8 



for m, n, p, etc., which will give the maximum value to the following 

 expression : 



amx -f- bny -f- cpz + 



where a, b, c, are price units, x,y,z, yield units, and 



m, n, p, the number of the units produced if each of different 



classes A, B, C, In the case of Egypt, where the limits of area 



of cotton cultivation are for the moment practically reached, we have 

 the further consideration that 



m -j- n -\- p 4- = k, a constant. 



The problem, so expressed, is clearly incapable of accurate 

 solution owing to the large number of variables ; but the attempt 

 is necessary if the maximum value is to be realized for the crop. 

 The need of a solution, if only an approximate one, is especially 

 necessary in a country like Egypt, in which practically the 'entire 

 wealth of the country is due to the one crop with which we are concerned. 



If, further, the interests of the individual producer are to be 

 protected, yet another algebraic problem must be solved. It will 

 here be necessary that : 



ax = by = cz = 



Unless this condition is fulfilled, supposing, that is, that 

 ax 7 by 7 cz 



the producer of B and, still more, the producer of C, will be placed at 

 a disadvantage as compared with the producer of A. Under such 

 conditions, unless local conditions exercise a selective influence, 

 the cultivation of B and, to a still greater extent, of 0, will diminish, 

 while the cultivation of A will extend. . 



The only alternative is the elimination of the economic factor 

 and for Government to control the proportionate cultivation of the 

 different classes a procedure hardly conceivable when such control 

 must react to the detriment of a proportion of the individual producers. 



We have here indicated the first problem to be solved with 

 relation to cotton growing. Diversity is an essential requirement, 

 and such diversity will only be maintained if 



ax = by = cz 



The absolute solution of this problem, the equalization of the 

 money returned by unit areas under the various types of cotton, is not 



possible, for the relative values of a, b, c vary from year to year. 



An approximate solution only can be attained, and may be sought 

 in two directions. The various types which yield the different classes 

 differ not only in regard to those lint characters which give these 

 cottons their distinctive features, but they differ in other characters 

 also. These characters we may term " physiological," thereby 

 implying a difference in reaction to environment. Egypt, in spite 



