98 
On the Variations in Personal Equation 
estimates {Ja% This is a result which we should anticipate, for the method of 
recording the estimate was the same in each experiment, and accidental errors of 
the same magnitude would occur in both cases ; on the other hand the observer 
was faced with a more difficult problem in estimating a third than in estimating 
a half, and this is shown by the greater vai'iability of his estimate in the former 
case ('07 against "OS)*. For the Timing experiments, we find no correspondence 
between the Jq-'s ; the great difference between the counting of ten seconds and 
the attempted concentration of mind on the passing of an unbroken ten second 
interval has been emphasized in the description of the experiments above, and a 
correspondence was hardly to be expected. The standard deviations are in terms 
of the factors ejp and must be multiplied by 10'2 if required in seconds. 
If now we turn to the values of r given in the last column of Table XIX, it 
will be seen that they lie near together, and although that for the Bisections 
is not an exact measure, there is a suggestion of close agreement between the ?''s 
in the pairs of similar experiments, for we have estimations of length with '71 
and '72, and estimations of time with '79 and '81. This coefficient is a measure of 
the rate at which the correlation of successive judgments falls off or the influence 
of previous estimates vanishes from the observer's mind : on the theory of zero 
partial correlation it is simply the coefficient of correlation between a true estimate 
freed from accidental errors and the preceding estimate. 
On any theory r would seem to be a fundamental constant not varying greatly 
for different types of observations, but perhaps varying considerably for different 
observers. The fact that it is so nearly the same for experiments with a five second 
interval between observations (Trisection and Bisection) and for others with an 
interval of ten seconds or more (Counting and Estimating) shows that the corre- 
lation of successive judgments is a function not only of the time interval between 
two judgments but also of the number of interveimig judgments. For if it were 
purely a function of the time interval we should expect to find a greater differ- 
ence between the values of r found for experiments with a five second interval and 
a ten second interval. Indeed if the experiments were exactly the same but for 
difference in interval, R/ for that with ten seconds would equal R/ for that with 
five seconds. Further experiments of the same type in which the interval between 
the recording of judgments was varied would undoubtedly throw much light on 
this point. 
XII. Prediction. 
If the values of " " successive judgments are known and there is no corre- 
lation between them, the " most probable " value of the {m + l)th judgment, that is 
the most reasonable guess at its value that can be made, is the mean of the "m" 
judgments. If however the successive judgments are correlated, then it is possible 
to predict the value of the {iii -\- ] )th with much greater expectation of accuracy. 
* This may be compared with the ratio of 3 to 2 given on p. 73 from a comparison of the 
S^'s before making any allowance for the accidental errors. 
