FERTILIZER PRACTICE 553 



Liebig. Wagner 1 later stated definitely that up to a 

 certain point the increase yield was proportional to the 

 increase in the application. This, however, evidently 

 cannot apply except over a very limited field, since it is 

 a matter of common observation that increased crop 

 yield becomes lower as the lacking element is supplied. 

 Recently Mitscherlieh 2 has formulated a law r3 which is a 

 logarithmic, rather than a direct, function of the increase 

 in the element occupying the position of the minimum. 

 Mitscherlich's law may be stated concisely as follows: 

 the increased grow r th produced by a unit increase of the 

 element in the minimum is proportional to the decre- 

 ment from the maximum. The following curve (see 

 Fig. 62) constructed from data obtained by Mitscherlieh, 4 

 shows the trend of the increased growth curve as governed 

 by increased applications of an element in the minimum, 

 other factors being, of course, under control. This curve 

 is maintained by Mitscherlich to approximate a theoretical 

 curve of a definite mathematical formula. 



1 Wagner, II. Beitrage zur Dungerlehre. Landw. Jahr.j 

 Band 12, Seite 691 ff. 1883. 



2 Mitscherlich, A. E. Das Gesetz des Minimums und das 

 Gesetz des Abnehmen den Bodenertrages. Landw. Jahr., 

 Band 38, Seite 537-552. 1909. 



Also, Ein Beitrage zur Erforschung der Ausnutzung des 

 im Minimum Vorhandenen Nahrstoffes durch die Pflanze. 

 Landw. Jahr., Band 39, Seite 133-156. 1910. 



-^ = (a y)k. Integrating, log (a y) = c kx. 

 dx 



y = total yield from any number of increments. 

 x = amount of any particular fertilizer constituent utilized. 

 a = maximum yield and is a constant. 

 k = a constant depending on y and x, variables. 

 4 Mitscherlich, A. E. Uber das Gesetz des Minimums und 

 die sieli aus dicsom Krgobonden Schlussfolgerungen. Landw. 

 Ver. Stat., Band 75, Seite 231-263. 1911. 



