CORRELATED VARIATIONS. 77 



cubit (18.05 inches), is about .6 inch. Let the devia- 

 tion of each value for stature from its median (67.20 

 inches) be now divided by the probable error of varia- 

 tion of stature (i. e., 1.75 inch), and each associated 

 mean deviation of cubit be divided by its probable error 

 (i. e., .56 inch). Then, by dividing each of these terms 

 for cubit by the corresponding term for stature, a series 

 of values is obtained, each representing the amount of 

 correlation between the various degrees of stature and 

 the cubit. These values would be approximately equal 

 in amount if a very large number of observations were 

 made, but with only moderate numbers they vary very 

 considerably. A mean of all of them may be called r, 

 or the average degree of correlation between cubit in 

 relation to stature. In a similar manner the individuals 

 must be split up into groups in respect of cubit, and the 

 associated deviation of stature determined. Another 

 series of correlation values will be obtained, represent- 

 ing stature in relation to cubit, of which the mean may 

 be called r a . This value is found to be approximately 

 equal to r l} and the mean of r^ and r a is called r, or 

 the correlation constant. 



The degree to which these individual correlation 

 values vary is best shown by means of a diagram. The 

 one given in Fig. 16 is taken from Professor Weldon's 

 paper on correlated variations in Crangon vulgaris* 

 and represents the correlation between the post-spinous 

 carapace length and the total carapace length in 

 Plymouth shrimps. 



The mean value of r found was .81. In this dia- 

 gram, the deviations of the organ whose value is fixed 

 *Proc. Roy. Soc., li. p. 2, 1892. 



