Karl Pearson 
25 
Now it will be seen that this consists of three parts 
(a) 
Vl - r 2 
90 c 
This is easy to table for all values of r. 
(b) ^l+«i)ltl-<O and 
H 
(o) 
K 
Both these (b) and (c) can be readily found from a single table rapidly formed from 
Sheppard's Table of the Probability Integral. The entry to the single table will 
be (a + c)jN or (a + b)/N, i.e. \ (1 + a). 
Thus a knowledge of the correlation r and the two division percentages (together 
with Miss Gibson's Table for , 67449/Vi\ r ), will enable us by the aid of the two 
new tables to rapidly write down four factors whose product gives the required 
probable error. I have tested the form (v) against the true probable error as found 
from (i). In all cases it gave results differing only from the true value at most by 
about one or two units in the third place of figures — a result amply accurate for 
all practical purposes. 
Illustration I. 
21125 
15375 
365 
152-75 
56025 
713 
364 
714 
1078 
The correlation was found to be '5557 + '0261 ; the probable error from the short 
formula was '0265. 
Illustration. II. 
1562 
383 
1945 
42 
94 
136 
1604 
477 
2081 
The correlation was found to be '5954 ± "0272 ; the probable error from the short 
formula was -0293. 
Illustration III. 
455 
622 
1077 
599 
1324 
1923 
1054 
1946 
3000 
The correlation was found to be '1811 + '0210; the probable error from the short 
formula was '0199. 
Illustration IV. 
849 
665 
1514 
205 
1281 
1486 
1054 
1946 
3000 
Biometrika ix 
