Vol. 62.] OF THE INTERIOR OE THE EARTH. 4:67 



that on wave-paths emerging at 30° from the origin the rigidity is 

 *385 of the bulk-modulus, for paths emerging at 60° it is *446, and 

 for those emerging at 90° it is '493 ; that is to say, the rigidity or 

 power of resisting distortion increases at a greater rate than the 

 solidity, or power of resisting compression. 



If absolute values of these two moduli are required, it is necessary 

 to make some assumption regarding the density of the medium 

 through which the waves are transmitted, and if it be assumed 

 that Laplace's law of densities is correct and that the mean density * 

 of the medium traversed is about the same as that at the greatest 

 depth reached by the chord, we get the following values for the 

 mean rigidity and bulk-modulus, both being measured in C.Gr.S. 

 units : — 



Assumed Modulus of Resistance to 



Arc. density. Compression. Distortion. 



30° 300 151-6 x 10 10 74-7 X10 10 



60° 4-25 2194 x 10" 132-3 x lO™ 



90° 620 322-4 x lO™ 223-2 x 10™ 



These figures should be regarded as arithmetical curiosities rather 

 than actual measures, for, apart from uncertainty regarding the 

 density of the medium, the mean apparent rate of propagation, as 

 measured along the chord, is certainly less than the true mean 

 rate, as measured along the actual wave-path, and the maximum 

 rate is greater than this again ; yet, despite this, the figures 

 indicate that the material traversed by the waves is endowed with 

 a very high degree of rigidity and resistance to compression. In 

 the case of the waves emerging at 90° from the origin, the material 

 traversed has, on the average, nearly 12 times the resistance of 

 granite to compression and 15 times its rigidity ; if the density 

 remains constant, these figures would be reduced by about three- 

 tenths, but on the other hand the maximum values will be higher. 



It must, however, be borne in mind that this high degree of 

 rigidity, as against stresses of very short duration, is quite compatible 

 -with the yielding to stresses of long duration, which is required 

 by known facts of structural geology, and need not necessarily be 

 inconsistent with those movements, of the nature of convection- 

 currents, which Mr. Eisher 2 believes to exist in the interior of the 

 earth. 



Turning now to the second quadrant, it wall be convenient to 

 take each phase separately, and to commence with the second 

 phase. 



The table (p. 464) shows that at 120° the increase in the mean 

 apparent rate of propagation is more than maintained, but too much 

 importance must not be attached to the exact figures, for the inter- 

 val at 120° is somewhat uncertain. Most of the records from about 

 this distance are late commencements, attributed to the second 



1 Strictly speaking, the square root of the mean of the squares of densities. 



2 ' Physics of the Earth's Crust' 2nd ed. (1889) chapters vi & xxiii. 



