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 



-fc = (A - f)k or log, (A - y] = c - k x, 



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. 1 



Mitscherlich's own experiments were made with oats grown in 

 sand cultures supplied with excess of all nutrients excepting phos- 

 phate. This 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. 33. 



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) . f , 



stants , ; - ~- ~- = . is a measure of the relative nutrient 

 k^ (mono-calcic phosphate) 



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

 (wirkungswert). There are some very attractive possibilities about 



1 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 # # 2 , 

 etc., the equations are 



log* (A ->>!)= C - **! . , . , . (l) 



log* (A - y 2 ) = c - kx a ..... (2) 



Then by subtraction log (A - yj - log (A - y^ k (x z - #,) . . . . . (3) 

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



.y 3 ) = *(* 3 -* 2 ) .... (4) 

 By subtracting (4) from (3) log* (A - y^ + log* (A - y s ) = 2 log* (A - y^ y 



(A - y,) (A - yi ) _ 

 *'" ' (A-^ a 



Since y it y* and y s are all numbers, the value of A is easily calculated. 

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



k = log ( A - yd - lp g g ( A - y*> . 



*3 ~ *1 



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. Fliigcl, Wasser und 

 Licht als V egetationsf actor en und ihre Beziehungen zum Gesetze von Minimum (Landw. 

 Versuchs-Stat., 1912, Ixxvi., 169 236. See also 226 c,). 



