108 



such data are considered, to which the calculus of probabilities (fre- 

 quency-curves, etc.. l ) can be applied, is a well-known fact (binomial 

 coefficients, etc.) This symmetry manifests itself for instance in the 

 numbers obtained by Gr. Mendel in his famous researches con- 

 cerning the heredity of properties in plant-hybrids, and in the 

 corresponding work of several other investigators. 2 ), 



Instances of this kind may easily be augmented; however it is 

 not our purpose to go into particulars here, but simply to draw the 

 attention of the reader also to these occurences, which represent 

 more especially a chapter of the general theory of numbers. 



About the symmetrical arrangement of some organs in plants, 

 a problem which is closely related to the kind of problems men- 

 tioned here, we will say something at the end of the next chapter. 



!) J. C. Kapteyn, Skewfrequency-curves in Biology and Statistics, Gro- 

 ningen, (1916). 



2) Gr. Mendel, Versuche ii. Pflanzenhybriden, Verb, naturf. Verein. Brunn, 

 4. 3-^7 (1865); Ostw.. Klass. d. ex. Wiss. No. 121. (1901), p. 17; Cf. also: 

 J. Tammes, Rec. des Trav. botan. Neerl. 8. 232. (1911). 



