Egon S. Pp:;arson 
91 
where is a constant not depending on the interval k. With this expression for 
the correlation we shall of course find an apparent partial correlation between the 
judgments at intervals greater than one ; for example the partial correlation 
(J (\ — Q) 
between yt and yt+i being constant, is ~- , and does not vanish unless 
5 = 1. According to the theory suggested this is however a spurious correlation 
due solely to the presence of the accidental errors. 
The next problem is to inquire how far a relation of the type of (xlvii) 
will fit the correlation coefficients which have been calculated for the Experiments 
A, B, G and D. In the first place, in order to get as smooth values for the 
coefficients as possible we must combine the 20 series, which we may do if we 
remove the secular change as represented by the variation in the series means ; 
this step is clearly necessary for we are considering the relationship between 
judgments made in close proximity and are not concerned for the moment with 
the variation in personal otpiation from day to day. We must therefore deal with 
the coefficients of correlation and endeavour to fit a curve z — qi-^ through the 
points x = k, z = Ri'. I will consider the different experiments in turn. 
(b) Application of Theofij to results of Experiments. 
Experiment A. 
The curve rej^r'esented by ^ = (p-^ is asymptotic to the x axis (as ?• < 1), so that 
if it is to fit the points {k, R^;') it is necessary that R^' should tend to zero as k 
increases. But the values of R^;' given in Table V, p. 58, appear to tend as A; 
increases, to a limiting value between + 16 and + "15 rather than to zero. 
I think that this results from the marked sessional changes which have been 
represented in mean form by a second order parabola (see Equation (xxx) and 
Figure 4), and that if there is a physiological significance in the distinction 
between the sessional change and the residual variations of the observations when 
freed from this change, it will be of interest to find out how the coefficients of 
correlation of these successive residuals — what have been termed the Rji,."'s — fall 
off as the interval or k is increased. Should it be found that the Ra:"'s follow 
the law 
Rfc" = 
the argument in favour of distinguishing the sessional change from the residual 
variations will be strengthened. 
It was found that the values of R/ given in Table V could be fitted closely by 
a curve of the form 
z=p + qr^ (xlviii), 
where p, q and r are constants. 
A rough trial gave the following approximate values : 
p, = -lb1, q, = -69, r„ = -73. 
Now if z = f{p, q, r) 
=f(lh, qo, n) + Bp + Bq p + Br to first order, 
= Po + qorj" + Bp + Tu'^Bq + kq^rj^^' Br, 
