444 Professor Cargill G. Knott [Feb. 14, 



Kne of distances. The distances at which the speed ceases to 

 increase and becomes constant for shorter distances from the earth's 

 centre is however different in the two cases. This is brono^ht ont by 

 the following approximate representation of the values of the speed r 

 in terms of the distance r from the earth's centre, the units being the 

 kilometre and second. (The earth's radius is 6378 kilometres.) 



The Primary Wave. 



Thus the speed of propagation reaches its maximum at a less 

 depth for the Secondary wave than for the Primary wave, less by 

 about 200 kilometres, or one-thirtieth of the earth's radius. 



This fact suggests a physical change in the material of the earth 

 which first affects the rigidity. As already mentioned no good 

 records of the advent of the Secondary wave are obtained at arcual 

 distances greater than about 110° from the epicentre. The depth 

 reached by a ray which emerges at this distance is not much more 

 than half the earth's radius. It thus appears that a ray of the 

 Secondary type of wave — that is, a ray of the distortional wave — cannot 

 penetrate deeper than about six-tenths of the earth's radius. The 

 material of the earth may be supposed to undergo a gradual change 

 from distance 0-5 of the earth's radius as measured from the centre 

 to distance ■ 4. At position ■ 5 the material behaves like an elastic 

 solid with the two elastic moduli of wave velocity A" + 4 n/i\ and 7i ; 

 but when the position ' 4 is reached the material has lost its rigidity 

 and has become what might be compared to a highly compressed 

 substance with incompressibility k and rigidity zero. Under these 

 conditions the distortional wave will be gradually stifled and 

 ultimately cease to exist. Its energy may pass into the compressional 

 form or it may simply be transformed into heat under the influence 

 of viscosity to shearing motion. 



Summary. 



For the first time, by a rigorous mathematical method, the forms 

 of the seismic rays have been deduced directly from the data of 

 observation. The seismic rays are on the whole concave outwards. 



