W. R. Macdonell 
209 
3'175 to obtain a true comparison for height, and find s = 1'14.32, which is still the 
greatest vahie of the 7 column. 
On this principle, then, the order is 1st, Face Breadth; 2nd, Head Breadth; 
3rd, Finger; 4th, Head Length; 5th, Foot; 6th, Cubit; and 7th, Height; it will 
be observed that this is the order of the standard deviations of the characters, but 
differs widely from the Scotland Yard order. 
I think, however, that JA/R is the correct criterion. We cannot read height 
to the same accuracy as head length, s for height = 3'6297, and for head length 
•5220, but head length is read to |- mm. and height to in- Now head length is 
hardly likely to be correct to more than 1 mm. or height to \ inch = 6 mm. say, or 
even to |-inch = 12 mm. ; hence I doubt if stature with aii s of 3"6 is really better 
than head length with a range of "5. The right piinciple seems to be to suppose 
each organ on its own s.D. equally useful, and then judge its efficiency by the 
extent to which that s.D. is altered by selection of the other characters. 
(19) Professor Pearson has pointed out to me that the ideal index characters 
would be given if we calculated the seven directions of uncorrelated variables, that 
is, the principal axes of the correlation "ellipsoid." Thus, given ijc^, a\, ... 
correlated variables, the seven uncorrelated variables are : 
Xi = ^ii^^i + li2^2 "h • • • H" ^17*7 
^2 ~ ^2V^1 "I" ^22^^^ 4" • • . 4" ^27*^7 
&c. &c. 
where the I's give the directions of the principal axes, and X^, X.,, ... Xy would be 
the proper index functions to identify criminals by if we have nothing better than 
the present correlated characters to work with. Of course this necessitates a 
preliminary determination of 49 numerical multipliers, but if these were once 
calculated, the uncorrelated characters of a criminal could be easily found from the 
measured correlated characters, and his identity established from an X-cabinet, 
into which we might enter m any order. I propose to return in a later paper to 
this calculation. 
(20) Reconstruction of Height from a knowledge of Finger, Cubit, and Foot, for 
medico-legal purposes. 
I now propose to consider in greater detail the four characters which have very 
high correlation, viz., Finger, Cubit, Foot and Height. For these four. 
A = 
1- -84638 -75871 -66084 
1- -79699 -79986 
-79699 1- -73636 
-84638 
-75871 
-66084 
•79986 -73636 1- 
■031586, 
Biometrika i 
19 
