194 
On Criminal Anthropometry 
Height and Head Breadth on which it is based. Comparing it with the worst 
value obtained above, "1562, we see that even in that case the difference is only of 
the order '02, or of the probable error of sampling. 
(9) I have next to find the standard deviations and means of the two 
characters ; this I shall do by applying the method explained in Professor Pearson 
and Dr Lee's memoir "On the inheritance of characters not capable of exact 
quantitative measurement" {Phil. Trans. Vol. 195, A., p. 82). Let us suppose our 
16-fold table reduced to a 9-fold table, and let n-^, ria, n^, the three classes of one 
character which are thus formed, be represented by the areas of the normal curve 
in the accompanying diagram. 
«2 
In all our investigations, the mean will fall within the area nj. Let Ox^=pi, 
Ox^—ps, be the distances of the mean from the boundaries of 112] then -1-^3 in 
absolute measurement is known, =r], say, being the range of the class n^. 
Remembering that the equation to the normal curve is of the form 
(T V27r 
where N is the total frequency and cr the S.D., we have 
where ^ = /^g = ^ . 
cr a 
Now the left-hand side is known, and from a table of the areas of the normal 
curve and are found. Therefore as o- = ^LlLEi = . ^ , , the standard devia- 
hi + % hi + /I3 
tion is known. Also, as pi = hicr, the distance of the mean from the left-hand 
boundary of n^, and therefore the mean itself, are known. 
To find the probable error of cr, we have 
77 ,5. 7) (Bhi + 
" — ocr = — 
hi + h,' ' ' {hi + h,y ■ 
