288 Prof. K. Pearson. Mathematical Contributions [Jan. 20, 



" Mathematical Contributions to the Theory of Evolution. — On 

 Homotyposis in Homologous but Differentiated Organs." By 

 Kael Peaesox, F.E.S., University College, London. Be- 

 ceivecl January 20,— Head February 19, 1903. 



(1.) In the paper on " Homotyposis in the Vegetable Kingdom,"* I 

 defined homotypes as ;£ undifferentiated like organs." In the course 

 of that paper, I endeavoured to indicate that I was not unconscious 

 of the influence of age, local environment, and position upon organism 

 in modifying homotypic correlation. The object of my memoir, how- 

 ever, was to obtain some general appreciation of the average intensity 

 of individuality in living forms, and to see if it approached the average 

 value of fraternal heredity in plant or animal life. For this purpose 

 I selected such material as was readily available, indicating the series 

 where I thought differentiation of a sensible amount was present owing 

 to the age, the situation, or the environment factors. 



From the standpoint of theory, however, we are not compelled to 

 adopt a mere indication of this kind. As soon as we can correlate 

 between: (ft) age and the quantitative character of the homologous 

 organs, (b) situation on the organism and this same character, or (c) 

 local environment and the character, we can allow for the differentiation 

 of homologous parts, or reduce them to pure homotypes. In other 

 words, homotyposis can be deduced from differentiated homologous 

 parts, if we correct for the differentiation due to (a), (b) or (c). The 

 test for the existence of such differentiation is simply the presence or 

 absence of the corresponding correlation. 



We have accordingly the following problems to find solutions for : — 



(i.) To find the correction to be made to the apparent homotypic 

 correlation, when the pairs of homologous parts are differentiated from 

 each other by their periods of growth. 



(ii.) To find the correction to be made to the apparent homotypic 

 correlation, when each pair of homotypes is differentiated by a common 

 period of growth from other pairs of homotypes. 



(iii.) To find the correction to be made to the apparent homotypic 

 correlation when the pairs of homologous parts are differentiated from 

 each other by situation on the organism. 



(iv.) To find the correction to be made to the apparent homotypic 

 correlation when each pair of homotypes is differentiated by the 

 environment of its organism from other pairs of homotypes. 



It will be seen that in problems (ii) and (iv) we are dealing with 

 true homotypes, but that the homotypic factor requires modifying for 

 the influence of age or environment on the organism. In (i) and (iii) 



* < Phil. Trans.,' A, vol. 197, pp. 285—379. 



