truth of the Copernican system. The discois owing to the accuracy and ingenuity of e late Dr. Bradley, astronomer royal; he was led to it accidentally by the result of some careful observations, which he had made with a view of determining the annual parallax of the fixed stars. The history of this discovery is related by the doctor himself, in No. 406′ of the Phil. Trans. Various explanations of the Bature of aberration have been given by different authors; but we know not where to find, or how to devise, one which will be more satis-gitude would be varied through all the points factory and familiar than that given by Dr. Huon in his Mathemat. and Philosoph. Dictionary, which is as follows: "This effect may be explained and familiarized by the moon of a line parallel to itself, much after the manner that the composition and resolution of forces are explained. If light have a progressive motion, let the proportion of its velocity to that of the earth in her orbit, be as the Le BC to the line A C (Pl. 5 fig. 1. ASTROMY:) then by the composition of these two motions, the particle of light will seem to deribe the line B A or D Č, instead of its real BC; and will appear in the direction AB or C D, instead of its true direction C B. that if AB represent a tube, carried with a el motion by an observer along the line AC, in the time that a particle of light would move over the space B C, the different places of the tube being A B, ab, cd, CD; and when the eye, or end of the tube, is at A let a particle of light enter the other end at B; then when the tube is at a b, the particle of light wil be at e, exactly in the axis of the tube; and when the tube is at c d, the particle of light will arrive at f, still in the axis of the the; and lastly, when the tube arrives at CD, the particle of light will arrive at the eye er point C, and consequently will appear to ere in the direction DC of the tube, instead of the true direction BC. And so on, one particle succeeding another, and forming a enntinue stream or ray of light in the apparent direction DC. So that the apparent are made by the ray of light with the line AE, is the angle DCE, instead of the true angle BCE; and the difference, BCD or ABC, is the quantity of the aberration. If Isht moved only one thousand times faster than the eye, and an object, supposed to be at an infinite distance, were really placed perpencicularly over the plane in which the eye is moving; it follows, from what has been said, that the apparent place of such object will always be inclined to that plane, in an angle of 56; so that it will constantly appear 3 from its true place, and will seem so much ss inclined to the plane, that way towards which the eye tends. That is, if BC be to AC as 1000 to 1, the angle B A C will be 89° 54, and the angle ABC 34 and 2 ABC will be 7, if the direction of the motion of the ye be contrary at one time to what it is at

another. If the earth revolve about the sun
annually, and the velocity of light were to the
velocity of the earth's motion in its orbit, as
1000 is to 1; then it is easy to conceive, that a
star really placed in the pole of the ecliptic,
would to an eye carried along with the earth,
seem to change its place continually; and neg-
lecting the small difference on account of the
earth's diurnal revolution on its axis, it would
seem to describe a circle about that pole, every
where distant from it by 34. So that its lon-

of the ecliptic every year, but its latitude would
always remain the same. Its right ascension
would also change, and its declination, ac-
cording to the different situation of the sun in
respect of the equinoctial points; and its ap-
parent distance from the north pole of the
equator, would be 7 less at the autumnal,
than at the vernal equinox. The greatest al-
teration of the place of a star, in the pole of
the ecliptic, or, which in effect amounts to
the same, the proportion between the velocity
of light and the earth's motion in its orbit,
being known, it will not be difficult to find.
what would be the difference, on this account,
between the true and apparent place of any
other star at any time; and, on the contrary,
the difference between the true and ap-
parent place being given, the proportion be-
tween the velocity of light, and the earth's
motion in her orbit, may be found." After
the history of this curious discovery related by
Dr. Bradley, in the places above referred to,
he gives the results of a multitude of accurate
observations made on a great number of stars
at all seasons of the year; and at the same time
he lays down a theory which corresponds in a
surprizing degree with the observations. He
likewise annexed to the theory, rules or for-
mule for computing the aberrations of the
fixed stars in declination and right ascension,
which have been variously demonstrated, and
reduced to other practical forms, by M. Clai-
raut in the Memoirs of the Academy of Sci-
ences for 1737; by Mr. Simpson in his Essays
in 1740; by M. Fontaine des Crutes in 1744;
and several other persons. The results of
these rules are as follow: Every star appears
to describe in the course of a year, by means
of the aberration, a small ellipse, whose greater
axis is 40′′, and the less axis, perpendicular to
the ecliptic, is equal to 40" multiplied by the
sine of the star's latitude, the radius being 1.
The eastern extremity of the longer axis, marks
the apparent place of the star, the day of the
opposition; and the extremity of the less axe,
which is farthest from the ecliptic, marks its
situation three months after.
The greatest
aberration in longitude is equal to 20′′ divided
by the cosine of its latitude. And the aber-
ration for any time, is equal to 20" multiplied
by the cosine of the elongation of the star
found for the same time, and divided by the
cosine of its latitude. This aberration is sub-

fractive in the first and last quadrant of the planet, considered as affected by aberration, argument, or of the difference between the appears in the place where it should have aplongitudes of the sun and star; and additive in peared at that instant which precedes the time the second and third quadrants. The greatest of observation, by the interval of time occupied aberration in latitude, is equal to 20" multi- by light in passing from the planet to the earth. plied by the sine of the star's latitude. And In the sun, the aberration in longitude is conthe aberration in latitude for any time, is stantly 20", that being the space moved by equal to 20" multiplied by the sine of the star's the sun, or rather by the earth, in the space of latitude, and multiplied also by the sine of the 8 m. 7 s. which is the time employed by light elongation. The aberration is subtractive be- in passing from the sun to the earth. And, fore the opposition, and additive after it. The knowing pretty nearly the distance of a pianet greatest aberration in declination, is equal to from the earth at any time, we shall have, as 20" multiplied by the sine of the angle of posi- the distance of the sun, to that of the planet; tion A, and divided by the sine of B the dif- so are 8 m. 7s. to the time of light passing ference of longitude between the sun and star from the sun to the earth: then, computing when the aberration in declination is nothing. the planet's geocentric motion in this time, in And the aberration in declination at any other longitude, latitude, right ascension, or declitime, will be equal to the greatest aberration nation, it will be the planet's aberration, for multiplied by the sine of the difference be- whichever of these the geocentric motion was tween the sun's place at the given time and calculated; and it will be subtractive or adhis place when the aberration is nothing. ditive, according as the planet's motion is Also the sine of the latitude of the star is to direct or retrograde. It is evident that the radius, as the tangent of A the angle of posi- aberration will be greatest in the longitude, tion at the star, is to the tangent of B, the and very small in latitude, because the planets difference of longitude between the sun and deviate in a very small degree from the plane star when the aberration in declination is no- of the ecliptic, or path of the earth; on this thing. The greatest aberration in right ascen- account, the aberration in the latitudes of the sion, is equal to 20' multiplied by the cosine planets is commonly neglected as nearly inof A the angle of position, and divided by the sensible; the greatest in Mercury being only sine of C the difference in longitude between 44", and it is considerably less than this in the the sun and star when the aberration in right other planets. As to the aberrations in decliascension is nothing. And the aberration in nation and right ascension, they must depend right ascension at any other time, is equal to on the position of the planet in the zodiac. the greatest aberration multiplied by the sine The aberration in longitude, being determined of the difference between the sun's place at the by the geocentric motion, will be nothing at given time, and his place when the aberration all when the planet is stationary; and greatest is nothing. Also the sine of the latitude of in the superiour planets when they are in opthe star is to radius, as the cotangent of A position to the sun, but in the inferiour planets the angle of position, to the tangent of C. when they are in their superiour conjunction. From the greatest variation in the place of the These maxima of aberration for the several stars, the doctor deduces the ratio of the velo- planets, when their distance from the sun is city of light to that of the earth in her orbit, least, are as follow: georgium sidus, 25′′; sasupposing both to be uniform, thus: in the turn, 27"; jupiter, 2978; mars, 37"8; venus, figure last refered to, BC is to AC, as the 432; mercury, 59′′; the moon, 3". Between velocity of light, to that of the earth in her these quantities and nothing the aberrations in orbit, and the angle ABC is 20"; so that the longitude, of the respective planets, vary acratio of those velocities, is that of radius to the cording to their situations. And as to the tangent of 20, or since the tangent has no aberration of the sun, in longitude, although it sensible difference from so small an are), as varies not (as before observed), yet it causes a radius to 20′′: but the radius of a circle is variation in the aberration in declination, equal to an are of 3710 nearly, or equal to which is greatest (about 8") at the equinoxes, 205260", therefore the velocity of light is to where the sun's motion is most inclined to the that of the carth, as 200260 to 20, or as 10313 equator; and is least (or absolutely nothing) to 1. Hunce the time in which light will pass in the solstices, where the sun's motion in the from the sun to the earth was easily deduced: ecliptic is for a short time parallel to the equafor this time is to one year, as AC or 20' to tor. A quantity of aberration is occasioned by 360°, or the whole circle; that is, 360°: 20" the diurnal rotation of the carth, but whether :: 36544: 8m. 7s.; therefore it appears, from we consider it with respect to the sun, planets, this discovery of Dr. Bradley's, that light or fixed stars, it is too small to be perceptible: passes from the sun to the earth in eight mi- for, in the space of eight minutes, a point on nutes seven seconds: thus confirming, in a the earth's surface moves through 32' of a devery satisfactory manner, the conclusion of gree; and since small optic angles are nearly M. Roemer, deduced from observations of a as the diameters they subtend, it is, as radius: totally different kind. See LIght. sine 32 875 (sun's parallax): 488, the ABERRATION ΟΓ THE PLANETS. A maximum of aberration from this cause.

On

subject of this article we have already erred to Simpson's Essays, and Mem. Roy. Acad. Scien. for 1737: the matter is farther pursued by M. Clairaut, in those Memoirs for 10. See also Robins's Tracts, vol. II. p. 276; 0. Gregory's Astronomy, chap. 22; La Lande's Astronomy, vol. III. 173-210, and Vince's Astronomy, vol. I. p. 332, &c. In the Philos. Trans. vol. 60, Dr. Price has phen Remarks on the effects of aberration on the transit of Venus.

P.

ABERRATION, in optics, that error or devation of the rays of light, when inflected a lens or speculum, whereby they are hinde from meeting or uniting in the same point, called the geometrical focus; it is either bural or longitudinal. The lateral aberration measured by a perpendicular to the axis of the speculum, produced from the focus, to set the reflected or refracted ray: the longidral aberration is the distance of the focus on the point in which the same ray intersects the axis. If the focal distance of any lenses be gm, their apertures be small, and the incitravs homogeneous and parallel, the londinal aberrations will be as the squares, as the lateral aberrations as the cubes of the Laar apertures. There are two species of tration, distinguished according to their fferent causes: the one arises from the Eure of the speculum or lens, producing a metrical dispersion of the rays, when these are perfectly equal in all respects; the other anes from the unequal refrangibility of the Ts of light themselves; a discovery that wis made by Sir Isaac Newton, and for this reason it is often called the Newtonian abernion. As to the former species of aberration, er that arising from the figure, it is well known that if rays issue from a point at a given distance; then they will be reflected into the other focus of an ellipse having the given luminous point for one focus, or directly tom the other focus of an hyperbola; and wil be variously dispersed by all other figures. But if the luminous point be infinitely distant, or, which is the same, the incident rays be parallel, then they will be reflected by a paracha mto its focus, and variously dispersed by all other figures. But those figures are very difficult to make, and therefore curved specula are commonly made spherical, the figure of which is generated by the revolution of a circular are, which produces an aberration of all rays, whether they are parallel or not, and dherefore it has no accurate geometrical focus which is common to all the rays. Let BVF (Pl. 7. fig. 1. OPTICS) represent a concave pherical speculum, whose centre is C; and ket AB, EF be incident rays parallel to the axis CV. Because the angle of incidence is equal to the angle of reflection in all cases, therefore if the radii CB, CF be drawn to the points of incidence, and thence BD making the angle CBD equal to the angle CBA, and

And

In

FG making the angle CFG equal to the angle
CFE; then BD, FG will be the reflected
rays, and D, G, the points in which they
meet the axis. Hence it appears that the
point of coincidence with the axis is equally
distant from the point of incidence and the
centre: for because the angle CBD is equal
to the angle CBA, which is equal to the al-
ternate angle BCD, therefore their opposite
sides CD, DB are equal: and in like manner,
in any other, GF is equal to GC.
hence it is evident that when B is indefinitely
near the vertex V, then D is in the middle of
the radius CV; and the nearer the incident
ray is to the axis CV, the nearer will the re-
flected ray come to the middle point D; and
the contrary. So that the aberration DG of
any ray EFG, is always more and more, as
the incident ray is farther from the axis, or
the incident point F from the vertex V; till
when the distance VI is sixty degrees, then
the reflected ray falls in the vertex V, making
the aberration equal to the whole length DV.
And this shews the reason why specula are
made of a very small segment of a sphere,
namely, that all their reflected rays may ar-
rive very near the middle point or focus D, to
produce an image the most distinct, by the
least aberration of the rays. And in like man-
ner for rays refracted through lenses.
spherical lenses, Mr. Huygens has demon-
strated that the aberration from the figure, in
different lenses, is as follows: 1. In all plano-
convex lenses, having their plane surface ex-
posed to parallel rays, the longitudinal aber-
ration of the extreme ray, or that most remote
from the axis, is equal to 2 of the thickness
of the lens. 2. In all plano convex lenses,
having their convex surface exposed to parallel
rays, the longitudinal aberration of the ex-
treme ray, is equal to Z of the thickness of the
lens. 3. In all double convex lenses of equal
spheres, the aberration of the extreme ray is
equal to of the thickness of the lens. 4. In
a double convex lens, the radii of whose
spheres are as 6 to 1, if the more convex sur-
face be exposed to parallel rays, the aberration
from the figure is less than in any other sphe
rical lens, being no more than 15 of its thick-
ness. Mr. Huygens has also shewn, that the
same aberration is produced by concave lenses
as by similar convex ones. It has been assert-
ed, chiefly on the authority of Sir Isaac New-
ton, that this species of aberration arising from
the figure of the glass, is very inconsiderable
when compared with that arising from the
unequal refrangibility of the rays of light;
nay, it has been stated (Smith's Optics, book
ii. cap. 6.) that the latter is to the former as
5449 to 1. Admitting the truth of this, it
was thought very strange that objects should
appear through refracting telescopes so dis-
tinctly as they are found to do: and indeed
many persons despaired of success in the use
and fabrication of lenses. But a little atten-