316 
A Study of the Negro Skull 
the chord and an approximate formula suffices. This is not true in the case of 
the nose, although more nearly true in the case of the Negro than in that of the 
European nose. For this reason a circular arc is by no means a good approximation 
to the nasal bridge. In fact in certain noses the subtense is more than half the 
chord and accordingly to use a circular arc supposes more than a semicircle ! After 
an examination of moulds of the bridge of the nose, it seemed to me that the 
bridge of the nose could be fairly closely represented in section by the common 
catenary with axis in the median plane. We might thus pass from arc and chord 
to subtense and chord by a simple table without much trouble and with sufficient 
accuracy for practical purposes. 
The equation to the common catenary is 
y = ^c{e c + e ~°), 
c being the parameter. 
Therefore i? : = arc/chord = \ (e c - e c ) 
if u be used to denote xjc. 
R 2 = subtense/chord = (y — c)/'2x 
= i2j x \ tanh \u. 
Hence if we use tables of the hyperbolic sine and cosine we can determine 
corresponding values of R 1 and R>. A table of corresponding values is given 
on pp. 338—9*. 100 (R 1 - 1) is the .Dacryal Index (3, and 100 R. 2 the Dacryal 
Index a, and the table is entered by these indices a and /3. In other words we 
have a means of passing from the measured arc and chord to a theoretical sub- 
tense. There is little doubt that the ratio of this theoretical subtense to the 
actual chord gives a fair approximation to the real shape of the bridge of the 
nose. 
It will be seen at once that our mesodacryal indices a and /3 include more than 
the nasal bones, for the nasal processes of the superior maxillary bones also con- 
tribute. But from the standpoint of the physiognomy of the living it is more than 
doubtful whether it is the form of the nasal bones only which is concerned in our 
classification of the nasal bridge — a feature which most certainly plays a large 
part in racial appreciation. In order to judge fully of the differentiation in this 
character between Negro and European races we have also measured the nasal 
bones alone, and obtained the index introduced by Merejkowsky, and which I 
venture to term the Simotic Index-f. In this case the shortest horizontal chord 
* Computed by Miss Julia Bell, M.A., from Gudermann's, Glaisher's and Newman's tables of the 
hyperbolic functions. 
t C. de Merejkowsky : " Sur un nouveau caractere anthropologique," Bulletins de la Societe d" Anthro- 
pologic, T. v. Troisieme serie, Paris, 1882, pp. 293 — 304. Merejkowsky calls this index " indice de la 
racine du nez." 
