M. Greenwood and J. D. C. White 
525 
indices thus obtained were analysed as usual. The same experiment was carried 
out in the case of 25's and lOO's. Tables XI, XI A and Graphs 6, 7 and 8, contain 
the constants and data of the distributions and Table XII the chances of obtaining 
indices within assigned limits deduced from the areas. 
TABLE XI A. 
Experimental Determination of Index Distributions. 
Samples op 25 
Samples of 50 
Samples op 50 
Samples of 100 
(Drawings not Eeplaced) 
(Drawings nut Replaced) 
(Drawings Keplaced) 
(Drawings 
not Eeplaced) 
Index 
Observed 
Calculated 
Observed 
Calculated 
Observed 
Calculated 
Observed 
Calculated 
■3- -4 
1 
- 
■4— -5 
3 
(1'454 ) 
j z 
•5— -6 
16-5 
11-243 
5 
(3-989 
3 
(3-007 
■6~ -7 
45 
40-468 
15-5 
13-990 
15-5 
15-308 
2 
{ 1-500 
•7— -8 
83-5 
89-850 
33-5 
37-969 
34-5 
39-863 
10-5 
1 1 -697 
■8— -9 
133-5 
121-939 
70 
66-729 
69 
65-497 
.35-5 
36-009 
■9—1-0 
130 
134-204 
79-5 
80-213 
71 
77-683 
55-5 
52-780 
1-0— 1-1 
105 
122-028 
66-5 
71-759 
78-5 
72-001 
41-5 
46-583 
1-1—1-2 
83 
96-635 
52-5 
51-973 
59-5 
54-817 
34 
29-0(13 
V2—1 ■S 
55-5 
69-188 
37-5 
32-676 
28 
35-425 
13 
14-177 
V3—1 ■It 
57-5 
46-012 
23-5 
18-792 
22 
19-873 
4 
5-850 
1 ■Jt—l -5 
37 
28-990 
6-5 
10-249 
13 
9-830 
2 
2-145 
1 ■S—l -6 
19-5 
17-560 
5 
5-452 
3 
4-334 
2 
S 1-00 
1 ■e—i -7 
11-5 
10-339 
1 
2-870 
1-5 
1-717 
\ 
1-7— V 8 
10-5 
5-967 
1 
1-512- 
1-5 
V8—1 ■£> 
4 
3-397 
2 
-803) 
1 -814 
1 ■9-2^0 
2 
1-918 
0 
-4.32 U -735 
2^0— 2-1 
2 
0 
( -5 ) 
2^1—2-2 
2^2— ^■S 
|2-0 
1 
{ 
Totals 
800 
803-265 
400 
399-908 
400 
400-169 
200 
203-744 
A comparison of these tables with nos. VIII — X indicates how far the limits of 
reliability are narrowed by a more complete study of actual conditions (see also 
Table XV infra). 
It will be noticed that these experiments do not assume any special distribution 
for the original variates. They merely afford a partial answer to this question — if 
we had two sets of 400—200, 800— samples exactly the same as the 400 (200, 800) 
actually counted and formed at random 400 (200, 800) indices from them, one set 
always furnishing the denominator and no sample being used more than once, how 
are the resulting indices likely to be distributed ? In strictness, therefore, these 
results are only applicable to our particular case. If, however, we assume that our 
counts are numerous enough and accurate enough to give the distributions of 
sample means of the size used, and for the emulsion used, with fair exactitude, 
then we can perform another experiment. 
Biometrika vii 67 
