478 Notices respecting New Books. 



cupies only thirty-seven pages, and therefore is little more than a 

 sketch, though doubtless very good so far as it goes. Its treatment 

 is so characteristic of the work that we will mention its contents. 

 In the first place it is shown that Kepler's laws follow from the law 

 of universal gravitation, the proofs being substantially the same as 

 those of Newton's 1st, 11th, and 15th propositions. The case of 

 two reciprocally attracting bodies is then briefly considered. In 

 the case of three bodies, expressions are found for the components of 

 the disturbing force along the radius, tangent, and at right angles to 

 the plane of the orbit respectively ; but that point attained, the ana- 

 lytical treatment of the question stops. The modifications of the 

 motion of the disturbed body under the action of these forces is 

 only considered generally, the kind of effect produced by each 

 being pointed out without any attempt to calculate its magnitude. 

 The remainder of the part, comprising the questions of the densi- 

 ties of the Planets, of the form and density of the Earth, and of the 

 Tides, is treated in an entirely popular manner. The last of these 

 questions is gone into in very considerable detail, considering the 

 space at the author's disposal, so far as the facts concerning the tides 

 at particular places are concerned. 



Perhaps the most valuable part of the work is the section devoted 

 to the solution of astronomical problems ; in every case worked ex- 

 amples are given, and the requisite Tables are contained in the 

 volume. In no branch of mathematics is it more necessary than in 

 astronomy that the student should be constantly referred back to 

 actual numerical results. It is very possible for a person to have 

 read a great deal about astronomy and yet to be puzzled when set to 

 do a very simple numerical question ; and, besides, numerical re- 

 sults impart a reality to knowledge which is not otherwise to be 

 attained. 



We ought to add that throughout the work accounts are given in 

 considerable detail of astronomical facts and appearances (as in the 

 case of the tides already mentioned), and that the physical theories 

 used to account for these phenomena are briefly but fully stated. 

 Such are the chapter on "Theories of the Evolution of Sidereal and 

 Planetary Systems," and the account of the author's speculations on 

 the formation of the tails of comets by the action of the sun's "■ re- 

 pulsive force." These portions are very properly printed in a dif- 

 ferent type from the body of the work. 



The treatise forms a handsome octavo volume ; the printing is le- 

 gible, and, so far as we have noticed, accurate. But exception must 

 be taken to the illustrations, which in some instances are coarsely 

 cut (e. g. figs. 19, 77, 95), and in others ill printed {e.g. figs. 76, 96). 

 This is a defect, though perhaps a minor defect, and certainly will 

 not seriously impair the usefulness of a very valuable work. 



