OF ERRORS OF JUDGMENT AND ON THE PERSONAL EQUATION. 
255 
phenomena. The true conclusion appears to be that the range of data upon which 
the personal equation is based must be very wide, so as to swamp as far as possible 
these sources of variation due to the “ atmosphere ” of a short consecutive series. 
But if such a personal equation be found, what will be its value ? It can hardly be 
applied satisfactorily to an isolated observation or to a short consecutive series of 
observations, for these will of course be influenced by their special atmosphere. It 
would only have value for a long series such as it was itself determined for, and such a 
series would rarely occur in practice. The fact that in both our series of experiments 
the differences between the values of the personal equation as found from short series 
are many times the probable error of sampling is very remarkable. I shall refer to it 
as “ the influence of immediate atmosphere,” where I understand the “ atmosphere ” to 
he compounded of all the little sources which affect either the observed thing or the 
observer more or less persistently during a short series. I am prepared to be told 
that the influence of immediate atmosphere was something peculiar to our own test 
experiments. But I shall require a good deal of the hard logic of exjjerimental facts 
to be convinced that it has no existence in astronomical observations. There are 
many determinations of astronomical personal equation, but in published data I have 
been unable to discover enough material to determine how far tlie admitted variations 
in personal equation for short series are or are not of the order of deviations due to 
random sampling. 
The following data will bring out the points of this discussion :— 
Table V.—-Personal Equation. 
First 
series. 
I 
Second series. 
Observer. 
Experi¬ 
ments. 
Bisection of lines. 
1 
1 
j Experi¬ 
ments. 
Position of bright line. 
1. 
2. 
3. 
1. 
2, 
3. 
Mean. 
500 
+ 01235 
- 00444 
- -00469 
! 519 
•06724 
-1-14906 
- -48563 
Ditto. 
1-250 
-t- 01424 
- 00173 
+ -00065 
1-266 
•09571 
-1-17282 
- -28940 
Ditto. 
251-500 
+ 01046 
- 00714 
- -01004 
j 267*-520 
•03731 
-1 •12-107 
- -69194 
Standard deviation . . 
500 
•02464 
•03068 
-02618 
[ 519 
1-19495 
1 •175-16 
1 -81599 
Probable error of mean 
500 
•00074 
■00093 
00079 
519 
•03538 
•03480 
•05377 i 
Ditto. 
250 
•00105 
00132 
■00112 
j 260 
•04998 
•04917 
•07596 
Ditto. 
25 
•00331 
■00416 
•00353 
30 
•14715 
•14475 
•22369 
* Experiment 291 omitted. 
This table shows us :— 
(a.) That the probable errors for the personal equations deduced from twenty-five 
bisections are such that the fluctuations of personal equation given in Table III. or 
Diagram 2 are in very many cases signiflcant. 
