330 W, C. VISSER 



against logx, than the curves are transformed into the type of curve of the 

 Mitscherhch equation. 



The Equation for Limiting Factors 



The productivity equations just discussed are not able to reproduce the 

 consequences of the assumption that the growth factor is taken up by the 

 plant in a fixed ratio to the amount of yield produced. If more of the growth 

 factor is present than the plant needs for the production of its substance a 

 part of the amount of nutritive material will not be taken up, or will be 

 used for luxury consumption. The functions discussed before, deal mainly 

 with this improper use of the nutritive material. The following assumption 

 takes also into account the fixed relation between the yield and the amount 

 of nutritive material that is necessary for plant growth. 



The formulae are the following : 



differential equation growth function 



^ = ^+'(3.1.) or ^='p5+i,(3.:6) {..-^)(A-,) = D 

 dq A— a a dq A—q a 



(3.2) 



Multifactorial equation 



ist solution 



{ax-q){hy-q){cz-q)...{A-q) = D (3.4) 



2nd solution 



{{ax-B) + {by-C) + {cz-E) + ...}{A-q)=D (3.5) 



The eqs. 3.4 and 3.5 are represented in Figs. 5 and 6. 



Discussion 



The yield increase is assumed to be constant and equal to ija, provided that 

 no other factor is Hmiting growth, nor should the growth be inhibited by 

 the hmit of expansion A of the plant. The differential equation may assume 

 two shapes, which may be derived from each other. Formula 2.1a is a 

 direct and logical expansion of the formulae i.i and 2.1. For x and q zero 

 the yield increase in the formula 3.16 is not dependent on the optimum 

 yield A. This seems more acceptable than the resulting value for the 

 formulae i.i, 2.1 and 3.1 a where the differential quotient for the minimum 

 yield depends on the optimal yield. 



In the multifactorial eq. 3.4 a new property is met. If only a few factors 

 are taken up the equation takes for each factor separately a shape which 



