324 
Anthropometry of Scottish Inmne, 
an accurate estimate can be formed as to the relative homogeneity of the general 
population, with respect to each separate character. If the whole population be 
homogeneous the relative differences between the general and local means should 
be expressed by a random distribution. It should be again noted that the relative 
local differences {RLD) are the differences between the general mean M and the 
local means m reduced to a common scale by dividing each difference by its 
standard deviation, i.e. the ratios 
for each character at each asylum are considered interlocally. If the population 
be a homogeneous one with respect to the character considered, the standard 
deviation of the distribution of these ratios interlocally, or s, will seldom differ 
from unity by a quantity greater than three times the probable error of s, or 
"67449 
s = lH — ^ where q is the number of districts considered Thus s is an 
~ ^2q 
interlocal constant determining the degree of homogeneity of the characters con- 
sidered or the degree of character homogeneity. An attempt has also been made 
to discover the degree of district or local homogeneity, using the values of the 
relative local differences intralocally, but the writer has failed to find a solution 
of this interesting problem. As Professor Pearson has pointed out no attempt can 
be successful which neglects intralocal correlations, and since head characters are 
all more or less highly correlated, the reasoning employed with respect to the 
relative local differences interlocally is not applicable intralocally. It is to be 
hoped that Professor Pearson will find time to furnish anthropometricians with 
a solution. 
The numerical portion of the following tables (Tables X. and XI.) gives the 
values of the interlocal constants, // being the mean of the distribution of (RLD) m 
interlocally and (s — 1) the deviation from homogeneity of the general population 
for the various characters shown in the table. In the body of the table the 
distinguishing feature of each character is shown for each asylum, the terms 
employed to describe significant excess or defect of local means from the general 
mean being those already referred to in C. D. Fawcett's memoir, except where 
new terms are used, as defined in the text and in the " synopsis of terms." 
Where the blanks occur in the table, approximations to the general mean are 
indicated. This table should be examined in conjunction with the character maps 
and the diagrams of relative local differences. Confining attention in the first 
instance to one character at a time, it has already been noted that if the population 
had been an entirely homogeneous one, the value of s — 1 = 0 and the groups at 
the various asylums would have simply been fair random samples of the whole. 
The magnitudes of many of the relative local differences show this is not the 
case. — The values of (s— 1) for the character H and $ ), viz. 8'89 and 3'95, 
compared with their probable errors, are very large, thus indicating a very 
significant deviation from homogeneity interlocally. The values of (s — 1) for all 
