If two plants which differ constantly in one or several characters be crossed, numerous experiments have demonstrated that the common characters are transmitted unchanged to the hybrids and their progeny; but each pair of differentiating characters, on the other hand, unite in the hybrid to form a new character, which in the progeny of the hybrid is usually variable. The object of the experiment was to observe these variations in the case of each pair of differentiating characters, and to deduce the law according to which they appear in the successive generations. The experiment resolves itself therefore into just as many separate experiments as there are constantly differentiating characters presented in the experimental plants.
The various forms of Peas selected for crossing showed differences in the length and colour of the stem; in the size and form of the leaves; in the position, colour, and size of the flowers; in the length of the flower stalk; in the colour, form, and size of the pods; in the form and size of the seeds; and in the colour of the seed-coats and the albumen [cotyledons]. Some of the characters noted do not permit of a sharp and certain separation, since the difference is of a “more or less” nature, which is often difficult to define. Such characters could not be utilised for the separate experiments; these could only be confined to characters which stand out clearly and definitely in the plants. Lastly, the result must show whether they, in their entirety, observe a regular behaviour in their hybrid unions, and whether from these facts any conclusion can be come to regarding those characters which possess a subordinate significance in the type.
The characters which were selected for experiment relate:
1. To the _difference in the form of the ripe seeds_. These are either round or roundish, the wrinkling, when such occurs on the surface, being always only shallow; or they are irregularly angular and deeply wrinkled (_P. quadratum_).
2. To the _difference in the colour of the seed albumen_ (endosperm)[25]. The albumen of the ripe seeds is either pale yellow, bright yellow and orange coloured, or it possesses a more or less intense green tint. This difference of colour is easily seen in the seeds as their coats are transparent.
[25] [Mendel uses the terms “albumen” and “endosperm” somewhat loosely to denote the cotyledons, containing food-material, within the seed.]
3. To the _difference in the colour of the seed-coat_. This is either white, with which character white flowers are constantly correlated; or it is grey, grey-brown, leather-brown, with or without violet spotting, in which case the colour of the standards is violet, that of the wings purple, and the stem in the axils of the leaves is of a reddish tint. The grey seed-coats become dark brown in boiling water.
4. To the _difference in the form of the ripe pods_. These are either simply inflated, never contracted in places; or they are deeply constricted between the seeds and more or less wrinkled (_P. saccharatum_).
5. To the _difference in the colour of the unripe pods_. They are either light to dark green, or vividly yellow, in which colouring the stalks, leaf-veins, and calyx participate[26].
[26] One species possesses a beautifully brownish-red coloured pod, which when ripening turns to violet and blue. Trials with this character were only begun last year. [Of these further experiments it seems no account was published. Correns has since worked with such a variety.]
6. To the _difference in the position of the flowers_. They are either axial, that is, distributed along the main stem; or they are terminal, that is, bunched at the top of the stem and arranged almost in a false umbel; in this case the upper part of the stem is more or less widened in section (_P. umbellatum_)[27].
[27] [This is often called the Mummy Pea. It shows slight fasciation. The form I know has white standard and salmon-red wings.]
7. To the _difference in the length of the stem_. The length of the stem[28] is very various in some forms; it is, however, a constant character for each, in so far that healthy plants, grown in the same soil, are only subject to unimportant variations in this character.
[28] [In my account of these experiments (_R.H.S. Journal_, vol. XXV. p. 54) I misunderstood this paragraph and took “axis” to mean the _floral_ axis, instead of the main axis of the plant. The unit of measurement, being indicated in the original by a dash (′), I carelessly took to have been an _inch_, but the translation here given is evidently correct.]
In experiments with this character, in order to be able to discriminate with certainty, the long axis of 6–7 ft. was always crossed with the short one of 3/4 ft. to 1-1/2 ft.
Each two of the differentiating characters enumerated above were united by cross-fertilisation. There were made for the
1st trial 60 fertilisations on 15 plants. 2nd " 58 " " 10 " 3rd " 35 " " 10 " 4th " 40 " " 10 " 5th " 23 " " 5 " 6th " 34 " " 10 " 7th " 37 " " 10 "
From a larger number of plants of the same variety only the most vigorous were chosen for fertilisation. Weakly plants always afford uncertain results, because even in the first generation of hybrids, and still more so in the subsequent ones, many of the offspring either entirely fail to flower or only form a few and inferior seeds.
Furthermore, in all the experiments reciprocal crossings were effected in such a way that each of the two varieties which in one set of fertilisations served as seed-bearers in the other set were used as pollen plants.
The plants were grown in garden beds, a few also in pots, and were maintained in their naturally upright position by means of sticks, branches of trees, and strings stretched between. For each experiment a number of pot plants were placed during the blooming period in a greenhouse, to serve as control plants for the main experiment in the open as regards possible disturbance by insects. Among the insects[29] which visit Peas the beetle _Bruchus pisi_ might be detrimental to the experiments should it appear in numbers. The female of this species is known to lay the eggs in the flower, and in so doing opens the keel; upon the tarsi of one specimen, which was caught in a flower, some pollen grains could clearly be seen under a lens. Mention must also be made of a circumstance which possibly might lead to the introduction of foreign pollen. It occurs, for instance, in some rare cases that certain parts of an otherwise quite normally developed flower wither, resulting in a partial exposure of the fertilising organs. A defective development of the keel has also been observed, owing to which the stigma and anthers remained partially uncovered[30]. It also sometimes happens that the pollen does not reach full perfection. In this event there occurs a gradual lengthening of the pistil during the blooming period, until the stigmatic tip protrudes at the point of the keel. This remarkable appearance has also been observed in hybrids of _Phaseolus_ and _Lathyrus_.
[29] [It is somewhat surprising that no mention is made of Thrips, which swarm in Pea flowers. I had come to the conclusion that this is a real source of error and I see Laxton held the same opinion.]
[30] [This also happens in Sweet Peas.]
The risk of false impregnation by foreign pollen is, however, a very slight one with _Pisum_, and is quite incapable of disturbing the general result. Among more than 10,000 plants which were carefully examined there were only a very few cases where an indubitable false impregnation had occurred. Since in the greenhouse such a case was never remarked, it may well be supposed that _Bruchus pisi_, and possibly also the described abnormalities in the floral structure, were to blame.
THE FORMS OF THE HYBRIDS.[31]
[31] [Mendel throughout speaks of his cross-bred Peas as “hybrids,” a term which many restrict to the offspring of two distinct _species_. He, as he explains, held this to be only a question of degree.]
Experiments which in previous years were made with ornamental plants have already afforded evidence that the hybrids, as a rule, are not exactly intermediate between the parental species. With some of the more striking characters, those, for instance, which relate to the form and size of the leaves, the pubescence of the several parts, &c., the intermediate, indeed, was nearly always to be seen; in other cases, however, one of the two parental characters was so preponderant that it was difficult, or quite impossible, to detect the other in the hybrid.
This is precisely the case with the Pea hybrids. In the case of each of the seven crosses the hybrid-character resembles[32] that of one of the parental forms so closely that the other either escapes observation completely or cannot be detected with certainty. This circumstance is of great importance in the determination and classification of the forms under which the offspring of the hybrids appear. Henceforth in this paper those characters which are transmitted entire, or almost unchanged in the hybridisation, and therefore in themselves constitute the characters of the hybrid, are termed the _dominant_, and those which become latent in the process _recessive_. The expression “recessive” has been chosen because the characters thereby designated withdraw or entirely disappear in the hybrids, but nevertheless reappear unchanged in their progeny, as will be demonstrated later on.
[32] [Note that Mendel, with true penetration, avoids speaking of the hybrid-character as “transmitted” by either parent, thus escaping the error pervading modern views of heredity.]
It was furthermore shown by the whole of the experiments that it is perfectly immaterial whether the dominant character belong to the seed-bearer or to the pollen parent; the form of the hybrid remains identical in both cases. This interesting fact was also emphasised by Gärtner, with the remark that even the most practised expert is not in a position to determine in a hybrid which of the two parental species was the seed or the pollen plant[33].
[33] [Gärtner, p. 223.]
Of the differentiating characters which were used in the experiments the following are dominant:
1. The round or roundish form of the seed with or without shallow depressions.
2. The yellow colouring of the seed albumen [cotyledons].
3. The grey, grey-brown, or leather-brown colour of the seed-coat, in connection with violet-red blossoms and reddish spots in the leaf axils.
4. The simply inflated form of the pod.
5. The green colouring of the unripe pod in connection with the same colour in the stems, the leaf-veins and the calyx.
6. The distribution of the flowers along the stem.
7. The greater length of stem.
With regard to this last character it must be stated that the longer of the two parental stems is usually exceeded by the hybrid, which is possibly only attributable to the greater luxuriance which appears in all parts of plants when stems of very different length are crossed. Thus, for instance, in repeated experiments, stems of 1 ft. and 6 ft. in length yielded without exception hybrids which varied in length between 6 ft. and 7-1/2 ft.
The hybrid seeds in the experiments with seed-coat are often more spotted, and the spots sometimes coalesce into small bluish-violet patches. The spotting also frequently appears even when it is absent as a parental character.
The hybrid forms of the seed-shape and of the albumen are developed immediately after the artificial fertilisation by the mere influence of the foreign pollen. They can, therefore, be observed even in the first year of experiment, whilst all the other characters naturally only appear in the following year in such plants as have been raised from the crossed seed.
THE FIRST GENERATION [BRED] FROM THE HYBRIDS.
In this generation there reappear, together with the dominant characters, also the recessive ones with their full peculiarities, and this occurs in the definitely expressed average proportion of three to one, so that among each four plants of this generation three display the dominant character and one the recessive. This relates without exception to all the characters which were embraced in the experiments. The angular wrinkled form of the seed, the green colour of the albumen, the white colour of the seed-coats and the flowers, the constrictions of the pods, the yellow colour of the unripe pod, of the stalk of the calyx, and of the leaf venation, the umbel-like form of the inflorescence, and the dwarfed stem, all reappear in the numerical proportion given without any essential alteration. _Transitional forms were not observed in any experiment._
Once the hybrids resulting from reciprocal crosses are fully formed, they present no appreciable difference in their subsequent development, and consequently the results [of the reciprocal crosses] can be reckoned together in each experiment. The relative numbers which were obtained for each pair of differentiating characters are as follows:
Expt. 1. Form of seed.--From 253 hybrids 7,324 seeds were obtained in the second trial year. Among them were 5,474 round or roundish ones and 1,850 angular wrinkled ones. Therefrom the ratio 2·96 to 1 is deduced.
Expt. 2. Colour of albumen.--258 plants yielded 8,023 seeds, 6,022 yellow, and 2,001 green; their ratio, therefore, is as 3·01 to 1.
In these two experiments each pod yielded usually both kinds of seed. In well-developed pods which contained on the average six to nine seeds, it often occurred that all the seeds were round (Expt. 1) or all yellow (Expt. 2); on the other hand there were never observed more than five angular or five green ones in one pod. It appears to make no difference whether the pods are developed early or later in the hybrid or whether they spring from the main axis or from a lateral one. In some few plants only a few seeds developed in the first formed pods, and these possessed exclusively one of the two characters, but in the subsequently developed pods the normal proportions were maintained nevertheless.
As in separate pods, so did the distribution of the characters vary in separate plants. By way of illustration the first ten individuals from both series of experiments may serve[34].
[34] [It is much to be regretted that Mendel does not give the complete series individually. No one who repeats such experiments should fail to record the _individual_ numbers, which on seriation are sure to be full of interest.]
Experiment 1. Experiment 2. Form of Seed. Colour of Albumen. Plants. Round. Angular. Yellow. Green.
1 45 12 25 11 2 27 8 32 7 3 24 7 14 5 4 19 10 70 27 5 32 11 24 13 6 26 6 20 6 7 88 24 32 13 8 22 10 44 9 9 28 6 50 14 10 25 7 44 18
As extremes in the distribution of the two seed characters in one plant, there were observed in Expt. 1 an instance of 43 round and only 2 angular, and another of 14 round and 15 angular seeds. In Expt. 2 there was a case of 32 yellow and only 1 green seed, but also one of 20 yellow and 19 green.
These two experiments are important for the determination of the average ratios, because with a smaller number of experimental plants they show that very considerable fluctuations may occur. In counting the seeds, also, especially in Expt. 2, some care is requisite, since in some of the seeds of many plants the green colour of the albumen is less developed, and at first may be easily overlooked. The cause of the partial disappearance of the green colouring has no connection with the hybrid-character of the plants, as it likewise occurs in the parental variety. This peculiarity is also confined to the individual and is not inherited by the offspring. In luxuriant plants this appearance was frequently noted. Seeds which are damaged by insects during their development often vary in colour and form, but, with a little practice in sorting, errors are easily avoided. It is almost superfluous to mention that the pods must remain on the plants until they are thoroughly ripened and have become dried, since it is only then that the shape and colour of the seed are fully developed.
Expt. 3. Colour of the seed-coats.--Among 929 plants 705 bore violet-red flowers and grey-brown seed-coats; 224 had white flowers and white seed-coats, giving the proportion 3·15 to 1.
Expt. 4. Form of pods.--Of 1,181 plants 882 had them simply inflated, and in 299 they were constricted. Resulting ratio, 2·95 to 1.
Expt. 5. Colour of the unripe pods.--The number of trial plants was 580, of which 428 had green pods and 152 yellow ones. Consequently these stand in the ratio 2·82 to 1.
Expt. 6. Position of flowers.--Among 858 cases 651 blossoms were axial and 207 terminal. Ratio, 3·14 to 1.
Expt. 7. Length of stem.--Out of 1,064 plants, in 787 cases the stem was long, and in 277 short. Hence a mutual ratio of 2·84 to 1. In this experiment the dwarfed plants were carefully lifted and transferred to a special bed. This precaution was necessary, as otherwise they would have perished through being overgrown by their tall relatives. Even in their quite young state they can be easily picked out by their compact growth and thick dark-green foliage.
If now the results of the whole of the experiments be brought together, there is found, as between the number of forms with the dominant and recessive characters, an average ratio of 2·98 to 1, or 3 to 1.
The dominant character can have here a _double signification_--viz. that of a parental-character, or a hybrid-character[35]. In which of the two significations it appears in each separate case can only be determined by the following generation. As a parental character it must pass over unchanged to the whole of the offspring; as a hybrid-character, on the other hand, it must observe the same behaviour as in the first generation.
[35] [This paragraph presents the view of the hybrid-character as something incidental to the hybrid, and not “transmitted” to it--a true and fundamental conception here expressed probably for the first time.]
THE SECOND GENERATION [BRED] FROM THE HYBRIDS.
Those forms which in the first generation maintain the recessive character do not further vary in the second generation as regards this character; they remain constant in their offspring.
It is otherwise with those which possess the dominant character in the first generation [bred from the hybrids]. Of these _two_-thirds yield offspring which display the dominant and recessive characters in the proportion of 3 to 1, and thereby show exactly the same ratio as the hybrid forms, while only _one_-third remains with the dominant character constant.
The separate experiments yielded the following results:--
Expt. 1.--Among 565 plants which were raised from round seeds of the first generation, 193 yielded round seeds only, and remained therefore constant in this character; 372, however, gave both round and angular seeds, in the proportion of 3 to 1. The number of the hybrids, therefore, as compared with the constants is 1·93 to 1.
Expt. 2.--Of 519 plants which were raised from seeds whose albumen was of yellow colour in the first generation, 166 yielded exclusively yellow, while 353 yielded yellow and green seeds in the proportion of 3 to 1. There resulted, therefore, a division into hybrid and constant forms in the proportion of 2·13 to 1.
For each separate trial in the following experiments 100 plants were selected which displayed the dominant character in the first generation, and in order to ascertain the significance of this, ten seeds of each were cultivated.
Expt. 3.--The offspring of 36 plants yielded exclusively grey-brown seed-coats, while of the offspring of 64 plants some had grey-brown and some had white.
Expt. 4.--The offspring of 29 plants had only simply inflated pods; of the offspring of 71, on the other hand, some had inflated and some constricted.
Expt. 5.--The offspring of 40 plants had only green pods; of the offspring of 60 plants some had green, some yellow ones.
Expt. 6.--The offspring of 33 plants had only axial flowers; of the offspring of 67, on the other hand, some had axial and some terminal flowers.
Expt. 7.--The offspring of 28 plants inherited the long axis, and those of 72 plants some the long and some the short axis.
In each of these experiments a certain number of the plants came constant with the dominant character. For the determination of the proportion in which the separation of the forms with the constantly persistent character results, the two first experiments are of especial importance, since in these a larger number of plants can be compared. The ratios 1·93 to 1 and 2·13 to 1 gave together almost exactly the average ratio of 2 to 1. The sixth experiment has a quite concordant result; in the others the ratio varies more or less, as was only to be expected in view of the smaller number of 100 trial plants. Experiment 5, which shows the greatest departure, was repeated, and then in lieu of the ratio of 60 and 40 that of 65 and 35 resulted. _The average ratio of 2 to 1 appears, therefore, as fixed with certainty._ It is therefore demonstrated that, of those forms which possess the dominant character in the first generation, in two-thirds the hybrid character is embodied, while one-third remains constant with the dominant character.
The ratio of 3 to 1, in accordance with which the distribution of the dominant and recessive characters results in the first generation, resolves itself therefore in all experiments into the ratio of 2 : 1 : 1 if the dominant character be differentiated according to its significance as a hybrid character or a parental one. Since the members of the first generation spring directly from the seed of the hybrids, _it is now clear that the hybrids form seeds having one or other of the two differentiating characters, and of these one-half develop again the hybrid form, while the other half yield plants which remain constant and receive the dominant or recessive characters [respectively] in equal numbers_.
THE SUBSEQUENT GENERATIONS [BRED] FROM THE HYBRIDS.
The proportions in which the descendants of the hybrids develop and split up in the first and second generations presumably hold good for all subsequent progeny. Experiments 1 and 2 have already been carried through six generations, 3 and 7 through five, and 4, 5, and 6 through four, these experiments being continued from the third generation with a small number of plants, and no departure from the rule has been perceptible. The offspring of the hybrids separated in each generation in the ratio of 2 : 1 : 1 into hybrids and constant forms.
If _A_ be taken as denoting one of the two constant characters, for instance the dominant, _a_, the recessive, and _Aa_ the hybrid form in which both are conjoined, the expression
_A_ + 2_Aa_ + _a_
shows the terms in the series for the progeny of the hybrids of two differentiating characters.
The observation made by Gärtner, Kölreuter, and others, that hybrids are inclined to revert to the parental forms, is also confirmed by the experiments described. It is seen that the number of the hybrids which arise from one fertilisation, as compared with the number of forms which become constant, and their progeny from generation to generation, is continually diminishing, but that nevertheless they could not entirely disappear. If an average equality of fertility in all plants in all generations be assumed, and if, furthermore, each hybrid forms seed of which one-half yields hybrids again, while the other half is constant to both characters in equal proportions, the ratio of numbers for the offspring in each generation is seen by the following summary, in which _A_ and _a_ denote again the two parental characters, and _Aa_ the hybrid forms. For brevity’s sake it may be assumed that each plant in each generation furnishes only 4 seeds.
Ratios. Generation _A_ _Aa_ _a_ _A_ :_Aa_ : _a_
1 1 2 1 1 : 2 : 1 2 6 4 6 3 : 2 : 3 3 28 8 28 7 : 2 : 7 4 120 16 120 15 : 2 : 15 5 496 32 496 31 : 2 : 31 _n_ 2^{_n_}-1 : 2 : 2^{_n_}-1
In the tenth generation, for instance, 2^{_n_}-1 = 1023. There result, therefore, in each 2,048 plants which arise in this generation 1,023 with the constant dominant character, 1,023 with the recessive character, and only two hybrids.
THE OFFSPRING OF HYBRIDS IN WHICH SEVERAL DIFFERENTIATING CHARACTERS ARE ASSOCIATED.
In the experiments above described plants were used which differed only in one essential character[36]. The next task consisted in ascertaining whether the law of development discovered in these applied to each pair of differentiating characters when several diverse characters are united in the hybrid by crossing. As regards the form of the hybrids in these cases, the experiments showed throughout that this invariably more nearly approaches to that one of the two parental plants which possesses the greater number of dominant characters. If, for instance, the seed plant has a short stem, terminal white flowers, and simply inflated pods; the pollen plant, on the other hand, a long stem, violet-red flowers distributed along the stem, and constricted pods; the hybrid resembles the seed parent only in the form of the pod; in the other characters it agrees with the pollen parent. Should one of the two parental types possess only dominant characters, then the hybrid is scarcely or not at all distinguishable from it.
[36] [This statement of Mendel’s in the light of present knowledge is open to some misconception. Though his work makes it evident that such varieties may exist, it is very unlikely that Mendel could have had seven pairs of varieties such that the members of each pair differed from each other in _only_ one considerable character (_wesentliches Merkmal_). The point is probably of little theoretical or practical consequence, but a rather heavy stress is thrown on “_wesentlich_.”]
Two experiments were made with a larger number of plants. In the first experiment the parental plants differed in the form of the seed and in the colour of the albumen; in the second in the form of the seed, in the colour of the albumen, and in the colour of the seed-coats. Experiments with seed characters give the result in the simplest and most certain way.
In order to facilitate study of the data in these experiments, the different characters of the seed plant will be indicated by _A_, _B_, _C_, those of the pollen plant by _a_, _b_, _c_, and the hybrid forms of the characters by _Aa_, _Bb_, and _Cc_.
Expt. 1.--_AB_, seed parents; _ab_, pollen parents; _A_, form round; _a_, form angular; _B_, albumen yellow. _b_, albumen green.
The fertilised seeds appeared round and yellow like those of the seed parents. The plants raised therefrom yielded seeds of four sorts, which frequently presented themselves in one pod. In all 556 seeds were yielded by 15 plants, and of these there were:--
315 round and yellow, 101 angular and yellow, 108 round and green, 32 angular and green.
All were sown the following year. Eleven of the round yellow seeds did not yield plants, and three plants did not form seeds. Among the rest:
38 had round yellow seeds _AB_ 65 round yellow and green seeds _ABb_ 60 round yellow and angular yellow seeds _AaB_ 138 round yellow and green, angular yellow and green seeds _AaBb_.
From the angular yellow seeds 96 resulting plants bore seed, of which:
28 had only angular yellow seeds _aB_ 68 angular yellow and green seeds _aBb_.
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_ + 2_ABb_ + 2_aBb_ + 2_AaB_ + 2_Aab_ + 4_AaBb_.
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_ + 2_Aa_ + _a_ _B_ + 2_Bb_ + _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[37]. 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_.
[37] [Note that Mendel does not state the cotyledon-colour of the first crosses in this case; for as the coats were thick, it could not have been seen without opening or peeling the seeds.]
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.
