ABERRATION AND NUTATION.] 



ASTRONOMY. 



933 



the star should occupy in the annual revolution of the 

 earth in its orbit. He was surprised to find that the 

 most distant position of the star from the pole of the 

 ecliptic did not occur when the sun was at S, but when 

 it was distant 90 from this point. His observations of 

 7 Draconis were commenced in December, 1725, when 

 the sun would be about the position S of our figure, and 

 the star in the position p ; but he found that it gradually 

 went towards the south, till it attained a position 20" 

 more southerly than in December. This occurred at 

 the beginning of March, 1726. It afterwards went 

 northerly, being in September more northerly by 39" 

 than it was in March. In the ensuing December the 

 star was found in the position of the previous December, 

 after making a proper allowance for the precession of the 

 equinoxes. 



Dr. Bradley did not, however, rest satisfied till he had 

 repeated the observations with another instrument, made 

 by one of the most celebrated artists of the day, Graham, 

 which included a larger range of zenith distance. The 

 same results as before mentioned were arrived at ; the 

 last instrument gave results identical with the three- 

 foot quadrant of Picard, and the twenty-four foot sector 

 of Molyneux. He endeavoured to trace the origin of 

 the difference to the effect of refraction, or a nutation of 

 the earth's axis, the latter of which corrections was then 

 unknown, with the exception of the trifling effect of 

 solar nutation, whose period was six months, and which 

 at its maximum, as determined by Newton, only 

 amounted to a fraction of a second. The cause was 

 certainly proved by Bradley not to be owing to nutation, 

 since a star, opposite in right ascension to 7 Dracouis, 

 and at the san.e distance from the pole, observed at the 

 same time of the year, exhibited differences only half 

 the amount of 7 Draconis. Had the cause been the 

 effect of nutation of the earth's axis, the same result of 

 fluctuation would have affected both stars by exactly the 

 same quantity. 



The effect of aberration may be thus explained. In 

 the figure, T T T", <fcc. (Fig. 38), represent as before ; 



Fig. 38. 



E is the place of the star. If we take with line S E, a 

 part S R, and another line Rr, parallel to the tangent 

 to the earth's orbit at T, which would be the direction 

 of the motion of the earth unless restrained by gravi- 

 tation, the proportion of R r to S R is that of the motion 

 of the earth in its orbit to the velocity of light. Thus 

 when the earth is at T, the star, to an observer immov- 

 .ible at the centre of the sun, would, by the effect of the 

 " aberration of light," be seen in the position S e, looking 

 at the star as if he had been on the earth at T. Thus, 

 by analogous reasoning, when the earth is at T', by 

 drawing R/ parallel to the direction of the earth's 

 motion, an observer at the sun will see the star in the 

 direction S e'; and so on. The star would then appear 

 to describe a curve in the heavens, e, e', e", e'". 



There is a great difference, theroiore, between the 

 two positions of the star, by taking into account the 

 effect of aberration. In the former case, the direction 

 of the visual ray was, for an observer, immovable at the 

 un, in a line parallel and equal to that joining the star 



with the earth in its orbit, and distant by the radius of' 

 the earth's orbit. la the latter case, the effect of aber 

 ration is to make the star appear in a line parallel to a 

 tangent of the earth in its orbit, and distant by a quantity 

 in proportion to the velocity of light, combined with that 

 of the earth in its orbit. 



Fig. 39 will show the real effect of aberration on the 

 position of 7 Draconis. By the preceding reasoning 

 Fig. 39. 



when the sun is at , tue star should appear at m, in the 

 small ellipse mp nt]_. The effect of aberration will there- 

 fore be to retard the position of the star by 90, which 

 will agree with Bradley's observation of December, 1725. 

 At March, 1726, the star had increased its polar distance 

 by 39", or was found in the position p, and so on, the suc- 

 cessive positions of the star agreeing precisely with 

 observation. 



NUTATION OF THE EARTH'S Axis. After the discovery 

 of the Aberration of Light, the indefatigable astronomer, 

 Dr. Bradley, prosecuted his observations at Oxford and 

 Greenwich, when his zeal and care were rewarded by the 

 discovery of another important inequality viz., Lunar 

 Nutation. After applying Precession and Aberration, he 

 found that, after a series of observations carried on from 

 1727 to 1745, an inequality existed, depending on the 

 longitude of the nodes of the moon, whose period was 

 18 years, the existence of which had been previously men- 

 tioned by Roe'mer, but of which no published account 

 had been given. Dr. Bradley communicated this "Nu- 

 tation of the Earth's Axis," in a Memoir, to the Royal 

 Society, in 1748 ; in which he mentioned, that in order to 

 reconcile it with his observations, it would be necessary 

 to assume that the pole of the equator described a small 

 ellipse about its mean plane, whose major and minor axes 

 were respectively 18" and 16". It was afterwards ex- 

 plained on Sir Isaac Newton's Theory of Gravitation, as 

 a necessary effect of the retrograde motion of the moon's 

 nodes, by which the moon's inclination to the equator 

 varies from 18 to 28. By this it is evident that this 

 variation of inclination will cause a considerable differ- 

 ence in the moon's attraction on the protuberant parts of 

 the earth's equator. Nutation is, then, an irregularity of 

 Lunar Precession, the mean value of which is 35" '9 an- 

 nually the remaining 14'~4 being principally due to the 

 sun or the whole amount of the precession of the 

 equinoxes being equal to 50" 3. 



The following explanation will clearly show the effect 

 of a nutation of the earth's axis on the position of a 

 star : 



It has been previously explained that the pole of the 

 equator makes a complete revolution around the pole of 

 the ecliptic in a term of about 25,000 years, and that it 

 is termed the "Precession of the Equinoxes." In Fig. 

 40 (which is not in exact proportion to the phenomena), 

 T K is the pole of the ecliptic, and T o the pole of the 

 equator, the angle K T o, or the obliquity of the ecliptic, 

 being 23 28'. In consequence, however, of nutation, 

 the pole of the equator, T o, does not preserve the same 

 inclination to the pole of the ecliptic, but moves on the 



