260 
PROFESSOR K. PEARSON ON THE MATHEMATICAL THEORY 
that the steadiness has substantially increased. The variations in correlations of 
judgments are noteworthy. Judged from the first series, or the second series, 
or the whole series, the correlation between the judgments of Dr. Lee and 
Dr. Macdonell remains sensibly the same, i.e., ’4 within the limits of the probable 
error ; there is sensibly no correlation between the judgments of Dr. Macdonell 
and myself as given by any of the three series. Between Dr. Lee and myself 
there is on the whole series a substantial correlation of ’16 fi: ’03, but the two 
half "series show us that it was on the wane during the course of the exjDeriments, 
having fallen from the comparatively high value of ‘26 to practically zero between 
the two half series. Whatever causes therefore produced the marked divergence 
of personal equation between Dr. Macdonell and myself, they seemed to have 
been combined in Dr. Lee, and—to speak metaphorically—the dominant set for 
Dr. Macdonell became after a struggle dominant for Dr. Lee ; her methods 
of judging in the course of the experiments became more and more like 
Dr. Macdonell’s and less like mine. 
We turn now to the relative judgments. These it must be remembered are the' 
only data which would be generally knovm in practice. Here it is only in the 
difference of Dr. Macdonell’s and my judgments (column 2-1) that there is any 
real approach to constancy in the relative personal equation. The differences of our 
judgments have sensibly the same value for the first, the second, and the whole series. 
The same remark applies also to relative steadiness of judgment.* On the other 
hand, the relative personal equations of Dr. Lee and Dr. Macdonell, or of Dr. Lee 
and me, differ substantially between the first half and the second half series. The 
relative steadinesses of judgment are less altered, being sensibly constant for Dr. Lee 
and myself, but possibly varying slightly for Dr. Lee and Dr. Macdonell. 
When we turn to the correlation of relative judgments, that of Dr. Macdonell’s 
and my judgments, referred to Dr. Lee’s as standard, shows sensible constancy 
throughout the three series; that of Dr. Macdonell’s and Dr. Lee’s, referred to 
mine as standard, shows not very large but sensible change ; and finally that of 
Dr. Lee’s and mine referred to Dr. Macdonell’s, shows very substantial modification. 
Now judged by size of personal equation I stand first and Dr. Macdonell last, 
judged by steadiness Dr. Macdonell and I are almost equal (within the limits 
of the probable error), and Dr. Lee last. The most constant results for absolute 
personal equation are found—as we might a 'priori exj)ect they would be—where 
the steadiness is greatest. But if we wish to obtain relative judgments whose 
relationship to each other will remain at closely the same value during a long 
series, then apparently we ought to refer not to the most steady, but to the least 
steady of the observers as a standard. 
* I may remind the reader of what this exactly means: The difterences of 1’72 and PGO, the standard 
deviations for (2-1) in the first and second series, from 1’66, the standard deviation in the whole series, 
are about ’06, and this is just about the magnitude of the probable error of these ditterences, f.e., 
(-035)2 + (-0,50)2} = -061. 
