Egon S. Pearson 
69 
55th observations in Series V and VI, would go far to account for the similar 
features in the yt diagram, the " y " scale of which is four times greater than that 
in Figure 11. 
Using the method of Correlation of Ranks*, the correlation between cti and pi 
has been calculated for the 20 Series ; the result is 
?V,,i = + -420 ±-124. 
Another coefficient which may be calculated, is that of the correlation between 
cTg, or the standai'd deviation of first differences of consecutive judgments, and ; 
using the same method as for r„^f,^, it is found that 
'""SPi = ~ '^^^ i "125 and again r^^a^ = + '465 + 'llS. 
Now pi, (Ti and as are not three independent quantities, as they are connected 
by the relation 
and it is open to question, which two are the most fundamental. In the ordinary 
theory of the Combination of Observations, where it is assumed that p^ is zero, 
it is natural to consider o-j (or a) as a fundamental constant, the measure of the 
accuracy of judgment ; as appears to have no special significance and merely 
equals V2cr. If however there is a correlation of successive judgments, a loses its 
importance ; if we take a small number, p, of successive observations and calculate 
their standard deviation, Sp, we can no longer say that Sp, subject to its probable 
error +"6745-^=, will be equal to a, the standard deviation of a long series of 
judgments. On the other hand there is every reason to expect that the as found 
from a few observations will give a fair approximation to the as found from a 
large number, a is dependent to a high degree on the sessional change ; for 
example it has been shown f that if this change can be represented by a straight 
line of the form y = ht, then a', or the standard deviation of the observations freed 
from this change is given by 
cr'^ = a=-^(H^-l). 
It is true that as is dependent to some extent on the sessional change, but far 
less so ; for instance in the case of the linear sessional change, as, the standard 
deviation of the first diflFerences of the successive residuals left after the removal 
of the line, is given approximately by the relation 
And for any form of sessional change which is likely to occur in experiments 
of the type we are considering, the correction to the difference between two 
successive observations necessary to get the corresponding difference between the 
* p. 52 and footnote, 
t Section V [h) p. 43. 
