GROWTH 287 



supposes that the extremities of an animal tend to become electro- 

 positive and thus favourable to oxidations, and this, he argues, is inimical 

 to growth. The evidence for the existence of such a situation (or for its 

 effectiveness if it does exist) is not very strong. Perhaps a more plausible 

 mechanism is to be found in auto-inhibitory effects, of an immunological 

 nature, such as those postulated by Rose and others (p. 193). 



Another aspect of the overall growth rate is its dependence on endocrine 

 secretions, particularly those of the pituitary. There is not space here to 

 deal with this subject, which belongs to endocrinology rather than embry- 

 ology. 



2. The relative growth of parts 



It is obvious that the different parts of an embryo do not always grow 

 at the same rate. Several different lines of attack on the problem have been 

 followed. 



Perhaps the simplest is that opened up by Huxley (summarised Huxley 

 1932, see also Medawar and Clark 1945, Symp. Soc. exp. Biol. 1948, 

 Zuckerman 1950). He showed that if x is the magnitude of a whole 

 organism and y that of some part of it, the relation between them can 

 often be represented by the equation 



y = bx'^ 

 or, what is the same thing, 



log y = log b -{- a log x. 



As the second equation shows, the two magnitudes will give a straight 

 line when their logs are plotted against one another (Fig. 13.3a). There is 

 no doubt that the formula does fit rather well to very many sets of data 

 and is a very useful generalisation. The phenomena has passed under a 

 variety of names, of which heterogony and allometry seem to be the most 

 usual. 



It is not at all easy to decide just what the formula means in biological 

 terms. Taking it from the simplest point of view, we may say that Hs a 

 relatively unimportant constant, which specifies the size of the organ y 

 when the whole organism x is unity. The other constant a is the one which 

 relates to the rate of growth of the organ: if the growth rate of both x and 

 y is proportional to their actual size we shall have 



dx dy 



-J- =Ax, / = Bx, 



dt dt 



whence y = bx^'"^, or y = bx^, when a = B/A. 



