J. I. Craig 
69 
people with the ancient Egyptians, and it is accordingly necessary to consider how 
far this is possible. 
Deniker* says: "La mesure principale, 1'indice cephalique, ne parait pas tou- 
jours correspondre sur le crane et sur le vivant. A priori la tete a l'etat vivant 
devrait avoir un indice un pen plus fort que la crane, les muscles de la region 
temporale etant plus epais que ceux de la region sus-occipitale et frontale ; 
cependant, les experiences faites a ce sujet sont contradictoires. D'apres Broca 
il faut soustraire deux unites a 1'indice pris sur le vivant pour obtenir 1'indice sur 
le crane ; c'est encore l'opinion de MM. Stieda et Houze', et d'un grand nombre 
d'anthropologistes, tandis que MM. Mantegazza et Weisbach preconisent la 
reduction de trois unites ; Virchow et Topinard n'en admettent aucune 
Cependant d'une facon generale on peut admettre la difference de deux unite's 
entre les indices du crane et du vivant." 
(8) It is reasonable to expect that there may exist a correlation between the 
shape of the head and that of the skull, and on certain assumptions the correlation 
may be demonstrated. 
Let I, b, be the length and breadth respectively of the head ; 
X, /3, the amounts to be subtracted from the length and breadth to obtain these 
measurements for the skull ; 
y, x, the cranial and cephalic indices respectively. 
Then by definition 
x = 100b/l, and y = 100 (b - /3)/(l - X) = (1006/0 * (1 - - V0- 
Since the magnitudes of ft/b and of X/l are of the order of 8*5/144 and 7/190 
respectively, we may write this equation : — 
y = x (1 — /3/b + X/l) — other terms. 
The other terms will be small, and may be allowed for by assigning a mean value, 
so that the equation becomes 
y = mx — c, 
where m = 1 — /3/b + X/l. 
The ratio of /S/6 is in general greater than that of X/l, so that m is a fraction 
slightly less than unity. In Egyptian bodies, Dr Douglas Derry has found that 
/3 = 8'5, X=7, 6 = about 144 and 1= 191 f. Hence in this case m = 0"976 approxi- 
mately, and the reduction is about 0 - 024« or about two units. 
(9) Since this theoretical reasoning suggests that the formula y = mx — c is 
capable of giving results not inconsistent with practice, I have assumed its truth, 
and have used it to find average values of m and c. Denikerj has given 43 cases 
* Races et peuples de la terre (Paris, 1900), p. 86. 
t Elliot Smith, loc. cit. p. '25. [Dr Derry' s results seem rather smaller than those for Europeans : 
see Lee and Pearson, Phil. Trans. Vol. 196, A, 1901, p. 250 et seq. Cf. Gladstone on post-mortem cases, 
Biometrika, Vol. iv. p. 110 et seq., however. Editor.] 
X Loc. cit. pp. 667 et seq. 
