86 MODERN SEITSMOLOGY 
periodicity with a maximum in winter and the diurnal period- 
icity with a maximum about noon obtained by Davison from 
earthquake statistics may be regarded as fairly well established. 
Although the small table at the beginning of this chapter 
is too limited to justify any general conclusion it will serve to 
illustrate the application of Schuster’s method. 
I find that the Fourier expression is given with sufficient 
accuracy by 
N = 20 (1 +04 cos ¢+ 120°+ O'1 cos 2¢+ 120°) 
where ¢ is the time reckoned from 1 January at the rate of 30° 
per month. 
The expentancy is 7/235 or 0°12, and we should thus 
argue that the semi-annual term is worthless while the annual 
term with its maximum at the end of August is important. 
The practical application of Fourier analysis to observational 
quantities is really very simple, and since it does not usually 
find a place in physical textbooks, a few remarks about it may 
not be out of place here. 
If the observed quantity fis to be expressed by means of 
a Fourier series 
n= ow 5 
f= tat _ (a, cos 20+ , sin 26) 
between the limits o and T where 0 = 27#/T, we have 
ip 
w= | adi 
0 
27rut 
ta,l -| x9 COS —7 at 
0 
Beal = io sin “dt 
0 
If f(o) =f(T) then no difficulty occurs; but if, as generally 
happens with observed quantities, (0) +-/(T) then the function 
fis not strictly periodic in time T, and this at once sets a 
limit. The series represents the function / between the limits 
but not at the limits, for the series then gives 4$/f(0)+/(T)} at 
the limits. 
This difficulty is often dealt with in practice by assuming 
that the difference f(o) f(T) is incident linearly, during the 
interval T and it is subtracted from / before analysing. This 
