816 Notice i respecting New Boohs, 



motion of oscillatory waves is expressed must remain con- 

 vergent until the height is so far increased that the outline 

 presents a singular point, namely the wedge of 120°. If this 

 be conceded, we have only to make the wave-length (in the 

 sense of the distance from crest to crest, not in that of the 

 distance from the point where one of the swells begins to 

 where it ceases to be sensible) infinite, in order to pass to the 

 case of a solitary wave uniformly propagated. 



XXXIX, Notices respecting New Books. 

 (i.) A Treatise on Trigonometry. (Fifth edition, pp. viii + 160.) 

 (ii.) A Treatise on Algebra. (Second edition, pp. viii-J-412.) 

 (iii.) Logarithmic Tables. (Third edition, pp. 96.) 

 HPHESE are three works, (i.) and (ii.) written by Profs. Oliver, 

 -*■ Wait, and Jones, of Cornell University , and (iii.) arranged by 

 the last-named gentleman, who has recently been on a visit to this 

 country with a view, we believe, to the preparation of a new 

 edition of th© Tables, (i.) is an excellent practical treatise on both 

 Plane and Spherical Trigonometry. w After eight years' use in the 

 class-rooms the book has been wholly rewritten." The aim in the 

 revision has been to make the book " simpler and more attractive 

 as a text-book, and to make it more thorough and exhaustive as a 

 treatise/' The new matter is thus noticed: — (1) Applications of 

 Trigonometry to surveyings astronomy, and navigation. (2) The 

 extension of the notion of directed lines, and the introduction of 

 such other conventions, particularly of directed surfaces,, as help 

 to interpret algebraic symbols by geometric maguitudes, and thus 

 to lay the foundation for the study of mathematical physics. 

 (3) Th© discussion of the general triangle, plane and spherical. 

 There is no lack of admirably drawn figures, and often the same 

 principle is illustrated by several figures: when this is the case, 

 " the first figure is easiest followed ; the others help the reader to 

 see the generality of the principle and of the proof." The text is 

 concise without being obscure. u Only the main lines of the sub- 

 ject are developed ; collateral matters are outlined in the examples 

 and left for the student to work out for himself." The authors 

 have freely used English text-books as well as American ones, and 

 largely drawn upon Senate-House Examination-papers. It is a 

 work especially adapted for practical students. There is a copious 

 Index of reference. 



(ii.) This edition appears to be almost, if not quite, identical 

 with the first edition, which we commended some few years since 

 in our Magazine. 



(iii.) is a very handy collection of most useful Tables. There is 

 an explanation of the Tables at the end of the work, and on the 

 title-page there is the promise of a dollar for the first notice of 

 every error in the Tables. 



The same three writers promise a text-book in Algebra whose de- 

 finitions and statements of principles are clear and 'precise, and whose 

 proofs are rigorous and so simple that any diligent pupil can read it 



