466 MR ROBERT WORTHINGTON. 



for any particular animal- deterniiae the form of this curve 

 are termed the constants of variation, or more briefly, the 

 variation of the given organ." 



As we have explained above, the constants used are M, 

 the mean, and a-, the standard deviation. In order, however, 

 to facilitate the comparison of variation, a coefficient of 

 variation (V) is subsequently formulated. 



V = fjlOO. 



That is to say, V is " the percentage variation in the mean ; 

 the standard deviation being treated as the total variation 

 in the mean." 



(2) Correlation. — "Two organs in the same individual, or 

 in a connected pair of individuals, are said to be correlated 

 when a series of the first organ of definite size being selected, 

 the mean of the sizes of the corresponding second organs 

 is found to be a function of the size of the selected first 



organ 



Consider two correlated organs A and B, of which a large 

 number of pairs are measured. The measures obtained are 

 sorted into groups, so that in each group the deviation a:; of A 

 from the mean of all A's is constant. The mean deviation 

 {y„^) of B from its mean (the mean of all B's) is determined 

 for the B's in each group, and it is found that 



ym=f{x), 



and similarly for constant values of B 



The function which is a measure of the degree to which 

 abnormality in A is accompanied by abnormality in B is 

 called the coefficient of correlation between A and B (Galton's 

 Function — rah). Its values must obviously lie between ±1 and 0, 

 according as there is complete or no interdependence between 

 the organs. In the paper on " Kegression, Heredity, and 

 Panmixia," Professor Pearson deals with the general theory 

 of correlation for n organs (where the frequency is normal). 



