38 Mr. EK. C. Snow. Correlations between Collaterals [June 3, 
a geometrical progression, and thus obeyed the fundamental principle 
of the Law of Ancestral Heredity, as deduced from observations on man 
and other living forms. 
(2) It is difficult to believe that the characters dealt with in the case of 
Mendelian investigations on animals can be largely affected by environment, 
but it is easy to allow for this influence by the method of partial correlation. 
If, in an investigatiun on any given character, the subscript 1 denote 
offspring, 2 the ancestor in any generation, 3 the offspring’s environment, 
and 4 the ancestor’s environment, then the correlation between 1 and 2 for 
constant 3 and 4 is given by 
sapie = rie(L ree!) Pasta? 1a'eg 1 M34 (T4728 + 13724) 
{ 1 — 123” — 134" — Toa? + 2 729/'34724 fF? { L—113°@— Tg? — 734? + 2713154714}? 
If we suppose the environment of a given stock to remain constant, this 
reduces to the simple form 
1—é’ 
where e is the correlation between character and environment.* This 
should be absolutely true for pairs of brothers reared in the same home 
e912 = 
conditions. 
Many investigations into the value of e for a great variety of characters 
in man have been carried out in the Statistical Laboratory at University 
College, and these show that the value of e is remarkably small. Its 
average value is 0°03, and it rarely reaches an intensity as high as 0-1. It 
can only introduce a second order correction into the correlation, and one 
well within the limits of the probable error of the determination. If e 
were 0:1, the change in fraternal correlation would only be from 0°50 to 
0-495. Thus, until the number and accuracy of observations have reached 
a much higher stage, the influence of environment need not be considered. 
(3) A noteworthy conclusion reached by biometric workers by actual 
measurements on man is that the correlation of brothers is not much 
larger than the correlation of parent and offspring. A priori, we 
* A German writer has recently given a formula for correcting fraternal correlation 
for the influence of environment. It differs from the above form, and consists in a 
factor multiplying 7,.. He assumes that the high values found for the parental and 
fraternal correlations in man as compared with those to be expected for somatic 
characters in the Mendelian hypothesis are due to the neglect of the influence of 
environment by the biometricians. He was probably unaware of the amount of attention 
which has been given by the biometric school to the determination of environmental 
correlations and to the comparison of the correlations for characters where environment 
is likely and unlikely to produce effect, e.g. heredity in stature ard forearm with heredity 
in eye colour and cephalic index. See W. Weinsberg, ‘ Zeitschrift fiir Vererbungslehre ’ 
1909, vol. 1. 
