BIOMETRICS 155 



This o- is not the same value as q, but one can be converted 

 into the other, for cr = ^-i- 0-6745. 



There are other variations which cannot be expressed 

 in a single flowing curve, but which give broken curves 

 with two or more humps. Such curves cannot be resolved 

 into a single mathematical formula. 



By some it has even been doubted whether discontinuous 

 variations, as exemplified by eye-colour, etc., are legitimate 

 material for the biometrician, as the Law of Probability 

 applies only to cases where a great number of small con- 

 current factors is involved. 



III.— CORRELATION AND REGRESSION. 



So far we have dealt with variations of a single character 

 for a given series of individuals, and found a measure of 

 its variability. But the organism is a whole ; its parts 

 are to a great extent interdependent, characters in one 

 part of the body being often closely related to certain 

 other characteristics in a different part of the body. 

 Variations in any such character cause simultaneous 

 variations to a greater or lesser extent in the correlated 

 character. This phenomenon of " Correlated Variation " 

 is a very common one, and has been made familiar by 

 Darwin, who described many curious cases. Thus, he 

 mentions that white cats with blue eyes are generally 

 deaf ; long-haired and coarse-haired animals are apt to 

 have long and many horns ; pigeons with feathered feet 

 have skin between their outer toes, etc. A relation is said 

 to exist, according to Beddoe, between the liability to 

 consumption and the colour of the hair, eye, and skin. 



Correlation regularly exists between homologous parts ; 

 indeed, it is the cause of the great degree of resemblance 

 between corresponding organs of the body — e.g., the right 

 and left side of most symmetrically-built animals— though 

 it is known that the resemblance is rarely complete, both 

 arms or both legs normally differing slightly from each 



