GROWTH IN TIME OF THE TOTAL ORGANISM 



191 



dimensions in general, and E = 75/3 for the linear dimension if "^. These equations 

 can be written in the following forms : 



3 



\' w*—{\yw*—'^/w)jc-'' 



(5-28) 



with w* and /" 



/ =/*_(/*_ge-^' (5.29) 



final weight and length, respectively. As can be seen, these 



equations contain only empirically testable parameters, namely, the final values 

 which can be determined from the growth curves, and the catabolic constant 

 which can be determined by physiological experiment. 



2 4 6 8 10 12 14 

 Time in weeks 



Fig. 10. Growth of Lebistes reticulatus in 

 semilogarithmic plot. See equation (5.31). 

 o weight, • length. Upper lines: 9, lower 

 lines: d. Constants: 



g: Calculated 



from weight: x = 0.285, t] = 2.64 

 from length : x = 0.256, v] = 2.38 



<5: Calculated 



from weight: x = 0.723, r\ = 4.06 

 from length : x = 0.708, t) = 4.04 



After Bertalanffy, 1938. 



10 20 304050 60 

 Time in days 



Fig. II. Regeneration of the tadpole tail; 

 Durbin's data. This example was one calcu- 

 lated by Pearl and Reed (1925) with their 

 cumbersome formula {cf. p. 176). The figure 

 shows (i) that graphical calculation ac- 

 cording to the simple equation (5.29) gives 

 satisfactory approximation (the discrepancy 

 of o. 1 3 mm in the last point would be experi- 

 mentally undetectable); (2) that regener- 

 ation may be considered as a re-establishment 

 of steady state, following the equations 

 discussed in the text. After Bertalanffy, 1934. 



The growth curves resulting by insertion of w = 2/3 into equation (5.18) have the 

 following main characteristics: I. Growth rates are decreasing and growth eventually 

 attains a steady state. 2. The curves for weight growth and linear growth are 



Literature p, 253 



