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A Study of the Negro Skull 
these two points, i.e. the geodesic. This 'false' margin gives usually abrupt 
changes of curvature at the terminals of the upper and lower orbital rims. I will 
term this the ' geodesic ' method. 
In either (i) or (ii), — which endeavour to maintain the Frankfurt Concordat 
idea of greatest breadth — the greatest measurement was to be taken, wherever 
found, an end being on the imaginary margin thus denned. While Fawcett 
used(i), Macdonell tells us he used (ii)*. He declares that in practice it is identical 
with following the curvature of the lower orbital rim to its furthest inward 
poiut, — but this is limited again by the statement that he does not cross the 
naso-frontal suture. This really appears to be not (ii) but a third definition, 
namely to produce the lower orbital rim from its last sensible point without change 
of curvature up to the naso-frontal suture and to measure from some point on this 
production. I admit that in many cases there is little change of curvature at the 
terminal of the lower orbital rim when the geodesic is drawn as described in (ii), 
but I do not think Macdonell's method is absolutely the same as Fawcett's geodesic 
method especially for male orbits, and thus we have new difficulties in forming 
racial comparisons. 
In Fawcett's paper the differences obtained in the orbital breadth by using 
(i) and (ii) for one series of crania are given as 1'9 mm. for males and 1*6 mm. for 
females. What difference, however, is there between the curvature method and 
the lacrymal point method ? The extraordinary uniformity of the breadth measured 
by the lacrymal point method in prehistoric Egyptians, Theban mummies and 
modern Copts (see Biometriha, Vol. I. pp. 426, 427) shows us that we may safely 
take for Egyptians, prehistoric to modern, the difference between the curvature 
method and the lacrymal point method as 4'8 mm. for males and 4'3 mm. for 
females. Hence to reduce Fawcett and Macdonell's measurements to a lacrymal 
point measurement we must roughly subtract 4'8 mm. and 4 3 mm. from Fawcett's 
values and 2 - 9 mm. and 2 - 7 mm. from Macdonell's values; the orbital index will 
then have to be taken as a ratio of means. I believe that this is the best 
that can be done ; I should have preferred to try and get a true orbital index as 
defined in the Frankfurt Concordat, but there are too many series to modify and 
too little is known of how they have really been measured. 
Dr Benington followed Macdonell in his orbital measurements and accordingly 
his maximum breadths 0 1 have to be reduced by 2 9 mm. and 2 - 7 mm. respectively 
for male and female. I have reduced his averages by these and recalculated the 
orbital indices from the modified averages. 
Before we look at the table thus modified we may compare the English 
(Macdonell) and Negro (Benington) results which were presumably measured by 
practically the same methods : 
* Biometriha, Vol. in. p. 201. 
