I9I5.] INTERIOR OF THE EARTH. 293 



but, thanks to a remarkable mathematical theorem of Abel, it is not. 

 It is clear that the time of arrival of an earthquake disturbance at a 

 distant station will depend on the path followed and the velocity in 

 different parts of the path, and if we make the reasonable assump- 

 tion, which is borne out by observation, that the velocity is every- 

 where the same at the same depth, then it is evident, if the velocity 

 increases continuously with the depth, that the transmission curves 

 will be continuous without breaks, and their curvatures will no- 

 where make a sudden change. The mathematical solution of the 

 problem has been obtained by Wiechert, Bateman and others, and 

 concrete results have been obtained by Wiechert and his assistants, 

 so that we now know the paths of the waves and their velocities with 

 a fair degree of accuracy, at least to a considerable distance below 

 the surface. But the questions arise : do the velocities increase 

 continuously with the depth; and if so, how? questions which 

 could be answered by the study of perfect transmission curves; but 

 even imperfect curves yield some information ; which, however, may 

 be so faulty that it must be received with great caution. Milne, who 

 has done such excellent pioneer work in seismology, was the first 

 to propose and attempt to answer these questions.^ He thought the 

 transmission curve could be satisfied by supposing the earth to con- 

 sist of a solid core having a radius of nineteen twentieths of the 

 earth's radius, and surrounded by a thin shell. The core was of 

 uniform density and elasticity, so that the velocity of propagation in 

 it was uniform, and the paths of the rays would be straight lines. 

 The velocity in the shell was much less than in the core. These 

 conditions satisfied fairly well the very imperfect transmission curve 

 of 1902, but they may be dismissed without further consideration, 

 for such an earth could not satisfy the astronomic requirements, 

 which exact, at the same time, the proper mean density and mo- 

 ment of inertia. 



Benndorff in 1906 thought he found evidence of a central core 

 of about four fifths the earth's radius, surrounded by two shells, 

 the outer one having the same thickness as Milne's.^ In the same 



5 Rep. of the Com. on Seismol. Investigation, B. A. A. S., 1903, p. 7. 



'^ " Ueber die Art der Fortpflanzungsgeschwindigheit der Erdbebenwellen 

 in Erdinnern," Mitt. d. Erdbeben Com. k. Akad. Wiss. in Wien, 1905, Nos. 

 XXIX. and XXXI. 



