PROBLEM OF THE EARTH'S RIGIDITY 193 



of treatment is novel and original in the highest degree. It is instructive 

 to see how by means of suitable and sufficiently obvious assumptions the 

 elastic wire and elastic thin plate can be discussed without the preliminary 

 laying down of the fundamental elastic principles. These are introduced, 

 in due course, as the authors pass on to the general theory of the equilibrium 

 and deformation of elastic solids. At the same time, a student reading 

 these sections for the first time will find them very hard to understand, 

 unless he has already some knowledge of the general theory of elasticity. 



In the sections on Elasticity, the important practical problems of twist 

 and bending of bars are completely solved, and then the solutions are 

 indicated of more general cases, such as the elastic deformation of spherical 

 shells and solid spheres subject to given surface tractions and body forces. 

 These problems afford interesting examples of the use of the spherical 

 harmonic analysis developed in the Appendix to the First Chapter. The 

 discussion ends with a promise of further illustrations under " Properties 

 of Matter," a promise which curiously enough still appears in the second 

 edition, in spite of the prefatory remark that the book was not to be 

 carried to completion. 



An important application of the laws of deformation of an elastic sphere 

 is made to our earth under the deforming stresses due to sun and moon ; 

 but, before this problem can be attacked, it is necessary to investigate the 

 deformation in a spheroid of incompressible fluid. This consideration forms 

 the transition from elasticity to hydrodynamics, and, after a brief discussion of 

 the more simple questions of equilibrium and flotation, Thomson and Tait 

 enter upon the final great series of problems connected with the equilibrium 

 of spheroidal rotating masses of fluid, the theory of the tides and tidal 

 stresses, and the closely related question of the rigidity of the earth. " To 

 promote an intelligent comprehension of the subject," all the polar harmonic 

 elements of the 6th and 7th orders are worked out, tabulated, and represented 

 graphically. The various kinds of tidal influence are then investigated ; and 

 it is shown by combined use of hydrostatic and elastic principles that if the 

 earth were only as rigid as steel it would as a whole yield to the tidal action 

 of sun and moon by an amount equal to about one-third of the yield in the 

 case of no rigidity. This concluding, highly original, part is greatly extended 

 by Sir George Darwin in the second edition of the book. 



The distinctive feature of the Treatise when compared with the earlier 

 great works on the same branches of Natural Philosophy, such as Lagrange's 

 T. 25 



