354 Illustrations of the Variate Difference Coi'r elation Method 
of reckoning quantities might enable us to put other and, perhaps, more kiminous 
interpretations on our results. But there can be small doubt that to proceed from 
the actual correlation of such indices to the cori'elations of their higher differences 
gives the feeling of clearing away the sand of the desert, and reaching all the 
ordered arrangements of an excavated town below; the slight undulations of the 
waste above are really fallacious, and enable us to appreciate nothing of the 
actual topography of the city. 
The method is at present in its infancy, but it gives hope of greater results 
than almost any recent development of statistics, for there has been no source 
more fruitful of fallacious statistical argument than the common influence of the 
time factor. One sees at once how the method may be applied to growth problems 
in man and in lower forms of life with a view to measuring common extraneous 
influences, to a whole variety of economic and medical problems obscured by the 
influences of the national growth factor, and to a great range of questions in 
social affairs where contemporaneous change of the community in innumerable 
factors has been interpreted as a causative nexus, or society assumed to be at 
least an organic whole ; the flowers in a meadow would undoubtedly exhibit 
highly correlated development, but it is not a measure of mutual causation, and 
the development of various social factors has to be freed from the time effect, 
before we can really appreciate their organic relationships. 
In the present paper we have dealt only with very sparse " populations " (only 
28 values of the variates), but this has enabled us to consider not only a very 
large number of correlations, but to see the practical influence of terminal con- 
ditions on our theory. This may we think be summed up in the statement that 
the Andersonian formidae for the standard deviations will hardly in many practical 
cases be more than very roughly approximated before the size of the population 
becomes too small to make the deductions reliable. Further in most cases our 
difference correlations have hardly even with the sixth differences reached a steady 
state. Possibly they have done so in the cases of Rail and Shipping, Shipping 
and Post, Shipping and Goal, Revenue and Post, International Commerce and 
Stamp Duties, International Commerce and Savings, Savings and Coffee, and in 
one or other additional pair. But in the great bulk of instances there is still a 
more or less steady rising or falling appreciable in the difference correlations, and 
all we can really say is that the final value, the true Vxr, will be somewhat 
greater or less than a given number. From an examination of the actual 
numerical working of the correlations, it appears to us that the terminal values 
are in the case of these short series of very great importance. It is further clear 
that the theoi-y as given by " Student " depends upon certain equalities which 
are not fulfilled in practice in short series. We await with much interest the 
complete publication of Dr Anderson's work, and hope to find a fuller discussion of 
the allowance to be made in short series for the influence of the terminal state of 
