In point of fact it is possible to demonstrate theoretically that this hypothesis would fully suffice to account for the development of the hybrids in the separate generations, if we might at the same time assume that the various kinds of egg and pollen cells were formed in the hybrids on the average in equal numbers[39]. [39] [This and the preceding paragraph contain the essence of the Mendelian principles of heredity.] In order to bring these assumptions to an experimental proof, the following experiments were designed. Two forms which were constantly different in the form of the seed and the colour of the albumen were united by fertilisation. If the differentiating characters are again indicated as _A_, _B_, _a_, _b_, we have: _AB_, seed parent; _ab_, pollen parent; _A_, form round; _a_, form angular; _B_, albumen yellow. _b_, albumen green. The artificially fertilised seeds were sown together with several seeds of both original stocks, and the most vigorous examples were chosen for the reciprocal crossing. There were fertilised: 1. The hybrids with the pollen of _AB_. 2. The hybrids " " _ab_. 3. _AB_ " " the hybrids. 4. _ab_ " " the hybrids. For each of these four experiments the whole of the flowers on three plants were fertilised. If the above theory be correct, there must be developed on the hybrids egg and pollen cells of the forms _AB_, _Ab_, _aB_, _ab_, and there would be combined:-- 1. The egg cells _AB_, _Ab_, _aB_, _ab_ with the pollen cells _AB_. 2. The egg cells _AB_, _Ab_, _aB_, _ab_ with the pollen cells _ab_. 3. The egg cells _AB_ with the pollen cells _AB_, _Ab_, _aB_, _ab_. 4. The egg cells _ab_ with the pollen cells _AB_, _Ab_, _aB_, _ab_. From each of these experiments there could then result only the following forms:-- 1. _AB_, _ABb_, _AaB_, _AaBb_. 2. _AaBb_, _Aab_, _aBb_, _ab_. 3. _AB_, _ABb_, _AaB_, _AaBb_. 4. _AaBb_, _Aab_, _aBb_, _ab_. If, furthermore, the several forms of the egg and pollen cells of the hybrids were produced on an average in equal numbers, then in each experiment the said four combinations should stand in the same ratio to each other. A perfect agreement in the numerical relations was, however, not to be expected, since in each fertilisation, even in normal cases, some egg cells remain undeveloped or subsequently die, and many even of the well-formed seeds fail to germinate when sown. The above assumption is also limited in so far that, while it demands the formation of an equal number of the various sorts of egg and pollen cells, it does not require that this should apply to each separate hybrid with mathematical exactness.