M. Greenwood 
79 
number arbitrarily, so that it seemed sufficient to give in tabular form the results 
of small samples after first samples of 50 and 100 without calculating the inter- 
mediate cases. 
The next question is as to whether, within the limited field chosen, interpolation 
can be trusted. Accurate methods of interpolation in the case of double-entry 
tables are a little complex* and not likely to appeal to the man in the laboratory. 
What is really material is whether simple interpolation is likely to lead to seriously 
erroneous conclusions. 
I now proceed to some tests. 
(1) A first sample of 17 having given 3 successes, required the probability 
that a second sample of 14 will contain 4 or more successes. 
From the tables for n = 20, p = 3, m = 10 and n = 15, p = 3, m = 10, we have 
for the proportional frequency of 4 or more successes in m trials, 
12 'SOU 2 
23-0040 
10i978 
which gives by simple interpolation for n = 17, p = 3, m = 10, 
18-92488 (a). 
Similarly interpolating between the values for n = 20, p = 3, m =15 and n = 15, 
p = 3, m = 15, we have for n = 17, p = 3, m = 15, 
3892372 (£). 
Interpolating between (a) and we reach for the proportional frequency of 
4 or more successes in 14 trials after n = 17, p = 3, 34 - 92. 
The true value obtained by direct calculation is 35'07G01, which gives an error 
of '43 % m the interpolated value, a difference of no importance for such 
purposes as the present. In the accompanying table I have grouped together the 
results of a number of random trials made in different parts of the table. 
A perusal of these results leads, I think, to the following conclusions. 
(1) For values of m and n ranging in each case up to 25, interpolation, when 
necessary, gives results of sufficient exactitude for all the purposes likely to be 
served by such tables. 
(2) For greater values of m and n, particularly when the latter is greater than 
50, the differences are too great to allow of interpolation and for such values the 
table can only provide the reader with a general impression (which is often enough 
sufficient) as to the limits within which possible variations from the proportions 
* Vide W. Palm Eldertou, "Interpolation by Finite Differences (Two Independent Variables)," 
Biometrika, 1903, Vol. n. p. 105 ; W. Palin Elderton, " Some Notes on Interpolation in n-dimension 
Space," ibid. 1908, Vol. vi. p. 94 ; also the Introduction to the British Association Tables of F (r, v) and 
H (r, v) Functions (issued by B. A. 1899, p. 56). 
