4 PROBLEMS OF RELATIVE GROWTH 



nature of factors which tend to limit the size of an organ 

 at high absolute sizes. 



Nor can genetics be left out. A constant partition of 

 growth-intensity between different regions implies constant 

 differences in their rates of growth. Thus any genes control- 

 ling relative size of parts will have to exert their action by 

 influencing the rates of processes, and so fall into line with 

 the numerous other rate-factors whose importance has been 

 summarized by Goldschmidt (1927) and by Ford and Huxley 

 (1929). The fact, however, that the ratios between growth- 

 rates, and not their absolute values, are the determining 

 factors introduces certain complications, whose discussion will 

 be found to have an interesting bearing upon the analysis of 

 other genetic ' characters '. 



Finally, the ancient problem of embryological recapitulation 

 will be found to be illuminated from a new angle ; and many 

 undoubted cases of recapitulation will be found to owe their 

 origin not to any mysterious phyletic law, but to embryological 

 convenience, adjusting evolutionary changes in the size of an 

 organ to the general rules of relative growth during individual 

 development. 



This brief introductory sketch will, I hope, have shown 

 some of the chief points of interest in the study of relative 

 growth. We must now come to grips with the subject, 

 and for the reasons above stated propose to do so by con- 

 sidering what at first sight seems a rather arid point — the 

 quantitative expression of the relation between the body as 

 a whole and an organ whose proportionate size changes during 

 life. 



§ 2. Constant Differential Growth-ratios 



Champy (1. c.) and others have pointed out that certain 

 organs increase in relative size with the absolute size of the 

 body which bears them ; but so far as I am aware, I (Huxley, 

 1924B) was the first to demonstrate the simple and significant 

 relation between the magnitudes of the two variables. In 

 typical cases, if x be the magnitude of the animal (as measured 

 by some standard linear measurement, or by its weight minus 

 the weight of the organ) and y be the magnitude of the dif- 

 ferentially-growing organ, then the relation between them is 

 y = ox k , where b and k are constants. 1 The constant b is 



1 This can also be written log y = log b + k log x, which means that 

 any magnitudes obeying this formula will fall along straight lines if 

 plotted on a double logarithmic grid. 



