1903.] 



to the Theory of Evolution. 



313 



Thus ?; diverges much from r pc and 2 M from zero. Indeed, a glance at 

 the diagram shows how far we are from true linear regression. If 

 we use Vpc as above instead of rj, i.e., (ix) instead of (x), we have 



R = 0-3511, 



a value very much below the actual value. This illustration will 

 suffice to emphasise the importance of testing the actual curve of 

 regression before we assume it to be linear and use equation (ix). 



(10.) The subject of differentiation due either to position or age is, 

 of course, a difficult one, but it does not seem at all beyond biometric 

 treatment. The greatest difficulty which it seems to me will have to 

 be encountered is not that of discovering and allowing for differentia- 

 tion due to serial position, but in ensuring that when this has been 

 allowed for, there is not remaining an organic correlation due to the 

 necessity of adjacent parts "fitting." On this account it is most 

 desirable that as large a number of homotypes as possible shall be 

 taken, so that the part of the correlation due to the homologous parts 

 having to fit, or, indeed, to serve a common end, should be reduced to 

 as small a quantity as possible. For example, if we suppose adjacent 

 whorls to have their number of branches influenced by an organic 

 relationship, this result will only bias nine out of the forty-five pairs we 

 should form in dealing with ten whorls. The question of separating 

 organic from homotypic correlation is one that I hope to return to at 

 a later date. Meanwhile the present paper will suffice to indicate how 

 partial correlation coefficients enable the biometrician to free himself 

 from the differentiation between individuals due to different periods 

 of growth, or to different positions on the organism. 



In conclusion I should like to thank Dr. Alice Lee and Mr. F. E. 

 Lutz for aid readily granted at one or other stage of this investiga- 

 tion. 



