G. MORANT 
315 
TABLE I. 
Lengths of Intervals in an indefinitely lung time, starting with a /S — '5 grouping. 
Frequency 
Lengths of intervals in seconds 
•5—1 -.5 
1 -5- 
2-5— 
3-5— 
4-5- 
5-5,^ 
(j-5 — 
8-5— 
!):5-- 
Observed 
Calculated 
106 
186-2 
1,217 
1,154-0 
845 
772-1 
475-5 
516-5 
353-5 
345-6 
221-5 
231-2 
143-5 
154-7 
95-5 
103-5 
65-5 
69-2 
59 
46-3 
29-5 
31 0 
Lengths of intervals in seconds 
10-5— 
11-5— 
12:5— 
13:5— 
U-5— 
15-5— 
16:5— 
17 -5- 
18:5— 
19:5— 
Over 
20-5 
Totals 
17-5 
20-7 
11 
13-9 
7 
9-3 
8 
6-2 
8 
4-2 
5 
2-8 
1 
1-9 
2 
1-2 
-5 
-8 
•5 
•6 
1 
1-1 
3,673 
3,673 
are not significant. The curve is shown fitted to the observed frequencies in the 
case when the first group is from ^ to 1 (Fig. I) and the areas are compared in 
Fig. II. Again there is a marked disagreement between the theoretical and 
observed frequencies of the first two groups ; combining these, as before, gives for 
goodness of fit P = '193, so that regrouping the material has not given a better fit. 
The curve does not fit the observations well, but there can be little doubt that this 
is due to the conditions of the experiment and not to the form of the curve or the 
methods of finding /3 and rn. /3 may have fluctuated considerably throughout 
the experiment and this would account for the bad fit at the beginning of the 
range ; the longer intervals not being affected. 
By finding the constants /3 and m from a sample only of the whole material we 
may get some idea of the way in which they were fluctuating. Taking two of the 
six tapes gave 
•354,020, 2-587,989. 
These values differ appreciably from those found from all the data, but as we 
have at present no knowledge of the probable errors of yS and m, it is not possible 
to say how significant these differences are. It would be more satisfactory if the 
above law of distribution of random intervals could be justified empirically with 
material which was more homogeneous and for which the " closed-time " ^ was 
more nearly constant. 
