No. 517] A BIMODAL VARIATION POLYGON 



with Chrysanthemum segetum. Pearson 7 in the first of 

 his "Mathematical (Vmtributions to the Theory of Evo- 

 lution" deals with the mathematical analysis of com- 

 posite frequency curves. 



Dimorphism referable to peculiar environmental con- 

 ditions has received considerable attention, but unfor- 

 tunately quantitative data are not numerous. For 

 seasonal dimorphism in Idotheca, CJadzikiewicz 8 has pub- 

 lished some figures which yield very different polygons 

 for the body length of September and March females. 



The above cases are illustrative merely and make no 

 pretense at completely setting forth the literature. 



Ludwig and his pupils have devoted a whole series of 

 papers 9 to the discussion of multimodal variation poly- 

 gons. De Vries in "Die Mutationstheorie" lays con- 

 siderable stress upon the Fibonacci series. More re- 

 cently Bitter 10 and Heyer 11 have taken up the questions 

 and the reader should consult these papers for a full 

 statement of the problems and the pertinent literature. 

 In any discussions in this field, the warnings set forth in 

 papers by Pearson 12 and by Pearson, Yule, Tower and 

 Lee 13 on the sources of apparent polymorphism in plants 

 should always be kept clearly in mind. 



Here I do not care to discuss the work of those who con- 

 clude that frequency curves have modes where they 



7 Pearson, K., Phil. Trans. Roy. Soc. Loud., A., Vol. CLXXXV, pp. 71- 

 110. 



h Gadzikiewicz. Hull. .trad. Sci. St. Pettish.. Vol. XXIV, pp. 263-272, 

 11,06 ; also Hiolog. C nimlhl.. Vol. XXVII, pp. 505-508, 1907. 



• A complete bibliography of this work is quite out of place here. The 

 reader may consult F. Ludwig, Biometrika, Vol. I, pp. 11-29, 1901, for a 



Ritter. 



'•Bitter, G., Beth. Bot. Centralbl., Abth. II, Vol. XXII, pp. 317-330, 

 1907; Abth. I, Vol. XXITI. pp. 273-319, 1908; Abth. I, Vol. XXV, pp. 1- 



11 Heyer, A.. Biometrika, Vol. VI, pp. 354 365, 1909. 



