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IIISTOEY OF PHYSICAL ASTfiONOMY.

quantity greatly exceeded the rate of diminution which had hitherto beendeduced from the observations of astronomers, Bradley was induced toascribe the phenomenon to an oscillation of the earth’s axis, occasioned bythe disturbing action of the moon upon the terrestrial equator. Beingunable, however, by means of observations, extending only over a periodof nine years, to judge whether the axis would recover its former position,he found it necessary to continue his observations throughout a wholerevolution of the moon’s nodes. In the year 1745, when the moon’sascending node had again arrived in Aries, he had the satisfaction to findthat the stars returned to the same position which they would haveoccupied, if the inclination of the terrestrial axis had been the same as itwas in 1737. This circumstance appeared to him an indubitable indica-tion that he had detected the true cause of the phenomenon.

Machin, to whom Bradley communicated an account of his discovery,devised a geometrical theory of the phenomenon, by the aid of which hecomputed a table of its numerical values. He supposed that while themean pole of the equator described a circle round the pole of the ecliptic,at the rate of 50" in a year, occasioning thereby the uniform motion ofprecession, the apparent pole of the equator described round the meanpole, a small circle whose radius was equal to 9", being in that part of thecircle which is farthest from the pole of the ecliptic when the moon’sascending node was in the beginning of Aries, and in the opposite pointwhen the same node was in Libra.

Bradley proceeded to establish a strict verification of his hypothesis, bycomparing it with a great number of his observations. The result ofthis comparison afforded a complete confirmation of his views. Havingcomputed the mean declination of y Draconis from 300 distinct obser-vations, by applying to each observation the appropriate corrections ofprecession, aberration, and nutation, he obtained a series of results whichpresented a remarkable agreement with each other. Eleven only werefound to differ so much as 3" from the mean of the whole, while notone differed so much as 3" from it. The result was equally satisfactoryin the case of several other stars, which he employed in testing his hypo-thesis *.

It has been stated that Bradley fixed the coefficient of nutation at 9".The researches of subsequent enquirers seem to indicate that the truevalue exceeds this quantity by a few tenths of a second. Maskelyne madeit 9".55. Laplace, by the aid of theory, deduced 9".40 as its most pro-bable value. Lindenau, by a discussion of a vast number of observations,extending from 1750 to 1815, and consequently including three completerevolutions of the moon’s nodes, obtained 8".989 for the coefficient ofnutation. This result is now generally supposed by astronomers to fallbelow the true value. Dr. Brinkley, by comparing 1618 observations ofdifferent stars, made it 9".35. Henderson, from the value of the moon’smass, indicated by his researches on the lunar equatorial parallax, deter-mined the coefficient of nutation to be 9".38. Dr. Robinson, from up-wards of 6000 observations with the mural circle, made by Pond atGreenwich, between the years 1813 and 1835, deduced 9".23913 as itsmost probable value. Various similar evaluations have been effected by-modern astronomers. Baily, by a careful comparison of all the results,came to the conclusion that the most probable value of the coefficient is9".25.

See the original Memoir of Bradley (Phil. Trans., 1748, p. 1 et seq.).