tions seem to indicate, at least in the opinion of Herschel, who supposes that it is moving northward, with considerable velocity, this must, in process of time, occasion an apparent change in the distances of the stars from each other. On this supposition, the stars which are nearest to us, must be most affected by such a motion, and therefore their relative distances would suffer the greatest change.

From the precession of the equinoxes, already explained, the stars appear to alter their longitude annually 50" of a degree, as it is counted from the intersection of the ecliptic and equator. But this does not alter their latitude, as the pole of the earth moves round the pole of the ecliptic, without sensibly approaching towards it.

Catalogue of variable Stars reduced to the beginning of 1786.

ABERRATION OF THE STARS.

THERE is also another apparent motion of the fixed stars, arising from the motion of the earth, and the progressive motion of light combined together, called their aberration; which causes their longitudes and latitudes, their right ascensions and declinations, to be different from what they are in reality; and as it depends upon the earth's motion, all the variations of it must be completed in the course of a year.*

It is known from the eclipses of Jupiter's satellites, that light takes 8' 7" of time to pass from the sun to the earth, in which time the earth moves in her orbit over an arc of 20".25; so that the velocity of light is to that of the earth, as radius to the tangent of 20".25. It is also known that the visibility of objects depends upon the impression made on the eye by the rays of light, which they transmit, and that we judge of the position of objects by the direction in which the ray enters the eye, without any regard to any motion of the eye, or any antecedent alteration in the direction of the ray. These things being premised, we now say, that the impression of a ray of light from a star upon the eye, is neither in the direction of the ray when

If the earth be at A* and moving from A to B in the time that a ray of light comes from the star in the direction CB; so that AB is, to AC, as the velocity of the earth is to the velocity of light; then the star will appear at D, in the direction BD parallel to AC. For if a telescope AC reaching to the star were carried parallel to itself, the ray of light emitted in the direction CB, would be still in the axis of the telescope until it should arrive at the eye at B, where it would appear to have come in the direction DB, of the telescope, and thereby represent the star at D, advanced before its true place C.

* See Plate 16, Fig. 3.

first emitted from the star, nor in the direction in which the earth is moving carrying with it the eye of the spectator; but like a body urged by two forces in two directions; so light is felt in the direction of a diagonal of a parallelogram, whose two sides are in the direc tions of the ray of light and of the earth's motion, and also proportional to the velocities of light and of the earth. So that the star's apparent place will be at that end of the diagonal of the parallelogram to which the earth is moving. Now as one side of this parallelogram is the line which joins the earth and star, and the other is the tangent to the earth's orbit, where she may be, the plane of the parallelogram will always be in this tangent; and as the direction of the tangent is conti nually changing, the plane of the parallelogram must, in the course of a year, revolve quite round the line that joins the earth and star. Hence the star's apparent place must always be in the periphery of an orbit, similar to that of the earth's, described round the star's true place as the center, and in a plane parallel to the earth's orbit, which may be considered as a circle. But if this circle of the star's aberration, were projected on any other plane oblique to the former, it would then become an ellipsis. Hence if the star were in the pole of the ecliptic, the heavens being there parallel to the plane of the ecliptic, the star's apparent path would be in the arc of a circle; and if the star were in the ecliptic, its course would be a right line, because its circle of aberration then passes through the eye. But in any intermediate place, between the pole and the plane of the ecliptic, the circle of aberraration, which is parallel to the ecliptic, must be projected into an ellipsis in the heavens, whose transverse axis is parallel to the ecliptic, and whose conjugate

is perpendicular to that plane. The transverse axis of the ellipsis of aberration of all the stars is the same, and found to be 40′′.5 of a degree, but the conjugate axis increases with the star's distance from the ecliptic; and therefore they are to each other as radius to the sine of the star's latitude; that is, as radius : S, star's latitude :: 40".5: the lesser axis of the ellipsis.

As the distance between the sun and the earth is so small in comparison with the distance of the stars, we may consider it as nothing: then the parallelogram above-mentioned, in the diagonal of which the star's apparent place is always found, may be considered as turning round on the line that joins the sun and star, as the earth moves round the sun, keeping its plane always parallel to the direction of the earth in her orbit. The star therefore revolves in the periphery of the ellipsis from west to east, being at the eastern extremity of the ellipsis when it is found in opposition with the sun, and at the western end when in conjunction. When the sun and star have the same longitude, the plane of the parallelogram of aberration is perpendicular to the plane of a circle of latitude, and the star is in the western extremity of its transverse axis; consequently its aberration is wholly in longitude, and then greatest, being, as far as possible, 20".25, removed from its true circle of latitude; and its aberration in latitude is nothing, as it is at the same distance with the center of its ellipsis from the ecliptic. But when the star is in quadrature with the sun, the plane of the parallelogram of aberration is parallel to the plane of the circle of latitude passing through the pole of the ecliptic and the star, and the star appears in the extremity of the lesser axis, so

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that its aberration is entirely in latitude, and nothing in longitude.

The same may be said with respect to the aberra tion in declination and right ascension. When the right ascension of the sun and star is the same, the plane of the parallelogram of aberration is parallel to, or coincident with, the plane of the circle of declination, and the aberration in right ascension is nothing; for the star appears in the plane of the true circle of declination. But when the plane of the parallelogram of aber. ration is at right angles with the plane of the circle of declination, the star appears in a parallel to the equator, and consequently has no aberration in declination. At any intermediate position, the aberration will be both in right ascension and declination. Yet the aberration in right ascension is not greatest when the aberration in declination vanishes, excepting in the solstitial colure, when a star is found in it, and vice versa. This is the case however with the aberration in longi. tude and latitude. The aberration in longitude is greatest, when the aberration in latitude is nothing, and vice versa.

From what has been said, we may easily compute the aberrations of a star for any particular time. As for example, let the aberrations of a star be required, whose latitude is 36° north, and longitude 12° in Taurus, at the time when the sun is in 26° of Leo.

With a radius taken from any scale of equal parts, =20′′.25, describe a circle to represent the ecliptic, and divide it into signs and degrees.* Through the star's place in the ecliptic draw a diameter; which shall represent a portion of a small circle parallel to the ecliptic, and the greater axis of the star's ellipsis

See Plate 19.