168 



MR. R. D. OL1MIAM ON THE PROPAGATION ( >!' 



paper, we find that the rigidity is 15 times, and the bulk modulus nearly \2 times, 

 greater than that of granite. If instead of a density of 3'5 we assume the more 

 probable density of 7'0, these values would have to be further increased by about 

 one-half, and would become 17 and 21 '5 times the corresponding constants for 

 granite. 



According to RUDZKI,* if the wave paths are circular arcs, the function of the 

 radial distance which represents the velocity of transmission takes the form 



V = A--BT 3 . 



Taking the value of V to be 14'5 kiloms. per second at a distance of 0'55 of the 

 radius, and equating this with the assumed initial velocity of 4 '5 kilom. per second, 



we get 



V = 18-5 14-r 2 , 



r being expressed as a fraction of the radius of the earth. For the distortional wave 



the formula becomes 



V = 11-5 9?-*. 



These formula give results in very fair accordance with those deduced from the 

 observations recorded, but cannot be accepted as more than empirical approximations. 

 They indicate that the maximum velocity of transmission at the centre of the earth 

 should be about 18 '5 kiloms. per second for the condensational, and 11 '5 kiloms. per 

 second for the distortional wave, if there is no sudden change in the increase of the 

 elastic constants below the depth of 3,000 kiloms. from the surface. 



It is, however, by no means certain that a regular increase of the elastic constants 

 to the centre of the earth is to be looked for ; on the contrary, a sudden change is to 

 be looked for where the wave path leaves the outer stony shell to enter the central 

 metallic core which may reasonably be supposed to exist. 



Though we have no direct knowledge of the constitution of the interior of the 

 earth, we do know not only its average density, but also approximately the rate of 

 increase of density from the surface to the centre. The estimates of this, made 

 by LAPLACE and WALTERSHAUSEN, give values for 0'5 and 0'6 of the radius as 

 follows : 



* GERLAND'S ' Beitragc z. Geophysik,' vol. 3, 1898, p. 518 



