4 BULLETIN 1280, U. S. DEPARTMENT OE AGRICULTURE 
When each of the three fertilizing elements of a mixed fertilizer is 
supplied by one or more simple constituent materials, with or without 
the addition of two or three constituent materials, considerable leeway 
is possible in the proportions of the like constituent materials which 
may be taken, and in such cases there is little or no advantage in 
the' use of a general formula for the calculation of such mixtures. 
As the number of materials, particularly single-constituent mate- 
rials, available for a fertilizer mixture is reduced, the range of fer- 
tilizer analysis formulae which they are capable of making is also 
reduced, and the difficulty of the" ordinary arithmetic method of 
calculating any given mixture may be greatly increased. 
It is likely that in the future fewer materials will be used in mixed 
fertilizers, and that the concentration of these materials will be 
greater. This condition is to be expected from reasons to be dis- 
cussed later. The object of the present bulletin is, therefore, to outline 
simple methods for determining the possible fertilizer ratios which 
may be made from concentrated fertilizer materials, and for calculat- 
ing' the quantities required for any given fertilizer analysis formula. 
THE TRIANGULAR SYSTEM FOR FERTILIZER MIXTURES 
From the trade standpoint the value of a complete fertilizer, in 
the present development of the fertilizer industry, is based entirely 
on the available ammonia, phosphoric acid, and potash present, and 
is independent of the number of materials in the mixture. Variations 
in the composition of mixed fertilizers may therefore be represented 
by use of a system of three coordinates corresponding to the three 
variables, ammonia, phosphoric acid, and potash. Such a system of 
coordinates is the triangular system 3 and the range of fertilizer ratios 
which can be made from fertilizer materials can be readily determined 
with the aid of triangular section paper as represented in Plate I. 
The corners A, B, and C of the triangle represent 100 per cent of 
NH 3 , P 2 5 , and K 2 0, respectively. The distance from each corner 
of the triangle to the opposite side is divided into 100 equal parts. 
The sum of the distances along the respective perpendiculars, from 
any point within the triangle to the opposite sides, will always amount 
to 100 of these divisions. Each point within the triangle will there- 
fore represent a definite mixture of all three constituents in such pro- 
portion as to total 100 per cent. Thus the point E, being 25, 50, 
and 25 divisions from the sides BC, CA, and AB, respectively, 
represents a mixture in which 25 per cent of the total fertilizing 
material is NH 3 , 50 per cent is P 2 5 , and 25 per cent is K 2 0. This 
point, therefore, represents a 25-50-25 fertilizer ratio, or any sub- 
multiple of this ratio, such as 4-S-4. Each side of the triangle 
represents varying mixtures of the two constituents represented by 
the adjacent corners but none of that of the opposite corner. Thus 
(he side AB represents mixtures containing varying amounts of 
XII. and P..O- but no K 2 0: and the side CA varying amounts of 
K.,() and XII., but no P 2 5 . Any particular point on a side repre- 
sents a definite mixture of the two constituents represented. The 
j.oint D on the side AB, for example, being 40 divisions from BC 
and 60 divisions from AC, corresponds to a fertilizer mixture which 
contains 10 per cent of the total fertilizing elements as X1I 3 , 60 per 
cenl as P 2 B and per cent Iy.,0. 
triangular diagram has been used bj Bchreiner and Skinner (J. Am. Soc. Agron. Vol. 10, pp. 225- 
l heir experimental u rtilizer mixtures for studying the effect on plants of different ratios of the 
fertilizing elements, ammonia, phosphoric wsid, and potash. 
