26 
Proceedings of the Royal Society of Edinburgh. [Sess. 
grounds that, from the evidence above quoted, the greatest stress must be 
laid upon the length-breadth coefficient of correlation, and the least upon 
that for breadth-height. 
An examination of our figures under the three heads for the races 
examined will show that they confirm Pearson and Lee as regards the 
relative stress to be laid upon the coefficients of correlation for length- 
breadth, height-length, and breadth-height. 
Turning lastly to the examination of these coefficients of correlations 
for the particular objects with which this research was undertaken, namely, 
the examination of the relative purity of type of the Tasmanian, Australian, 
and Papuan, our final results are set forth in Table XII. 
In this table the probable error of the difference of any two coefficients 
of correlation is calculated in the usual way as the square root of the sum 
of the squares of the probable errors of the coefficients themselves. 
In Table XI. of the coefficients of correlation for breadth-height and 
height-length it is seen that the figures apparently indicate a greater con- 
stancy in shape of head for the Papuans than for the Australians, being 
practically the same as for the Tasmanians on the first count, and intermedi- 
ate to the Tasmanians and Australians on the second. But these figures 
must be read in conjunction with their respective probable errors (see 
Table XII.), when it is at once seen that in all those cases where the differ- 
ences as taken have negative values they are quite overshadowed by their 
probable errors, and therefore the chances are that such differences are due 
to random sampling, and consequently are not indicative of any real differ- 
ence at all. 
With regard to the correlation of breadth-height, the coefficients for all 
three races are, within the limits of the probable errors, constant. 
In the case of height-length the Tasmanians show a coefficient higher 
than for either of the other two races, the difference in each case being 
greater than the probable error. On this count, therefore, the figures show 
that the Tasmanian is of a more uniform type than are either of the other 
two races. 
As might naturally be expected from the evidence already adduced as to 
the relative values of breadth-height, height-length, and length-breadth, the 
last-mentioned shows, in our results, the most striking differences. The 
length-breadth coefficient of correlation for the Tasmanians exceeds that for 
the Australians by from two to three times the probable error of the excess, 
and the excess of the Australian coefficient over the Papuan coefficient is 
considerably greater than its probable error. 
It follows from this investigation that, for the three races considered, 
