September -25, 1903.] 



SCIENCE. 



401 



the two recessive characters (ab), and so 

 conceal no liidden i*ecessives. They may at 

 once be set aside as pure. But in the other 

 three classes nothing but actual breeding 

 tests will serve to show which individuals 

 are pure and which impure or hybrid. To 

 each pure individual possessing one domi- 

 nant and one recessive character there 

 will be two others, exactly like it in ap- 

 pearance, but hybrid in one pair of char- 

 acters. This statement applies to the two 

 classes, rougli-white and smooth-pig- 

 mented, in which the impure individuals 

 would be designated A(a)b and aB(b) 

 respectively. Such impure animals bred 

 inter se would produce, in Ihe ease of 

 rough-white parents, both rough-white and 

 smooth-white offspring, and in the case of 

 smooth-pigmented parents, both smooth- 

 pigmented and smooth-white offspring. 



In the class of rough-pigmented second- 

 generation offspring, which combines the 

 two dominant characters, there will be to 

 each pure individual (AB) eight which 

 are impure in one or both characters. Two 

 of the eight will be hybrid in one character 

 only, as in the rough vs. smooth charac- 

 ter they form the class A(a)B; two 

 other individuals will be hybrid in the 

 other character, albino vs. pigmented, 

 forming the class AB(b) ; while the re- 

 maining four will be hybrid in both char- 

 acters, exactly like the entire first genera- 

 tion of offspring, AB(ab). 



The task of the practical breeder who 

 seeks to 'establish' or 'fix' a new variety, 

 produced by cross-breeding, in a case involv- 

 ing two variable characters, is simply the 

 isolation and propagation of that one in 

 each sixteen of the second-generation off- 

 spring which will be pure as regards the 

 desired combination of characters. Men- 

 del's discovery by putting the breeder in 

 pos.session of this information enables him 

 to attack his problem systematically, with 



confidence in the outcome, whereas hitlierto 

 his work, important and fascinating as it 

 is, has consisted largely of groping for a 

 treasure in the dark. 



The greater the number of separately 

 variable characters involved in a cross, the 

 greater will be the number of new combina- 

 tions obtainable ; the greater, too, will be 

 the number of individuals which it will be 

 necessary to raise in order to secure all 

 the possible combinations ; and the greater, 

 again, will be the difficulty of isolating the 

 pure, i. e., stable forans from such as are 

 similar to them in appearance but still 

 hybrid in one or more characters. Mendel 

 has generalized these statements substan- 

 tially as follows: In eases of complete 

 dominance, when the number of dift'erences 

 between the parents is n, the number of 

 different classes into which the second gen- 

 eration of offspring fall will be 3" of 

 which 2" will be pure (stable) ; the re- 

 mainder will be hybrid, though indis- 

 tinguishable from pure individuals. The 

 smallest number of individuals which in 

 the second hj-brid generation will allow of 

 one pure iudividual to each visibly differ- 

 ent class will be 4» . (See Table IV.) 



The law of Mendel reduces to an exact 

 science the art of breeding in the case most 

 carefully studied by him, that of entire 



