272 



NA TURE 



[January 18, 1906 



handle with a strong leather covering. One illustra- 

 tion here reproduced represents a corps a corps a la 

 Japonaise, and, judging from the photograph, it is 

 allowable to combine a trip with a hit, as one fencer 

 is trying to knock his opponent over with a hit at 

 the neck, at the same time taking his leg from under 

 him with a sort of jujitsu trip. 



The last chapter describes the sumo or wrestling 

 of the Japanese— to many a most repulsive spectacle 

 on account of the enormously fat bodies of the par- 

 ticular class of men who follow this profession; but 

 a fight between two expert sumotori is for the 

 Japanese an event of almost national importance, and 

 they flock in thousands to the huge amphitheatre in 

 the centre of which the tussle takes place. The second 

 illustration shows two combatants in a crouching 

 position waiting for a chance to spring at each other. 



The last few pages of the book are devoted to 

 jujitsu, but as nothing new is said on this subject 

 and the photographs are very poor there is no need 

 to enter into detailed description. For the rest, a 



very pleasant hour may be spent over the perusal of 

 this interesting little book. E. W. 



THE MOTION OF THE MOON.' 

 DER ARDUA AD ASTRA should be the motto for 

 a cultivator of the lunar theory. There is no 

 austerer road to prove oneself a man of mettle. 

 Incredibile studium atque indefessus labor was Euler's 

 summary upon it, and improvement of method since 

 Euler's time has diminished neither studium nor 

 labor. The work now brought to completion has 

 occupied Prof. Brown (and a computer) since 1S95, 

 almost to the exclusion of other researches, and for 

 some years before that he was busied with developing 

 its methods. Moreover, the present stage is only a 

 level whence he can take breath to proceed. 



It is a fact to remember in mathematical astronomy 

 that problems mathematically identical are often 

 astronomically opposite as the poles. The theory of 

 the moon from a geometer's point of view is simply 

 the theory of one of the planets. It is the special 

 values of the constants alone which distinguishes the 



1 " Theory of the Motion of the Moon." By Krnest W Erown F R <; 

 n the Memoirs of the Royal Astronomical Society, vols, liii., liv., ivii 



no. 1890, VOL. 7$\ 



case. The astronomer seeks a correct ephemeris, but a 

 mathematical instinct seeks to solve the question as 

 a case of the problem of three bodies, and Delaunay's 

 two enormous volumes will show what labours may 

 be undertaken to obtain full literal development of 

 the moon's coordinates which shall be approximate 

 enough to meet the needs of the observer. Unfor- 

 tunately the expressions when obtained are in many 

 cases so imperfectly convergent that they give neither 

 a solution of the three-bodies-problem nor do they 

 surpass the observations in precision, as calculation 

 should. _ It seems that unless some wholly new 

 device is found we must be content to separate the 

 problem into two parts, leaving literal developments 

 for special mathematical researches throwing light 

 upon the problem of three bodies, such as G. YV. 

 Hill's investigations of periodic moons of different 

 mean motions, and making the developments essen- 

 tially numerical when they are designed to form the 

 basis for tables, although by so doing the former 

 part loses all observational interest and the latter 

 nearly all that is mathematical. Prof. 

 Brown's theory is neither wholly 

 numerical like that of Hansen nor 

 wholly literal like that of Delaunay. 

 The mean motion alone is treated as 

 numerical, the other constants as eccen- 

 tricities and inclination appearing in 

 literal form. This was a plan Adams 

 always urged, and from time to time he 

 made considerable studies to give effect 

 to it. When there otherwise remain four 

 parameters according to powers of which 

 each coefficient must converge, it is 

 clearly an immense gain to omit a fifth 

 when that fifth is answerable for all the 

 worst cases of slow convergence ; and 

 while the mean motion may be con- 

 sidered known, it is hardly the case with 

 the other constants, the lunar eccen- 

 tricity, for example, and the ratio of the 

 mean distances of the sun and moon 

 being uncertain within the limits over 

 which debate ranges, so that it is 

 essential that the calculator should not 

 be tied to a single set of elements at the 

 outset. 



Besides this idea Prof. Brown's re- 

 search rests upon two clear and 

 solid supports. First is the use of rectangular 

 moving axes of reference, which he points out — 

 and otherwise it seems to have passed from 

 memory — was developed by Euler. But perhaps 

 as much as anything his success is due to the 

 brilliant transformation of the equations of motion 

 given by G. W. Hill. It detracts not the least from 

 Prof. Brown's achievement that his main ideas 

 and methods are derived from earlier masters. The 

 tools were ready to hand for one who had the learn- 

 ing and judgment to use them. Anyone who has 

 faced a similar task knows that there remain 

 abundant calls for resource and invention, as well as 

 for comprehensive patience, in fitting given plans 

 together and working them out abreast in every 

 remote ramification of a subject, without fidgeting 

 about "originality." 



The work is not yet at a stage to put to proof by 

 calculation of- an ephemeris, which indeed would 

 need the calculation of lunar places for a great many 

 years backwards and forwards to prove that it is 

 superior to Hansen, cr to Hansen plus Newcomb. 

 But even now it is almost certain that it will be so. 

 First its methods are more intelligible and above 



