The first example to be considered is obviously the assumption that the parents of a cross differ from each other in respect to two characters. A good illustrative example is afforded by the thorn-apple. I have crossed the blue flowered thorny form, usually known as _Datura Tatula_, with the white thornless type, designated as _D. Stramonium inermis_. Thorns and blue pigment are obviously active qualities, as they are dominant in the hybrids. In the second generation both pairs of characters are resolved into their constituents and paired anew according to Mendel's law. After isolating my hybrids during the period of flowering, I counted among their progeny: 128 individuals with blue flowers and thorns 47 individuals with blue flowers and without thorns 54 individuals with white flowers and thorns 21 individuals with white flowers and without thorns ---- 250 The significance of these numbers may easily be seen, when we calculate what was to be expected on the assumption that both characters follow Mendel's law, and that both are independent from each other. Then we would have three-fourths blue offspring and one-fourth individuals with white flowers. Each of these [301] two groups would consist of thorn-bearing and thornless plants, in the same numerical relation. Thus, we come to the four groups observed in our experiment, and are able to calculate their relative size in the following way: Proportion Blue with thorns 3/4 X 3/4 = 9/16 = 56.25% 9 Blue, unarmed 3/4 X 1/4 = 3/16 = 18.75% 3 White with thorns 1/4 X 3/4 = 3/16 = 18.75% 3 White, unarmed 1/4 X 1/4 = 1/16 = 6.25% 1 In order to compare this inference from Mendel's law and the assumption of independency, with the results of our experiments, we must calculate the figures of the latter in percentages. In this way we find: Found Calculated Blue with thorns 128=51% 56.25% Blue unarmed 47=19% 18.75% White with thorns 54=22% 18.75% White unarmed 21= 8% 6.25% The agreement of the experimental and the theoretical figures is as close as might be expected. This experiment is to be considered only as an illustrative example of a rule of wide application. The rule obviously will hold good in all such cases as comply with the two conditions already premised, viz.: that each character agrees with Mendel's law, and that both are wholly independent of each other. It is clear that our figures show the numerical composition [302] of the hybrid offspring for any single instance, irrespective of the morphological nature of the qualities involved.