106 Relationshq) of IntdU<jence to Size and Shape of Head 
(ii) The measurement and observation of considerably more than 5000 school 
children. This material was collected by the aid of many teachers, and with 
assistance from the Government Grant Committee*. 
The present investigation deals with the girls as well as the boys, who alone 
were considered in the earlier papers. Further, it gives the results in as complete 
a form as they admit of being tabulated in, and reduces them therefore by a more 
ample theory than was previously possible. We have investigated the mean and 
variability of each grade of intelligence for each measurable character. From 
these means we have deduced the fundamental constant, the correlation ratio rj, 
which becomes identical with tlie coefficient of correlation when the regression 
is linearf. The value of rj must of cour.-<e depend to some extent on the nature 
of the intellectnal grading, but the results now obtained are : (i) in good agree- 
ment with those of the preliminary papers deduced by a totally different statistical 
process, (ii) in good accordance with each other. 
While thej' largely extend, they yet in every respect confirm our previous 
main conclusion that : While there exists a slight but sensible relation between 
size of head and intelligence, there is no possibility of using this relation to make 
even rough individual predictions. 
In the present memoir the full results are for the first time published, and 
there will be found some discussion of each character taken in order. 
(2) On the Expression of Intelligence hy a Quantitative Scale. 
In dealing with the Cambridge graduates we classified our material into four 
grades only : (i) First Glass Honours, (ii) Second Class Honours, (iii) Third Glass 
Honours, and (iv) Pass Degrees. 
In the case of the school data we classified into (i) Quick Intelligent, (ii) Intelli- 
gent, (iii) Sloiu Intelligent, (iv) Slow, (v) Sloio Bull, (vi) Very Bull. 
Now, for the purposes of determining the correlation ratio between intelligence 
and the physical characters, it is unnecessary to make any assumpti<m as to the 
extent to which these grades fit into any quantitative scale. But in order to 
exhibit the results graphically, it is needful to have some scale of intelligence 
to plot our average physical characters to. We have accordingly selected, as the 
normal scale of intelligence, that which would be given if the frequency distribu- 
tion of intelligence followed the normal or Gaussian curve of errors. Whatever 
the true scale may be, it can only be a more or less — probably less — distorted 
form of this scale. Such horizontal distortion has no effect on the value of the 
correlation ratio for the plotted physical character, and an a priori justification of 
* Fuller particulars as to the schedules and method of collectiug will be found in my Huxley 
Memorial Lecture : see Bionietrika, Vol. iii. pp. 131 — 190. 
t " Mathematical Contributions to the Theory of Evolution, XIII, On the Theory of Contingency 
and its Eelatiou to Association and Normal Correlation." Drapers' Companij Research Memoirs, 
Dulaii and Co. 
