l68 GROWTH PRINCIPLES AND THEORY 2 



dajdt = ka^'- {a* - a) (4.5) 



(a* — final size of area). In this case, the initial area («q) enters into the parameter 

 a* : Oq.E' = a*, i.e. the maximal area eventually reached is proportional to the 

 initial area. This is obvious because in this case growth is limited by the resources 

 lying in the explant itself. Introducing new constants, equation (4.5) can be 

 written : 



dajdt = rir - XV (4-6) 



which is a modification of equation (5.24). Equation (4.6) implies i. that the 

 growth of volume of a tissue culture is nearly equal to growth in surface because 

 growth in thickness is negligible; 2. it differs from equation (5.24) insofar as 

 according to the latter, total surface is responsible for growth while according to 

 the first, only the periphery is responsible because mitoses are confined to it. 

 Equation (4.6) is written in a somewhat diflferent way by Ephrussi and Teissier 

 (1932). The slight modification made here shows that the growth equation 

 proposed by these authors is a special case of the general growth equation and 

 model used in the present study. 



V. GROWTH IN TIME OF THE TOTAL ORGANISM 



(a) Definitions 



The course of growth in time is expressed by the growth curve where the 

 magnitudes investigated, such as weight, length, etc. are plotted against time. 

 Some frequently used measures require definition. 



Absolute growth rate is the increase of size per unit of time (dy/d/) ifj is a measure 

 of body size such as weight (w) or length (/). 



Specific growth rate is the increase in size per unit of time and unit of size, hence 

 dylydt. 



The following measures of specific growth rate are frequently used: 



J. Minot's formula. IfjVo andy are two sizes (weights, lengths) at times t^ and t, 



the average increase per time unit is jv — y^jt — f^, or if the interval {t — t^) is 



equal to i : y — y^. 



Hence, specific growth rate according to Minot is : 



^■-=^-^ (5.0 



dt y y 



i.e. increase in size divided by initial size. If specific growth rate is indicated in 

 per cent, this value is to be multiplied by 100. 



This formula is inexact because the increase in size is related to a constant 

 value at the beginning of the time period under consideration. In fact, body size 

 increases continually. The error committed by calculation of growth rates after 

 Minot's formula is the greater the larger is growth rate and the longer the 

 intervals. 



