Notices respecting New Boohs. 307 



our language being Prof. Unwin's article in the * Encyclopaedia 

 Britannica.' 



But Mr. Basset puts off the consideration of viscosity and fluid 

 friction to a second volume, and contents himself for the present 

 with the motion of the so-called perfect fluid. 



The general equations of motion are due originally to Euler and 

 Lagrange ; but these equations have undergone considerable deve- 

 lopment at the hands of Stokes, Helmholtz, and Clebsch, in their 

 discussion of the distinction between irrotational and rotational 

 motion ; the physical and geometrical interpretation receiving also 

 great benefit from Sir W. Thomson's investigations. 



The character of the motion set up in a liquid by the motion of a 

 solid body through it receives careful treatment in this book, and 

 the author has exhausted all possible means of discovering new 

 cases by the employment of electric and magnetic analogies ; but 

 as the matter stands at present, the only bodies for which the 

 problem can be considered solved are the sphere, bodies made up 

 of parts of a sphere, and the ellipsoid. 



To George Green is due the credit of the solution (in 1833) for 

 the case of the motion of translation of the ellipsoid, while lately 

 Mr. W. M. Hicks has extended the case of two spheres as far as 

 modern analysis will allow. 



The curious cases of plane discontinuous motion discovered by 

 Helmholtz and Kirchhoff are discussed in chapter vi. ; and in 

 this direction the subject should yield some interesting develop- 

 ments to the investigator. 



The splendid modern dynamical principle of the " ignoration of 

 coordinates," due to Dr. Eouth, enables us to apply the Lagrangian 

 and Hamiltonian equations to the motion of a solid through liquid, 

 and chapters viii., ix., x., and xi. are occupied with the appli- 

 cation of these principles to all the interesting problems yet 

 discussed. 



A second volume is promised containing the theory of circular 

 vortices, on the lines of Prof. J. J. Thomson's essay ; on the motion 

 of a liquid ellipsoid under its own attraction, including the most 

 recent work of Poincare and G. H. Darwin, in addition to Biemann 

 and Dirichlet ; a chapter on liquid waves and tides ; and concluding 

 with the theoretical investigation of the effect of viscosity, a sub- 

 ject in which the author himself has made valuable researches. 



The author shirks no mathematical difficulties, and his work 

 should prove stimulating to the pure mathematician in directing 

 his attention to parts of analysis requiring development, as well as 

 to the student of physical science and applied mathematics. 



A. G. Greenhill. 



Sunlight. By H. P. Malet. 

 (8vo, pp. i-xii and 1-180.) Trubner & Co. : London. 



By way of enabling our readers to form some notion of this book 

 of extraordinarv views, which it would be of little use to criticize 



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