24 SOIL CONDITIONS AND PLANT GROWTH 



of the lacking factor is added, and goes up all the further, the lower it 

 had previously fallen. Mitscherlich puts this as follows : the increase 

 of crop produced by unit increment of the lacking factor is propor- 

 tional to the decrement from the maximum. The advantage of this 

 form is that it can be expressed mathematically : — 



dy 



-^={K - y)k ox log, (A - y) = c- kx, 



where y is the yield obtained when x = the amount of the factor 

 present and A is the maximum yield obtainable if the factor were 

 present in excess, this being calculated from the equation.^ 



Mitscherlich's own experiments were made with oats grown in 

 sand cultures supplied with excess of all nutrients excepting phos- 

 phate. Tlus constituted the valuable x : the yields actually attained 

 when monocalcium phosphate was used and those calculated from the 

 equation are shown in Table IV. (p. 25). It will be noticed that there 

 is a kink in the curve at the point where 0"2 grammes of phosphate 

 is supplied. This kink seems to invariably occur, and is dealt with 

 on p. 32. 



Experiments were also made with di- and tri-calcic phosphates and 



constants were calculated corresponding to k. The ratio of these con- 



. . k„ (di-calcic phosphate) . r ^1. t x- ^ ■ ^ 



stants -; — ^ ^-^ — =-^^ — J — ^ IS a measure of the relative nutrient 



>?i (mono-calcic phosphate) 



efficiency of the two salts ; k is therefore called the efficiency value 



(wirkungswerf). There are some very attractive possibilities about 



' The method of calculation is as follows : Obtain two equations by substituting two 

 of the numerical values of x and y obtained experimentally. Calling these numbers xy, x^, 

 etc., the equations are 



log« [A -yi) = c - kxi (i) 



loge (A - y^) = c - kx^ (2) 



Then by subtraction log (A - y^) - log (A - yj!) = k (x^ - x{) (3) 



Obtain another equation like (3) but select the numerical values so that 



^3 ~ X2 ^ x^ — ^ 

 log, (A - y^) - log, (A -y3) = k (x, - x,) . . . . (4) 

 By subtracting (4) from (3) log, (A - ;»,) + log, (A - jVa) = 2 log, (A - y^, 

 . (A - y^) (A - y,) 



(A - y,)" - '• 

 Since ^j, ^3, and;*, are all numbers, the value of A is easily calculated. 

 The value of k is then found from equation (3) 



J = log (A - >i) - log« (A - y,) . 



X, - Xi 



As all the quantities on the right-hand side are numbers the value of k is readily obtained. 

 This method is further discussed by Th. Pfeiffer, E. Blanck and M. Flugel, Wasser und 

 Licht als Vegetationsfactoren und ihre Beziehungen zum Gesetze von Minimum (Landw. 

 Versuchs-Stat., 1912, Ixxvi., 169-236). 



