Ernest Warren 
137 
Professor Pearson* has introduced a formula for the purpose of extracting this 
"spurious correlation." If --, are two indices; Vj, v^, v^, coefficients of 
. , . /standard deviation , „ ^ . , 
variation x 100 oi x^, x.., x^, x^ respectively; r,„, r->,, v., 
\ mean / i ^ - - 
coefficients of correlation between x^ and x.,, x.^ and x^, x.^ and x^ respectively 
and p the coefficient of correlation between the indices, then 
P = 
Applying this to the present case 
B. CD '^AB '^CD f^AB '^AB 
P = 
Vab '^v\.o + V'j^s-2r, 
CD, AB f'cD '^AB 
Now, if the correlation (r^^,^^^) be supposed to disappear the expression neverthe- 
less does not vanish but becomes 
= Po, 
V v%r> + V'ab 
v^B=8-25H7, 1)00 = 12-9682, 
.-. Po = --o'^n, 
and p- po = -3200 + ■5372 = + -8572. 
Assuming that the expression p — po has a definite meaning, we conclude that 
there is a strong correlation between the ratio and the size of the body in the 
adult animal. 
(7) The Variability of the Race. 
The coefficient of variation of any organ has been defined by Professor Pearson f 
standard deviation ■ ■ , .■ n ■ i -i-. i -i i 
as X 100 ; it is thus a ratio-measure oi variability while the 
mean 
standard deviation is an absolute measure of the same. In the accompanying 
table the standard deviations and coefficients of variation are given for parents and 
offspring. 
The variability of the second generation (fourth and fifth columns, Table V.) is 
greater than that of the parents, and this we should expect since certain selective 
influences v^^ould doubtless be less active than among wild aphides. The fact that 
the mothers are weighted with their fertility will have no appreciable effect on 
the standard deviation, since as was mentioned above fertility is only slightly 
correlated with any of the dimensions. 
* Proe. Roy. Soc. 1897. 
t Phil. Trans, of the Roy. Society, Vol. 187 (1896) a, p. 277. 
Biometrika i 10 
