R. Ciiewdson Benington 
297 
imaginary surface tangential to the inner alveolar surfaces of the mesial incisors ; 
Gi = length from base of spine. The reader should consult Biometrika, Vol. I. 
p. 429 and Vol. ill. p. 201, for obscurities in different systems of measuring the 
palate length*: — G 2 = breadth of palate between the inner alveolar walls at the 
second molars ; B 2 = breadth of palate, from end to end of palato-maxillary suture ; 
GL = profile or basi-alveolar length, from basion to alveolar point. fml = length 
of foramen magnum ; fmb = greatest breadth of foramen magnum. In order to 
determine the flattening of the bridge of the nose, Dr Benington at my suggestion 
started to measure the transverse distance from dacryon to dacryon with the 
callipers and also the corresponding minimum arc with the tape. The ratio of 
the excess of the mesodacryal arc over the mesodacryal chord to the mesodacryal 
chord, i.e. DA — DC to DO forms a measure of the flattening of the bridge of the 
nose. Possibly a better measure than this ratio would be the ratio of the subtense 
of this arc to the chord and a means of determining this is discussed later. These 
two ratios may be called the Mesodacryal or more shortly the Dacryal Indices. 
It might be anticipated that they would show very considerable differences 
between European and negro races. 
P£=Bi-pteric breadth, measured from the hinder extremity of one spheno- 
parietal suture to the other. St = Bi-stephanic breadth. 
The indices calculated are : the cephalic indices 100 B/L, 100 H/L and 
100 B/H; the upper facial index 100 G'HjGB ; the nasal index 100 NBjNH; the 
right and left orbital indices 100 0 2 /0j; the palate index 100 G^/Gx) the occipital 
S I S ft nJ) 
indexf Oc.I= 100^4 x / a . , 0 3 c ; the foraminal index 100~- , ; and the dacryal 
& 3 V z4 (o 3 — o 3 ) fml 
indices, a and ft, as defined above. 
On the mandibles, where available, were measured : Wx = condylar width, or 
greatest width from outside one condyle to outside of second; W 2 = greatest width 
at angles from outside one angle to outside of other; A 1 = greatest height, from 
lowest median projection to top of alveolar margin between mesial incisors ; and 
f— distance between foramina mentalia. 
* The following comparative results are of interest : 
Length of spina nasalis posterior. 
Naqada Skulls Male 5-05, Female 4-00. Fawcett 
English Skulls, Whiteehapel ... Male 3-61, Female 3-60. Macdonell 
Negroes, Congo Male 3 - 09, Female 2-93. Benington 
Negroes, Gaboon, 1864 ... Male 3 -73, Female 3 -37. Benington 
It will be noticed that the spine is sensibly longer in the Egyptian than in the English or Negro 
series. I presume Shrubsall bas measured G x , but in many cases craniologists do not precisely define 
what they understand by palate length. 
t This index, which I now term the Occipital Index, was suggested by me to Dr Macdonell and 
misnamed by me at that date as the Cerebellar Index. 
Biometrika viii 38 
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