8 Proceedings of Royal Society of Edinburgh. [sess. 
basion, but the limits within which this difference in level varies 
will be discussed later. At any rate, the thickness of the soft 
tissues of the scalp and the hair must quite compensate for it, if 
they do not cause the vertical height, taken as described, to be 
slightly greater, as is possible, than the true basi-bregmatic height. 
It is very unlikely, however, that in more than two cases at most 
the basi-bregmatic height of the individuals under discussion 
would equal their parieto-squamosal breadth in the skull, and it 
is improbable that this would be found to be the case, could the 
skulls be measured, in a single instance. In the living men the 
mean breadth-height index of the head is 87*9, and the extremes 
are 98*6 and 77*9; the mean height is 136*4, and the extremes 
are 151 and 126 mm. 
The length of the face, measured directly with the callipers 
between the bridge of the nose and the tip of chin, varies from 
134 to 106 mm., with a mean of 122*3 mm., while the interzygo- 
matic (or bizygomatic) breadth varies between 156 and 152 mm. ; 
in two cases out of twenty the length of the face is greater than 
the bizygomatic breadth, and in one the two measurements are 
equal. The complete facial index, calculated from these two 
measurements, varies from 10T8 to 77*9, and the man with the 
shortest face, which is considerably shorter than any other in the 
series, has the lowest index, though the man with the longest face, 
which is not so much longer than any other, has only the third 
index, the breadth being equal to the length. The measurements 
for the cephalic and vertical indices are easy to take with a fair 
degree of accuracy, and do not depend upon the play of the sub- 
ject’s features ; but it is far otherwise with those for the facial 
index — an unfortunate fact, seeing that, provided all the measure- 
ments are taken by the same person, no index is of greater import- 
ance as a racial character. It makes all the difference in the 
world whether the length of the face is taken directly, or by pro- 
jection from the vertex to the nasion and to the chin and by sub- 
sequent calculation, and it makes just as much difference whether 
the features of the subject are perfectly at rest or in any way 
distorted. I am not aware in what manner exactly Dr Jprgensen 
obtained what he calls the “longitudo naso-menthalis,” or what 
degree of pressure he exerted in measuring his “ latitudo bizygoma- 
