364 



W. C. VISSER 



is a dynamic representation, in which the properties that influence the 

 cropping pattern are variable. The type of farming depends on a great 

 many internal and external factors, economic, organisational as well as 

 physical. This complex relation may as a first approximation be described 

 as a multiple probability distribution. Eventually skew chance distributions 

 might be needed, but the nature of the data with respect to their restricted 

 accuracy often make it unnecessary to introduce this comphcation. 



Frequency "U 

 70r- 



60- 



20 



OATS/BARLEY MIX 



OATS 

 POTATOES 



75 



125 175 225 275cm minus soil surface 



Mean depth of ground-water 

 table in summer 



Fig. 6. The parabola for the cropping pattern makes possible a reconstruction of the 

 frequency percentage -groundwater depth diagram by changing back the logarithmic 

 scale aiid reversing the horizontal and vertical shifts. The graphical and numerical 

 results of the influence of groundwater depth on the frequency of occurrence of each 

 crop is given above. 



One single probabihty distribution diagram is able to comprise the 

 frequency curves for all the crops by choosing for every crop separately 

 the right situation of the co-ordinate system for the frequency and for the 

 production parameter. But this apphes only if the logarithm of the 

 frequency is used. Logarithmic plotting of the probability percentage 

 transforms the frequency distribution curve into a parabola. The multiphca- 

 tion factor a^ in the parabola -see formula 2- may be assumed to be con- 

 stant for a certain area. This constant represents the reaction of the joint 

 farmers to a decrease in productivity due to sub-optimal circumstances. 



