Difference Problem 
399 
and from (xxii)...(xxiv) : 
Cj=0, C2=-017,699, --003,081, 
X=sx 1-127. 
Since the next term vanishes, I believe this result is probably true to the last figure. Anyhow 
I think we may say that if the individuals be taken at random from a population, then the 
probable value of the standard deviation of that poijulation is nearly | of the difference between 
the two individuals. Thus by averaging the differences between pairs of individuals taken at 
random we can obtain fairly readily an appreciation of the standard deviation, i.e. the variability 
of the general population. Further, if we take individuals, not quite at random, bvit from 
correlated groups, e.g. pairs of brothers selected at random, the |f th of the average difference of 
the pairs will be the standard deviation of the correlated groups, e.g. a group of brethren ; 
hence the degree of relationship between such correlated individuals may be determined. This is 
only a suggestion of one of the many possible uses of Galton's difference problem. It opens up, 
indeed, many new methods of inquiry, the effectiveness of which, however, can only be tested by 
their application in actual statistical practice. It must suffice for the present to have indicated 
that this difference problem marks a new, and very probably a most important, departure in 
statistical theory. 
KARL PEARSON. 
