248 
A First St udy of the Burmese Skull 
appreciation of racial resemblance or racial difference by treating each, character as 
an independent judgment, i.e. omitting the influence of correlation. 
Accepting this principle as a tem-jjorary working condition, we can reach for every 
pair of races, characterised by m measured characters, a single numerical coefficient; 
and can at the same time give its probable error. This coefficient will measure the 
probability that the two groups of crania under consideration are samples of one 
and the same population : it may be termed the Coefficient of Racial Likeness (C.R.L.). 
Such a coefficient will enable us to compensate for the smallness of a cranial series 
by measuring a large number of characters. The advantage to the craniologist 
will be considerable. This coefficient is defined as follows: 
Let m characters be measured, and let the sth character in the first race have 
Mg for mean and Og for standard deviation, these two constants being based on Ug 
individual measurements. Let the corresponding characters for the second race 
be ilf/, Og' and ng'. 
Then if the two races were really samples of the same population, the following 
expression should be sensibly zero : 
[ S(3Ig~-Mg'f \ 
[ Ug Hg ) 
and the probable error of its deviation from zero will be -67449/^2?^. 
Now, for most cranial samples we have not adequate numbers to enable us to 
determine ag and a/ : but there is not a very great difference in variability between 
one race and another. It will therefore suffice, for a first approximation, to put 
o^s = o's' == the value found for the standard deviation of this character in the 
longest series of homogeneous crania available. It is only needful to use the ap- 
propriate a for the appropriate sex. 
Thus our coefficient of racial likeness becomes: 
•67449 
V2m 
I have calculated the C.R.L. for the Whitechape! Plague Pit Crania of the Biometric 
Laboratory which were measured by Macdonnell* ; also for the Long Barrow British 
of the Oxford University Museum as measured by Schusterf . I have also compared 
the Whitechapel Crania with the measurements of the skulls of French prisoners 
dying in Germany in 1871*. I have compared Bavarians* with Wlirtembergers* 
and Prehistoric Egyptians as measured by FawcettJ with Congo negroes measured 
by Crewdson Benington§, using for these comparisons male skulls only. 
The table on p. 249 gives us at once a much better appreciation of the degree 
of resemblance between the seven races they represent than could have been obtained 
from a comparison of seven columns of means for twenty to thirty individual 
characters. 
* Blometrika, Vol. ill. ij. 208. f Ibid. Vol. v. p. 104. 
t Ibid. Vol. I. p. 426. § Ibid. Vol. vm. p. 298. 
C.R.L.= l^{3V„r^--^-T[- 
m [ng + ng \ cxg ) ] 
1 ± 
