THE HEREDITARY FACTORS AND DIFFERENTIATION 415 



this gradient. In the second place, one of the main differences 

 between wild species, unimproved domesticated breeds, and im- 

 proved domesticated breeds, consists in larger carcass, shoulder, 

 and thigh size (and therefore greater proportion of meat) in rela- 

 tion to limb size in the improved breeds, and this on analysis is 

 found to depend on an accentuation of the slope of the original 

 gradient. Owing to this, the relative growth-intensity of the 

 terminal portions of the limb is decreased, that of the central por- 

 tions in the region of the limb-girdles is increased. In improving 

 the meat qualities of the sheep, it is necessary to search for genes 

 affecting the growth-gradients of the limbs. 



In a similar way, it will undoubtedly be found that there are 

 genes which affect the primary gradient-fields of the early embryo, 

 and therefore the relative sizes of the chemo-differentiated fields 

 in the next stage, and thus consequently the proportions of the 

 developed animal. 



Thus a knowledge of the nature and effects of gradient-fields will 

 guide the geneticist in his search for Mendelian gene- differences 

 and his analysis of the way in which they exert their effects. 



§9 

 In the analysis of the genetics of qualitative characters, a know- 

 ledge of developmental processes may be of very great importance 

 to the geneticist. In many cases, for example, the relative size of 

 a part does not vary in linear relation with the absolute size of the 

 body, but is proportional to the size of the body raised to a power. 

 In such a case, to take percentage size of part as a "character" to 

 be analysed could only lead to erroneous conclusions. To put it 

 mathematically, if developmental study shows that the growth- 

 formula of the part (y) relative to the body (x) is of the form 

 y = ax^, then the geneticist must search for genes modifying not 

 only the value of the constant a, but also that of b : and if he does 

 not know the formula, he is not likely to search for the right con- 

 stants. 



Again, linear dimensions would appear to be the simplest "cha- 

 racters" to deal with in making a genetical analysis of quantitative 

 differences in the size and proportions of an organ. But develop- 

 mental analysis appears to show that the two main variables which 



