68 



Prof. C. Gr. Knott on Reflexion and Refraction of 



Rock. 



m. 



a. 



». ! 



Marble 



4-68x10" 

 4-35x10" 

 2-44x10" 

 366X10" 

 6-07x10" 



1-44x10" 

 1-3 XlO" 

 1-31X10" 

 1-94x10" 

 2-45x10" 



4--2S 

 + •29 

 -•08 

 -07 

 + •16 



Tuff 



Clay-Rock 



Slate 





Two of the ratios come out negative, which means physically 

 that, if the substance be perfectly elastic, an extension of the 

 substance by a pnll in a given direction is accompanied by an 

 extension at right angles to this direction. It also means that 

 the ratio of the velocities of the two waves is distinctly smaller 

 than in the other cases. This diminished ratio, it will be 

 noticed, exists along with a diminished resistance to com- 

 pression, while the rigidity continues to have much the same 

 value as those which hold for the other rocks. In the cases 

 of the tuff and clay-rock we may have to do with either 

 a considerable compressibility, or a sluggishness in recovery 

 due to the viscosity of the material. Such a viscosity might 

 well show itself more distinctly in compression than in 

 distortion. 



If we calculate from Milne's values of wave-velocities 

 obtained from his experiments on artificial earthquakes, we 

 find for the ratio s in two different cases the values +'154 

 and — *152, and for the corresponding ratios of m to n the 

 values 2'43 and 1*76. 



In the calculations to be described presently, I have taken 

 the following values of the several constants involved as a 

 fair approximation to what might reasonably be regarded as 

 somewhat near the truth, when the elastic properties of fairly 

 solid rock are to be considered. 



Density p =3 



Rigidity n =l'5xl0 n 



Ratio of the wave-moduli m/n = 3 

 Poisson's ratio .... s = '25 



We now pass to the consideration of the transmission of 

 waves in an elastic solid ; and first I desire to call attention 

 to Lord Rayleigh's short paper " On Waves Propagated 

 along the Plane Surface of an Elastic Solid " *. To show 



* ' Proceedings of the London Mathematical Society,' vol. xvii. 

 (1885-86). 



