22 Proceedings of the Royal Society of Edinburgh. [Sess. 
Numbers 165 to 171 and Number 183 are from Sir William Turner’s 
“ Decorated and Sculptured Skulls from New Guinea ” (20). 
Numbers 172, 173, 174, and 184 are from some hitherto undescribed 
decorated New Guinea skulls in the Anatomical Museum of the University 
of Melbourne. 
Numbers 175 to 182 and 185 to 191 are from Dorsey and Holmes’ 
“ Observations on a Collection of Papuan Crania ” (21). 
In view of the limited number of Tasmanian crania available, we deemed 
it unnecessary to multiply the numbers of Papuan crania, though it would 
have been easy to do so, as, for example, by incorporating Meyer’s (31) 
hundred and thirty-five Papuan skulls, and others. 
Such being the material, it now becomes necessary to say something of 
the biometrical methods adopted in its examination. It is unnecessary for 
us to make any attempt to extenuate the employment of biometrical 
methods in a craniological investigation, since the magnificent work of 
Professor Karl Pearson and his school has proved that no other method can 
now be legitimately employed in such work. Nor is it necessary for us to 
make any examination of the literature of the method to be found in the pages 
of Biometrika, and also scattered throughout the pages of the Philosophical 
Transactions of the Royal Society of London ; for whilst all of that work is 
important, but little of it has a direct bearing on the subject-matter in hand. 
Of the special adaptation of Professor Pearson’s methods to the present 
research, the following is an outline 
The principal quantities determined are the means, standard deviations, 
coefficients of variation, and, in particular, the coefficients of correlation, 
these last being taken as measures of the constancy of type in the respective 
groups of crania. 
In comparing this constancy of type, or purity of any two groups of 
crania, the coefficients of correlation of a selected pair of measurements, as, 
for example, length and breadth, are calculated, and the difference between 
the respective values in the two groups under consideration, together with 
the probable error of that difference, is determined. A difference greater 
than its probable error indicates a real difference, and not one due merely 
to random sampling ; and as the ratio of the difference to its probable error 
increases, so also does the probability that the difference is a real one, but 
much more rapidly. A discussion as to which pair of characteristics should 
be chosen for this purpose follows later. 
In the actual calculations, provisional means, which are whole numbers, 
are in all cases initially adopted, to be afterwards suitably corrected to give 
the true values. In this way whole numbers only have to be manipulated. 
