Klastic Waves, with Seismologieal Applications. 67 



If we write m instead of k + ^n*, we obtain for the value 

 of the Poisson ratio the expression 



m — 2n 



2(m— n) 



The possible values of s range from + \ to — 1 ; the former 

 being its value in an incompressible elastic body, the latter 

 its value in a body of infinite rigidity but finite compres- 

 sibility. The luminiferous pether appears to be a substance of 

 infinite resistance to compression ; but of the other limiting- 

 kind of elastic material we have no example. 



The velocities of the condensational and distortional waves 

 are given respectively by the expressions sjmjp and \/n/p, 

 p being the density of the material. 



There are experimental methods for measuring the quan- 

 tities m and n ; and from them the two velocities can easily 

 be calculated. Or, if the two velocities are known, it is 

 possible to calculate from them the two moduli. Now it is 

 quite obvious that m must always be greater than n ; the 

 ratio indeed varies from 00 for the case of the incompressible 

 body to tj- for the case of the infinitely rigid body. Of course, 

 in the latter case, both waves travel with an infinite speed ; 

 but the speed of the distortional wave can never become 

 equal to the speed of the condensational wave, however large 

 it is made to be. 



In deducing the true values of m and n from the two wave- 

 velocities, we must know the density of the material. The 

 only values I have been able to find for wave-velocities of 

 both types in rocks are those given by Messrs. Milne 

 and Gray. These velocities were originally obtained from 

 direct measurements of the elastic moduli of the rocks in 

 question. The moduli themselves Professor Milne has 

 recently furnished me with. In the following table they 

 are given f, expressed in C.G.S. units, along with the Poisson 

 ratio s. 



* This m is not the same as the m used by Thomson and Tait ; but 

 for our present purpose it is convenient to use one symbol for the 

 mixed modulus which determines the speed of the condensational 

 wave. 



f In the notes given me by Professor Milne the numbers here 

 tabulated under m are headed " Young's Modulus." This, I am inclined 

 to think, is a mistake. Professor Milne himself, not having the complete 

 records in possession, is doubtful. At any rate, these numbers give the 

 velocities of the normal vibrations as tabulated by Messrs. Milne and 

 Gray (see Phil. Mag., November 1881). Further, if they really were 

 Young's Moduli, we should have in granite and marble examples of 

 substances which expand when compressed ! 



F2 



