ecliptic, and it is possible to calculate where the planet was in each year. It was thus seen that in the year 1690 the planet was situated in that part of the ecliptic where Flamsteed was at the same date making his observations. It was natural to search the

observations of Flamsteed, and see whether any of the so-called stars could have been Uranus. An object was found in the "Historia Cœlestis" which occupied a position identical with that which Uranus must have filled on the same date. Could this be Uranus? A decisive test was at once available. The telescope was directed to the spot in the heavens where Flamsteed saw a sixthmagnitude star. If that were really a star, then would it still be visible. The trial was made: no such star could be found, and hence the presumption that this was really Uranus could hardly be for a moment doubted. Speedily other confirmations flowed in. It was shown that Uranus had been unconsciously observed by Bradley and by Tobias Mayer, and it also became apparent that Flamsteed had observed Uranus not only once, but that he had actually measured its place four or five times between the years 1690 and 1715. Yet Flamsteed was never conscious of the discovery that lay so nearly in his grasp. He was of course under the impression that all these observations related to different stars. A still more remarkable case is found among the observations of Lemonnier. After Uranus had been discovered, Lemonnier turned to examine his former observations, and among them he found that he had really observed Uranus no less than three times, on each occasion, of course, recording it as a distinct star. But Uranus had in reality a still narrower escape from being detected by Lemonnier. Another astronomer on going again over Lemonnier's work found no fewer than nine additional observations of Uranus, and of these four had been made on consecutive nights. How close, indeed, was Lemonnier to the discovery which would have immortalised him! During the intervals between those four nights, the planet of course moved, and was of course taken for a different star each night. If Lemonnier had only carefully looked over his own work; if he had perceived, as he might have done, how the star he observed

yesterday was gone to-day, while the star visible to-day had moved away by to-morrow, there is no doubt that Uranus would have been discovered, and William Herschel would have been anticipated. Would Lemonnier have made as good use of his fame as Herschel did? This is a question hard, perhaps, to answer; but those who estimate Herschel as the present writer thinks he ought to be estimated, will probably agree in thinking that it was most fortunate for science that Lemonnier did not compare his observations.*

These early accidental observations of Uranus are not merely to be regarded as matters of historical interest or curiosity. That they are of the deepest importance with regard to the science itself a few words will enable us to show. It is to be remembered that Uranus requires no less than eighty-four years to accomplish his mighty revolution around the sun. The planet has completed one entire revolution, since its discovery, and up to the present time (1885) has accomplished nearly one-third of another. For the careful study of the nature of the orbit, it was desirable to have as many observations as possible, and extending over the widest possible interval. This was in a great measure secured by the identification of the early observations of Uranus. proximate knowledge of the orbit was quite capable of giving the places of the planet with sufficient accuracy to identify it when met with in the catalogues. But when by their aid the actual observations have been discovered, they tell us precisely the place of Uranus; and hence, instead of our knowledge of the planet being limited to but little more than one revolution, we have at the present time information with regard to it extending over considerably more than two revolutions.

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From the observations of the planet the ellipse in which it moves can be ascertained. We can compute this ellipse from the observations made during the time since the discovery. We can also compute the ellipse from the early observations made

* Arago says that "Lemonnier's records were the image of chaos." Bouvard showed to Arago one of the observations of Uranus which was written on a paper bag that in its time had contained hair-powder.

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before the discovery. If Kepler's laws were rigorously verified, then, of course, the ellipse performed in the present revolution must differ in no respect from the ellipse performed in the preceding, or indeed in any other revolution. We can test this point in an interesting manner by comparing the ellipse derived from the ancient observations with that deduced from the modern ones. These ellipses closely resemble each other; they are nearly the same; but it is most important to observe that they are not exactly the same, even when allowance has been made for every known source of disturbance in accordance with the principles explained in the next chapter. The law of Kepler seems thus not absolutely true in the case of Uranus. Here is, indeed, a matter demanding our most earnest and careful attention. Have we not repeatedly laid down the universality of the laws of Kepler in controlling the planetary motions? How then can we reconcile this law with the irregularities proved beyond a doubt to exist in the motions of Uranus?

Let us look a little more closely into the matter. We know that the laws of Kepler are a consequence of the laws of gravitation. We know that it is in virtue of the sun's attraction that the planet moves in an elliptic path around the sun, and we know that the ellipse will be preserved without the minutest alteration if the sun and the planet be left to their mutual attractions, and no other force intervene to disturb them. The conclusion is irresistible. Uranus does not move solely in consequence of the sun's attraction and that of the planets of our system interior to Uranus; there must therefore be some further influence acting upon Uranus besides those already known. To the development of this subject the next chapter will be devoted.

CHAPTER XV.

NEPTUNE.

Discovery of Neptune-A Mathematical Achievement-The Sun's Attraction-All Bodies Attract-Jupiter and Saturn-The Planetary Perturbations-Three Bodies Nature has Simplified the Problem-Approximate Solution-The Sources of Success-The Problem Stated for the Earth-The Discoveries of Lagrange The Eccentricity-Necessity that all the Planets Revolve in the same Direction-Lagrange's Discoveries have not the Dramatic Interest of the more Recent Achievements-The Irregularities of Uranus-The Unknown Planet must Revolve outside the Path of Uranus-The Data for the ProblemLe Verrier and Adams both Investigate the Question-Adams Indicates the Place of the Planet-How the Search was to be Conducted-Le Verrier also Solves the Problem-The Telescopic Discovery of the Planet—The Rival Claims-Early Observation of Neptune-Difficulty of the Telescopic Study of Neptune--Numerical Details of the Orbit-Is there any Outer Planet ?—Contrast between Mercury and Neptune.

WE enter in this chapter into a discovery so extraordinary that the whole annals of science may be searched in vain for a parallel. We are not here concerned with technicalities of practical astronomy. Neptune was first revealed to us by profound mathematical research rather than by telescopic investigation. We must develop the account of this striking epoch in the history of science with the fulness of detail which is commensurate with its importance; and it will accordingly be necessary, at the outset of our narrative, to make an excursion into a difficult but most attractive region of astronomy, to which we have as yet made little reference.

The supreme controlling power in the solar system is the attraction of the sun. Each planet of the system experiences that attraction, and, in virtue of it, the planet is constrained to move around the sun in an elliptic path. The efficiency of the sun as an attractive agent is directly proportional to its mass, and as its mass is more than a thousand times as great as the mass of Jupiter, which, itself, exceeds that of all the other planets collectively, the

attraction of the sun is necessarily the chief determining force of all the movements in our system. The law of gravitation, however, does not merely say that the sun attracts each planet. Gravitation is a doctrine much more general, for it asserts that every body in the universe attracts every other body. In obedience to this law each planet must be attracted, not only by the sun, but by innumerable bodies, and the movement of the planet must be the joint effect of all the attractions. As to the influence of the stars on our solar system, it may be at once set aside as inappreciable. The stars are no doubt enormous bodies, in many cases possibly transcending our sun in magnitude, but the law of gravitation tells us that the intensity of the attraction decreases with the square of the distance. Most of the stars are a million times as remote as the sun, and consequently their attraction is so slender as to be absolutely inappreciable in the discussion of this question. The only attractions necessary to consider are those which arise from the action of one body of the system upon another. Let us take, for instance, the two largest planets of our system, Jupiter and Saturn. Each of these planets moves mainly in consequence of the sun's attraction, but each planet also attracts the other, and the consequence is that each planet is slightly drawn away from the position it would otherwise have occupied. In the language of astronomy we would say that the path of Jupiter is perturbed by the attraction of Saturn; and, conversely, that the path of Saturn is perturbed by the attraction of Jupiter.

For many years these irregularities of the planetary motions presented problems which astronomers were not able to solve. Gradually, however, one difficulty after another has been vanquished, and though there are no doubt some small irregularities still outstanding which have not been completely explained, yet all the larger and more important phenomena of the kind are well understood. The subject is one of the most difficult which the astronomer has to encounter in the whole range of his science. He has here to calculate what effect one planet is capable of producing on another planet. Such calculations bristle with the most