[ 525 ] 



LIX. Notices respecting New Books. 



A Treatise on Hydrodynamics, luith numerous Eojamples. Vol. II. 



By A. B. Basset, M.A. Cambridge : Deighton, Bell, and Co., 



1888. 



"VXTE have not had long to wait for the completion of this impor- 



'* tant work, and now we possess a valuable treatise on 



Hydrodynamics carefully brought up to date. Considering the 



great advances made by the recent work of Lord Bayleigh, Poincare, 



Hicks, J. J. Thomson, Gr. H. Darwin, and Love, the author must 



have devoted much time and trouble to the task of embodying their 



results and processes in a concise form in this second volume. 



So many analytical difficulties of pure mathematics block the way 

 to future progress, that the present work is necessarily only addressed 

 to advanced mathematicians, conversant with Bessel, Elliptic, Sphe- 

 rical Harmonic, Spheroidal, and Toroidal Functions ; and incident- 

 ally in the course of the hydrodynamical investigations many 

 elegant theorems in Pure Mathematics drop out, important enough 

 to set up in his business a pure mathematician. 



Chapter xii. of the present volume is a resume of the chief 

 properties of these functions, required in chaps, xii. and xiv. on the 

 properties of rectilinear and circular vortices, the latter embodying 

 the most important reseai'ches of J. J. Thomson. 



In chapter xv. the motion of a rotating liquid ellipsoid under 

 the influence of its own attraction is discussed, from the points of 

 view of Jacobi, Biemann, Dirichlet, Sir W. Thomson, Poincare, 

 and Gr. H, Darwin. The discussion of the stability of the motion 

 is one of the most refined operations of modern analysis, and 

 important in its bearing on the subject of the Figure of the Earth, 

 and Greueral Cosmogony, including the Grenesis of the Moon, 

 recently investigated by Mr. Love, too recently, however, to be 

 embodied in the present volume. 



Chapter xvii. treats of all the hitherto solved questions on 

 Liquid Waves, and here analytical difficulties still restrict us to 

 the consideration of waves of small displacement. This restriction 

 is, however, a legitimate working hypothesis when we come to the 

 grand Theory of the Tides, chapter xix., with which the names of 

 Newton, but principally of Laplace are associated; and now 

 recently undertaken afresh by Prof. Gr. H. Darwin. 



The remainder of the volume is devoted to the investigation of 

 the simple cases of liquid motion it is possible to discuss mathe- 

 matically at present, when the disturbing effect due to a viscosity 

 in the liquid in motion is taken into account. Some important 

 experiments made recently by Prof. Osborne Reynolds have re- 

 directed attention to this important question, and shown the path 

 for theoretical investigation. 



We venture to defend again the expression " with numerous 

 examples " appearing on the title-page, an expression which will 

 call forth disapproval in certain quarters. These examples are 

 carefully selected and verified ; they afford a welcome recreation to 



PliiL Mag. S. 5. Vol. 27. No. 169. June 1889. 2 N 



