Part 14

From 108 round green seeds 102 resulting plants fruited, of which:

35 had only round green seeds Ab 67 round and angular green seeds Aab.

The angular green seeds yielded 30 plants which bore seeds all of like character; they remained constant ab.

The offspring of the hybrids appeared therefore under nine different forms, some of them in very unequal numbers. When these are collected and co-ordinated we find:

38 plants with the sign AB 35 " " " Ab 28 " " " aB 30 " " " ab 65 " " " ABb 68 " " " aBb 60 " " " AaB 67 " " " Aab 138 " " " AaBb.

The whole of the forms may be classed into three essentially different groups. The first embraces those with the signs AB, Ab, aB, and ab : they possess only constant characters and do not vary again in the next generation. Each of these forms is represented on the average thirty-three times. The second group embraces the signs ABb, aBb, AaB, Aab : these are constant in one character and hybrid in another, and vary in the next generation only as regards the hybrid character. Each of these appears on an average sixty-five times. The form AaBb occurs 138 times: it is hybrid in both characters, and behaves exactly as do the hybrids from which it is derived.

If the numbers in which the forms belonging to these classes appear be compared, the ratios of 1, 2, 4 are unmistakably evident. The numbers 32, 65, 138 present very fair approximations to the ratio numbers of 33, 66, 132.

The developmental series consists, therefore, of nine classes, of which four appear therein always once and are constant in both characters; the forms AB, ab, resemble the parental forms, the two others present combinations between the conjoined characters A, a, B, b, which combinations are likewise possibly constant. Four classes appear always twice, and are constant in one character and hybrid in the other. One class appears four times, and is hybrid in both characters. Consequently the offspring of the hybrids, if two kinds of differentiating characters are combined therein, are represented by the expression

AB + Ab + aB + ab + 2ABb + 2aBb + 2AaB + 2Aab + 4AaBb.

This expression is indisputably a combination series in which the two expressions for the characters A and a, B and b, are combined. We arrive at the full number of the classes of the series by the combination of the expressions:

A + 2Aa + a B + 2Bb + b.

Second Expt.

ABC, seed parents; abc, pollen parents; A, form round; a, form angular; B, albumen yellow; b, albumen green; C, seed-coat grey-brown. c, seed-coat white.

This experiment was made in precisely the same way as the previous one. Among all the experiments it demanded the most time and trouble. From 24 hybrids 687 seeds were obtained in all: these were all either spotted, grey-brown or grey-green, round or angular. From these in the following year 639 plants fruited, and, as further investigation showed, there were among them:

8 plants ABC. 22 plants ABCc. 45 plants ABbCc. 14 " ABc. 17 " AbCc. 36 " aBbCc. 9 " AbC. 25 " aBCc. 38 " AaBCc. 11 " Abc. 20 " abCc. 40 " AabCc. 8 " aBC. 15 " ABbC. 49 " AabbC. 10 " aBc. 18 " ABbc. 48 " AaBbc. 10 " abC. 19 " aBbC. 7 " abc. 24 " aBbc. 14 " AaBC. 78 " AaBbCc. 18 " AaBc. 20 " AabC. 16 " Aabc.

The whole expression contains 27 terms. Of these 8 are constant in all characters, and each appears on the average 10 times; 12 are constant in two characters, and hybrid in the third; each appears on the average 19 times; 6 are constant in one character and hybrid in the other two; each appears on the average 43 times. One form appears 78 times and is hybrid in all of the characters. The ratios 10, 19, 43, 78 agree so closely with the ratios 10, 20, 40, 80, or 1, 2, 4, 8, that this last undoubtedly represents the true value.

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, 3^{n} gives the number of terms of the combination 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 embraces, if the original stocks differ in four characters, 3^4 = 81 of 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 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.

The uniformity of behaviour shown by the whole of the characters submitted to experiment permits, and fully justifies, the acceptance of the principle that a similar relation exists in the other characters which appear less sharply defined in plants, and therefore could not be included in the separate experiments. An experiment with peduncles of different lengths gave on the whole a fairly satisfactory result, although the differentiation and serial arrangement of the forms could not be effected with that certainty which is indispensable for correct experiment.

THE REPRODUCTIVE CELLS OF HYBRIDS.