Alice Lee 
545 
statisticians, and ought never to be used where hard work can produce larger 
numbers. But in annual returns, as has been indicated by others, a period of 
30 to 50 years is often the maximum attainable, and we must take what we can 
get. In the present case the probable errors of the difference correlations — -based 
on the Andersonian formulae for steady conditions — show us that we can form 
fairly legitimate conclusions from the results reached. 
A second test that we have applied is the approach to the theoretical values 
in the function o-^s ^/o^'s ^ where SmX is the mth difference of the variate x. 
The following table shows that there is a reasonable approach to these 
theoretical values in the calculated standard deviations of the diffei-ences, and 
suffices to justify the application of the variate difference method within the 
limits of practical statistics. We have continued the differences beyond the 
values used in some of the correlation results to indicate the sort of irregularities 
"... . 
which may be expected to occur when using high differences in small populations. 
Terminal irregularities then begin to affect the uniform rise of a'^ x/'^'s c- 
