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XXXIII. Notices respecting New Books. 



A Treatise on Hydrodynamics, with numerous Examples. By A. B. 

 Basset, M.A., of Lincoln's Inn, Barrister-at-Law ; Fellow of the 

 Cambridge Philosophical Society, and formerly Scholar of Trinity 

 College, Cambridge. Vol. I. Cambridge : Deighton, Bell, and 

 Co. London : George Bell and Sons. 1888. 

 "PiUBING- the last nine or ten years, since the appearance of 

 -"-^ Lamb's ' Treatise on the Motion of Fluids,' so much progress 

 has been made in this fascinating subject of Hydrodynamics, and 

 so many new problems of interest have been attacked, that the 

 appearance of the present treatise is very welcome, containing, as 

 it does, the results of the most important investigations in the 

 mathematical theory of Hydrodynamics which have been made in 

 modern times, carefully brought down to date as closely as possible. 

 The subject is a difficult one, and taxes to the utmost the ana- 

 lytical resources of the mathematician ; and so we find this treatise 

 bristling with formulas involving all the functions yet invented ; 

 not only the algebraical and circular functions of the ordinary 

 elementary text-books, but also the hyperbolic, elliptic, spherical, 

 spheroidal, conical, and cylindrical functions of Gudermann, Abel, 

 Jacobi, Weierstrass, Legendre, Lame, Bessel, Mehler, and others. 

 To read such a treatise with profit the student must have gone 

 through a thorough course of pure mathematics on these advanced 

 functions. We fear that such students are becoming rarer, now 

 that the course of mathematical subjects at Cambridge has been so 

 much curtailed of late for the examination in mathematical honours, 

 and that so few are encouraged to proceed to the study of the 

 higher subjects. 



It is the fashion at present to decry collections of examples as 

 undignified in an advanced textbook of mathematics ; but to the 

 properly trained student, examples and problems are a source of 

 instruction and delectation, and by their introduction the book can 

 be considerably condensed ; the prolixity of foreign mathematical 

 treatises is thus avoided, and foreign writers are now beginning to 

 perceive this and to take a leaf out of our book by themselves in- 

 troducing collections of illustrative examples, generally appropriated 

 from our examination-papers. 



While the theory of Hydrostatics dates back to the time of 

 Archimedes, the scientific treatment of Hydrodynamics, or the 

 Motion of Fluids, arose only two or three hundred years ago, from 

 the hydraulic requirements of Italian gardening and ornamental 

 waterworks, by which Torricelli and Bernoulli were led to the dis- 

 covery of the theorems bearing their names. So far as the flow of 

 liquids in pipes or channels is controlled by fluid friction, their 

 investigation under the name of Hydraulics is important from 

 the practical engineering point of view ; and numerous treatises 

 exist in French and German, the most modern and complete in 



