Researches into the theory of probabiUty. 



39 



I have extended the method here named the abridged one to the prohleni 

 concerning the dissection of frequency curves into three components. Tlie solution 

 is then dependent on a certain septic. 



It may occur also that there is reason to consider a given frequency curve 

 as the resultant of two curves of type B. Such is for instance the case with many 

 multimodal curves ohtained in botany. The ray flowers of Chrysanthemuin segetum 

 belong to this class of curves, as may be found from some statistics gathered by 

 Hugo de Veies and Ludwiu ^). During this summer I have counted in a field (where 

 peas were cultivated) the ray flowers of 1015 individuals of this flower. The result 

 is shown from the following - table. 



Ninth Example. Distribution of freciuency of ray flowers of 1015 specimens 

 of Chrysanthemum segetum. 



Number of ray flowers 



8 



9 



10 



11 



12 



13 



14 



15 



16 



17 



Class 



—5 





—3 



2 



— 1 



0 



+ 1 



+ 2 



+ 3 



+4 



Frequency 



2 



2 



3 



5 



16 



265 



189 



108 



77 



77 



Number of ray flowers 



18 



lii 



20 



21 



22 



23 



24 









Class 



+ 5 





+ 7 





+ 9 



+ 10 



+ 11 









Frequency 



57 



6() 



50 



88 



2 



1 



1 









It is very probable that we here have to do with a com[>osite frequency 

 curve, consisting of two curves of type B, the one having its summit at 13 rays 

 the other at 21. Fig. 19 shows how these com[)onents could be constituted. A 

 biological research here can give a definite answer 



For solving such a problem we can proceed in the following manner, that 

 may be considered only as a preliminary to a definite solution. 



Calling the x coordinates of the stimmits of the components Cj and Cg, and 

 designating with and Ic^ two unknown constants, we may write the frequency 

 curve in the form 



(50) F(:r) = y^,-K('^^"^i) + ^2'P.(c,--4 



where 'j>j and ']>2 with the characteristics and respectively designate two curves 

 of type B. More generally we may consider the scales coj and different (and 

 differing from unity) for the two curves. Limiting ourselves to the form (50), we may 

 consider and as known (coinciding with the coordinate for 13 and 21 ray 

 flowers in fig. 19), and hence have four constants Xj^, X^, Ic^ and to determine from 

 the frequency curve. 



') Compare the bibhography in Davenport's »Statistical Methods». 



^) If tlie collection of flowers in question should be composed in the manner indicated by 

 the figure, it follows that the offspring of plants with 23 and 24 ray flowei's would generally be- 

 long to the 13-type, whereas plants with 11, 10, 9 and 8 ray flowers should give rise to an off- 

 spring belonging to the 21-type. 



