her calculated place, a result which seemed to show that there was some oscillation of long period which had been overlooked. He made two conjectural explanations of this inequality, but both were disproved by subsequent investigators. The question, therefore, remained without any satisfactory solution till 1846, when Hansen announced that the attraction of Venus produced two inequalities of long period in the moon's motion, which had been previously overlooked, and that these fully accounted for the observed deviations of the moon's position. These terms were recomputed by Delaunay, and he found for one of them a result agreeing very well with Hansen's. But the second came out so small that it could never be detected from observations, so that here was another mathematical discrepancy. There was not room, however, for much discussion this time. Hansen himself admitted that he had been unable to determine the amount of this inequality in a satisfactory manner from the theory of gravitation, and had therefore made it agree with observation, an empirical process which a mathematician would never adopt if he could avoid it. Even if observations were thus satisfied, doubt would still remain. But it has lately been found that this empirical term of Hansen's no longer agrees with observation, and that it does not satisfactorily agree with observations before 1700. In consequence, there are still slow changes in the motion of our satellite which gravitation has not yet accounted for. We are, apparently, forced to the conclusion either that the motion of the moon is influenced by some other cause than the gravitation of the other heavenly bodies, or that these inequalities are only apparent, being really due to small changes in the earth's axial rotation, and in the consequent length of the day. If we admit the latter explanation, it will follow that the earth's rotation is influenced by some other cause than the tidal friction; and that, instead of decreasing uniformly, it varies from time to time in an irregular manner. The observed inequalities in the motion of the moon may be fully accounted for by changes in the earth's rotation, amounting in the aggregate to half a minute or so of time-changes which could

be detected by a perfect clock kept going for a number of years. But, as it takes many years for these changes to occur, no clock yet made will detect them.

Yet another change not entirely accounted for on the theory of gravitation occurs in the motion of the planet Mercury. From a discussion of all the observed transits of this planet across the disk of the sun, Leverrier has found that the motion of the perihelion of Mercury is about 40 seconds in a century greater than that computed from the gravitation of the other planets. This he attributes to the action of a group of small planets between Mercury and the sun. In this form, however, the explanation is not entirely satisfactory. In the first place, it seems hardly possible that such a group of planets could exist without being detected during total eclipses of the sun, if not at other times. In the next place, granting them to exist, they must produce a secular variation in the position of the orbit of Mercury, whereas this variation seems to agree exactly with theory. Leverrier explains this by supposing the group of asteroids to be in the same plane with the orbit of Mercury, but it is exceedingly improbable that such a group would be found in this plane. There is, however, an allied explanation which is at least worthy of consideration. The phenomenon of the zodiacal light, to be described hereafter, shows that there is an immense disk of matter of some kind surrounding the sun, and extending out to the orbit of the earth, where it gradually fades away. The nature of this matter is entirely unknown, but it may consist of a swarm of minute particles, revolving round the sun, and reflecting its light, like planets. If the total mass of these particles is equal to that of a very small planet, say a tenth the mass of the earth, it would cause the observed motion of the perihelion of Mercury. The evidence on this subject will be considered more fully in treating of Mercury.

With the exceptions just described, all the motions in the solar system, so far as known, agree perfectly with the results of the theory of gravitation. The little imperfections which still exist in the astronomical tables seem to proceed mainly

from errors in the data from which the mathematician must start in computing the motion of any planet. The time of revolution of a planet, the eccentricity of its orbit, the position of its perihelion, and its place in the orbit at a given time, can none of them be computed from the theory of gravitation, but must be derived from observations alone. If the observations were absolutely perfect, results of any degree of accuracy could be obtained from them; but the imperfections of all instruments, and even of the human sight itself, prevent observations from attaining the degree of precision sought after by the theoretical astronomer, and make the considerations of 66 errors of observation" as well as of "errors of the tables" constantly necessary.

§ 7. Relation of the Planets to the Stars.

In Chapter I., § 3, it was stated that the heavenly bodies belong to two classes, the one comprising a vast multitude of stars, which always preserved their relative positions, as if they were set in a sphere of crystal, while the others moved, each in its own orbit, according to laws which have been described. We now know that these moving bodies, or planets, form a sort of family by themselves, known as the Solar System. This system consists of the sun as its centre, with a number of primary planets revolving around it, and satellites, or secondary planets, revolving around them. Before the invention of the telescope but six primary planets were known, including the earth, and one satellite, the moon. By the aid of that instrument, two great primary planets, outside the orbit of Saturn, and an immense swarm of smaller ones between the orbits of Mars and Jupiter, have been discovered; while the four outer planets-Jupiter, Saturn, Uranus, and Neptuneare each the centre of motion of one or more satellites. The sun is distinguished from the planets, not only by his immense mass, which is several hundred times that of all the other bodies of his system combined, but by the fact that he shines by his own light, while the planets and satellites are dark bodies, shining only by reflecting the light of the sun.

A remarkable symmetry of structure is seen in this system, in that all the large planets and all the satellites revolve in orbits which are nearly circular, and, the satellites of the two outer planets excepted, nearly in the same plane. This family of planets are all bound together, and kept each in its respective orbit, by the law of gravitation, the action of which is of such a nature that each planet may make countless revolutions without the structure of the system undergoing any change.

Turning our attention from this system to the thousands of fixed stars which stud the heavens, the first thing to be considered is their enormous distance asunder, compared with the dimensions of the solar system, though the latter are themselves inconceivably great. To give an idea of the relative distances, suppose a voyager through the celestial spaces could travel from the sun to the outermost planet of our system in twenty-four hours. So enormous would be his velocity, that it would carry him across the Atlantic Ocean, from New York to Liverpool, in less than a tenth of a second of the clock. Starting from the sun with this velocity, he would cross the orbits of the inner planets in rapid succession, and the outer ones more slowly, until, at the end of a single day, he would reach the confines of our system, crossing the orbit of Neptune. But, though he passed eight planets the first day, he would pass none the next, for he would have to journey eighteen or twenty years, without diminution of speed, before he would reach the nearest star, and would then have to continue his journey as far again before he could reach another. All the planets of our system would have vanished in the distance, in the course of the first three days, and the sun would be but an insignificant star in the firmament. The conclusion is, that our sun is one of an enormous number of self-luminous bodies scattered at such distances that years would be required to traverse the space between them, even when the voyager went at the rate we have supposed. The solar and the stellar systems thus offer us two distinct fields of inquiry, into which we shall enter after describing the instruments and methods by which they are investigated.

PART II-PRACTICAL ASTRONOMY.

INTRODUCTORY REMARKS.

SHOULD the reader ask what Practical Astronomy is, the best answer might be given him by a statement of one of its operations, showing how eminently practical our science is. "Place an astronomer on board a ship; blindfold him; carry him by any route to any ocean on the globe, whether under the tropics or in one of the frigid zones; land him on the wildest rock that can be found; remove his bandage, and give him a chronometer regulated to Greenwich or Washington time, a transit instrument with the proper appliances, and the necessary books and tables, and in a single clear night he can tell his position within a hundred yards by observations of the stars." This, from a utilitarian point of view, is one of the most important operations of Practical Astronomy. When we travel into regions little known, whether on the ocean or on the Western plains, or when we wish to make a map of a country, we have no way of finding our position by reference to terrestrial objects. Our only course is to observe the heavens, and find in what point the zenith of our place intersects the celestial sphere at some moment of Greenwich or Washington time, and then the problem is at once solved. The instruments and methods by which this is done may also be applied to celestial measurements, and thus we have the art and science of Practical Astronomy. To speak more generally, Practical Astronomy consists in the description and investigation of the instruments and methods employed by astronomers in the work of exploring and measuring the heavens, and of