86 



TEXTBOOK OF PLANT PHYSIOLOGY 



the yield may be observed only within comparatively narrow limits 

 and that with an increase of the amount of a given element, the 

 effect of increasing applications of this element decreases and 

 finally ceases to affect the yield. This dependence of yield on a 

 certain limiting element cannot be expressed graphically by a 

 straight line, as in the case of a simple proportionality, but by a 

 logarithmic curve (Fig. 36). Mathematically, Mitscherlich ex- 

 presses this relationship by the formula 



* - (A - y)K 



ax 



180 

 160 



» wo 



E 



g 120^ 



£ I0( 

 CD 



'5 80 



D 60 



o 



40 



20 







1.0 



2.0 



3.0 

 N,P 2 5 ,K 2 



4.0 



5.0 



p IG- 36. — The influence of increasing doses of fertilizer on the yield, according to 



Mitscherlich. 



where A is the maximum yield obtainable under given conditions, y 

 the yield actually obtained,, x the amount of fertilizer used, and 

 K a constant. By integrating and transforming, the following 

 formula, convenient for calculations, is obtained : 



log (A - y) = log (A - Y ) - Kx, 



where Y is the magnitude of yield on unfertilized soil. Knowing 

 this magnitude, as well as the amount of substance applied and the 

 yield obtained after its application, it is possible to calculate the 

 constant K. According to Mitscherlich, this constant is wholly 

 independent of the plant, being determined exclusively by the 

 factor of yield obtained. This formula shows that when definite 

 amounts of a fertilizer are gradually supplied, the yield increases 



