EVOLUTION 397 



slope of AB, is termed the correlatioti, and the letter r is 

 conveniently used to represent it. In our case of the 

 poppy capsules r = .56. We should accordingly say that 

 a correlation of .56 represents the degree of resemblance 

 of like parts in the individual poppy plant. 



Now theory shows us that if we take the standard 

 deviation of an array ^ about the corresponding point on 

 the line of regression, then the mean value of the ^ for 

 all the arrays will be cr{\ —r-') ; but further, if the regres- 

 sion be truly linear, and we assume certain hypotheses as 

 to the origin of variability,^ then (7 sj \ — r'^ is the standard 

 deviation of each array about its mean, or this is the same 

 for all arrays. In other words, we may in this case obtain 

 the variability of an array from the racial variability by 

 multiplying by the quantity ^i — r-. Thus the co- 

 efficient of correlation determines the reduction in varia- 

 bility as we pass from the general population to a special 

 array of it. Clearly, when the correlation is very high, i.e. 

 AB nearly coincides with DE, or r is nearly unity, then the 

 variability of the array becomes very small, or the distri- 

 bution concentrates itself along DE. Thus the higher 

 the correlation, the more certainly we can predict from 

 one member what the value of the associated member 

 will be. This is the transition of correlation into causa- 

 tion. Causation tells us that B will accompany A ; 

 correlation tells us the proportion of cases in which B 

 accompanies A, and as r approaches unity this will be 

 more and more nearly 100 per cent." 



Now so far we have been dealing with two associated 

 like organs, two poppy capsules or two beech leaves from 

 the same individual. But a little reflection will show the 

 reader that this is quite unnecessary. In the diagram of 

 the regression line on p. 395 our two scales are identical, 



1 These hypotheses are {a) that variability takes its rise in an indefinitely 

 great number of groups of causes ; (l>) that such groups of causes are in- 

 dependent of each other ; and {c) contribute only a small amount individually 

 to the total variation. These are the foundations of the Gauss-Laplace 

 theory of deviations, which we may possibly look upon as a first approxima- 

 tion to an exact theory of variability. 



2 See also footnote, p. 407. 



