66 Prof. H. Nagaoka on the Elastic Constants of 



amplitude. By it will be found disturbances which come 

 through various strata, and probably those travelling through 

 the stratum of maximum velocity of propagation. 



Seismic waves travelling through strata of heterogeneous 

 elasticity and density will generally be not purely longi- 

 tudinal as in the case of sound, nor purely transversal as in 

 the case of light, but a mixture of these two kinds. The 

 velocity of propagation expressed as a function of elastic con- 

 stants and density is not a simple problem ; and moreover we 

 do not possess sufficient experimental data to test the result 



of calculation. The formula V ; -= \f — for longitudinal 



waves in a thin rod will give a rough estimate of the velocity. 

 From records taken in Italy and Japan, Prof. Omori con- 

 cludes that the velocity of the first tremor is almost always 

 equal to 13 kilometres per sec. The question naturally arises : 

 how can we account for such an enormous rate of propagation ? 

 The velocity of plane longitudinal waves in an infinite 

 medium of steel is about 6'2 kilometres per second ; if we 

 take a rod of steel in place of an uniform medium and give 

 a blow to one of its ends, the longitudinal wave will travel 

 with a velocity of 5*3 kilometres ; if the same experiment be 

 repeated on a piece of iron pyrites cut parallel to its axis of 

 greatest' elasticity, the velocity will be 8*4 kil. per second; 

 in topaz, it will amount to \) kilometres. Thus even with 

 substances easily accessible on the earth's surface, w T e have 

 instances of elastic waves travelling with a velocity of some- 

 thing like 10 kilometres. In the present experiments the 

 velocity in several primeval rocks ranges from 6 to 7 kil. 

 per second ; as we go deeper in the crust, we may not fail to 

 find those rocks whose elastic constants are several times 

 greater than those near the surface. So far as I am aware, 

 iron pyrites has the greatest mHnlus of elasticity among the 

 substances which have till noty been placed under experi- 

 mental test ; it is about 1*6 times greater than in steel, and 

 amounts to 3 - 5 x 10 12 C.G.s. uvtits (Voigt). If we now 

 imagine a stratum in which Y/ntig's modulus exceeds that 

 of iron pyrites as much as that of iron pyrites exceeds that of 

 steel, we shall obtain a velocity arrived at by seismologists, if 

 density is not at the same time increased so much as to bring- 

 down the rate of propagation. The velocity of 13 kilometres 

 per second, which is that calculated from the preliminary 

 tremors, roughly corresponds to E = 6'0 X J 13 and p= 3*5. To 

 speak of the relation between density and elastic constant 

 might seem a little absurd, but in the rocks so far examined, 



