that the perturbing effects of Neptune were increasing in intensity from year to year; and hence no set of elements could correctly represent the places of Uranus, because the observations did not extend back far enough to embrace the disturbed places of the planet at the former conjunction in 1651. No correct solution was then possible until the perturbations should reach their maximum value, which occurred in 1822, when the planets were in conjunction, and subsequently to which period the planet Uranus would slowly return to its computed orbit as it receded further and still further from the influence of the disturbing body, as may be more clearly seen from the figure below, in which the smaller circle may represent the orbit of Uranus, the larger one the orbit of Neptune. For a long while prior to con

junction in 1822, Uranus would be slowly overtaking Neptune, during which time the direction of the disturbing force would be such as to accelerate the orbital motion of Uranus, and to increase its distance from the sun. The acceleration would cease at conjunction, and would there be changed into equal and opposite retardation, as is manifest from the figure, while the increase of the distance of Uranus must continue to increase even after conjunction, but the disturbing force must rapidly decline in power as the interval

between the planets increases. Thus the great problem demanded the position of a disturbing planet at a given time, which could account for the known perturbations, all of which were crowded into a few years, say 25, before and after the conjunction in 1822. While this narrowing of the limits of sensible perturbation increased the chances of directing the telescope to the unknown disturber, it seems to have really increased the difficulty of assigning to this disturber his exact orbit. Indeed, even with circular orbits, several might have been chosen, such that by varying the mass of the unknown, the perturbations might have been tolerably well represented; but, in case elliptical orbits are chosen, then our limits are much extended, and the mean distance may be made to vary within very broad limits, provided the eccentricity may be chosen at pleasure. Thus the ellipse shown in the figure coincides between N and N' very nearly with the circular orbit, and in case a planet revolving in the circle could account for the anomalies of Uranus, the same would be tolerably well represented by the effects of a planet with a very different period and mean distance revolving in the elliptic orbit. Now, this was exactly the case as developed in the final history of this grand discovery. The great geometers chose an elliptic orbit of such eccentricity, and having its major axis in such position, that the computed and true orbits agreed with each other in a most remarkable manner during the twenty years before and after conjunction. Their efforts were thus crowned with the success which they so eminently deserved; and although the computed orbit came finally to differ greatly from the true one, yet, for the time when the computed orbit was required to represent the places of the unknown, and to point the telescope to its actual location, the computed orbit responded nearly as perfectly as the true one could have done, even had it been then known.

It has been already stated that after the discovery of Uranus, when the elements of its orbit had been obtained with sufficient accuracy to render it possible to trace the

planet backwards among the fixed stars, it was ascertained that it had been observed and its place recorded as early as 1690, and had been seen many times subsequently and prior to its discovery, being always mistaken for a fixed star; so we find in the case of Neptune, a like examination by Professor Walker led to the discovery that the new planet had been twice recorded in position by La Lande, in May, 1795. These two observations were found to be outside the path which had been assigned the planet by the theory of both Le Verrier and Adams; and such was the deep confidence in the accuracy of the elements assigned by these two geometers, that it was with great difficulty that some of the ablest astronomers could be induced to believe that the missing star twice observed by La Lande could be the new planet. The identity was, however, soon demonstrated, and hence arose the discussion which led to the declaration by an eminent mathematician, that the discovery of Neptune was the result of a happy accident; but we have seen that the grand problem propounded by both the French and the English astronomer, and which each resolved with such astonishing precision, was to point the telescope in the direction of the unknown, which had produced the late excessive perturbations of Uranus. It remains, so far as I know, yet to be decided whether the data in possession of Adams and Le Verrier can be so treated by analysis, as to give an orbit to the unknown more nearly agreeing with that of the known planet.

NEPTUNE'S SATELLITE. The vast distance to which Neptune is buried in space will perhaps render it impossible to learn how many satellites revolve about this remote primary. The great refractors have certainly discovered the existence of one satellite, and another is suspected. The discovery of this one satellite of Neptune becomes, under all the circumstances, a matter of deep interest, as it enables us to determine the mass or weight of the primary-a matter of the first moment in computing the effects of the planet as disturbing body. The satellite is found to perform its

revolution about the primary in a period of about five days. and twenty-one hours, and at a mean distance of 232,000 miles, or nearly equal to the distance of our moon from the earth. In case these distances are assumed to be exactly equal, then, as at the same distance the centrifugal force increases as the square of the velocity; and as the velocity of Neptune's moon is about four and a half times greater than that of our moon, its centrifugal force in its orbit must be 4.5 x 4.5, equal to about twenty times the centrifugal force of the moon. Now, the attractive force of Neptune is exactly proportioned to its weight or mass; and hence, to counterbalance this centrifugal force in his satellite, which is twenty times as great as that of the moon, the mass of Neptune must be twenty times as great as that of the earth. Thus has been revealed, not one world, but two-the one containing a mass of matter sufficient to form no less than twenty worlds as heavy as our earth-the other a satellite, indeed, of the first, yet sufficiently large to send back to us, at a distance of 3,000,000,000 of miles, the light of the sun, enfeebled by its dispersion over this vast distance to the onethousandth part of the intensity it pours on our earth. We have reached the known boundary of that mighty confederation of revolving orbs which, whilst they acknowledge in the most specific manner a mutual dependence, are all controlled by the predominating influence of the sun, which occupies the common focus of all their orbits, and around which they all roll and shine in obedience to the grand law of universal gravitation.

We shall now retrace our steps toward the sun, and consider a remarkable class of bodies, which for ages were regarded as evanescent meteors, suddenly blazing athwart the sky, and as suddenly fading from the vision, never more to reappear. Modern science has given to these bodies determinate orbits, and in some instances, as we shall see, has assigned them a permanent place among the satellites of the suu.

CHAPTER XIV.

THE COMETS.

Objects of Dread in the Early Ages.-Comets obey the Law of Gravitation and revolve in some one of the Conic Sections.-Characteristics of these Curves.-Comet of 1680 studied by Newton.-Comet of 1682 named "Halley's Comet."-Its History.-Its Return Predicted.-Perihelion Passage computed.-Passes its Perihelion 13th April, 1759.-Elements of its Orbit. -Physical Constitution.-Nucleus. - Envelopes. -Tail.— Intense Heat suffered by some Comets in Perihelio.-Dissipation of the Cometic Matter.-Encke's Comet.-A Resisting Medium.-Deductions from Observation.-Biela's Comet.—Divided.—Number of Comets.

IN all ages of the world these anomalous objects have excited the deepest interest, not only among philosophers, but among all classes of men. The suddenness with which they sometimes blaze in the sky, the vast dimensions of their fiery trains, the exceeding swiftness with which they pursue their journey among the stars, the rapid disappearance of even the grandest of these seeming chaotic worlds, have all combined to invest these bodies with a power to excite a kind of superstitious terror which even the exact revelations of science cannot wholly dispel. History records the appearance of these phenomena; and in general they were regarded as omens of some terrible scourge to mankind, the precursors of war or pestilence or famine, or at the very least announcing the death of some prince or potentate. Some of the ancients, of course, rose above these superstitious ideas, and the Roman philosopher Seneca even entertained the opinion that these erratic bodies would some day fall within the domain of human knowledge, that their paths among the stars would eventually be traced, and that they would be found in the end to be permanent members of the solar system. How remarkably this prediction has been verified will appear in the concise sketch we are about te resent.