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XXXIV. Notices respecting Neio Books. 

 Recent Cambridge Mathematical Works. 



Examples of Analytical Geometry of Three Dimensions. Collected by 

 I. ToDHUNTER, M.A., Felloto and Assistant Tutor of St. John's 

 College, Cambridge. Cambridge : Macmillan and Co. 1858. 



Plane Trigonometry for the Use of Colleges and Schools. With nume- 

 rous Examples. By I. Todhunter, M.A. Cambridge: Mac- 

 millan and Co. 1859. 



A Treatise on Hydrostatics and Hydrodynamics. By W. H. Besant, 

 M.A., Felloto and Assistant Tutor of St. John's College, Cambridge. 

 Cambridge : Deighton, Bell and Co. London : Bell and Daldy. 

 1859. 



^"^HE first of the above three books is a most useful contribution 

 •*- to mathematical literature. It is rather strange that this should 

 be, as we believe it is, 'the first collection of problems (with their 

 answers) in so interesting a department as that of geometry of three 

 dimensions. Mr. Todhunter has given 406 examples, with their 

 results, and occasional hints for their solution. Such a book has long 

 been very much wanted ; and there are few persons who could have 

 supplied the want better than Mr. Todhunter. 



The second book on the list is a very good text-book for the Cam- 

 bridge student, containing, as it does, the most recent view of the 

 subject as treated in the College Lectures, with a considerable num- 

 ber of improved methods scattered here and there throughout the 

 treatise, and a large collection of examples with their answers. We 

 should have been glad, however, if IVlr. Todhunter had stepped a 

 little out of the old beaten track so long trodden by Cantabs on this 

 subject, and introduced more practical information into his book, 

 such as would meet the wants of those who study trigonometry 

 chiefly for its uses in surveying, &c. 



Of Mr. Be?ant's ' Hydrostatics and Hydrodynamics,' we have 

 nearly the same remarks to make as of the preceding work by his 

 fellow-tutor at St. .lohn's. It is a very good book to " get up " for 

 the College and Senate-house examinations; and this was probably the 

 chief, if not the only olyect of its author. The theories of displacement 

 and oscillation of floating bodies ; tension of flexible surfaces ; equili- 

 brium of a revolving fluid, with apj)lictition to the figure of the earth ; 

 the general equations of hydrodynamics ; the propagation of sound, 

 and tlie vibrations of musical instruments, are treated at greater 

 length than is usual in elementary works ; but, as a set-off" against 

 this, the description of all the common hydrostatical and pneumatical 

 apparatus, such as pumps, hydrometers, &c., is entirely omitted. 

 We regret also that Mr. Besant has not followed tlie example of 

 Mr. Todhunter in giving the answers or solutions to the problems 

 he lias collected in illustration of the subject. Hfn short, the book 

 must be considered as merely a supplement to other works on the 

 same subject already in use at Cambridge. 



