STATISTICAL 87 
merely confuses the issue, and it is less objectionable to take 
the function fas observed and to remember that in so far as 
J(o) differs from f(T) the representation is incomplete. 
The data are, however, usually presented in the form of 
hourly values in solar time or lunar time according to the 
source we have reason to suspect as contributing to the effect. 
If thenf,, fi. . . fa represent the values of / for the various 
hours the formule become 
3 
24a,=4f+fu)t%,, - 
m =I 
Ven 
Mm = 23 ° 
12an=4$(fotSoa) + > ey Jm COS (mn 15°) 
126,= 5) 
M = 23 
Tm Sit. (em. 15). 
m=t1 
The numerical process is simple since the terms collect 
into groups with the same numerical coefficients. 
In these expressions /,, may be the actual value at the 
hour 7 or the mean for an hour centering at 7. Neither is 
strictly correct for an infinite Fourier series although the 
former is correct for a limited series, ending with z= 24. 
Here again the representation is incomplete when /, +/,. 
Unless the quantity / varies in a very regular manner, one 
day’s observations would not be sufficient, and the hourly 
values are then averaged for say a month. A similar process 
would then be applied to the coefficients so obtained to de- 
termine their annual periodicity. 
This method, however, fails unless the day or the year are 
real periods of the phenomena; and may, as we have seen, give 
a false impression of periodicity unless Schuster’s criterion can 
be applied. 
The only general method of detecting periodicity is due to 
Schuster) quote from) his’ paper (Proc, Ra Saale) skowet ly 
be a function of ¢, such that its values are regulated by some 
law of probability, not necessarily the exponential one, but 
acting in such a manner that if a large number of values of 
¢ be chosen at random there will always be a definite fraction 
of that number depending on 4 only, which lie between ¢, and 
t,+ I, where T is any given time interval. 
