friend of Arago, Leverrier's Cometary Investigations, and more especially his researches of the motions of Mercury, had gained for him the confidence of this distinguished savant, and Arago urged on his young associate the importance of the great problem presented in the perturbations of Uranus, and induced him to abandon other investigations, and concentrate all the energies of his genius on this profound and complex investigation.

The extraordinary powers of Leverrier as a mathematical astronomer had been so successfully displayed in his researches of the motions of Mercury, that it deserves a passing notice. The old tables of this planet, Leverrier believed to be defective. He therefore set about a thorough examination of its entire theory, and after a rigid scrutiny, deduced a new set of tables, from which the places of the planet might be predicted with greater precision.

The transit of Mercury across the sun's disc, which occurred on the 8th day of May, 1845, presented an admirable opportunity to test the truth of the new theory of the young astronomer. Most unhappily for his hopes, all observations in Paris were rendered impossible by the clouds, which covered the heavens during the entire day on which the transit took place. While the computer was sadly disappointed, I was more fortunate, for a pure and transparent atmosphere favored this, the first astronomical observation I ever made. A slight reference to this occurrence may be pardoned. For three years I had been toiling to complete a most difficult and laborious enterprise, the erection of an astronomical ob servatory of the first class, in a country where none

had ever existed. Amid difficulties and perplexities which none can ever know, the work had moved on, and at length I had the high satisfaction of seeing mounted one of the largest and most perfect instruments in the world. I had arranged and adjusted its complex machinery-had computed the exact point on the sun's disc where the planet ought to make its first contact-had determined the instant of contact by the old tables, and by the new ones of Leverrier, and with feelings which must be experienced to be realized, five minutes before the computed time of contact, I took my post at the telescope to watch the coming of the expected planet. After waiting what seemed almost an age, I called to my friend how much time was yet to pass, and found but one single minute out of five had rolled heavily away. The watch was again resumed. Long and patiently did I hold my place, but again was forced to call out, how speeds the time? and was answered that there was yet wanting two minutes of the computed time of contact.With steadfast eye, and a throbbing heart, the vigil was resumed, and after waiting what seemed an age, I caught the dark break which the black body of the planet made on the bright disc of the sun. Now! I exclaimed; and within sixteen seconds of the computed time did the planet touch the solar disc, at the precise point at which theory had indicated the first contact would occur.

The planet was followed across the disc of the sun, round and sharp, and black, and every observation confirmed the superior accuracy of the new tables of Leverrier. While the old tables were out fully a minute and a half in the various contacts, those of Le

verrir were in error by only about sixteen seconds as

a mean.

The great success of this investigation encouraged the young astronomer to accept the difficult task which Arago proposed for his accomplishment, and he earnestly set about preparing the way for a full discussion of the grand problem of the perturbations of Uranus. The importance of the subject demanded the greatest caution, and having determined to rely solely on his own efforts, he at once rejected all that had been previously done, and commenced the problem at the very beginning. New analytic theories were formed; elaborate investigations of the planets Jupiter and Saturn, as disturbing bodies, were made, and an entire clearing up of all possible causes of disturbance in the known bodies of the system was laboriously and successfully accomplished, and the indefatigable mathematician finally reached a point where he could say, here are residual perturbations which are not to be accounted for by any known existing borly, and their explanation is to be sought beyond the present ascertained limits of the solar system.

As early as the 10th of November, 1845, M. Leverrier presented a memoir to the Royal Academy of Sciences in Paris, in which he determined the exact perturbations of Jupiter and Saturn on Uranus. This was followed by a memoir, read before the academy on the 1st of June, 1846, in which he demonstrates that it is impossible to render an exact account of the perturbations of Uranus in any other way than by admitting the existence of a new planet exterior to the orbit of Uranus, and whose heliocentric longitude he fixes at 325° on the 1st of January, 1847. On the

30th of August, 1846, a third memoir was presented to the academy, in which the elements of the orbit of the unknown planet are fixed, together with its mass and actual position, with greater accuracy, giving on the 1st of January, 1847, 326° 32′ for its heliocentric longitude. Finally, on the 5th of October, 1847, a fourth memoir was read, relative to the determination of the plane of the orbit of the constructive planet.

It is quite impossible to convey, in popular form, the least idea of the profound analytic reasoning employed by M. Leverrier in this wonderful investigation. None but the rarest genius would have dared to reach out 1,800,000,000 of miles into unknown regions of space, to feel for a planet which had displaced Uranus by an amount only about equal to four times the apparent diameter of the planet Jupiter, as seen with the naked eye-a quantity so small that no eye, however keen and piercing, without telescopic aid, could ever have detected it. Yet from this minute basis was the magnificent superstructure to be reared which should eventually direct the telescope to the place of a new and distant world. To many minds, the resolution of such a problem may appear utterly beyond the powers of human genius, and without one ray of light to illumine the midnight darkness which surrounds it to them, they are disposed to reject the entire subject. An attentive examination of the following train of reasoning may at least demonstrate that the problem is not quite so hopeless as it would at first appear.

It was not necessary to extend researches to all quarters of the heavens indifferently, in an effort to find the unknown body. All the planets revolve

in planes nearly coincident with the plane of the earth's orbit, and more especially do the distant ones. Jupiter and Saturn and Uranus revolve in orbits but little inclined to the plane of the ecliptic.Hence, it was fair to conjecture that the new planet, should it ever be found, would not violate this general law, and a search for it was properly limited to a narrow belt near the plane of the earth's orbit.— The limits of research were thus brought down to a narrow zone, sweeping around the entire heavens indeed, but insignificant in extent, when compared with the whole celestial sphere.

The next point of examination was the probable distance of the unknown planet. Here, again, analogy came to the aid of Leverrier. The empirical law of Bode, already explained in a former lecture, showed that the remote planets increased their distances by a very simple law. Saturn was twice as remote as Jupiter; Uranus was at double the distance of Saturn, and it was fair to conclude that the unknown planet would be about twice as far from the sun as Uranus. As a first approximation, then, its distance was fixed at about 3,600,000,000 of miles from the sun. Kepler's law, regulating the ratio be tween the distances and periods of the planets, gave at once the time of revolution of the new planet, in case its distance had been correctly assumed. In the next place, it was fair to conclude that the orbit of the new planet, like those of Jupiter, Saturn, and Uranus, would not differ greatly from a circle. These conjectures were, in some degree, confirmed by a very simple train of reasoning with reference to the distance of the disturbing body. If it revolved in an