466 MR. E. D. OLDHAM ON THE CONSTITUTION- [Aug. I906, 



separately, dealing first with the wave-paths which emerge at 

 distances up to 90° from the origin, and then with those which 

 emerge at distances beyond that. 



If the rate of propagation through the earth were uniform in all 

 directions and at all depths, the wave-paths would be straight lines, 

 and the mean apparent rate of transmission, along the chord, would 

 be the same for all distances. It is obvious that this is not so, for 

 the apparent rate of propagation, as measured along the chord, 

 increases continuously up to 90°, in the case of both first and second 

 phase-waves. This means that the waves travel faster as they 

 penetrate to greater depths, and consequently the wave-paths 

 are not straight lines, but curves whose convexity is directed 

 towards the centre. Besides this, .the fact that the increase in 

 apparent rate of propagation is proportionately greater in the case 

 of the second phase, shows that the curvature of its wave-paths is 

 greater than in the case of the first-phase waves. 



It must, however, be noticed that, although the increase in 

 apparent rate of propagation is greater in the one case than in 

 the other, yet the rate of increase as between 30°, 60°, and 90° is 

 practically the same in both cases. The actual figures are as 

 follows : — 



Increase of apparent velocity First Phase. Second Phase. 



along the chord 30° to 60° *055 -118 



Ditto 60° to 90° -036 -075 



Ratio of increments "65 '64 



These figures show that the apparent rate of propagation increases 

 with the distance about twice as rapidly in the case of the second 

 as in that of the first-phase waves ; that the rate of increase is not 

 uniform, but diminishing with increasing distance ; and that in both 

 cases this alteration is in the same direction and at the same rate. 

 This suggests that the increase in rate of propagation with increase 

 in depth of the wave-paths is not due to their passage through 

 material of a different character, but may be merely the effect of 

 increased pressure and temperature, and consequently, that the 

 substance of which the earth is composed — below the outer crust — 

 undergoes no material change in composition or physical condition, 

 at least to the depths reached by the wave-paths of earthquake- 

 waves emerging at 90° from the origin. 



This much is independent of any assumption regarding the 

 nature of the wave-motion, but without making some assumption 

 regarding this, no further information is attainable. I shall take 

 it that the first-phase waves are condensational — this being generally 

 acknowledged — and that the second-phase waves are distortional, 

 an assumption which I regard as more than probable, and on 

 these assumptions it is possible to estimate the proportion which 

 the modulus of rigidity bears to the bulk-modulus, or resistance 

 to compression. In making this estimate we may take the wave- 

 paths for the two waves as being so nearly coincident that there is 

 no material difference in the density of the medium. The calcu- 

 lation being simple, it is only necessary to state the results, which are 



