OF ERRORS OF JUDGMENT AND ON THE PERSONAL EQUATION. 
283 
(11.) (b.) Agreement between Theory and Observation m the General Distribution 
of Errors of each 'particular size. 
Now ill the ‘Philosophical Magazine’ for July, 1900, I have worked out a very 
simj^le criterion for the goodness of fit of any frequency distribution to a theoretical 
curve. 1 have measured the probability that the divergence from a given curve is 
one which may be attributed to random sampling. The test is of the following 
kind ; Calculate the squares of the differences of the observed and theoretical 
frequencies, and divide each such square by the corresponding theoretical frequency ; 
the sum of all such results, written -f, is the constant from which we can easily 
determine whether the probability, P, is large or small that the observed system 
of divergences or a still more divergent system would arise by random sampling. 
In Table XIX. below are recorded for the case of the Inight-line expeiiments the 
values of n', or the nundjsr of frequency groups, and P, the above-mentioned 
probability. 
Tx\ble XIX.—Motion of Bright Line. 
1. 
2. 
3. 
i 3-2. 
! 
1-3. 
2-1. : 
<D 
11 
18 
16 
20 
24 
23 
23 
o 
X-' 
12-07 
19-72 
15-88 
60-24 
20-37 
40-17 
p 
•7959 
•1829 
•6653 
•000,035 
•5599 
•0103 
n' 
18 
16 
20 
24 
24 
23 
o 
X" 
P 
42 • 85 
•0006 
83-50 
•000,000 
21 -82 
•2933 
154-41 
•000,000 
34-46 
•0441 
99-79 
•000,000 
Some words are necessary as to the meaning of this table, n' gives the number 
of groups of frequency upon which the determination of was based. This had 
to be somewhat arbitrary when there Avere outlying observations, as in cases (2), (3), 
(2-1). The calculation of the frequencies within the range of each group was 
found partly by meclianical integration of carefully drawn diagrams of the 
iis to these sources. When one advances into a new country one is apt not to see all things at once in 
their due proportions, and I may well have laid more stress than was justifiable on the importance of range, 
for example. This was not because a determination of range, if it exists, is not of most primary 
importance, but because I had not till the fourth memoir of the series ascertained a method of determining 
the probable error of the determination of range, and seen that in certain cases it is considerable. The 
critic—to whom I hope to reply elsewhere—seems to have failed to perceive the aim of my investigations 
i.e., to find a simple description of frecpiency, which will describe the great bulk of cases within the errors 
of random sanijiling. 
2 o 2 
