CROSSINGS IN MELANIL'M-VIOLETS 273 



Skcwiiess ill the variation of the characters of organisms may 

 depend on different causes. Ql'etei>et and Peahson state that causes 

 resulting in a »tendency to deviation of one side of the mean unequal 

 to the tendency to deviation on the other side» should give a skew 

 curve. The normal distribution of the variants should thus (biologi- 

 cally) be expressed by the development of the binominal formula 



{a-\-b)", or (9 + 9)", if a + /) = /. The positive and the negative 



deviation from the mean are equal, or about equal, and the causes 

 of the deviations (n) in eitlier very numerous (properly = oo I. If a 



and b are very different, for example |j -\- ^r these authors state a 



dissymmetrical arrangement of the variation. However, this is the 

 case only for very moderate values for n. If the causes of the varia- 

 tion are very numerous (which always may be the case in nature) 

 and independent of each other the result becomes a normal frequency 

 curve. As stated by Kapteyn (1916) already a value of n ^ 20 gives 

 an almost normal curve. 



Kapteyn states that skew curves result under tlie influence of 

 factors acting with unequal force on small and large individuals. It 

 is very possible that a factor favourable for the growth in size of a 

 berry, such as a rain, for example, increases the volume of a berry of 

 5 mm. diam. 0,73 mm.^. Another berry of 10 mm. diam. would in- 

 crease 6,00 mm.'. The cause of such a different behaviour of these 

 berries may depend on the fact that the reactions of the organisms 

 probably arc much influenced by previous reactions. 



In the cross here treated the nearness of the mean of Fj to that 

 of V. arvensis may depend on the greater influence of the inhibiting 

 factor than that of the positive factors for the size of the corolla, and 

 the effect of environmental influences. The effect of these latter factors 

 may increase the skewness in such a manner as assumed by Kapteyn, 

 The positive factors for the length of the petals, on the contrary, may 

 probably influence the size in the opposite direction. 



However, Fj-generations must always show a skewness on 

 account of another cause. Suppose that Fo-individuals with a »ge- 

 notypical length» of the petals = 6 mm. are realized as phenotypes. 

 On account of the modification the length of the petals in these phe- 

 notypes would vary between 5 and 7 mm. although their geno- 

 typical constitution is the same. Another type has the »genoty- 

 pical length» of 11 mm. When realized as phenotypes those plants 

 would show a length of 8 — 14 mm. The frequency curve of the length 



