100 



SCIENCE. 



[Vol. V., No. 104. 



The discussion of the records of part ii. and 

 part iii., together with the meteorological data 

 of the expedition, is in course of preparation 

 by Professor Tait and Mr. Buchan. 



PUBLICATIONS OF THE NAUTICAL 

 ALMANAC OFFICE. 



In the first part of this volume, Professor 

 Newcomb presents a detailed development of 

 the perturbative function which is applicable 

 to all cases, except extreme ones, in which a 

 general development of planetaiy inequalities 

 in terms of the time is sought, and by which 

 any required derivatives of the function ma} T 

 be found with great facility. In order to 

 afford some idea of its range of application, 

 he compares this development with others 

 having the same general object ; viz., those of 

 Laplace, De Pontecoulant, Peirce, Leverrier, 

 Hansen, and Cauchy. The method of this 

 development has previously been indicated b} T 

 Professor Newcomb, in the American journal 

 of mathematics, vol. iii. The second part of 

 this volume of the ' Astronomical papers ' 

 (pp. 201-344) is a determination of those in- 

 equalities of the moon's motion which are 

 produced by the figure of the earth, and is by 

 Dr. G. W. Hill, assistant in the office of the 

 Nautical almanac. 



In Delaunay's ' Theorie du mouvement de 

 la lune,' the perturbations of the moon by the 

 sun were fulh' treated ; but subordinate portions 

 of the theory were in some cases unfinished, 

 and in others untouched. Having waited more 

 than ten }'ears for the promised filling of these 

 gaps by French astronomers, Mr. Hill has in 

 this paper taken up, in his masterful wa}', the 

 discussion of the perturbations which the moon 

 undergoes on account of the figure of the 

 earth, the appreciable character of which was 

 first brought to light by the analysis of Laplace. 

 In his ' Darlegung der theoretische berech- 

 nung,' etc., Hansen has dealt with these in- 

 equalities in a very thorough way ; but Mr. 

 Hill has investigated these perturbations to the 

 same degree of algebraical approximation that 

 Delaunay adopted in determining the solar per- 

 turbations, viz., to terms of the seventh order 

 inclusive ; and his memoir is thus most appro- 

 priately entitled ' A supplement to Delaunay's 

 theory of the moon's motion.' 



The third part of the same volume (pp. 345- 

 371), by Professor Newcomb, treats of the 



Astronomical paper's prepared for the use of the American 

 ephemeris. Vol. iii. parts i.-iii. Washington, Government, 

 1884. 371 p. 8°. 



motion of Hyperion. In several papers pub- 

 lished during the past five years, Professor 

 Asaph Hall has shown a remarkable retrograde 

 motion in the peri-Saturnium of its orbit, the 

 period of its revolution being about eighteen 

 years. At first sight, this result appears incon- 

 sistent with the law of gravitation ; for it is 

 easily shown that in the case of a bod}- moving 

 in an eccentric orbit, and disturbed by another 

 moving in a nearly circular one, the secular 

 motion of the peri- centre will alwa} T s be direct. 

 As Titan is much the brightest, and much the 

 nearest to Hj^perion, of all the satellites of 

 Saturn, Professor New comb investigates the 

 results of its attraction upon this satellite, 

 and shows that the ordinary theory of secular 

 variations is entirely inapplicable to the mutual 

 action of these satellites, and that we have 

 here an entirely new case in celestial mechanics. 

 The ordinary theory of secular variations pre- 

 supposes" that the mean motions of any two 

 bodies to which it is applied are incommen- 

 surable ; so that to any given mean longitude 

 of the one, will correspond, in the course of 

 time, every mean longitude of the other. The 

 conjunctions of the two bodies will thus be 

 scattered through every part of the orbit. But 

 four times the mean motion of Hyperion is 

 nearly equal to three times that of Titan ; so 

 that, if the two satellites are in conjunction at a 

 given time, when Hyperion has completed three 

 revolutions, Titan will have completed four, 

 and another conjunction will occur at very 

 nearly the same point. In its outer form, this 

 relation between the two satellites is some- 

 what analogous to that among the satellites 

 of Jupiter ; but it is quite different in its cause. 

 Professor Newcomb develops the modified for- 

 mulae applicable to this case ; and among other 

 results of interest is the determination of the 

 mass of Titan equal to i^ioQ part that of 

 Saturn. 



FORCHHEIMEWS TUNNEL-BUILDING 

 IN ENGLAND. 



Dr. Forchheimer visited England in the 

 spring of 1883, by ministerial authority, to in- 

 spect and report upon the class of engineering- 

 work represented by the title below, confining 

 himself, for the most part, to tunnels in prog- 

 ress or recently completed. Several most in- 

 structive examples are to be seen there, and 



Englische tunnelbauten bei untergrundbahnen, sowie unter 

 ■fiussen und meeresarmen : ein reisebericht. Von Dr. Philipp 

 Forchheimer, ingenieur, privatdocent an der konigl. tech- 

 niscben hochschule zu Aachen. Aachen, Mayer, 1884. 8 + 69 

 p., 14 pi. 8°. 



