161 
1918-19.] The Propagation of Earthquake Waves. 
equation (11), did not seem prepared to make any better suggestion than 
to express T in ascending powers of 0, deduce therefrom the corresponding 
values for p and f(p), and obtain an integrable form for the integral either 
as a whole or in bits. 
What seemed to be most desirable was a direct way of evaluating the 
integral without any assumption of a functional relation between T and 6 
or p and 0 . I hoped to hit upon some analytical method, but in this I 
was baffled. Fortunately I was able to discuss the problem with Professor 
Whittaker, who is thoroughly at home not only in the theory of integral 
equations, but also in all the best modes of numerical calculation in higher 
mathematics. He at once pointed out one general line of attack, the only 
objection being the length of time required to carry it out efficiently. 
After a few preliminary trials I decided to carry through the calculations 
in the manner now to be described. This description is given under three 
headings, namely, the data used, the reduction of these data to a form 
suitable for application to the integral equation (11), and the evaluation 
of the integral and of all the quantities involved. 
(1) The Bata Used . — These are given in the tables familiar to all 
seismologists, in which times of transit of the primary and secondary 
waves are expressed in terms of the arcual distances of the stations of 
observation from the source or (to be quite accurate) the epicentre. John 
Milne was the first to put these data of observation in tabular form and 
to draw an average curve giving the relation between time and distance 
(see B.A. Reports for 1899 and following years). With the accumulation 
of earthquake records this average curve underwent continuous corrections, 
and Milne’s final values did not differ essentially from the values prepared 
by Wiechert and Geiger in 1907 from what they regarded as the best 
statistics then available. Milne tabulated the times of transit against the 
corresponding arcs measured in degrees ; Wiechert and Geiger translated 
the degrees over the earth’s surface into kilometres, 10,000 kilometres to 
the quadrant. For some years Professor H. H. Turner, chairman of the 
Seismological Committee of the British Association, has published Wiechert 
and Geiger’s values in a modified form, following Milne’s original method 
of expressing arcual distances. It is this modified table which I have 
used in the main calculations. 
Lately Dr Klotz of Canada has collated a valuable set of tables for 
use by seismologists, adopting, however, somewhat smaller values of the 
times of transit of the Primary waves iii accordance with a recent dis- 
cussion by Dr Mohorovicie of Agram. The times of transit of the 
Secondary waves he obtains by simply adding to those for the Primary 
VOL. xxxix. 11 
