1849.] ་ The Planet Le Verrier. 457 ART. VIII.-THE PLANET LE VERRIER. Comptes-Rendus des Séances de l'Académie des Sciences.—Paris, 1846, 1847, 1848. No discovery in science ever caused so great a sensation, among those capable of estimating its importance, as that of the Planet to which the name of Neptune has been given by some, but which will hereafter be distinguished by that of Le Verrier. The circumstances of this discovery may be briefly stated as follows:-In comparing the observed motions of the planet Herschel with the places indicated by theory, and after allowing for all the disturbances produced by the influence of the known bodies of the solar system, certain anomalies and discrepancies were detected. It required little skill to infer that these differences between the calculated ephemerides and the results of direct observation, must be caused by the action of some body or bodies as yet unknown to astronomers. In this opinion, therefore, almost all who considered the subject in a proper light concurred, and hopes were entertained that, by means of th recent improvements in the construction of the two kinds of telescope, and the systematic mapping of the heavens now going on in various observatories, some wandering body might be detected, which, after observations of sufficient duration, would be found to account for the anomalies in the motions of Herschel. No one, however, as far as we know, ventured, prior to 1845, to state that, from the consideration of these irregularities themselves, the place, the distance, and the mass of the disturbing body, might be inferred approximately. It was even farther from the hopes of the most sanguine cultivators of physical astronomy that such investigations might be pursued so successfully, that a telescope might, by their aid, be directed to the heavens, with a certainty, almost absolute, of finding the body in question within its field of view. The scientific world was therefore startled with the intelligence that a German observer, acting under the published directions of a French analyst, did, at the first trial, find the planet whose influence on Herschel had been indicated by the irregularities of which we have spoken. The surprise was even enhanced by the fact, that the same discovery had nearly been made by means of indications furnished by a mathematician of English birth. A discussion hence arose between France and England for the merit of priority; but, however hard it may be to the Englishman who was so near the prize, the honours must be awarded to the Frenchman. This is more justly his due, because he had from time to time, at the weekly sittings of the Academy of Sciences, made public the progress of his investigations, and it was not until the fourth of his communications that he reported such progress as would serve for the guide of the practical astronomer. The earlier of these papers might have served as a guide to others; and one who had published nothing on the subject, whatever may have been his real merit, could not with propriety assert a superior claim to one who had made known every step of his investigation. The Frenchman to whom we refer was Le Verrier. On the 31st of August, 1846, he made his fourth communication to the Academy. Referring to his preceding paper, read 1st of June, wherein he had pointed out the probable longitude of the planet, he states that delays and difficulties had attended the determination of its mass, and its periodic time. These, he states, he hopes to overcome, and will endeavour to do so as speedily as possible. With this salvo for any errors which might remain in his investigations in relation to these points, he proceeds to expose in a succinct manner the methods he was employing, and then gives his results. These two elements, from his very mode of stating them, were still doubtful, and with them must have been also in doubt the distance from the sun, the eccentricity of the orbit, and the line of the apsides. His object in publication, while his theory was yet incomplete, was obviously the risk of postponing the search for the planet for a whole year. "The opposition of the planet is now taking place," says he, "yet, happily, the researches of astronomers furnished with powerful telescopes will be possible for three months to come." After stating the mean distance, the periodic time, the longitude of the perihelion, the eccentricity of the orbit, and the mass, all obviously with the salvo we have mentioned, he goes on to give a more accurate determination of the position of the planet than he had previously been able to reach, and states that this determination, founded on more accurate and precise data, placed the body about four degrees to the east of the star & Scorpionis. From his estimate of this mass he next inquires into the possibility of seeing the body in question, and distinguishing it by a visible diameter from a fixed star, and infers that at the time of its opposition it ought to subtend an angle of 3".3. That he should have had such confidence in his methods as to venture on so positive a statement, must still strike us with astonishment. We must consider that he commenced his researches with no other known fact than that there were disturbances in the motion of Herschel that had not been explained. He was therefore compelled at first to extend his researches to every part of the zodiac, and it was not until after June 1st, 1846, that he had been able to eliminate such positions of Herschel as were of no importance to his racy. inquiry, and select such as must lead to a tolerable degree of accuEven with these, it became necessary to employ the calculus of probabilities, for some of the observations were ancient, and made with imperfect instruments, while others were the product of the highest art and the most accomplished observers. 400 Let us now see the result of this publication of the paper read 31st August, 1846. It reached Berlin, in a letter from Le Verrier to Galle, 23d September. The same night that observer, directing his telescope to the place indicated, found a star, which did not appear in the maps, ascertained that it had a visible diameter, and that this diameter was 3". On reducing the observed place, by means of Le Verrier's approximate periodic time, to the epoch of 1st June, 1847, the difference between the observed and calculated position was less than a degree, or, more accurately, 52'. Considering thus that Le Verrier had, in beginning, the whole circumference of the ecliptic to work upon, the error amounted to no more than¿õ. The new planet, thus happily discovered, became the immediate object of attention in all observatories. Its motions were carefully watched, its diameter repeatedly measured. From the first of these, probable positions at former periods were inferred, and recorded observations of stars that appeared to have vanished from the heavens were sought for, in the hopes of their being found to exhibit ancient positions of the planet. In these researches the astronomers of Cambridge, Mass., and of Washington, bore no small part, and were so well seconded by the skill in calculation of their associates, that the names of Maury and Walker, Bond and Peirce, will be necessarily associated with that of Le Verrier in this brilliant page of the history of astronomic science. In particular, Mr. Walker, by long and laborious researches, conceived that he had identified a star seen by La Lande, May 10th, 1795, with the new planet. A similar inference was made about six weeks afterwards by Mr. Petersen, of Altona, with this difference, that Mr. Walker states his inference as certain, Mr. Petersen as a subject for further inquiry. We conceive that there was, and perhaps is still, a reason for a doubt. The star in question does not, as we shall see, correspond to the theory given by Le Verrier, and we conceive that the observations of the new planet were not yet of such a character as to authorize a conclusion in opposition to that theory. It had not, at the time of Mr. Walker's inference, been observed for more than a third of a year. During a part of the time it had been retrograde, and its whole direct motion could not have amounted to more than about twothirds of a degree. We therefore venture to say that sufficient data had not yet been attained to infer the probable position; at a prior epoch, distant more than fifty years. From this assumed position, and the observations of fourteen weeks, Mr. Walker then proceeded to calculate the elements of the orbit, &c. In these calculations he has exhibited his profound skill; and, admitting that he was right in conceiving the star of La Lande to have been the planet of Le Verrier, they are to be received as entitled to all the confidence to which the value of the data he had at his command will entitle them. These, however, we consider to have been totally insufficient to serve as the basis of any accurate theory of the planet's motions. Three observed geometric places of any newly observed body are indeed sufficient data on which to found the calculation of the elements of its orbit. But the results of such a calculation, however perfect, do not necessarily give these elements with absolute accuracy. They are, at best, approximations of greater or less closeness, and the approach to certainty will depend upon the relations between the two angles contained between the three observed places. Now it requires no knowledge of the method itself to be able to infer, that when one of these angles is at least one hundred times as great as the other, the chance of approximation to absolute truth, in the determination of the circumstances of an elliptical orbit, must be amongst the most remote that can well occur in such an investigation. It is only by successive approximations that the elements of the orbit of a new planet can be reached; and Mr. Walker knows this fact too well to have presented his results for more than the first of these approximations, made at the earliest period at which such an attempt was possible. The great mass of readers, and, it would appear, many scientific men, seem not to have been aware of this fact. They have received the orbit of Mr. Walker, as if it were definitely fixed as the true path of the planet; and remarking great differences between it and the predicted orbit of Le Verrier, have been almost led to conclude that the discovery of a planet so near the place indicated by Le Verrier, was rather the result of a singularly happy chance, than the legitimate consequence of his analytic investigations. Going a step farther, a scientific rival ventured to assert, at a meeting of the Academy of Sciences, that "the identity of Neptune with the theoretic planet is no longer admitted by any one." We consider it due to Le Verrier that this impression, which we fear is very prevalent, should be removed, and his merit exhibited in a full and just light. Before entering into the discussion, we think it proper to state, for the information of those who have not entered deeply into the history of astronomy, that all the facts which we now possess have been reached by slow and laborious steps. In fact, theory and the * methods of observation have kept up a march almost exactly corresponding to each other; and it may even be suspected that, if our present instruments had been invented at an earlier epoch in the history of the theory, they might have retarded, rather than accelerated, the progress of astronomical knowledge. Thus, in early ages, it was found sufficient for all purposes to consider the planets as moving in circular orbits. The introduction of instrumental observation by Hipparchus showed the errors of such an hypothesis, and led to the introduction of the epicycle, in which it was supposed that the planet moved on the circumference of one circle whose centre was carried around upon another. When Tycho planned instruments by which observations could be made to minutes of a degree, the hypothesis of the epicycle was shown to be erroneous; and Kepler, by the collation of Tycho's observations, discovered the elliptical form of the orbits, and the law of areas by which they were described. But, had this discovery been announced at the present day for the first time, the disturbances in the elliptic motion would have appeared so enormous to our instruments, that we much doubt whether Kepler's theory would not have been rejected, if the resources of the celestial mechanics had not been at hand to explain them. In the history of that last-named and sublime science, all can learn how observation and analysis have mutually aided each other, and in what manner our existing knowledge has been gradually reached, through steps each of themselves erroneous, but each approaching more and more nearly to truth. Even in the body nearest to us, the moon, absolute certainty has not yet been attained, and the further correction of the lunar tables is still desirable. We may, even in advance of our discussion, state here, that the errors in the prediction of an eclipse, or of the distance of the moon from a star, were, not half a century back, greater than the differences between the elements of the orbit of Neptune, as derived from observation, and those inferred from the analysis of Le Verrier. The difference in the two cases, however, is great; for all the errors of the lunar tables were included and compensated within the space of a single lunation, while the differences in the case of the planet go on during the whole of its long revolution. Le Verrier inferred the position of Neptune by a method the converse of those employed in relation to bodies which had been the subject of observation. The data for his calculations were irregularities very small in themselves, and it is allowing their determination a greater degree of accuracy than it is entitled to, to admit their possible error to be no more than one-tenth of their assumed amount. If, then, the difference between the results of actual observation, and |