1903.] 



to the Theo ry of Evolu tion. 



289 



we are not dealing with homotypes at all, but with homologous parts, 

 and we wish to reduce them to homotypes by correcting for differ- 

 ences between them due to growth or to situation on the organism. 



I propose at present to deal only with problems (i) to (iii), not 

 because (iv) does not admit of theoretical treatment, but because we 

 have not thus far obtained data to illustrate satisfactorily the correlation 

 between character and the immediate environment of the individual 

 organism. Experimental determinations of homotyposis in plants, 

 when the individuals are subjected to a graduated environmental 

 scale, e.g., in depth of soil or quantity of moisture allowed would be 

 fairly easy to carry out, and most interesting in result. I hope it may 

 be possible to arrange experiments of this kind for the coming sum- 

 mer. We can then illustrate the fourth proposition from actual obser- 

 vation, and the publication of its theoretical solution will be of greater 

 value. 



(2.) To find the correction to be made to the apparent homotypic correla- 

 tion when the pair of homologous parts are differentiated from each other 

 by their periods of growth. 



Let x and y denote the characters in the two homologous parts 

 quantitatively determined, and t h t 2 their respective periods of growth. 

 Then we have four variable quantities x, y, ti, t 2l no one of which 

 fixes absolutely any other, for individuals will have different charac- 

 ters even with the same period of growth. The proposition accord- 

 ingly reduces to this : What is the correlation R between x and y for 

 constant values of the variables, i.e., selected values of, t\ and t 2 % 



This problem is answered in formulae (lviii), (lix) and (lx) of my 

 memoir : "On the Influence of Natural Selection on the Variability 

 and Correlation of Organs."* 



Let us write in those formulas t Y for the subscript 1, t 2 for 2, x for 3, 

 and y f or 4 ; we have at once 



v 9 .o 1 - *V, 2 - Tjctl - r x , 3 2 + 2r tlti r xtl r xh ( 



y 2 _ '2 1 ~ r ht? - *W ~ r*t* + 2r ht2 r yh r ytl ( . { 

 ~y~ — °y i _ 2 ^ h 



•m v p ^ ^ r -v ( 1 - *V, 2 ) - r **i 7 Vi ~ r *h r vk + r h h (r xtl r yh + r yh r xh ) ({ . {) 



l ~ r hh 



Now if we deal with direct and not cross-homotyposis, i.e., with the 

 correlation of the same character in two homologous parts, we can put 

 these results more simply. We in this case render our correlation 

 tables symmetrical by entering each one of a pair of homologu.es first 

 as an x and then as a y. We may then write 



VOL. LXXI. 



* ' Phil. Trans.,' A, vol. 200, p 30. 



Y 



