COMPUTATION OF FERTILIZER MIXTURES 15 
If it is desired to combine a fourth material in a mixture with 
three others containing two fertilizing elements each, such as mono- 
ammonium phosphate, monopotassium phosphate, and potassium 
nitrate, two special cases may be considered, depending on whether 
the fourth material contains one, or two, fertilizer constituents. 
A nitrogen compound such as ammonium nitrate is represented 
in the triangle of Plate IV by the point A. By plotting the points 
D, E, and F as before to represent the ammonium and potassium 
phosphates and potassium nitrate, the area ADEF will inclose all 
possible fertilizer ratios that can be prepared from mixtures of these 
materials. 
If the fourth material has a composition similar to tankage (con- 
taining 8.5 per cent of NH 3 , and 5 per cent of P 2 5 ), it may be repre- 
sented in the figure by the point P, and only fertilizer ratios falling 
within the area PDEF can be made from these four materials. 
In calculating the quantities of the four materials required for a 
ton of any given analysis formula, such as the 8-6-6 mixture repre- 
sented at the point X, the two NH 3 -P 2 5 materials may be taken 
arbitrarily in any proportion such that the point Q representing the 
mixture will form the apex of a triangle on the base EF inclosing L. 
It is apparent from the figure that the location of the point Q may 
vary from P (representing the tankage alone) to the point Q' , which 
becomes the apex of the triangle when the side FQ' passes through L. 
The relative quantities of the two materials required to form a mix- 
ture containing a given ratio (r) of NH 3 : P 2 5 corresponding to Q is 
determined as follows: 
Let x = quantity of the first material. 
y = quantity of the second material. 
a = percentage of NH 3 in first material. 
a' ' = percentage of NH 3 in second material. 
b= percentage of P 2 5 in first material. 
~b" = percent age of P 2 5 in second material. 
Then; «E±pL =r 
' ox + o y 
or 
a—rb 
For monoammonium phosphate and tankage, 
a=14.8; a" = 8.5; 6 = 61.72; andZ>" = 5 
For monoammonium phosphate and ammonium nitrate, 
a = 14.8; a" = 42.55; 5 = 61.72; and&" = 
If a ratio of NH 3 : P 2 5 in the mixture is selected corresponding to 
the point Q, which represents 55 parts of NH 3 to 45 of P 2 5 , r= 55/45: 
whence for tankage with monoammonium phosphate, y = 2oA x, and 
for ammonium nitrate with monoammonium phosphate, ?/ = 1.43 x. 
Mixtures corresponding to the point Q may therefore be prepared 
from 25.4 pounds of tankage, or 1.43 pounds of ammonium nitrate, 
with one of monoammonium phosphate. 
