332 W. C. VISSER 



The Use of the Growth Equation 



The correct use of the growth equation requires careful consideration about 

 the nature of a growth factor and of the different solutions of the equation. 

 Soil properties, as clay content or soil structure, are not growth factors. 

 They are only in some ways related to them. Rainfall, for instance, is in 

 itself not a growth factor, but it may constitute a part of the factor water. 

 We will call these empirical productivity characteristics growth para- 

 meters. A definition of what a growth factor is seems hard to give. We will 

 understand the meaning of such a designation here as an outside influence 

 expressed in such a way that irrespective of the level of any other growth 

 factor it exerts the same significance for the crop yield. 



The aim of the construction of a growth equation is to describe how the 

 level of a growth parameter, determined outside the plant, defines the 

 actual importance of the factor as it acts inside the plant. If the observations 

 of the value of the growth factors are made inside the plant, then the 

 formulae may serve to defme the activity of such factors. A further aim is to 

 define how a growth factor influences the effect of other growth factors. 



A growth factor now may be a function of the growth parameter and 

 the growth parameter may constitute a part of the growth factor. Further, 

 the growth parameter may bear a complex relation together with other 

 parameters to the growth factor, but also the parameter may contribute to 

 more than one growth factor. 



If the parameter is indicated with p and the factor with/ then in the 

 formulae the following expressions may have to be used to obtain a good 

 representation of the yield function. These linear or functional expressions 

 should fit from a mathematical as well as from a plant physiological 

 standpoint : 



f=S{p){4.i) f=ap^+bp^{4.2) f=gi{pi)+S2{P2)+gz{P3) + --- (4-3) 



fi-gi{Pi)+g2{P2)+ ■••] (,A 



f2=sM+sM+---y ^^'^^ 



An instance of formula 4.1 with the factor a function of the parameter, 

 might be the groundwater depth. The logarithm of that productivity 

 parameter fits better into the growth equations than the depth itself If this 

 logarithm is inserted in formula 1.2, this changes into formula 2.2. 



Formula 4.2 represents cases as the combined influence of natural rain 

 and sprinkhng, where the artificial rain will be given in dry spells only and 

 will be more efficient as a productivity factor, shown by a higher constant 

 a, whilst natural rain is less effective because it also falls in wet periods and 

 has to be given a lower constant b. 



