Vol. 65.] ANNIVERSARY ADDRESS OF THE PRESIDENT. lxXXV 



very interesting chapter in the history of mathematics, as applied to 

 a geological problem ; after encountering and overcoming numerous 

 difficulties it has at length reached a successful conclusion, and 

 Lord Kelvin's original contention that the earth is almost as rigid 

 as a globe of steel, is found to have been an under-estimate rather 

 than an over-estimate of the fact. 



Fresh light was thrown on this question in 1900 from an 

 unexpected quarter. Up to that time, notwithstanding a vast 

 accession of novel and precise observations, the view which found 

 general acceptance with respect to the nature of seismic waves was 

 that of Mallet, who regarded them as wholly compressional. That 

 distortional waves may be involved had been suggested by Wertheim 

 in 1849, and maintained by Cancani in 1894, but the merit of 

 rightly identifying such waves belongs exclusively to 11. D. Oldham, 1 

 who attributed a distortional nature to the movements of the second 

 phase : those of the first phase being compressional, and the large 

 waves of the third phase, superficial, and possibly of the same nature 

 as what are known as liayleigh's waves. 



Distortional waves, however, cannot be propagated otherwise 

 than through a solid medium, and consequently, since in the case of 

 great earthquakes such waves actually pass right through the 

 substance of the planet, from the seismic focus to its antipodes, 

 it follows necessarily that this substance must on the whole be 

 solid. 



Love 2 has carried the argument a step further, and from cal- 

 culations based on the velocity of the waves combined with the 

 assumption of uniform density, has arrived at the conclusion that 

 the seismic rigidity of the earth must be about as twice as great 

 as that of steel, and its compressibility (linear elasticity) about 

 half as great. Wiechert, making a different assumption as to the 

 density, obtains a rigidity four times as great as that of steel, 

 and a compressibility more than four times less. 



Thus we seem to have arrived at something like demonstrative 

 proof. Our conclusion entirely depends, however, on the truth of 

 the fundamental proposition, i.e., that the waves of the second 

 phase are in fact distortional. This has been challenged by the 

 Rev. Osmond Fisher, whose arguments, however, by their very 



1 E. D. Oldham, 'On the Propagation of Earthquake-Motion to Great 

 Distances ' Phil. Trans. Roy. Soc. ser. A. vol. cxciv (1900) pp. 135-74. 



2 A. E. H. Love, Phil. Trans. Roy. Soc. ser. A. vol. ccvii (1907) p. 215. 



