158 
Biometric Constants of English Brain-weights 
averages of Gladstone's groups, which were composed of post-moi'tem, work-house, 
and professional class measurements *. 
Generally we see that the woman has a rather higher capitulo-statural index 
than the man ; absolutely it is about equally variable, but its coefficient of 
variation is less. These coefficients, however, have very much the values which 
have been found for other bone measurements on man. The drop of this index 
per centimetre of stature is almost identical in male and female. 
For anthropometric purposes the index appears to be of little value, for the 
change in the diametral product with stature is given at once by the regression 
coefficient tabled in Table XIX., where the reader will also find the influence 
of age and horizontal circumference on this product. In fact, the theory of linear 
correlation shows that we should expect for a given S to be closely of the form 
= CiS' + Co, and accordingly if C« is positive we might not unnaturally anticipate 
that P^jS would decrease with S. Such an index would only be of value if Cj 
were zero, and up to the present a wide experience shows that even a sensible 
approach to zeio in C.,, if it ever does occur, is an occurrence of the most marked 
variety f . 
(12) On tJie Index = Ratio of Diametral Product to Brain-weight. 
What we have said at the conclusion of the previous article applies with a 
good deal of force to the index : Diametral Product/Brain-weight, which we will 
represent by the letter z. All the properties of it are involved in the correlations 
already tabled between the diametral product, the brain-weight, and the other 
characters. Still there is a physical side to this index which may be of some 
interest. It measures in a rough sort of way the ratio of volume to weight of 
enclosed brain-matter. We will investigate how far this index changes with 
age. All the requisite constants are given in Table XXIV. 
The results were deduced, as in the case of the capitulo-statural index, from 
the formulae : 
Vf = {100a,lzf = V/ + - 2VpV,,rp,„ (iii), 
r^A = {VprpA - Vw'>'wa) (iv), 
* If we apply the above formula to male giants and dwarfs (see Gladstone, p. 117), we find : 
Individual and Stature 
Gladstone's Value 
Formula 
Irish Giant, O'Brian, 231'1 cms. 
7-12 
6-46 
American Giant, Freeman, 205-7 cms. 
7-77 
7-59 
Dwarf from Kiel, 121-9 cms. 
11-1.5 
11-29 
Dwarf from Holstein, 97-8 cms. 
13-78 
12-35 
but quite different values have been given by other authorities for these statures and accordingly 
no great stress can be laid on such divergences as occur between the formula and " observed " values. 
+ Cf. Lewenz and Pearson, Biometrika, Vol. iii. pp. 373 and 374. 
