ECOLOGICAL REACTION OF CROP YIELDS 327 



the ecological properties and that the activity constants in the formulae 

 should not be influenced by any other magnitude than the nature of the 

 productivity factor. It v^^as not considered to be necessary that in the growth 

 function itself the plant physiological basis should be easily recognisable. 

 It has not been possible to prove these theories. This raises the questions 

 whether the formula was not right or v/hcther it was not apphed in the 

 right way. 



The fundamental equation will have to express as general statement, that 

 the differential equation can only be a function of the yield and of the 

 growth factor. This may be described by 



Three formulae will be discussed as examples of this general formula. 



The Mitscherlich Equation 



In the Mitscherhch equation the differential quotient was supposed to be 

 only dependent on the yield. The following equations resulted : 



differential equation growth function typical form 



^^ -^ (i.i) q = A{i-c-^^^^)'c) (I.,) log^^= -^ (1.3) 



Multifactorial equation 

 ist solution 



^ = A(i-e-<^-«'i)/'^i)(i-e-<2/-«'2)/c2)(i_e-(3-&3)/c3) ... (1.4) 



2nd solution 



q = A(i — e-i^-h)/ci-(y-b2)c2-(.z-b3)c3 . . .) (1.5) 



The solutions of eqs. 1.4 and 1.5 are represented in Figs, i and 2. 



Discussion 



In I.I the increase in yield is a function of the deficit with respect to the 

 highest attainable yield A. The maximum increase for ^ = o is equal to A/c. 

 It seems questionable that the yield increase for q = o should be a function of 

 the maximal yield A. The equation 1.3 shows that the logarithm of the 

 yield deficit in parts of the maximal yield is a linear function of the level of 

 the growth factor. This is an important property for graphical treatment. 



