OF ERRORS OF JUDGMENT AND ON THE PERSONAL EQUATION. 
259 
that I have worked out all the constants for the second series, for the whole set 
of experiments, and for its first and second moiety. 
They are given in the accompanying table. 
Table VI.—Influence on Constants of Fluctuations in Personal Equation. 
All Ohservations. 
First Series 
Second Series. 
1-520 (without 291). 
1 - 
-266 inclusive. 
267-520 (without 291). 
Observer. 
1 
2 
3 
1 
2 
3 
1 
2 
3 
Mean . . - 
r 
•0672 
-1-1491 
- -4856 
•0957 
-1-1728 
- -2894 
•0373 
-1 ■1241 
- -6919 
L 
± 0364 
± -0348 
± -0537 
± 0514 
± -0520 
± -0778 
± 0484 
± 0459 
± -0728 
S.D. . . 
f 
1 -1949 
1-1755 
1 -8160 
1 -2428 
1 -2563 
1 -8815 
1 1417 
1 -0833 
1 -7205 
± -0250 
± -0246 
± -0380 
± 0363 
± 0367 
± 0550 
± 0342 
± 0325 
± 0516 
Correlation < 
r 
•3819 
•1571 
•0139 
3677 
•2594 
•0530 
•4123 
■0256 
- -0308 
± 0253 
± -0289 
± 0296 
± 0355 
± 0386 
± 0412 
± 0352 
± 0424 
± 0423 
Observers. 
3-2 
1-3 
2-1 
3-2 
1-3 
2-1 
3-2 
1-3 
2-1 
Mean . . - 
•6634 
•5529 
-1 -2163 
•8834 
•3851 
-1 -2685 
•4321 
•7292 
-1 -1614 
± -0517 
± -0595 
± 0493 
± 0760 
± -0814 
± 0711 
± -0683 
± 0865 
± 0680 
S.I). . . . 
1 -7462 
2-0109 
1 -6645 
1 -8385 
1 -9676 
1 -7198 
1 -6114 
2 -0406 
1 -6026 
± 0366 
± -0421 
± 0348 
± 0538 
± -0575 
± -0503 
± -0483 
± 0612 
± -0481 
Correlation ■ 
•5625 
•3055 
•6154 , 
•5085 
■3900 
•5935 
•6323 
•1938 
•6375 
± -0202 
± -0268 
± 01841 
± -0307 
± -0351 
± -0268 
± 0255 
± 0408 
± -0252 
In the row in absolute judgments, entitled “ Correlation,” the correlation, rjj, of the judgment of the second and third 
observers is entered in column fl), rjj in column (2), r,] in column (3). In the row in relative judgments, entitled 
“ Correlation,” the correlation of the judgments of the second and third observers referred to the first observer as 
a standard, or p,, 03 , is entered in column (1), pj, 31 in column (2), and p^, 12 in column (3). 
The figures in antique type give the probable eiTors of each constant, and the probable errors in the differences of the 
constants can be found in the usual way as the square root of the sum of the squares of these. 
Dealing first with the absolute observations, we note that the personal equations 
of Dr. Macdonell and myself, (2) and (1), are within tlie limits of the probable 
errors the same for either half series and for the whole series. Both of us appear to 
have improved by about ’03, but whether this is a real improvement between the 
first and second series it is impossible to say, for the probable error of the half series 
is as much as '05. In my own case, in the second series my personal equation is less 
than its probable error, and accordingly on the basis of 253 experiments—a number 
be it noted far larger than could ever be made in actual practice—it would be 
impossible to say whether I had a personal equation or not. I mention this point, 
because it seems to me a sine qud non of all investigations of personal equation that 
the probable error of the results should be given, and in most cases one seeks for it 
in vain. 
Dr. Lee’s personal equation has increased substantially between the first 
and second series. All three observers have grown apparently steadier in their 
judgment. The probable errors, however, of the S.D.’s do not allow of the assertion 
2 L 2 
