OF EREOKS OF JUDGEMENT AND ON THE FERSONAL EQUATION. 
281 
Thus while two of the cases might reasonably be considered symmetrical distribu¬ 
tions, to fulfil axiom (a), and one of the cases might with some improbability 
(10 or 11 to 1) be supposed to. have = 3, i.e., to fulfil axioms (y8) and (y), no 
single case can be supposed, with any reasonable degree of probal)ility, to fidfil all 
three, or to be capable of rej)resentation by a normal curve. The third moment, 
the distance from mean to mode, tlie skewness and the magnitude and sign of the 
criterion K are quantities which, one or more or all, are in each individual case sensible 
and quite inconsistent with the result of random sampling from “ normal material.” 
I now give a similar talde for the bisection experiments. 
Table XVIII.—Bisection of Lines. 
! 1. 
1 
2. 3. 
2-3. 
3-1. 
1-2. 
H 
6-0258 
9-3966 
6-8915 
10-4745 
11-3987 
12-3817 
IH 
- 1-732G 
-9779 
-3-8272 
2-2447 
-4-6402 
2-6583 
+ 1-0929 
+ 2-1283 
+ 1-3367 
+ 2-5048 
+ 2-8435 
+ 3-2191 
/u 
118-0048 
267-1088 
124-7219 
301-1530 
.352-0688 
450 - 2880 
-0137 
-0012 
-0448 
-0044 
-0145 
-0037 
-0000 
-0000 
-0000 
-0000 
-0000 
-0000 
3-2499 
3-0251 
2-6261 
2-7448 
2-7096 
2-9372 
+ -1478 
+ -1478 
+ -1478 
+ -1478 
+ -1478 
+ -1478 
,1 
+ -1254 
- -0512 
+ -4045 
-1310 
+ -2605 
- -1125 
+ -0907 
+ -1132 
+ -0970 
+ -1196 
+ -1247 
+ -1300 
Sk. 
-0511 
-0006 
-1541 
- 0405 
-0772 
-0511 
+ -0369 
+ -0369 
± -0369 
+ -0369 
+ -0369 
+ -0369 
S, 
-1171 
-0.340 
-2115 
-0662 
-1206 
-0610 
+ -0739 
± -0739 
+ -0739 
+ -0739 
+ -0739 
+ -0739 
K 
- -4587 
- -0468 
+ -8821 
+ -5235 
+ -6243 
+ -1368 
+ -2955 
± -2955 
+ -2955 
± -2955 
± -2955 
± -2955 
Now it will be seen by a most cursory glance at tins table tliat the distribution of 
errors in tbe case of the l)isection of right lines can be far more nearly represented 
by a normal curve than in the case of judgment as to the position of a bright 
line. In the case of every one of the constants for the distribution of my own 
errors of judgment (he., (2)), they differ Ijy less than their probable error from 
their value on the normal theory. I can therefore treat my judgments as following 
the normal law and represent them by this curve. In Mr. Yule’s case (he., (3) ), 
the distance from his mode to his mean is more than four times its prol^able error ; 
or, only once in 332 trials, say, should we expect such a divergence from normality 
in a random selecting. It is thus very improbal)le that his judgments follow the 
normal law so far as symmetry is concerned. Further, the value of ydo differs from 
3 by about 2‘53 times its prolmlde error, or tlie odds against such a value are 
about 22 to 1, or, since can, unlike d and Sk., differ from its normal value either 
in excess or defect, say 10 or 11 to 1. On both counts, then, Mr. Yule’s judgments 
VOL. CXCYIII.-A. 2 O 
