138 LAMBERT: CONSTITUTION OF THE EARTH 



Thus we see that if we assume uniform density, we overestimate 

 the rigidity necessary to produce a given effect; if we assume, 

 as we have done, incompressibihty also, we underestimate the 

 rigidity, though as nearly as can be made out not to as great an 

 extent as we overestimated it in the first case.-^ If we wish to 

 take account of a variation in the modulus of rigidity as well as 

 in the density, about our only resource is the Wiechert hypothesis 

 of density and with different moduli for nucleus and shell. This 

 introduces an extra unknown, and we cannot determine both 

 moduH from the latitude variation alone. If we try to satisfy 

 the tidal observations also, and use the value of h — k = 1/3 

 formerly current, we get a modulus of 20 X 10^^ for the nucleus, 

 and I X 10^^ only for the shell. -^ Since a representative rigidity 

 of natural rock at ordinary pressure is about 2.4 X 10", the 

 rigidity of the shell seems too low. There seems to be a tendency, 

 however, towards smaller values of h — k than the 1/3 used above, 

 of which Michelson's 0.29 is an example.^'' If these smaller 

 values be accepted, it is easier to reconcile the modulus from the 

 variation of latitude with that from the tidal observations, 

 and with the known properties of rock. We should thus get a 

 value of about 16 X 10^^ for the nucleus and about 4 X 10^ "^ 

 for the shell. You will understand by this time, I think, some- 

 thing of the difficulties of the subject and the many assumptions 

 that lie back of the statement, "The rigidity of the earth is thus 

 and so." 



There are, as you know, two theories of elasticity; one favored 

 chiefly on the continent of Europe, which may be called the 

 "rari-constant" theory and the other generally accepted in Eng- 

 land, the "multi-constant" theory. According to the first theory 

 there is only one independent elastic constant for an isotropic 

 elastic body, and the modulus of rigidity of such a body is 3/5 

 of its modulus of compressibility. According to the second, the 



-* Love. Problems of geodynamics, Chap. YIll. Cambridge, 191 1. 



-3 Love. Proc. Royal Soc. 82: S2. 1909. Scuweydar. Beitnige zur Geophysik. 

 9: 76. 1908. 



5" For a downward revision of Schweydar's h - k, see Mem. Coll. Science and Engi- 

 neering, Kyoto Imp. Univ., 4: 114. 1912. 



