G. MORANT 
317 
m and 13 are rigidly constant quantities, but in actual practice they fluctuate 
slightly during the experiments or observations, and also the material is probably 
subject to fairly large errors of random sampling. Thus it by no means follows 
that the values of ^ and m found from the whole of the data will agree very closely 
with those obtained in another phase of the investigations when only a portion of 
the data can be used. It is therefore very essential to obtain m and /3 from each 
phase of the work independently, and to test the accordance of the values thus 
obtained. If the material given refer only to a limited period, the moment 
method of finding /3 and m, from the frequency of intervals in an indefinitely long 
time, cannot be used. 
Fig. II. Lengths of intervals in an indefinitely long time. 
1200t 
1000 
800- 
600 
400 
200 
/ff=-363 
m = 2-496 
P = -19 
OBSERVED 
- CALCULATED 
10 
Seconds 
15 
20 
We have to investigate the probability of ?i occurrences in a limited time T on 
the hypothesis that there was not an occurrence within the " closed-time " /3 before 
the beginning of the period T. Let the times of occurrence be f,, L... tn from the 
beginning of the period and let di^, dU ... dt,,, be indefinitely small intervals round 
