II2 BOTANICAL GAZETTE [FEBRUARY 



ratio of 3p:iw. The ratio of purple to white in family no. 05213 

 can have no significance, since one of the two purple plants used as the 

 pollen parents was probably a D and the other a DR. 



To test the assumption that family no. 05114 represented the 

 cross DRXDR, and to get further evidence on the Mendelian char- 

 acter of the purple color in this species, a series of over eighty crosses 

 was made within this single family. All of the pistillate plants 

 received pollen from a single white staminate plant, and pollen from 

 each of the staminate plants was used to fertilize the different flowers 

 of a single white pistillate plant. 



This method was employed because it is the simplest way in which 

 the correct classification of every individual of the first generation of 

 hybrids may be attained. Every single cross in the series had the 

 recessive white as one of its members, so that only three possible com- 

 binations could occur among the resultant hybrid families, namely, 

 DxR, DRXR, and RxR, giving respectively, according to expecta- 

 tion, 100 per cent., 50 per cent., and o per cent., of purple-flowered 

 offspring, in the ratio 1:2:1. About 50 plants from each of these 

 83 crosses were reared to maturity in 1907, and, when classified accord- 

 ing to the percentage of purple individuals in each family, showed 13 

 families with more than 95 per cent, purple, 48 having 30-70 per cent, 

 purple, and 22 with less than 5 per cent, purple, the expectation being 

 21 with 100 per cent, purple, 42 with 50 per cent, purple, and 21 with 

 o per cent, purple. The result is close enough to expectation to 

 demonstrate the correctness of the Mendelian law in regard to the 

 flower-color of Lychnis dioica L. 



The diagram (fig. 4) showing the distribution of percentages of purple 

 individuals in the heterozygote families may be used to call attention 

 to what we ought to mean by "Mendelian expectation." Very often 

 when a rather small series of observations shows a considerable depart- 

 ure from the ratios 1:1, 1:2:1, 3:1, 9:3:4, or whatever other ratio 

 represents the theoretical limit appropriate to the conditions of the 

 particular experiment in hand, the statement is made that the results 

 are not in accord with "Mendelian expectation." When the number 

 of observations is small, such a statement is usually due to the fact 

 that too much is expected. This will become clear when attention is 

 called to the fundamental basis of the Mendelian ratios. Equal 



