280 
Miscellanea 
With a view to confirming the theoretical results, a practical random sampling was made in 
the following way. A circle, about 20 inches in diameter, was carefully divided into sectors 
whose angles (and therefore areas) were proportional to the class-frequencies given in Table II. 
For each sampUng a pointer was placed at random inside the circle and the number of the sector 
in which it was placed was noted. It appeared that, if the observer kept his eyes shut and 
rotated the cu-cle for a time between each pointing, the method would give quite satisfactorily 
random sampUng. In this way an ordered series of 648 samples was made and by taking samples 
of two by pauing in accordance with three different rules, the series of numbers given in Table III 
were obtained. Alongside of each series in the Table is given the ratio of the number in each 
set to the total. These ratios are to be compared with the "theoretical chances." In all three 
samples the number with standard deviation 0 is considerably less than the theoretical numbers, 
but from the values of the Goodness of Fit "P " given at the ends of the columns it appears that this 
can be accounted for by the variations of random sampling. 
TABLE III. 
Frequency distribution of Standard Deviations of Samples of Two 
Capsules from the Shirley Poppy Series. 
Experimental Results 
Standard 
Deviation 
Theoretical 
Chance 
I 
II 
I 
II 
(a) 
(b) 
Number of 
samples 
Chance 
Number of 
samples 
Chance 
Number of 
samples 
Chance 
U 
•1522 
•1478 
39 
•1204 
38 
•1172 
37 
•1142 
•5 
•2820 
•2760 
102 
•3148 
99 
•3056 
109 
•3364 
1 
•224!) 
•2246 
75 
•2315 
75 
•2315 
74 
•2284 
1-5 
•1553 
•1594 
55 
•1698 
58 
•1790 
44 
•1358 
2-0 
•0937 
•0986 
26 
•0802 
26 
•0802 
31 
■0957 
2-5 
•0503 
•0532 
7 
•0216 
15 
■0463 
15 
■0463 
30 
■0243 
•0250 
12 
•0370 
5 
■0154 
8 
■0247 
3f< 
•0108 
•0102 
5 
•01.54 
5 
■0154 
5 
■0154 
4-0 
•0043 
•0037 
3 
•0093 
2 
■0002 
0 
■0000 
4-5 
•0015 
•0011 
0 
•0000 
1 
•0031 
I 
■0031 
5-0 
•0005 
•0003 
0 
•0000 
0 
•0000 
0 
■0000 
5-^ 
■0001 
•0001 
0 
•0000 
0 
•0000 
0 
•0000 
Using Theoretical Chance (a) 
P=^18 
/ = 8-3, 
P=-69 
x2=10-5. 
P=-49 
Using Theoretical Chance (6) 
P=^12 
X^ = 8^9, 
P=63 
X^ = ll-3, 
P=-42 
The mean standard deviations given by these sets are for I, 1^06, for II, 1-07, for III, 1-05, 
while those derived from the half-Gaussian and from the "theoretical chances" are 1011 and 
1^050 respectively. It will be noticed also that although the calculated chances (a) appear to 
give a better fit than the half-Gaussian, the differences in the " P's " are very slight, and the 
half-Gaussian would sufflce for most purposes. These results form a strong confirmation of the 
correctness of the theory. 
