16H MR. R. D. OLDHAM ON THE PROPAGATION OF 



iu other words, the initial velocity of propagation in the case of an earthquake, is not 

 far removed from 4'5 kiloms. per second in the case of condensational, and 2*6 kiloms. 

 per second in the case of distortion; il waves. 



These values are in close accord with the ones obtained from the curve given by 

 distant observations, the difference being no greater than might easily be made to 

 vanish by a slight manipulation of the extrapolated portion of the curve. We may 

 consequently adopt the conclusion that the first phase represents the arrival of con- 

 densational, and the second that of distortional waves, which have travelled through 

 the earth from the origin to the place of record. 



6. If the curves drawn on the diagram represent the true time curves, it should be 

 possible to deduce from them the relation between the variation of velocity of trans- 

 mission and depth below the surface. Until a larger number of observations have 

 been collected, and it is certain that the true curve does not exhibit irregularities, 

 not shown by the few records as yet available, it does not seem advisable to attempt 

 this ; but a tentative investigation of the results obtained at a distance of 85, where, 

 owing to the number of observations available, the curves are fixed with great 

 certainty, will not be unprofitable. 



For a distance of 85, or about 9,500 kiloms. from the origin, the time intervals 

 are very close to 15 m and 25 m respectively. These intervals give apparent mean 

 velocities of 10 '5 kiloms. and 6 '3 kiloms per second, and as the wave path is a curve 

 convex towards the centre of the earth, these are probably nearer the true average 

 velocities than the mean apparent velocities as measured along the chord, which are 

 9*5 kiloms. and 57 kiloms. per second respectively. 



The maximum velocity is necessarily greater than the mean, and we shall pro- 

 bably be not far wrong in assuming that the maximum excess over the initial velocity 

 is about double the mean excess. To be on the safe side the apparent mean velocities 

 as measured along the chord may be taken ; here the mean excess is 5'0 kiloms. and 

 3'1 kiloms. per second respectively. Adding the doubles of these to the initial 

 velocities of 4 '5 and 2 '6, we obtain a maximum velocity of 14 '5 kiloms. per second 

 for the condensational, and 8 '8 kiloms. per second for the distortional waves respec- 

 tively. 



If we put V, for the initial velocity, and V w for the maximum, then 



V,-/sin a, = V'/sin ' = V"/sin a" = V M /sm a m , 



where a, is the initial angle of incidence, or what may be called the plunging angle 

 at which the particular ray or wave path leaves the focus, and a m is the angle of 

 refraction where the maximum velocity is attained. But a m is necessarily 90, the 

 maximum velocity being attained where the wave path is tangent to a circle drawn 

 round the centre of the earth. Hence 



V,/V M == sin a,. 



