. /•: Becker— Proof of tin Earth's Rigidity. 387 



most important in physical geology, bat u it 1ms been treated 

 l>\ physicists, the subject la one of peculiar difficulty. Sir 

 William Thomson baa shown that the earth exhibits to the 

 attractive forces of the sun and moon a resistance s<> great aa to 

 implv that ir ia solid throughout To roach thia concinaion it 

 i> necessary to determine separately the resistance t<> deforma- 

 tion which a solid sphere presents because of the mutual attrac- 

 tion of its parts, and the resistance duo to the clastic forces 

 which arc called in play when deformation occurs. 



The resistance due to gravitation ia thoroughly well under- 

 •d and this portion of the subject is not hard to master. On 

 the other hand, the determination of the elastic resistance is 

 very difficult. The general theory of the statics of elastic 

 bodies is highly complex, and physicists are by no means 

 Bed as to whether the general equations involve 21 or only 

 15 independent constants. " : - Both schools accept as the empir- 

 ical basis of calculation Hooke'a law, which experiments show 

 to be only approximately true for small pressures, while for 

 high pressures it is morally certain that the so called constants 

 assume other values, and no physicist professes to be able to ob- 

 tain results which are strictly accurate excepting for infinites- 

 imal deformations. — On the basis of the general elastic theory, 

 Lame investigated the equilibrium of an elastic sphere by the 

 method of spherical harmonics. There seems to be no doubt 

 that this investigation is a masterpiece of genius. Thomson's 

 inquiry is based upon Lame's. He has considerably simplified 

 the discussion, but without rendering it either short or easy ; 

 and he has applied it to the case of a homogeneous, isotropic 

 sphere, of the size and mean density of the earth, without 

 mutual gravitation of its parts, but subject to the attraction of 

 a distant external body such as the sun or the moon. That 

 even this application of Lame's problem is laborious may be 

 inferred from the fact that Thomson himself refers to the 

 "tedious algebraic reductions" which he omits. 



The result, so far as the earth is concerned, is an extremely 

 simple formula for the ellipticity of an elastic sphere. 



When this formula is once reached, Thomson's argument for 

 the great effective rigidity of the earth presents no difficulty 

 which may not be made intelligible to any geologist. It is not 

 strange, however, that there has been some reluctance in geo- 



* B. de Saint-Yenant, probably the greatest elastician up to this time (he died 

 in 1886), followed Poisson in maintaining that eolotropic elasticity involves only 

 15 moduluses and that isotropic elasticity involves but I constant. On the other 

 hand, Green, Stokes. Thomson, and others, starting from a different view of the 

 molecular constitution of matter, argue that 21 and 2 moduluses respectively are 

 requisite. Lame adopted the molecular theory which leads to uniconstant iso- 

 tropy, but expresses his results by biconstunt formulas. These are certainly the 

 more convenient, for they can at once be reduced to uniconstant forms. See Tod- 

 hunter's History of Elasticity. 



