74 



NA TURE 



[May 



897 



this collection of papers would indicate that he took no 

 notice of it for thirty years. He then points out that the 

 objection would be valid if it were sought to explain the 

 perturbations of Uranus throughout one or more whole 

 synodic periods of the planet. Practically, and for the 

 purposes of the particular solution, the action of the 

 disturbing planet on the motion of Uranus is limited to 

 some twenty years before and after 1822, when the two 

 planets were last in conjunction. The preceding con- 

 junction took place in 1650, some forty years before 

 Flamsteed's earliest observation, and the sensibly elliptic 

 orbit in which Uranus was moving from that time to the 

 beginning of the century, was the elliptic orbit on which 

 the perturbations of Neptune at the last conjunction had 

 been impressed. The outstanding discrepancy exhibited 

 by Flamsteed's observation, in 1690, from the place 

 indicated by the theories of both Adams and Le Verrier, 

 arose from the inadequacy of those theories to represent 

 the place of the planet in the remote past, owing to the 

 erroneous distance assigned to the hypothetical planet. 



Passing over a few short papers generally referring to 

 the orbits of comets and of double stars, we come to 

 Adams's work on the Moon. The papers on this subject 

 refer to lunar parallax, the secular acceleration of the 

 moon's mean motion, and critical notices on the lunar 

 theory, both theoretical and numerical. The work on 

 lunar parallax includes an entire revision of the 

 equations from which the parallax is deduced in the 

 tables of Burckhardt and Damoiseau, as well as in the 

 theories of Plana and Pontecoulant. Henderson had 

 found a difference of i"-3 in the value of the mean 

 parallax deduced from observation, according as he 

 employed the tables of Damoiseau or Burckhardt. 

 Clausen had also called attention to discrepancies in the 

 equations of parallax between the same two authorities, 

 but had not pursued the subject, probably on account of 

 the labour involved. But Adams not only instituted a 

 rigorous comparison between the coefficients employed, 

 and traced the errors of Burckhardt to their source, but 

 added a table of corrections to the daily values of the 

 parallax given in the Nautical Almanac from 1840-1855. 

 This heavy piece of work, demanding as much nicety in 

 its mathematical investigation as patience in its numerical 

 application, Dr. Glaisher describes as characteristic of 

 the author. No part of the work is given ; the method of 

 procedure is briefly sketched, and the final conclusions 

 are stated in the fewest words, and simplest manner 

 possible. 



The discussion of the secular acceleration of the 

 moon's mean motion is known almost as well as the 

 history of the discovery of Neptune. Fierce controversy 

 has centred round this question, and forced it on public 

 notice. It is difficult to understand now, and impossible 

 to explain briefly, the reason for the controversy called 

 forth by Adams's paper in 1853. This somewhat 

 acrimonious debate was carried on with undiminished 

 force for some years, though Adams took little part in it 

 beyond practically settling the fray in i860. To Adams, 

 and to mathematicians of the present day, the problem 

 is purely one of dynamics. Given that the eccentricity 

 of the earth's orbit changes at a slow uniform rate, to 

 determine the corresponding rate of change in the 

 mean motion of the moon. The solution of this 

 NO. 1439. VOL. 56] 



problem is, as Adams pointed out, to be effected by 

 means of a purely algebraical process, the validity of 

 each step of which, admits of being placed beyond all 

 possible doubt. Here there would seem to be no room 

 for dispute. But the question did not present itself quite 

 in this simple manner to Laplace and others of his time. 

 They always had before them the necessity of explaining 

 on purely gravitational grounds the observed motion of 

 the moon. The complete vindication of the Newtonian 

 theory was dear to the hearts of the schoolmen of the 

 last century. Many triumphs had been successively 

 won by investigations undertaken with this object, the 

 greatest of which was due to Laplace, who was believed 

 to have satisfactorily explained and laid to rest the last 

 difficulty, revealed by the complicated motion of the 

 moon. In his paper of 1853, Adams joined issue with 

 Laplace, and in shovving that the work of the earlier 

 astronomer was incomplete, he not only destroyed the 

 harmony that was so long supposed to exist between 

 observation and theory, but practically impeached the 

 judgment of those who upheld the authority of Laplace. 

 M. de Pontecoulant seems to have urged, as a reason for 

 the non-acceptance of Adams's value, the fact that it 

 had "I'inconvenient d'alterer profondement I'expression 

 analytique admise jusqu'k present, au coefficient de cette 

 equation." 



It is curious to reflect on what slender grounds the 

 observed value of 10" assigned lo the secular acceleration 

 was based, and, consequently, how little increased weight 

 it could add to any theoretical value with which it 

 chanced to accord. We may take Dunthorne's investi- 

 gation as typical of the others made with the same 

 purpose. He computed from the lunar tables in use in 

 his time, probably those published in 1739, and in which 

 the moon's centennial mean motion would have a con- 

 siderable error, the circumstances of the eclipses recorded 

 by Tycho Brahe, by Regiomontanus (14 78-1490), by 

 Ebn Jounis (977-8), the eclipse of Theon (364), and 

 those of Ptolemy, Not one of these sources is un- 

 objectionablCj or possesses the necessary accuracy. 

 Ptolemy's catalogue of eclipses was probably selected by 

 him to satisfy a preconceived theory. Theon says that he 

 computed the time of the beginning of the eclipse, and 

 found the observation agreed with his calculation. This 

 agreement is suspicious. The Arabian observations, 

 eye determinations of the beginning and end of the 

 phenomena, are the best suited to the purpose ; though 

 here the error in the moon's mean longitude must be 

 considerable, and a secular acceleration of 7" will satisfy 

 the observations. Those of Regiomontanus and Tycho 

 Brahe, still made without a telescope, must have ap- 

 proximately the same error, and are too near in point of 

 time to gain the advantage of accumulation. 



It is scarcely necessary now to point out the source ot 

 the error in Laplace's theory. In this error he was followed 

 by Damoiseau and Plana, who, while extending the 

 method to include the square and higher powers of the 

 disturbing force, failed to detect the incompleteness of 

 the reasoning which vitiated the earlier portion of the 

 work. Laplace only took into account directly the radial 

 component of the disturbing action of the sun. 



This neglect of the tangential disturbing force, or the 

 assumption that the area described in a given time by 



