270 
PEOFESSOE K. PEAESOX OX THE MATHEMATICAL THEOEY 
billed with spurious correlation according to the special manipulation used in the 
reduction of the errors. 
Takino’ into account what we have learnt as to the nature of fluctuations in 
o 
personal equation, I think we may conclude broadly as follows :— 
The errors of judgment of apparently independent observers are not as a rule 
indejiendent. The immediate atmosphere of each single observation or of each short 
series of observations affects in a differential manner the factors of the personality, 
causing variations in the personal equation which are not of the order of those 
due to random sampling. Certain factors affected b}^ the immediate atmosphere 
seem to be common elements of two or more personalities, and there results from this 
a tendency in each pair of observers to judge in the same manner. If we enlarge the 
concept of “ immediate atmosphere ” to embrace not only the objective side of the 
phenomena, but the physical and mental state of the percipient, we may simply state 
that certain elements of this immediate atmosphere are common to each pair of 
observers and produce a correlation between their judgments. Their personal equa¬ 
tions fluctuate in sympathy. This swnjjathetic fluctuation of personal equations 
leading to correlation of judgments is really visible on insj^ection, as the reader will 
at once see on examinino- Diao’rams II. and III. 
Dia^rc^m in. Persona,!, Equa,C/on 
Numbers of Observa.Cions. MoCion <jf Bn6hb Line. 
Continuous PoLygon = Values of Personal Equation as based upon Z7 Co 37 Observations. 
Continuous Curve = Approach •• " Co its Mean Value for 513 -> 
This quite s\d:)-conscious sympathetic fluctuation of personal equation in the case of 
apparently independent observers is not only of fundamental importance when we 
have to combine obseiwations of the same phenomenon by different observers, and 
assign tlie weight of the combination, but it appears to have an even wider bearing 
