214 PROFESSOR A. E. H LOVE ON THE 



X+2/i, which was found in the case of lateral disturbances, is assumed to be the 

 critical mean value of X + 2fi for a planet in which the mass is condensed towards the 

 centre, then we may say that, if the mean modulus of compression were about equal 

 to that of glass, and there were very little rigidity, the planet would be unstable as 

 regards lateral disturbances ; but, if there were considerable rigidity, it would be 

 stable. If, on the other hand, the mean modulus of compression were decidedly less 

 than that of glass, though not so small as that of mercury, the planet would be 

 unstable as regards lateral disturbances, even though it possessed a considerable mean 

 rigidity. 



40. In order to settle the question of the gravitational stability or instability 

 of the Earth, we must assign the appropriate values to the constants X and p.. 

 Lord KELVIN'S theory of elastic tides in a solid sphere led to the result that the tidal 

 effective rigidity of the Earth is not less than that of steel. This result suggests 

 that fi should not be taken to be less than 8'19x 10" C.G.S. units; but, since it was 

 obtained by treating the Earth as incompressible, it affords no means of determining 

 the value of A.. JEANS (1903) proposed to deduce the values of X and /u, from the 

 observed velocities of propagation of earthquake shocks. In a homogeneous elastic 

 solid body, free from gravitation and initial stress, irrotational waves of dilatation are 

 propagated with the velocity [(X + 2ju,)//3 ] i , where /3 is the density, and equivoluminal 

 waves of distortion are propagated with the velocity [j*/pvj, while waves of a third 

 type are propagated over the surface with a velocity approximately equal to 

 (Q"9)[j*/Ptf- When a great earthquake takes place, the disturbance received at a 

 distance from the source consists of three sets of disturbances : two sets of 

 " preliminary tremors," and the " main shock." The first set of preliminary tremors 

 is received at distant places at such times as it would be if it travelled directly through 

 the Earth with a velocity of about 10 kiloms. per second. The second set of tremors 

 is propagated apparently in a rather less regular fashion, but the times at which it 

 can be observed at distant stations are nearly the same as they would be if it travelled 

 directly through the Earth with a velocity of about 5 kiloms. per second. The main 

 shock is received at distant places at such times as it would be if it travelled over the 

 surface of the Earth with a velocity of about 3 kiloms. per second.* The identification 

 of the three sets of disturbances with the three sets of waves which are theoretically 

 known seems to be inevitable, and the discrepancy between the ratio of velocities of 

 equivoluminal and superficial waves and the ratio of velocities of the second set of 

 tremors and the main shock may be explained by the supposition that, while the 

 velocity of transmission of these tremors depends upon the mean rigidity of the Earth 

 as a whole, the velocity of transmission of the main shock depends upon the average 



* Reference may be made to a Memoir by R. D. OLDHAM, " On the Propagation of Earthquake Motion 

 to great distances," London, 'Phil. Trans. Roy. Soc.,' ser. A, 194, 1900, and to the Reports of the 

 Seismological Committee of the British Association, in particular that published in ' Brit. Assoc. Rep.,' 

 1902. 



