ceivable effect upon them. Therefore, in proportion as our distance from the masts is increased, so in proportion will it require a greater change in our own position to produce the same apparent change in their position.

Thus it is with all visible objects. When a multitude of stationary objects are viewed at a distance, their relative position will depend upon the position of the observer; and if the station of the observer be changed, a change in the relative position of the objects must be expected; and if no perceptible change is produced, it must be inferred that the distance of the objects is incomparably greater than the change of position of the observer.

Let us now apply these reflections to the case of the earth and the stars. The stars are analogous to the masts of the ships, and the earth is the station on which the observer is placed. It might have been expected that the magnitude of the globe, being eight thousand miles in diameter, would produce a change of position of the observer sufficient to cause a change in the relative position of the stars, but we find that such is not the case. The stars, viewed from opposite sides of the globe, present exactly the same appearance; we must, therefore, infer that the diameter of the earth is absolutely nothing compared to their distance.

But the astronomer has still a much larger modulus to fall back upon. He reflects, as has been already observed, that he is enabled to view the stars from two stations separated from each other, not by 8000 miles, the diameter of the earth, but by 200 millions of miles, that of the earth's orbit. He, therefore, views the heavens on the 1st of January, and views them again on the 1st of July, the earth having in the meanwhile passed to the opposite side of its orbit, yet he finds, to his amazement, that the aspect is the same. He thinks that this cannot be that so great a change of position in himself cannot fail to make some change in the apparent position of the stars;-that, although their general aspect is the same, yet when submitted to exact examination a change must assuredly be detected. He accordingly resorts to the use of instruments of observation capable of measuring the relative positions of the stars with the last conceivable precision, and he is more than ever confounded by the fact that still no discoverable change of position is found.

For a long period of time this result seemed inexplicable, and accordingly it formed the greatest difficulty with astronomers, in admitting the annual motion of the earth. The alternative offered was this; it was necessary, either to fall back upon the Ptolemaic system, in which the earth was stationary, or to suppose that the immense change of position of the earth in the course of half a year, could produce no discoverable change of appearance in the

stars; a fact which involves the inference that the diameter of the earth's orbit must be a mere point compared with the distance of the nearest stars. Such an idea appeared so inadmissible that for a long period of time many preferred to embrace the Ptolemaic hypothesis, beset as it was with difficulties and contradictions.

Improved means of instrumental observation and micrometrical measurement, united with the zeal and skill of observers, have at length surmounted these difficulties; and the parallax, small indeed but still capable of measurement, of several stars has been ascertained.

169. Methods of ascertaining the parallax of fixed stars. -It will easily be imagined that astronomers have diligently directed their observations to the discovery of some change of apparent position, however small, produced upon the stars by the earth's motion. As the stars most likely to be affected by the motion of the earth are those which are nearest to the system, and therefore probably which are brightest and largest, it has been to such chiefly that this kind of observation has been directed; and since it was certain that, if any observable effect be produced by the earth's motion at all, it must be extremely small, the nicest and most delicate means of observation were those alone from which the discovery could be expected.

One of the earlier expedients adopted for the solution of this problem was the erection of a telescope, of great length and power, in a position permanently fixed, attached, for example, to the side of a pier of solid masonry erected upon a foundation of rock. This instrument was screwed into such a position that particular stars, as they crossed the meridian, would necessarily pass within its field of view. Micrometric wires were, in the usual manner, placed in its eye-piece, so that the exact point at which the stars passed the meridian each night, could be observed and recorded with the greatest precision. The instrument being thus fixed and immovable, the transits of the stars were noted each night, and their exact places when they passed the meridian recorded. This kind of observation was carried on through the year; and if the earth's change of position, by reason of its annual motion, should produce any effect upon the apparent position of the stars, it was anticipated that such effect would be discovered by these means. After, however, making all allowance for the usual causes which affect the apparent position of the stars, no change of position was discovered which could be assigned to the earth's motion.

170.

Professor Henderson's discovery of the parallax of a Centauri.—Notwithstanding the numerous difficulties which beset the solution of this problem, by means of observations made with the ordinary instruments, Professor Henderson, during his resi

dence as astronomer at the Royal Observatory at the Cape of Good Hope, succeeded in making a series of observations upon the star designated a in the constellation of the Centaur, which, being afterwards submitted by him to the proper reductions, gave a parallax of about 1". Subsequent observations made by his successor, Mr. Maclear, at the same observatory, partly with the same instrument, and partly with an improved and more efficient one of the same class, have fully confirmed this result, giving o'9187, or ths of a second as the parallax.

It is worthy of remark, that this conclusion of Messrs. Henderson and Maclear is confirmed in a remarkable manner, by the fact that like observations and computations applied to other stars in the vicinity of a Centauri, and therefore subject to like annual causes of apparent displacement, such as the mean annual variation of temperature, gave no similar result, showing thus that the displacement found in the case of a Centauri could only be ascribed to parallax.

Since the limits of error of this species of observation affecting the final result cannot exceed the tenth of a second, it may then be assumed as proved, that the parallax of a Centauri is about 1", and consequently that its distance from the solar system is such that light must take more than three years to move over it.

171. Parallax of a few stars ascertained. Notwithstanding the great number of stars to which instruments of observation of unlooked-for perfection, in the hands of the most able and zealous observers, have been directed, the results of such labours have hitherto been rather negative than positive. The means of observation have been so perfect, and their application so extensive, that it may be considered as proved by the absence of all measurable displacement consequent upon the orbital motion of the earth that, a very few individual stars excepted, the vast multitude of bodies which compose the universe and which are nightly seen glittering in the firmament, are at distances from the solar system greater than that which would produce an apparent displacement amounting to the tenth of a second. This limit of distances is, therefore, ten parallactic units, or about two million times the space between the earth and sun.

The parallax of the following stars has been determined within some degree of probability from the observations of MM. Henderson, Bessel, Krüger, Struve, and C. A. F. Peters. The names and amount of parallax of each star are a Centauri, o"976; 61 Cygni, o"348; Lalande 21258, 0260; OeltzenArgelander 17,415-6, 0247; Groombridge 1830, 0" 226; a Lyræ, o" 155; Sirius, o"150; Ursa Majoris, o"133; Arcturus, o" 127; Polaris, o"067; and Capella, o"046.

The parallax of the first nine of these stars may be considered as having been ascertained with tolerable certainty and precision. The very small amount of that of the last two is such as to render it more doubtful. What is certain, however, in relation to these is, that the actual amount of their parallax is less than the tenth of a second.

CHAPTER IX.

PRECESSION AND NUTATION.

172. Effects which would be produced if a satellite were attached to the surface of the earth at the equator. If the earth were attended by a second satellite, revolving close to its surface and in the plane of its equator, the periodic time of the satellite would be considerably less than that of the moon, in a ratio which is easily ascertained.

But such a satellite would be subject to the disturbing action of the sun, which would produce in its orbit inequalities similar in kind to, but different in magnitude from, those produced by the sun's disturbing force on the moon's orbit. Its nodes, that is, the equinoxial points (inasmuch as its orbit is by the supposition the plane of the equator), would receive a slow regressive motion; and its inclination, that is, the obliquity of the ecliptic, would be subject to a variation whose period would depend on that of the successive returns of the sun to the same equinoxial point.

This satellite would also be subject to the disturbing action of the moon, which would affect it in a manner nearly similar; since, in that case also, the disturbing body would be exterior to the disturbed. It would impart to the line of nodes of the supposed satellite, that is, to the intersection of the plane of its orbit with the plane of the earth's equator, a retrograde motion upon the former plane; and since that plane is inclined at a very small angle to the plane of the ecliptic, this would produce a like retrograde motion of the equinoxial points upon the ecliptic.

A variation of the inclination of the plane of the equator to that of the moon's orbit, and, therefore, to the plane of the ecliptic, would also be produced, the period of which would depend on the moon's motion.

But the moon's orbit would also be disturbed by the attraction of the supposed satellite. A regressive motion would be imparted to the line in which the plane of its orbit intersects that of the equator,

and a periodical variation of inclination would likewise be produced, depending on the period of the supposed satellite.

Let us now imagine that the supposed satellite, instead of revolving in a short period, moves with a much slower motion, and revolves in 23 hours and 56 minutes, the time of the earth's rotation. The inequalities which it suffers and which it produces, will then be changed only in their magnitudes and periods, but will retain the same general character. But the supposed satellite now having the same motion precisely as the surface of the earth close to which it is placed, may be imagined to adhere to that surface, so as to form, in fact, a part of the earth, without in any way deranging the conclusions which have been deduced above.

173. Like effects would be produced by any number of such satellites, or what would be equivalent, by the spheroidal form.—But the same observations would be equally applicable to any number of satellites similarly placed and similarly moving, which might, therefore, be imagined to be successively attached to the surface of the globe at and near the equator, until such a protuberance would be formed upon it, as would in effect convert it into the form of an oblate spheroid, such as the form of the earth is known to be.

It is, however, to be further considered, that the effects of the disturbing forces which thus act upon this protuberant matter, are necessarily modified by the inertia of the spherical mass within it, to which it is imagined to be attached. The protuberant mass which alone is acted on by the disturbing forces, cannot obey any action of these forces, without dragging with it this vast spherical mass to which it is united. The motions and changes of motion, therefore, which it receives, will be rendered slower in proportion to the mass with which such motions must be shared.

These observations are obviously applicable equally to any of the other planets, which being attended by satellites, have the spheroidal form.

174. Precession of the equinoxes. Since, therefore, we may consider the spheroidal protuberance round the terrestrial equator as a satellite attached to the earth, it will follow that the general effect of the sun's disturbing force acting upon it, will be to impart to its nodes, that is, to the equinoxial points, a retrograde motion, which will be much slower than that which they would receive from the same cause, if this protuberant matter were not compelled to carry with it the mass of the earth contained within it.

The moon exercises a like disturbing force which produces a like regression of the nodes of the equator on the moon's orbit; and that orbit being inclined at a small angle to the ecliptic, this is attended with a like regression of the equinoxial points.