APPENDIX 337 



Experimentally, therefore, the theory is confirmed that the pea 

 hybrids form egg and pollen cells which, in their constitution, represent 

 in equal numbers all constant forms which result from the combination 

 of the characters united in fertilisation . 



The difference of the forms among the progeny of the hybrids, 

 as well as the respective ratios of the numbers in which they are 

 observed, find a sufficient explanation in the principle above 

 deduced. The simplest case is afforded by the developmental series 

 of each pair of differentiating characters. This series is repre- 

 sented by the expression A + ^Aa + a, in which A and a signify 

 the forms with constant differentiating characters, and Aa the 

 hybrid form of both. It includes in three different classes four 

 individuals. In the formation of these, pollen and egg cells of the 

 form A and a take part on the average equally in the fertilisation; 

 hence each form [occurs] twice, since four individuals are formed. 

 There participate consequently in the fertilisation 



The pollen cells A -\- A -{- a ■\- a 

 The egg cells A -\- A -\- a -]r a. 



It remains, therefore, purely a matter of chance which of the two 

 sorts of pollen will become united with each separate egg cell. 

 According, however, to the law of probability, it will always hap- 

 pen, on the average of many cases, that each pollen form, A and a, 

 will unite equally often with each egg cell form, A and a, conse- 

 quently one of the two pollen cells A in the fertilisation will meet 

 with the egg cell A and the other with an egg cell a, and so likewise 

 one pollen cell a will unite with an egg cell A, and the other with 



egg cell a. 



Pollen cells A A a a 



\ .\ i 



Egg cells A A a a 



The result of the fertilisation may be made clear by putting the 

 signs for the conjoined egg and pollen cells in the form of fractions, 

 those for the pollen cells above and those for the egg cells below the 



line. We then have 



A A a a 



_ I — _i_ — J- - . 



A^ a^ A^ a 



In the first and fourth term the egg and pollen cells are of like kind, 

 consequently the product of their union must be constant, viz. A 



