148 



SECTIONAL ADDRESSES. 



and breadth and 5-5 mm. to their auricular height. All those living 

 heads or skulls, on the other hand, the auricular height of which has been 

 measured by a craniometer or head-spanner which fits into the middle 

 of the ear-holes, have had 6 mm. deducted from that height, because at 

 the Frankfurt agreement it was decided that the auricular height should 

 be taken from the top of the auditory opening. 



Columns 1, 2, and 3, therefore, give the length, breadth, and height 

 averages of the heads with the soft parts in position, and the figures in 

 parentheses represent the number of heads upon which the averages are 

 based. Column 4 is the proportion of the breadth to the length, or the 

 cephalic index. Column 5 is the sum of the length, breadth, and auricular 

 height, of which the three succeeding columns are fractions ; while 

 columns 6, 7, and 8 show the proportions which the length, breadth, and 

 height bear to the sum of the three in column 5. 



The following lists show how little difference there is between an 

 index constructed from the length, breadth, and height of the skull and 

 one constructed from the cube root of the product of the three measure- 

 ments. Whichever index is used the relative positions of the various 

 groups of skulls remain unchanged ; and for this reason I do not think 

 that the extra time and labour needed in working out the product index 

 is repaid in any way. 



