TIT] 



OF HETEROGONY 



211 



Once again we find close agreement between the observed and 

 calculated values, although the observations are somewhat few and 

 the equation is arrived at in a simple way. We may take it as 

 proven that the relation between the two growth-rates is essentially 

 linear. 



A compound-interest law of growth occurs, as Malthus knew, 

 in cases, and at times, of rapid and unrestricted growth. But 

 unrestricted growth occurs under special conditions and for brief 



50 100 



Length of cranial portion (mm.) 



150 



Fig. 56. Relative growth of the cranial and facial portions of the 

 skull in the sheepdog. Cf. Huxley, p. 18, after Becher, 



periods; it is the exception rather than the rule, whether in a 

 population or in the single organism. In cases of diiferential 

 growth the compound-interest law manifests itself, for the same 

 reason, when one of the two growth-rates is rapid and "unre- 

 stricted," and when the discrepancy between the two growth-rates is 

 consequently large, for instance in the fiddler-crabs. The compound- 

 interest law is a very natural mode of growth, but its range is 



