26 
AMERICAN JOURNAL OF BOTANY 
[Vol. io. 
when grown in sand and water cultures, use has been made of the triangular 
diagram in discussing these results. This scheme was first suggested for 
this kind of work by Schreiner and Skinner (17) and was later modified and 
perfected by Tottingham (25), Shive (19), McCall (10), and Trelease (26). 
The details of the arrangement of the cultures in the triangle are given by all 
of the above-named authors and also by the plan of the committee (23). 
The triangular diagrams for the dry weights of tops and roots for water 
and sand cultures are shown in figure 1. The five cultures lying in the 
high-yielding areas, marked H in table 2, are plotted on the triangles with 
small + signs. Similarly, the five cultures lying in the low-yielding areas, 
marked L in table 2, are plotted on the triangles with small circles. This 
method was suggested by Shive (19). The culture having the highest yield 
in each diagram is marked with a circle. 
In figure 1, comparing first the triangles representing the dry weight of 
tops of wheat plants grown in water and sand cultures, the five high-yielding 
water cultures (15.82-9.44) occupy the lower left position of the triangle, 
whereas the five high-yielding sand cultures (8.99-7.84) assume the upper 
right central portion of the triangle. Thus it is seen, as noted by McCall 
(10), that the water cultures and sand cultures show a marked difference 
in the salt proportions that are required to produce their respective maxi¬ 
mum yields of tops. At only one point, that of R3S2, do the areas overlap, 
and this is the lowest culture of the five in both cases. The highest-yielding 
water culture (R2S1) has the following molecular proportions: 2, KNO 3 ; 
1, Ca(H 2 P0 4 )2; and 5, MgS0 4 . The partial volume-molecular concentra¬ 
tions are 0.0054 KN0 3 , 0.0027 Ca(H 2 P 0 4 ) 2 , and 0.0135 MgS 0 4 . In other 
words, the solution is made with 18.90 cc. (1.0 M) KN0 3 , 94.5 cc. (0.1 M) 
Ca(H 2 P 0 4 ) 2 , 47.25 cc. (1.0 M) MgS 0 4 , and 3 mg. FeP 0 4 , made up to 1 liter 
with distilled water. The highest-yielding sand culture (R3S3) has the 
following molecular proportion: 3, KN0 3 ; 3, Ca(H 2 P 0 4 ) 2 ; and 2, MgS 0 4 . 
The partial volume-molecular concentrations are 0.0067 KNO 3 , 0.0067 
Ca(H 2 P 0 4 ) 2 , and 0.0045 MgS 0 4 . This solution is made with 23.45 cc. 
(1.0 M) KN0 3 , 234.5 cc. (0.1 M) Ca(H 2 P 0 4 ) 2 , 15.75 cc. (1.0 M) MgS 0 4 , 
and 3 mg. FeP 0 4 made up to 1 liter with distilled water. 
The five low-yielding water cultures (0.125-0.412) occupy the extreme 
lower right apex of the triangle, and the same is true for the five low-yielding 
sand cultures (0.856-3.94). 
A comparison of the triangles representing the dry weight of roots of 
the sand and water cultures also shows a wide difference in salt proportions, 
though not as great as in the case of the tops. Four of the five high-yielding, 
water cultures (3.86-2.74) are located on the line of cultures deriving two 
eighths of their total molecular proportions from Ca(H 2 P 0 4 ) 2 . The highest- 
yielding culture (marked with a circle) is characterized by having two 
eighths of its total diffusion tension due to Ca(H 2 P 0 4 ) 2 ; three eighths due 
to KN 0 3 ; and three eighths due to MgS 0 4 . The area of the high-yielding 
