Miscellanea 
183 
If we suppose a number of variates /< to be uucorrelated with each other, but correlated 
''ill) '02) •■■ '"iitt with another variable .Iq, then wc have from the determinant as given below 
A = 
1 
'ill) 
= - ''nr - 'W' - • ■ • ''nn)^a 
'•,«, I , 0 , ... 0 
'•2(1) 0 , 1 , ... 0 
»Vu) 0 , 0 , ... 1 
. • . R'^ = '•]„- + rjo^ + . . . + 'n..^ 
or ll = sjn J v+'-^+^-^'-o'^ . 
Therefore, if n variable.s, uncorrelated among themselves, be correlated with an additional 
variable, it is necessary that the root mean square of their correlations should be less than 
— AVe see therefore that it must either be impossible to find a large number of variables 
uncorrelated among themselves, which are correlated with an additional variable, or else their 
correlations with this variable must be extremely low. The last result shows us the fallacy 
of supposing that correlations are simply added together for a combined effect ; clearly when 
the variates are uncorrelated among themselves, we add by the sum of the squares. For 
example, if roi = >'o2=...= = "03 07ie hundred such variables would only raise R to "30. On 
the other hand if the variates are highly correlated togethei', say e=-81, an indefinitely great 
number of such variables would only raise the multiple correlation to '0333, if the individual 
correlation were '0300. 
We are now in a position to apply our results to the problem of the relative intensity of 
heredity and environment. This problem has been singularly misunderstood especially by the 
2)opular exponents of Eugenics. Some illustrations of this may Ije given here. Major Leonard 
Darwin writes as follows in the Journal of the Eugenics Education Society : " It is impossible 
to compare heredity as a whole with environment as a whole as far as their effects are 
concerned ; for no living being can exist for a moment without either of them*. Moreover, 
in order to compare two things so as to be able to use the words more or less in connection 
with such a comparison, we must have a common unit of measurement applicable to them 
both. But what is the unit by which both heredity and environment may be measured ? 
I myself have no idea. May we not be discussing questions as illogical as enquiring what 
portion of the area of a rectangle is due to its width and what to its length I Is it ever wise 
to use words in scientific literature without endeavouring to attach a definite meaning to thein\ ? 
It is hard to conceive a paragraph of the same length more full of evidence of complete 
ignorance of the methods ased in modern science for comparing correlated variates ! Yet it 
goes out as the opinion (jf the President of a Society which is endeavouring to spread the 
scientific doctrines of Eugenics among the people I Major Darwin begins by stating that it is 
needful to have a common unit of measurement in order to compare two variates. To begin 
with we are not comparing two things, but we are comparing the influence of two things on 
* There would in ovu- sense be no heredity if the average child born to noteworthy parents was equal 
to the average child of the whole community. Yet it is perfectly easy to understand how living beings 
could exist under such a law of reproduction. Major Darwin seems to be confusing two things, the fact 
that a man is born true to bis species, aud the fact that he resembles his immediate ancestry. It is 
the latter fact only which concerns us when we compare heredity and environment, i.e. how variation of 
immediate ancestry affects the individual's physical or mental characters. But without such heredity 
individuals might quite well exist. 
t The Eugenics Review, Vol. v. p. 152. The italics are mine. 
