200 Applications of Physics and Mathematics to Seismology, 



and suppose them to be respectively 12*5 and 2*5 kilometres 

 per second, this appearing a fair estimate. 

 Then, in absolute C.G.s. measure, 



V(m + n)lp = 125 x 10 4 , Vn~fc= 25 X 10 4 . 



Taking p = 5'5 for the earth, we have the approximate 

 results, 



n = wi/24 = 35 X 10 7 grammes wt. per sq. cm. 



For E, Young's modulus, and &,the bulk modulus (resistance 

 to compression), we have similarly, 



E = n(3—n/m) = 10 x 10 8 grammes wt. per sq. cm., 



k = m -n/3 =83xl0 8 „ „ „ 



The rigidity and Young's modulus — the quantities from 

 whose magnitudes our conception of a material's elasticity is 

 usually derived — are in no ways remarkable, being much 

 below the average magnitude observed in iron. The only 

 abnormal feature is the enormous resistance to compression. 

 Any one, however, who considers the enormous pressures 

 presumably in continuous operation on the earth's deep- 

 seated material, will appreciate the probability that it responds 

 uncommonly little to any slight increase in pressure. 



A difference between the velocities calculated at stations 

 near and distant from the epicentre is only what we should 

 expect. Lord Rayleigh* has shown that waves with a 

 velocity somewhat less than s/n/p may be propagated 

 through the material close to the surface of a medium 

 bounded by an infinite plane ; and a similar phenomenon 

 may be expected in a sphere, so long at least as the distance 

 from the epicentre is small compared to the radius. In 

 such waves the velocity must depend mainly on the density 

 and elastic properties of the surface material, which in 

 general must differ largely from the corresponding quan- 

 tities in the deep-seated material. Thus the velocities calcu- 

 lated from the observed effects must depend largely on 

 whether the waves propagated along the surface or those 

 propagated through the interior are the dominant ones ; in 

 other words, on whether the distance of the station from the 

 epicentre is or is not small compared to the earth's radius. 



* Proc. London Math. Soc. vol. xvii. (1886). See also Love's 

 < Treatise,' vol. i. pp. 328-330. 



