ON SEISMOLOGICAL INVESTIGATIONS 255 



was found to give good results, with the reservation that any particular earth- 

 quake is liable to show a systematic deviation from the formula at all the 

 antipodal stations. (A is the distance in degrees from the end of the diameter 

 through the epicentre. The name ' hypocentre ' was used for this point; but 

 Mr. Davison calls attention to the fact that this name has been used, especially 

 in Italy, for the focus ; and it may therefore be better to use ' anticentre ' for 

 the antipodal point.) It was suggested that this systematic deviation is due to 

 variation in depth of the focus ; and this suggestion was reduced to numerical 

 form by the help of the calculations made by Professor C. G. Knott. It would 

 thus appear that, if we call d the unknown depth of the focus corresponding 

 to the adopted tables, the depth for different earthquakes in the years 1913 to 

 1916 varied from d—.021 to d+.061, the earth's radius being unity. Hence 

 rf-.021. 



The investigation has been printed as No. 1, Vol. I, of a series of Geo- 

 physical Supplements to the IMonthly Notices of the Royal Astronomical Society, 

 to which further reference may be made. 



Another contribution to the discussion was made by Dr. Dorothy Wrinch, 

 of which she has kindly supplied the following summary : — 



In a problem such as that of the depth of earthquake foci, in which there 

 is a tremendous variety of relevant data, it is important to select for first con- 

 sideration those data which are the most fundamental. The data with respect 

 to the speeds of P and S waves near the surface of the earth appear to be of 

 prime importance in the discussion of this problem. 



1. The records of the Oppau explosion last year at Strasbourg, Zurich, 

 Munich, and De Bilt give a value of 5.4 km. /sec. for the speed of the P 

 waves. 1 (The data in question were obtained by the kind assistance of the 

 Director of the Meteorological Office.) 



2. From the density and elastic constants deduced from the observations of 

 Adams and Coker and others a speed of 5.38 km. /sec. was calculated for the 

 P waves and a speed of 2.99 km. /sec. for the S waves near the surface of the 

 earth. 



Assuming these results, we may obtain an upper limit for the depth of the 

 focus of an earthquake from P or S observations. It is well known that the 

 speed of P and S waves increases when their paths are no longer restricted to 

 the surface layer of the earth. An upper limit to the focal depth of any single 

 earthquake can therefore evidently be obtained from the observations of that 

 earthquake, if we find the depth at which the focus would lie if we use these 

 observations and assume that the waves are propagated throughout their path 

 with the velocity which they have in the surface layer. Making this assumption, 

 we can deduce that if d is the depth of the focus. R the radius of the earth, 

 V the velocity of the wave in question (P or S), the time t to a distance A is 

 given by 



'-^-•+4'~iB-Al.O- 



if terms of relative order (A/R)^are neglected. Now, in the case of earth- 

 quake records taken at stations near enough to the distui'bunre for the terms 



of order ( 1 to be of no significance, when the probable experimental error 



of the records is taken into account, we obtain an upper limit for the depth of 

 the focus of the earthquake by applying the formula above to the observations 

 and inserting the values of v for P or S already agreed upon. This procedure 

 in the case of the observations of the Calabrian earthquake of 1905, September 8. 

 taken at stations at distances of between 40 and 220 km., yields 40-50 km. as 

 an upper estimate of the depth. The same method applied to the observations 

 of stations in the neighbourhood of the two Formosa earthquakes of 1906, 

 April 14, yields a depth of order of 450 km. as an upper limit. (These investi- 

 gations will be published in full shortly.) 



With this method of obtaining iiifininatioii about an earthquake focus only 

 the observations at different stations of one disturbance are used in any one 



1 Cf. a forthcoming paper in collaboration with Dr. H. Jeffreys on this 

 problem. 



1922 T 



