CROPPING PATTERN AND WATER RELATIONS 357 



because the unit of decision for the cropping pattern is not the field but the 

 farm. The study of the influence of moisture relations on the cropping 

 pattern will have to account for disturbiag factors such as farm size, 

 availabihty of labour, accessibUity of the field, etc. A great many data of 

 separate fields from a large number of farms will be needed. But the large 

 number of farms may cover such a vast area, that the comparabihty of the 

 farms to be included in the survey may be impaired, due to economic 

 influences such as distance to markets or railheads. 



This means that the data have to be collected from a relatively small 

 area. The cropping pattern to be described has to be based upon a restricted 

 number of observations, which are by their nature moreover, of a restricted 

 accuracy. Therefore a method of treatment of the observations has to be 

 devised, which enables a condensation of the information contained in the 

 data as much as possible, and the elimination of random deviations as far 

 as possible. This means a general formula has to be devised that is vahd for 

 every crop and fertihty factor and requires the minimum amount of 

 constants. 



The Formula for a Cropping Pattern 



An acceptable assumption is, that for every crop within the cropping system 

 an optimal value for the production parameter wlU exist. The more the 

 actual fertihty level diverges from this optimum, the less frequently the 

 crop will be planted. If the assumption is made that the frequency of 

 occurrence is linearly related to the difference x — Xq between the actual 

 and the optimal level of the production parameter x this means that the 

 probabihty of occurrence F% of the crop is governed by the normal 

 probabiHty distribution : 



This may be written as 



hiF% = - a%x- Xo)2+ In^ (2) 



Formula 2 expresses that by plotting the logarithm of the frequency 

 against the production parameter a part of a parabola will be found, which 

 is described by three constants, two of which — Irt^ and Xq — may be 

 accounted for by shifting the co-ordinate axes. 



The value of Xq and hA depends on the crop and the production 

 situation. If the value o(a were constant, then, by shifting the co-ordinate 

 axes, the curves of every crop might be brought to coincidence with the 

 curve for any other crop. 



