APPENDIX 331 



twos and threes were united as hybrids : all yielded approximately 

 the same results. There is therefore no doubt that for the whole 

 of the characters involved in the experiments the principle applies 

 that the offspring of the hybrids in which several essentially different 

 characters are combined exhibit the terms of a series of combinations, 

 in which the developmental series for each pair of differentiating 

 characters are united. It is demonstrated at the same time that the 

 relation of each pair of different characters in hybrid union is inde- 

 pendent of the other differences in the two original parental stocks. 



If n represents the number of the differentiating characters in the 

 two original stocks, 3 n gives the number of terms of the combina- 

 tion series, 4 n the number of individuals which belong to the series, 

 and 2 n the number of unions which remain constant. The series 

 therefore contains, if the original stocks differ in four characters, 

 3 4 = 81 classes, 4 4 = 256 individuals, and 2 4 = 16 constant forms; 

 or, which is the same, among each 256 offspring of the hybrids 

 there are 81 different combinations, 16 of which are constant. 



All constant combinations which in Peas are possible by the 

 combination of the said seven differentiating characters were 

 actually obtained by repeated crossing. Their number is given by 

 2 7 = 128. Thereby is simultaneously given the practical proof 

 that the constant characters which appear in the several varieties of a 

 group of plants may be obtained in all the associations which are pos- 

 sible according to the [mathematical] laws of combination, by means of 

 repeated artificial fertilisation. 



As regards the flowering time of the hybrids, the experiments are 

 not yet concluded. It can, however, already be stated that the 

 time stands almost exactly between those of the seed and pollen 

 parents, and that the constitution of the hybrids with respect to 

 this character probably follows the rule ascertained in the case of 

 the other characters. The forms which are selected for experiments 

 of this class must have a difference of at least twenty days from the 

 middle flowering period of one to that of the other; furthermore, 

 the seeds when sown must all be placed at the same depth in the 

 earth, so that they may germinate simultaneously. Also, during 

 the whole flowering period, the more important variations in tem- 

 perature must be taken into account, and the partial hastening or 

 delaying of the flowering which may result therefrom. It is clear 

 that this experiment presents many difficulties to be overcome and 

 necessitates great attention. 



