1112 
MR. C. DAVISON ON THE ANNUAL 
length is one-fifth of a year are eliminated, provided the interval over" which the 
seismic record extends consists of an integral number of years. 
8 . The curves in fig. 1 exhibit the close agreement in the results obtained by the 
different methods of determining the semi-annual period, the seismic record chosen 
being that by Professor Milne of the earthquakes felt in Tokio during the years 
1873-1881 and 1883-1890. , The continuous curve is that obtained by Dr. Knott’s 
Fig. 1. 
method, every ordinate being first, however, multiplied by — l)/2, or '65, so as 
not to alter the ratio of the amplitude to that of the annual period. The broken 
curve is that obtained by the method used in this paper, the earthquakes being 
grouped in half-months, while the dotted curve is that obtained by the same method 
when the earthquakes are grouped in months. 
9. Connection hetioeen the Amplitude of the Annual Period and the Winter-to- 
Suinmer Ratio in the Number of Earthquakes. —In discussions on earthquake frequency, 
it is usual to estimate the ratio between the number of shocks felt during the six winter 
months (October to March) to the number felt during the six summer months (April 
to September). The ratio so obtained is, of course, only valuable when, as is fre¬ 
quently the case, the maximum of the annual period occurs either at the end of June 
or the end of December. Greater uniformity would be secured by evaluating the 
ratio of the number of shocks felt during the six months bisected by the maximum 
epoch to the number felt during the six months bisected by the minimum epoch. In 
the present paper, I have substituted the amplitude of the annual period for the last- 
named ratio, and it seems desirable to point out briefly the connection between them. 
In fig. 2 let the distance AC represent the average number of earthquakes per 
month, and let the curve represent the annual seismic period. Let PM and QN 
represent the average length of the ordinates during the maximum and minimum 
halves of the year respectively. Then the ratio of the number of shocks felt during 
the maximum half to the number felt during the minimum half of the year is equal to 
PM : QN, i.e., to the ratio of 1 + 2a/7r to 1 — ^ajir, where a is the amplitude of the 
annual period, the average number of shocks felt during each month of the year being 
taken as unity. 
For instance, in the case of the European earthquakes of 1865-1884 as tabulated 
by Fuchs (see § 19), the maximum of the annual period occurs at the end of 
