320 
On Random Occurre^ices in Space and Time 
To find the /3 and m we proceed as follows : 
Accordingly 
f = Ne "' , and write a = — e>" , b = ~ e" 
m. ni 
and 
Xn 
lib. 
The weight Wn of Xn will be inversely as the square of its standard deviation. But 
and fn and /„ being frequency groups, 
Mean (8fjf) = --^-^. 
Thus approximately 
Xn' «M/A NJ /oV NJ N fnfoj 
1( - - 
.(xiii). 
Accordingly we may take 
to fn / * \ 
W« = — -f^-TT- (XIV). 
Xn (Jo +Jn) 
To find the best values of a and b we have thus to make 
= S (a — nb — XnT '^n a minimum, 
or we reach 
aS (tVn) - bS (mVn) S (%nW,i) 
0 0 
aS (mvn) - bS (nhVn) = S {nxnWn) 
.(XV). 
These equations have not been found too laborious in practice. When a and h 
are determined, we have 
/S = -r (xvi) 
a 
and then if 2^ = — , we must find z and eventually to from 
m •' 
b = (xvii). 
(c) The above method of finding /S and m cannot be used when the observed 
frequency fn is zero, and we should not expect it to give good results if were 
small. A more general method is required to cover these cases. 
