Mathematical Contributions to the Theory of Evolution. 325 



can be extended so as to readily apply to such cases, we shall have 

 much widened the field within which we can make numerical investiga- 

 tions into the intensity of heredity, as well as much lessened the labour 

 of collecting data and forming records. 



The extension of theory required for such investigations is provided 

 in a separate memoir. It is found that the sole conditions for applying 

 this theory are : (1) that an order of intensity must exist even if there 

 be no quantitative scale ; (2) that the correlation must be supposed 

 normal. If these assumptions are made, individuals may even be classi- 

 fied into only two groups of less and greater intensity, and the corre- 

 lation still found. For example, the correlation between stature and 

 hair-colour could be found by classifying all individuals simply into 

 short and tall, light and dark haired, although for convenience of 

 judgment a medium class in each case might be introduced. For the pur- 

 pose of ascertaining the relative variability of the characters involved, 

 this third or medium class at least must be introduced and a ninefold 

 division made of the correlation table. In the introduction to the 

 present memoir the probable errors of all the quantities involved 

 are considered, and illustrations given of their values for selected 

 cases. 



(2) The bulk of the memoir, however, is concerned with the appli- 

 cation of this theory to two special cases, those of inheritance of the 

 coat-colour of horses''^ and of the eye-colour of men. 



There are three recognised chief types of inheritance : the blended 

 heritage, the exclusive heritage, and the particulate heritage, to which 

 latter two may possibly be added the reversionary heritage as a modify- 

 ing factor. 



In the blended heritage the character of the parents and the ancestry 

 in the direct line are in the average offspring mingled in certain pro- 

 portions. This heritage seems in broad lines to be described by the law 

 of ancestral heredity. 



In exclusive heritage the offspring takes the character of one parent 

 to the exclusion of that of the other. While in blended heritage, rever- 

 sion becomes very difficult, if not impossible, to distinguish from excep- 

 tional variation, here reversion becomes an easily detected feature ; 

 and studies on reversion ought if possible to deal with exclusive heri- 

 tage. Lastly, in particulate heritage, we have a mixture, not a blend, 



* The twelye tables of coat-colour inheritance have been extracted for me by 

 Mr. Leslie Bramley-Moore out of Weatherby's Studbooks. He first pointed out 

 to me the difficulties attending my method of proportioning, which led to my 

 withdrawing and rewriting this paper. The twenty-four tables of eye-colour 

 inheritance I have extracted from eye-colour data most generously placed at my 

 disposal by Mr. Francis Gralton, The arithmetic on these tables is chiefly due to 

 Miss Alice Lee, D.Sc, but Mr. L. N. G-, Filon, M.A., Mr. Bramley-Moore and Miss 

 C. D. Fawcett, B.Sc, have given us friendly aid. 



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