| Number | % | Calculation | |
| Hairy and red | 70 | 44 | 56.25% |
| Hairy and white | 23 | 14 | 18.75% |
| Smooth and red | 46 | 23 | 18.75% |
| Smooth and white | 19 | 12 | 6.25% |
For the combination of pubescence and the capacity of flowering in the first year I found:
| Number | % | Calculated | |
| Hairy, flowering | 286 | 52 | 56.25% |
| Hairy without stem | 128 | 23 | 18.75% |
| Smooth and red | 96 | 17 | 18.75 |
| Smooth and white | 42 | 8 | 6.25% |
Many other cases have been tested by different writers and the general result is the [303] applicability of Mendel's formula to all cases complying with the given conditions.
Intentionally I have chosen for the last example two pairs of antagonisms, relating to the same pair of plants, and which may be tested in one experiment and combined in one calculation.
For the latter we need only assume the same conditions as mentioned before, but now for three different qualities. It is easily seen that the third quality would split each of our four groups into two smaller ones in the proportion of 3/4 : 1/4.
We would then get eight groups of the following composition:
| 9/16 X 3/4 = 27/64 | or | 42.2% |
| 9/16 X 1/4 = 9/64 | " | 14.1% |
| 3/16 X 3/4 = 9/64 | " | 14.1% |
| 3/16 X 1/4 = 3/64 | " | 4.7% |
| 3/16 X 3/4 = 9/64 | " | 14.1% |
| 3/16 X 1/4 = 3/64 | " | 4.7% |
| 1/16 X 3/4 = 3/64 | " | 4.7% |
| 1/16 X 1/4 = 1/64 | " | 1.6% |
The characters chosen for our experiment include the absence of stem and flowers in the first year, and therefore would require a second year to determine the flower-color on the perennial specimens. Instead of doing so I have taken another character, shown by the teeth of the capsules when opening. These curve outwards [304] in the red campion, but lack this capacity in the evening-campion, diverging only until an upright position is reached. The combination of hairs, colors and teeth gives eight groups, and the counting of their respective numbers of individuals gave the following:
| Hairs | Flowers | Teeth of capsules | Number | % | Calculated |
| Hairy | Red | curved | 91 | 47 | 42.2% |
| Hairy | Red | straight | 15 | 7.5 | 14.1% |
| Hairy | White | curved | 23 | 12 | 14.1% |
| Hairy | White | straight | 17 | 8.5 | 4.7% |
| Smooth | Red | curved | 23 | 12 | 14.1% |
| Smooth | Red | straight | 9 | 4.5 | 4.7% |
| Smooth | White | curved | 5 | 2.5 | 4.7% |
| Smooth | White | straight | 12 | 6 | 1.6% |
The agreement is as comprehensive as might be expected from an experiment with about 200 plants, and there can be no doubt that a repetition on a larger scale would give still closer agreement.
In the same way we might proceed to crosses with four or more differentiating characters. But each new character will double the number of the groups. Four characters will combine into 16 groups, five into 32, six into 64, seven into 128, etc. Hence it is easily seen that the size of the experiments must be made larger and larger in the same ratio, if we intend to expect numbers equally trustworthy. For [305] seven differentiating marks 16,384 individuals are required for a complete series. And in this set the group with the seven attributes all in a latent condition would contain only a single individual.
Unfortunately the practical value of these calculations is not very great. They indicate the size of the cultures required to get all the possible combinations, and show that in ordinary cases many thousands of individuals have to be cultivated, in order to exhaust the whole range of possibilities. They further show that among all these thousands, only very few are constant in all their characters; in fact, it may easily be seen that with seven differentiating points among the 16,384 named above, only one individual will have all the seven qualities in pure active, and only one will have them all in a purely dormant condition. Then there will be some with some attributes active and others latent, but their numbers will also be very small. All others will split up in the succeeding generation in regard to one or more of their apparently active marks. And since only in very rare cases the stable hybrids can be distinguished by external characters from the unstable ones, the stability of each individual bearing a desired combination of characters would have to be established by experiment [306] after pure fertilization. Mendel's law teaches us to predict the difficulties, but hardly shows any way to avoid them. It lays great stress on the old prescript of isolation and pure fertilization, but it will have to be worked out and applied to a large number of practical cases before it will gain a preeminent influence in horticultural practice.
Or, as Bailey states it, we are only beginning to find a pathway through the bewildering maze of hybridization.
This pathway is to be laid out with regard to the following considerations. We are not to cross species or varieties, or even accidental plants. We must cross unit-characters, and consider the plants only as the bearers of these units. We may assume that these units are represented in the hereditary substance of the cell-nucleus by definite bodies of too small a size to be seen, but constituting together the chromosomes. We may call these innermost representatives of the unit-characters pangenes, in accordance with Darwin's hypothesis of pangenesis, or give them any other name, or we may even wholly abstain from such theoretical discussion, and limit ourselves to the conception of the visible character-units. These units then may be present, or lacking and in the first case active, or latent.
[307] True elementary species differ from each other in a number of unit-characters, which do not contrast. They have arisen by progressive mutation. One species has one kind of unit, another species has another kind. On combining these, there can be no interchange. Mendelism assumes such an interchange between units of the same character, but in a different condition. Activity and latency are such conditions, and therefore Mendel's law obviously applies to them. They require pairs of antagonistic qualities, and have no connection whatever with those qualities, which do not find an opponent in the other parent. Now, only pure varieties afford such pure conditions. When undergoing further modifications, some of them may be in the progressive line and others in the retrogressive. Progressive modifications give new units, which are not in contrast with any other, retrograde changes turn active units into the latent condition and so give rise to pairs. Ordinary species generally originate in this way, and hence differ from each other partly in specific, partly in varietal characters. As to the first, they give in their hybrids stable peculiarities, while as to the latter, they split up according to Mendel's law.
Unpaired or unbalanced characters lie side by side with paired or balanced qualities, and they [308] do so in nearly all the crosses made for practical purposes, and in very many scientific experiments. Even Mendel's peas were not pure in this respect, much less do the campions noted above differ only in Mendelian characters.
Comparative and systematic studies must be made to ascertain the true nature of every unit in every single plant, and crossing experiments must be based on these distinctions in order to decide what laws are applicable in any case.
[309]
D. EVER-SPORTING VARIETIES