238 Notices respecting New Books, 



to make the treatise sufficient in itself — with such subjects as 

 would be treated of once for all in a systematic work on the Prin- 

 ciples of Natural Philosophy like Thomson and Tait's, to which 

 preliminaries Mr. Love's first five chapters are devoted. 



In Chapter vi. the treatment of concrete problems is commenced 

 with the " Equilibrium of Beams," in solving which St. Venant and 

 Clebsch are, of course, mainly followed. The analogy between 

 the problem of the resistance of a cylindrical beam to flexure and 

 the hydrodynamic question of the motion of frictionless liquid in 

 a rotating cylindrical vessel is explained. There follow the " Tor- 

 sion and Flexure Problems," very fully and clearly worked out in 

 the practicable cases suitable for a text-book, with references to 

 the sources for further recent developments. In a note at the end 

 of vol. i. are some valuable remarks on iEolotropy ; wherein the 

 typographical slip of " luminated " for " laminated " may be pointed 

 out, into which perhaps the printer was led by the occurrence of 

 " luminiferous " lower down. 



Chapter vii. is devoted to an exposition of " Curvilinear Coordi- 

 nates," first introduced by Lame in the 0. R. for 1838. The 

 method Mr. Love adopts is one founded on Mr. Webb's as given 

 in his very able paper " Stress and Strain in Cylindrical and Polar 

 Coordinates," Messenger, vol. xi. Some examples in illustration 

 follow. 



" General Solutions " occupy Chapters viii. and ix., wherein Betti, 

 Cerruti, and Boussinesq are mainly followed: the solid strained, 

 the dilatation and small motions in which are sought, being of no 

 special form. 



Chapter x. is occupied with the most recent generalization of 

 Lame's problem of the displacements of an elastic spherical shell ; 

 viz. a gravitating sphere subject to surface-tractions. Some account 

 of the application of these results to the case of the elastic tides 

 of the solid earth as discussed by Lord Kelvin and Prof. Darwin 

 conclude the chapter. 



Prof. Lamb's solution of the problem of the vibrations of an 

 elastic sphere and spherical shell (Proc. L. M. S. xxiii., xxiv.) 

 forms the subject of Chapter xi., as a particular example of the 

 general theory explained in Chapter viii. 



The subject of the application of curvilinear coordinates is 

 further illustrated in the concluding chapter of vol. i. ; and the ap- 

 plication of conjugate functions to problems of elastic equilibrium. 

 In the second volume of Mr. Love's treatise are considered " in 

 greater detail the special problems that arise when some linear 

 dimensions of a body are small in comparison with others." The 

 bending of rods in one plane ; of rods and wires, with twisting, in 

 three dimensions and the general theory of the same, as treated 

 by Kirchhoff in particular, form the matter of Chapters xiii., xiv., 

 and xv. ; the theory of the small vibrations of thin rods that of xvi. 

 Chapter xvii., treating of Resilience to Impact and Voigt's and 

 Hertz's theories of Impact — the former taking account of the 

 motions set up in the surface-films, the latter of the compression 



