of the ancient eclipses which have been handed down to us, could be completely accounted for as a consequence of planetary perturbation. This was regarded as a great scientific triumph. Our belief in the universality of the law of gravitation would, in fact, have been seriously challenged unless some explanation of the lunar acceleration had been forthcoming. For about fifty years no one questioned the truth of Laplace's investigation. When a mathematician of his eminence had rendered an explanation of the remarkable facts of observation which seemed so complete, it is not surprising that there should have been but little temptation to doubt it. On undertaking a new calculation of the same question, Professor Adams found that Laplace had not pursued this approximation sufficiently far, and that consequently there was a considerable error in the result of his analysis. Adams, it must be observed, did not impugn the value of the lunar acceleration which Halley had deduced from the observations, but what he did show was, that the calculation by which Laplace thought he had provided an explanation of this acceleration was erroneous. Adams, in fact, proved that the planetary influence which Laplace had detected only possessed about half the efficiency which the great French mathematician had attributed to it. There were not wanting illustrious mathematicians who came forward to defend the calculations of Laplace. They computed the question anew and arrived at results practically coincident with those he had given. On the other hand certain distinguished mathematicians at home and abroad verified the results of Adams. The issue was merely a mathematical one. It had only one correct solution. Gradually it appeared that those who opposed Adams presented a number of different solutions, all of them discordant with his, and, usually, discordant with each other. Adams showed distinctly where each of these investigators had fallen into error, and at last it became universally admitted that the Cambridge Professor had corrected Laplace in a very fundamental point of astronomical theory.

Though it was desirable to have learned the truth, yet the breach between observation and calculation which Laplace was believed to have closed thus became reopened. Laplace's investigation, had it been correct, would have exactly explained the observed facts. It was, however, now shown that his solution was not correct, and that the lunar acceleration, when strictly calculated as a consequence of solar perturbations, only produced about half the effect which was wanted to explain the ancient eclipses completely. It now seems certain that there is no means of accounting for the lunar acceleration as a direct consequence of the laws of gravitation, if we suppose, as we have been in the habit of supposing, that the members of the solar system concerned may be regarded as rigid particles. It has, however, been suggested that another explanation of a very interesting kind may be forthcoming, and this we must endeavour to set forth.

It will be remembered that we have to explain why the period of revolution of the moon is now shorter than it used to be. If we imagine the length of the period to be expressed in terms of days and fractions of a day, that is to say, in terms of the rotations of the earth around its axis, then the difficulty encountered is, that the moon now requires for each of its revolutions around the earth rather a smaller number of rotations of the earth around its axis than used formerly to be the case. Of course this may be explained by the fact that the moon is now moving more swiftly than of yore, but it is obvious that an explanation of quite a different kind might be conceivable. The moon may be moving just at the same pace as ever, but the length of the day may be increasing. If the length of the day is increasing, then, of course, a smaller number of days will be required for the moon to perform each revolution even though the moon's period was itself really unchanged. It would, therefore, seem as if the phenomenon known as the lunar acceleration is the result of the two causes. The first of these is that discovered by Laplace, though its value was overestimated by him, in which the perturbations of the earth by the planets indirectly affect the motion of the moon. The remaining part of the acceleration of our satellite is apparent rather than real, it is not that the moon is moving more quickly, but that our time-piece, the earth, is revolving more slowly, and is thus actually losing time. It is interesting to note that we can detect a physical explanation for the apparent checking of the earth's motion which is thus manifested. The tides which ebb and flow on the earth exert a brake-like action on the revolving globe, and there can be no doubt that they are gradually reducing its speed, and thus lengthening the day. It has accordingly been suggested that it is this action of the tides which produces the supplementary effect necessary to complete the physical explanation of the lunar acceleration, though it would perhaps be a little premature to assert that this has been fully demonstrated.

The third of Professor Adams' most notable achievements was connected with the great shower of November meteors which astonished the world in 1866. This splendid display concentrated the attention of astronomers on the theory of the movements of the little objects by which the display was produced. For the definite discovery of the track in which these bodies revolve, we are indebted to the labours of Professor Adams, who, by a brilliant piece of mathematical work, completed the edifice whose foundations had been laid by Professor Newton, of Yale, and other astronomers.

Meteors revolve around the sun in a vast swarm, every individual member of which pursues an orbit in accordance with the well-known laws of Kepler. In order to understand the movements of these objects, to account satisfactorily for their periodic recurrence, and to predict the times of their appearance, it became necessary to learn the size and the shape of the track which the swarm followed, as well as the position which it occupied. Certain features of the track could no doubt be readily assigned. The fact that the shower recurs on one particular day of the year, viz., November 13th, defines one point through which the orbit must pass. The position on the heavens of the radiant point from which the meteors appear to diverge, gives another element in the track. The sun must of course be situated at the focus, so that only one further piece of information, namely, the periodic time, will be necessary to complete our knowledge of the movements of the system. Professor H. Newton, of Yale, had shown that the choice of possible orbits for the meteoric swarm is limited to five. There is, first, the great ellipse in which we now know the meteors revolve once every thirty three and one quarter years. There is next an orbit of a nearly circular kind in which the periodic time would be a little more than a year. There is a similar track in which the periodic time would be a few days short of a year, while two other smaller orbits would also be conceivable. Professor Newton had pointed out a test by which it would be possible to select the true orbit, which we know must be one or other of these five. The mathematical difficulties which attended the application of this test were no doubt great, but they did not baffle Professor Adams.

There is a continuous advance in the date of this meteoric shower. The meteors now cross our track at the point occupied by the earth on November 13th, but this point is gradually altering. The only influence known to us which could account for the continuous change in the plane of the meteor's orbit arises from the attraction of the various planets. The problem to be solved may therefore be attacked in this manner. A specified amount of change in the plane of the orbit of the meteors is known to arise, and the changes which ought to result from the attraction of the planets can be computed for each of the five possible orbits, in one of which it is certain that the meteors must revolve. Professor Adams undertook the work. Its difficulty principally arises from the high eccentricity of the largest of the orbits, which renders the more ordinary methods of calculation inapplicable. After some months of arduous labour the work was completed, and in April, 1867, Adams announced his solution of the problem. He showed that if the meteors revolved in the largest of the five orbits, with the periodic time of thirty three and one quarter years, the perturbations of Jupiter would account for a change to the extent of twenty minutes of arc in the point in which the orbit crosses the earth's track. The attraction of Saturn would augment this by seven minutes, and Uranus would add one minute more, while the influence of the Earth and of the other planets would be inappreciable. The accumulated effect is thus twenty-eight minutes, which is practically coincident with the observed value as determined by Professor Newton from an examination of all the showers of which there is any historical record. Having thus showed that the great orbit was a possible path for the meteors, Adams next proved that no one of the other four orbits would be disturbed in the same manner. Indeed, it appeared that not half the observed amount of change could arise in any orbit except in that one with the long period. Thus was brought to completion the interesting research which demonstrated the true relation of the meteor swarm to the solar system.

Besides those memorable scientific labours with which his attention was so largely engaged, Professor Adams found time for much other study. He occasionally allowed himself to undertake as a relaxation some pieces of numerical calculation, so tremendously long that we can only look on them with astonishment. He has calculated certain important mathematical constants accurately to more than two hundred places of decimals. He was a diligent reader of works on history, geology, and botany, and his arduous labours were often beguiled by novels, of which, like many other great men, he was very fond. He had also the taste of a collector, and he brought together about eight hundred volumes of early printed works, many of considerable rarity and value. As to his personal character, I may quote the words of Dr. Glaisher when he says, "Strangers who first met him were invariably struck by his simple and unaffected manner. He was a delightful companion, always cheerful and genial, showing in society but few traces of his really shy and retiring disposition. His nature was sympathetic and generous, and in few men have the moral and intellectual qualities been more perfectly balanced."

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