13 



ABERRATION. 



ABERRATION. 



U 



AC of the star; whence, as the earth changes the direction of its 

 motion in going round the sun, the direction of the aberration will also 

 change. 



3. That we have committed an error in supposing the lines A c and 

 B a to be parallel, since they meet at the star ; which error, on account 

 of the star's enormous distance, will be imperceptible. 



4. That AB is not properly the spectator's motion round the sun 

 only, but compounded of that and his motion round the earth's axis ; 

 the latter, however, being at most not one-third of a mile in a second 

 while the former is nineteen miles per second, the maximum effect of 

 the diurnal aberration amounts to only a fraction of a second of space. 



5. The real direction AC of (the light may be considered as the 

 i-.ime at every part of the earth's orbit, on account of the distance of 

 the star. 



6. The aberration always throws the star apparently nearer to the 

 earth's course, that is, A a is always within the angle CAB. 



7. The aberration is greater or less according as the angle c A B is 

 nearer to, or further from, a right angle, and is greatest when c A B is a 

 right angle. This result may readily be proved by those who under- 

 stand trigonometry, if they recollect that A B and a A are given, being 

 the velocity of the earth and the apparent velocity of light, and that 



AB . AB . 



sin AOB, or sin CAB = sin BBA = sui CAB. 

 A OA 



Let us suppose, which will be exact enough for our purpose, that 

 the earth moves in a circle (the ecliptic), of which the sun is in the 

 centre. The line s A, perpendicular to the plane of the ecliptic, looks 

 towards the pole of the ecliptic. Let 8 B be the direction of a star, 

 p s Q perpendicular in the plane of the ecliptic to s B, and R s T perpen- 

 dicular to PS Q. in the same plane. When the earth is at E, it is 

 moving in the direction E M, perpendicular to s E, and the star, from its 

 great distance, is in the direction r. c parallel to s B. Hence the aber- 



Fig. S. 



ration takes place in the plane c E M, that is, the star is a little lowerec 

 towards EM, and appears in the direction ED. Let the needle 8X 

 move round the circle with the earth, so as always to indicate the 

 direction in which the earth is moving, that is, 8 N is always parallel to 

 E M, and perpendicular to s E. The plane B s N being parallel to the 

 plane OEM, is the plane in which aberration would appear to take 

 place if the spectator were at 8, and 8 was moving ; but as the spec 

 tator does not perceive his own motion, let us suppose him placed al 

 8, and the same aberration to take place in the plane B 8 N, which 

 really does take place in c E M. By what has been said, the aberration 

 is greatest when the needle points to q or p, that is, when the earth is 

 at T or R ; and least, when the needle points to T or B, that is, when 

 the earth is at P or q ; because the angle B 8 N is a right angle when 

 in at p or q, and differs most from a right angle when u is at T or R 

 Hence the aberration increases as the earth moves from P to T, dimi 

 nishes from T to Q, increases from Q to B, and decreases again from 

 R to P. The line in which the star appears, moves round s B in th 

 course of a year, and describes a cone, while the star appears to describe 

 a small oval or ellipse about B, the greater axis of which is parallel tc 

 p <J, and the lesser to R T ; such as p r q I, in which p is the apparen 

 place when the earth is at P, and so on. This deviation ia completec 

 in the course of a year. 



When the star itself is in the pole of the ecliptic, or is seen in th 

 direction s A, the angle A aw, is always a right angle, the aberration 

 always of the same magnitude, and the apparent path of the star is 

 circle. As we take stars in which 8 B is more inclined to the ecliptic 

 the oval become* flattened in proportion to it length, so that when th 

 star is in the ecliptic, it appears to vibrate backwards and forwards in 

 straight line, going and returning once in each year. 



If the star be on the solstitial colure, the points P and Q will be th 



noxes, and R and M the solstices. The aberration will consequentl 



be greatest at the solstices, and least at the equinoxes. We shall refe 



to thin caw presently. 



The Un appear to us to lie on a large sphere, of which we are at th 

 centre. [SPHERE.] We may represent the phenomenon on a commo 

 globe, by drawing a small ellipse or oval round the star, the majo 

 axis of which is parallel to the ecliptic, and the figure of whic 

 U more or less flattened, as the star in nearer to, or further fron 



le ecliptic. The major axis will always be an arc of 41", and 

 le minor axis will be 41" multiplied by the sine of BSM or the 

 ar's latitude. 



Previously to entering upon the quantity of aberration, we shall give 

 ome account of the discovery, which is one of the most remark- 

 ble in the history of science. The arguments for the motion of the 

 arth, though tolerably conclusive, were yet principally derived from 

 le great simplicity of this hypothesis in comparison with others, 

 ince all the phenomena then observed could be equally well explained 

 pon the supposition, that the other planets moved round the sun, at 

 be same time that the sun moved round the earth. It remained, 

 berefore, to find some experimentum, crucis, some phenomenon, which 

 admitted of no other explanation except what could be derived from 

 he earth's motion. The first idea which suggested itself to astronomers 

 as, that if the earth really moved, the stars would appear to change 

 heir places ; though they did not count much upon this, since they 

 rnew that the distance of the stars might be so great, that the whole 

 liameter of the earth's orbit would be too small a change of position 

 a cause any perceptible change of place. [PARALLAX.] 



However, the great improvements effected in practical astronomy 

 /owards the close of the 1 7th century, enabled astronomers to detect 

 certain small changes in the apparent places of the stars, which hat! 

 litherto escaped observation, but which could not be satisfactorily 

 explained by the parallax depending on the annual motion of the earth, 

 looke, indeed, from observations of y Draconis, made with a zenith 

 sector of his own construction, was led to assign a parallax of sensible 

 magnitude to that star, but the result at which he arrived was not 

 ;enerally admitted by astronomers. About the same time Picard 

 remarked that the apparent place of the pole star was subject to a 

 variation of which he could give no satisfactory account. Flamsteed, 

 who independently detected the same phenomenon, attributed it to 

 ;he effects of annual parallax, but Cassini showed that the direction 

 in which the displacement occurred, was not in accordance with the 

 iffect which would result from the annual motion of the earth.* It 

 may be mentioned also that Rb'mer, a contemporary of Flamsteed, 

 remarked certain changes in the declinations of the stars which, 

 according to his pupil Horrebow (' Basis AstronomifC,' p. 66) he was 

 unable to explain either by parallax or refraction. 



In the year 1725, Bradley, Savilian Professor of Astronomy at 

 Oxford, and afterwards Astronomer Royal, and Molyneux, the son of 

 Locke's well-known friend of that name, resolved to verify Hooke's 

 observations of y Draconit. This star had been selected by Hooke for 

 his researches on annual parallax, because it passed very near the 

 zenith of Gresham College, London, the place where his observations 

 were made, and therefore would not be sensibly affected by refraction. 

 The star manifestly offered the same facility of investigation to Bradley 

 and Molyneux, whose observations were originally made at Kew. The 

 instrument with which their observations were made was also a zenith 

 sector, which, indeed, at that time was the most correct instrument for 

 measuring very small angles [ZENITH SECTOR] ; and a very large one, 

 having a telescope 24 feet long, made by Graham, one of the most 

 celebrated artists this country has produced, was erected at the 

 place just mentioned, under the direction of Molyneux. Before 

 proceeding further let us consider what would be the effect pro- 

 duced on the apparent place of y Draconis by the aberration of 

 light. This star happens to be situate within about 16 of the pole of 

 the ecliptic ; it will, therefore, in accordance with the preceding account 

 of aberration, appear to describe nearly a small circle about the place 

 it would have if the earth had no motion, which is called its mean 

 place. In the maps of the stars, published by the Useful Knowledge 

 Society, the little circle, which represents y Draconw, will do well 

 enough to give an idea of the path which it describes every year. By 

 measuring the star's zenith distance when on the meridian, its polar 

 distance was also measured, since the zenith and pole are both points of 

 the meridian, distant from one another by the colatitude of the place 

 [COMPLEMENT] ; in other words, by adding the difference between 90 

 and the latitude of Kew to the meridional zenith distance of the star at 

 that place, we obtain its polar distance. In fg. 4, s represents the mean 

 place of the star and t> s a w the small ellipse, nearly a circle, described 

 by the star in one year. The reader must imagine this circle placed 

 in the heavens, and the line P s bent over his head, so that z is his 

 zenith and p the pole. We must now show how to find the points of 

 the ellipse v s aw, answering to the four principal periods of the year 

 namely, the solstices and equinoxes. Referring back to fij. 3, in 

 which we finally placed the spectator at s, the sun will appear to 

 describe the circle which the earth really describes; that is, as the 

 earth moves from Q to R, the sun will appear to move from p to T. 

 Hence, when the earth is at Q, the aberration, throwing the apparent 

 place of the star towards SB, 90 before the earth, throws it also 

 towards a line 90 behind the sun's apparent place. Let E, fig. 5, be 



* The displacement remarked by Flamsteed was evidently due to aberration. 

 This has recently been established beyond doubt by Dr. Peters, who, by a dis- 

 cussion of Flamstecd's observations of the pole star, found the maximum value 

 of aberration tobc 20"'fl76, with a probable error of l"'ll. The close agreement 

 of this result with the mean of the most trustworthy values of the same element 

 hitherto obtained, furnishes a favourable proof of the accuracy of Flamsteed's 

 observations. 



