52 



GROWTH 



mals examined j and not only for growth in weight, but also for 

 growth in many physiological functions as, for example, growth 

 in milk secretion shown in Figure 24. 



The mathematically-minded reader may be interested to 

 know that equation (2) is the integral form of the equation 



dW 



= k(A-W) (3) 



dt 



dW 



Ag- 



in which -3— is the instantaneous velocity of growth. The other 

 dt 



symbols have the same mean- 

 ing as in equation (2). Ac- 

 cording to equation (3), the 

 velocity of growth is not de- 

 pendent on age, but on the 

 growth remaining to be made 

 to reach the mature weight A. 

 Data on delayed growth ob- 

 tained by Osborne and Men- 

 del (cf. Figure 34) indicate 

 that within certain limits the 

 velocity of growth is, indeed, 

 independent of age. 



3. The course of growth 

 during the self-accelerating 

 phase of growth. Growth cy- 

 cles versus metamorphosis. — 

 We have found that the course 

 of growth of the self-inhibit- 

 ing phase of growth is rela- 

 tively simple: The time rate 

 of growth declines at a con- 

 stant percentage rate as indi- 

 cated by equations (2) and 

 (3). The situation is somewhat 

 more complex as it relates to 



Figure 34. Growth as a function of the ma- 

 ture weight, and not of age. One of the 

 curves on the left (k = .383) represents 

 the course of growth of Dr. King's 16-25 

 generations inbred series of female rats. 

 The other curve on the left (k = .707) 

 represents the course of growth of the fe- 

 male rats of Sherman and McLeod. The 

 curve on the right was plotted from data 

 of female rat 2033 of Osborne and Mendel. 

 By means of a decreased food supply, this 

 rat was kept at a constant body weight of 

 55 grams from the age of 1.3 months (cor- 

 responding to about 3 to 4 years in man), 

 to the age of 17.1 months (corresponding to 

 about 43 years in man). When an adequate 

 food supply became accessible, the rat be- 

 gan to grow at a rate characteristic of its 

 weight and not of its age, thus indicating 

 that, within certain limits, growth is inde- 

 pendent of age. k is a measure of the steep- 

 ness of the curve, that is, of the rapidity 

 with which the mature weight is reached. It 

 is evident that the slope of the experimental 

 rat of Osborne and Mendel is of the same 

 order as of the normal rats. 



