Page:Science vol. 5.djvu/114

 PTOL. v.. No. KM.

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��The diaciissioii of llio records of part ii. aud part iii.. together with the uietporologk-ul ilaia of tilt expedition, is ic course of pi-eiiarntioti liv Professor Tait .ind Mr. liudiau.

��In the first part of this volume, I'l-ofeBaor Newcomb preaeiita a detailed development of the perturhative function which ia applicable to all cases, except cstrenic ones, in which a general development of planelarj' inequalities ill terms of the time ia sought, and by which any retjuired derivatives of the function may be found with great facility. In order to atl'ord some idea of its range of npiilicaiion, he compares this development with otiiers having the same general object; viz., those of Laplace, De I'out^coulant. Peirce, Leverrier, Hansen, and Cnncby. The method of this development has previously Iwen indicated by Professor Kcwcomh. in the American journal of mathemaUat. vol. iii. The second part of this volume of the 'Astronomical papers' (pp. 201-34-4) 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.'llill, assistant in the ofHce of the Nautical oJinunac.

In Delaunay's ' Th^orie du mouvement de la lune,' the perturbations of the moon by the Bun were fully treated ; but subordinate portions of the theory were in some cases unfinished, and in others untouched. Having waited more than ten years for the promised filling of these gaps by French astronomers, Mr. Hill has in this paper taken up, in his masterful way, the discussion of the perturbations which the moon imdei^oes 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 Iheorctische berech- nung,' etc., Hansen has dealt with these in- equalities in a very thorough way ; but Mr- Hill has investigated these jicrLurbations to the same degree of algebraical ai>proximation that Delaunay adopted in determining the solar per- turbations, viz., to terms of the seventh order inclusive ; and his memoir is thus most appro- jniately entitled ' A supjtlement tu Delaunay's theory of the moon's motion.'

The third part of the same volume (pp. :)45-
 * f71). by Professor Newcomb, treats of the

AntnmamSall papfrn prrparrd /or (he mka t/ tj\f Amrriritn

��motion of Hyi>ei"ioi). In several papers pub- lished during the past five years. Professor Asaph Hall has shown a remarkable retrograde motion in the [teri-Saturniura of its orbit, the period of its revolution being about eighleioi years. At first sight, lliis result appears incon- sistent with the law of gravitation ; for it is easilj' shown that in the case of a body moving in an eccentric orbit, and disturbed b}' another moving in a nearly cii'cular one, the secular motion of the peri-centre will always be direct. As Titan is much the brightest, and mucli the nearest to Hyperion, of all the satellites of Saturn, Professor Newcomb imestigates the results of its attraction upon this satellite, and shows that the ordinary theorj' of secular variations is entirely inapplicable to the mutual action of these satellites, and that we have here an entirely new mse in celestial mechanics. The ordinary theory of secular \'ariations pre- supposes that the mean motions of an}' two bodies to which it is applieil are incommen- surable ; so thai to any given mean longitude of the one, will correspond, in the course of lime, every mean longitude of the other. The conjunctions of the two bodies will thus be scattered through eveiy part of the orbit. But four times the mean motion of Hyperion is nearly equal to three limes that of "Titan ; so that, if the two satellites are in conjunction at a given time, when Hyperion has completed three revolutions, Tilan will have completed four, and another conjunction will occur ftt very nearly the same jxtint. In its out«r form, this relation between the two satellites is some- what analogous to that amoug the satellites of Jupiter ; but it is quite different in its cause. Professor Newcomb develops the modified for- mulae apphcable to this case ; and among othei ■ results of interest is the determination of t' mass of Titan equal to xsico P"^* ^^^ ' Saturn.

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��FORCHBEIMER'S TUNNEL-BUILDING \ IN ENGLAND.

Db. FoHCHUEiMBB visited England spring of 18H3, by ministerial authoritj', to itt-^ sped 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

fiiiJ!S UHil'vntriUr>t>iH: ein "r^irrtcM. Voo'or. Phiuit

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