136 MENDELISM chap. 



primarily upon the number and variety of the factors that 

 existed in the two gametes that went to its building. 

 Now most species exhibit considerable variation and exist 

 in a number, often very large, of more or less well-defined 

 varieties. How far can this great variety be explained in 

 terms of a comparatively small number of factors if the 

 number of possible forms depends upon the number of the 

 factors which may be present or absent ? 



In the simple case where the homozygous and hetero- 

 zygous conditions are indistinguishable in appearance 

 the number of possible forms is 2, raised to the power of 

 the riumber of factors concerned. Thus where one factor 

 is concerned there are only 2^ = 2 possible forms, where 

 ten factors are concerned there are 2^° = 1024 possible 

 forms differing from one another in at most ten and at 

 least one character. Where the factors interact upon one 

 another this number will, of course, be considerably in- 

 creased. If the heterozygous form is different in appear- 

 ance from the homozygous form, there are three possible 

 forms connected with each factor ; for ten such factors the 

 possible number of individuals would be 3^° = 59,049 ; for 

 twenty such factors the possible number of different in- 

 dividuals would be 3^° = 3,486,784,401. The presence 

 or absence of a comparatively small number of factors in 

 a species carries with it the possibility of an enormous 

 range of individual variation. But every one of these in- 

 dividuals has a perfectly definite constitution which can 



