May 27. 1897] 



NATURE 



75 



the moon about the earth undergoes no permanent 

 alteration, introduced a considerable error in the co- 

 efficient of iii^ in the expression for the true longitude. 

 Correcting the whole of the coefificients in the expansion 

 as far as /;/', Adams assigned a value to the secular 

 acceleration that has not been sensibly disturbed by any 

 subsequent investigation. This value is 5"7, a quantity 

 only about one-half of that assigned by Laplace, or of that 

 which seemed to be demanded by observation. The 

 minuteness of the quantity sought afifords a good illus- 

 tration of the powers of analysis. The acceleration of 

 the moon's motion implies, of course, an approach to the 

 earth, but the amount is less than one inch per annum, 

 and this minute quantity is determined by theory to 

 within about one-thousandth part of its true amount. 



Such an investigation as this last, exhibits the patient 

 examination which Adams was prepared to give to a term, 

 the value of which has been frequently under review by 

 methods that have long been pursued. It shows a con- 

 fident reliance upon the accuracy of his judgment, the 

 completeness of his work, and a refusal to be led by 

 authority. But some later papers on the general method 

 of treating the lunar theory will be belter appreciated, 

 as showing, perhaps, greater originality, and illustrating 

 the application of the results of more modern mathe- 



tmatical inquiry to obtain greater accuracy with less 

 expenditure of labour. It is curious to notice that but 

 for a lucky accident, this peculiar method of treating the 

 lunar motion, and which is likely to be much developed 

 _^ in the future, would not have been published by Adams 

 himself. In 1877, Mr. Hill published his inquiry into 

 the motion of the moon's perigee, in which is sought 

 an absolutely accurate value of that part of c (the ratio 

 of the synodic to the anomalistic months) which depends 

 upon ;;/ alone. This is the historic problem that Clairaut 

 successfully solved by adding the term depending upon 

 w^ and thus supplying a confirmation of the Newtonian 

 theory when it was most needed. Delaunay has since 

 determined the numerical value of the series as far as 

 ?«^ and possibly human patience could get little further 

 by this process. Mr. Hill had recourse to quite a different 

 method, which, as applied, gives the same accuracy that 

 would be attained by carrying the series to ;;/-". The 

 sight of this paper by Mr. Hill, seems to have reminded 

 Prof Adams that some ten years previously he had been 

 at work on similar lines in order to arrive at an accurate 

 value of g, which is related to the motion of the node in 

 the same way that c is to the perigee. The differential 

 equation which determines z, the moon's coordinate 

 perpendicular to the ecliptic, is 



Prof. Adams puts 

 J + -^ = (« - «')■■{'/ + 2r/j COS 2{n - n')( + 



2^.^cos4{n - n')t + 2^/3 cos 6(« - n')t -t- &c.I, 

 and on solving this equation was led to the form that 

 Mr. Hill had employed in his work. For Mr. Hill had 

 made the general equations of motion depend upon a 

 single differential equation having the form 



dT- 

 NO. 1439, VOL. 56] 



where r denotes the mean angular distance between the 

 Sim and moon, and can be developed in a periodic 

 series of the form 



00 + ©1 cos 2 r + ®., COS 4T + &c. , 



leading to the same infinite determinant in both cases. 

 This is developed in a series of powers and products of 

 small quantities, the coefficient of each term being given 

 in a finite form. The similarity of method pursued in- 

 dependently by the two mathematicians, and the greater 

 accuracy obtainable with less labour, seem to point to a 

 new departure in the method of treating the lunar theory. 

 Prof Adams has indicated what appears to him the most 

 advantageous method of treating this problem. 



We can but barely mention one other of Adams's in- 

 vestigations, the discussion of the orbit of the November 

 meteors. It is well known that the late Prof. Newton 

 left undecided the periodic time in which the meteors 

 revolved about the sun, indicating, however, the method 

 which might lead to the settlement of the question by 

 the discussion of the observed amount of secular perturb- 

 ation of the node. By a method given by Gauss in his 

 " Determinatio Attractionis," it is shown how to deter- 

 mine the attraction of an elliptic ring, such as the meteors 

 form, on a point in any given position. By dividing the 

 orbit of the meteors into a number of small portions, and 

 summing up the changes corresponding to these portions, 

 Adams found the total secular changes of the elements 

 produced in each of the five possible periods that Prof 

 Newton showed might be assigned as the meteoric path. 

 With only one of these periods, that of about thirty-three 

 years, was it possible for the node to advance in the 

 manner required by the several historical accounts of 

 the meteoric display. With a thirty-three years' period, 

 and with no other, the longitude of the node is increased 

 20' by the action of Jupiter, 7' by that of Saturn, and i ' by 

 Uranus, thus 28' in all, giving a mean annual motion of 

 52", agreeing with the observed motion, and thus satis- 

 factorily settling the periodic time in which the November 

 meteors revolve. 



Several other papers possess great interest, and 

 evidence among other things much painstaking arith- 

 metic. Such is the calculation of thirty-one of Bernoulli's 

 numbers, and the computation of the Eulerian constant 

 to 263 places of decimals. These may have been the 

 occupation of his leisure moments. The reputation of 

 Adams will ever rest upon the determination of the 

 inverse perturbations of Uranus, the work on the lunar 

 theory, and his inquiry into the period of the November 

 meteors. 



A CYCLOP.i£DIA OF BIOLOGICAL THEORY. 

 Les Theories sin T HMdit^ et les grands problhiies de la 

 Biologic generate. Par Yves Delages, Professeur k la 

 Sorbonne. Pp. xiv -I- 878. (Paris : Reinwald, 1895.) 



PROFESSOR DELAGES has produced in this 

 large volume of 880 pp. royal octavo, a valuable 

 exposition and critical discussion of the modern theories 

 bearing upon the great problems of biology. The work 

 is remarkable for the ability with which so vast a variety 

 of theories and observations are epitomised and con- 

 sidered. Whilst the author does not profess to give 



