The development of the hybrids when the original parents differ in three characters results therefore according to the following expression:

ABC + ABc + AbC + Abc + aBC + aBc + abC + abc +
2 ABCc + 2 AbCc + 2 aBCc + 2 abCc + 2 ABbC + 2 ABbc +
2 aBbC + 2 aBbc + 2 AaBC + 2 AaBc + 2 AabC + 2 Aabc +
4 ABbCc + 4 aBbCc + 4 AaBCc + 4 AabCc + 4 AaBbC +
4 AaBbc + 8 AaBbCc.

Here also is involved a combination series in which the expressions for the characters A and a, B and b, C and c, are united. The expressions

A + 2 Aa + a
B + 2 Bb + b
C + 2 Cc + c

give all the classes of the series. The constant combinations which occur therein agree with all combinations which are possible between the characters A, B, C, a, b, c; two thereof, ABC and abc, resemble the two original parental stocks.

In addition, further experiments were made with a smaller number of experimental plants in which the remaining characters by 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 represent the terms of a series of combinations, in which the developmental series for each pair of differentiating characters are associated. It is demonstrated at the same time that the relation of each pair of different characters in hybrid union is independent of the other differences in the two original parental stocks.

If n represent the number of the differentiating characters in the two original stocks, 3n gives the number of terms of the combination series, 4n the number of individuals which belong to the series, and 2n the number of unions which remain constant. The series therefore embraces, if the original stocks differ in four characters, 34 = 81 of classes, 44 = 256 individuals, and 24 = 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 27 = 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 possible 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 period stands almost exactly between those of the seed and pollen parents, and that the constitution of the hybrids with respect to this character probably happens in the same way as 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 temperature 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.

If we endeavour to collate in a brief form the results arrived at, we find that those differentiating characters which admit of easy and certain recognition in the experimental plants, all behave exactly alike in their hybrid associations. The offspring of the hybrids of each pair of differentiating characters are, one-half, hybrid again, while the other half are constant in equal proportions having the characters of the seed and pollen parents respectively. If several differentiating characters are combined by cross-fertilisation in a hybrid, the resulting offspring form the terms of a combination series in which the permutation series for each pair of differentiating characters are united.