218 Proceedings of the Royal Society of Edinburgh. [Sess. 
increases, is not one which can be readily admitted in these days. The 
evidence seems to be all the other way. 
In 1905 and 1906, Benndorf * published two important papers, in the 
second of which he works out a law connecting speed of propagation with 
depth, starting from the angles of emergence as measured by Schliiter. 
Before I knew of these papers of Benndorf, I had myself returned to 
the problem of nine years ago, and after some trials had obtained a form 
of solution which seemed to satisfy all the known phenomena. It is this 
which forms the subject of the present paper. 
It is recognised by all seismologists that the records obtained at stations 
outside the destructive area of a large earthquake consist of two well- 
marked portions — called by Milne the “ preliminary tremors ” and the “ large 
waves.” In all well-developed seismograms two distinct phases of the 
preliminary tremors can be distinguished, a fact first clearly discussed by 
Oldham ; and Omori, the Professor of Seismology in Tokyo, further divides 
the large waves into five distinct phases. 
Here I consider only the two phases of the preliminary tremors, 
regarding the nature of which there has been a good deal of controversy. 
The most obvious view regarding these is that they are elastic waves 
propagated from the earthquake source through the body of the earth. 
This is the view I have always held along with Milne and Oldham ; but 
it is not the view favoured by the Japanese seismologists. Benndorf s 
second paper, already referred to, strongly supports the view now to be 
presented. 
When an earthquake occurs it sends forth in all directions seismic 
disturbances apparently of three distinct kinds. Two of these, the phases, 
namely, of the preliminary tremors, are transmitted by brachistochronic 
paths through the earth with speeds of propagation which are determined 
by the elastic constants and the density of the earth. The large waves, on 
the other hand, pass round the circumference as surface waves, taking fully 
two hours to reach the antipodal point after the epoch of the earthquake. 
This is proved by the fact that the time of transit from the epicentre to 
any station is proportional to the arcual distance of the station. But the 
time of transit of the preliminary tremors does not follow this simple law. 
The times of transit for various distances are given below when the results 
of the calculation are compared with the results of observation. 
In the following investigation I assume — 
1. That the source of disturbance is close to the surface of the globe. 
* Mitt. d. Erdbeben-Kommission (Kaiserl. Akad. der Wissens., Vienna), Nos. xxix., 
xxxi. 
