May 10,1924 Factors Influencing Binding Power of Soil Colloids 509 
The next series of briquettes was made up of 25 per cent colloid with three 
different mixtures of sand of various grades. The results are shown in Table 
VI and indicate that the binding power of the colloid depends upon the grading 
as well as the size of the material. Mixtures A and B were prepared by mixing 
the indicated amounts of the relative sand sizes; mixture C was a quartz flour, 
the composition of which was determined by mechanical analysis. 
Table VI .—Effect of the grading of the noncolloidal material on the breaking 
strength of the briquettes , 25 per cent Sharkey colloid 
Mixture of noncolloidal grains—mechanical analyses 
Weight 
Average 
Load per 
Load per 
Name 
Coarse 
sand 
Medium 
sand 
Fine 
sand 
Very 
fine sand 
Silt 
Clay 
of dry 
briquette 
load per 
briquette 
gram of 
briquette 
gram of 
colloid 
A_ 
30.0 
25.0 
20.0 
15.0 
10.0 
0.0 
Grams 
24.9 
Kilograms 
526 
Kilograms 
21.1 
Kilograms 
84.6 
B. 
10.0 
15.0 
20.0 
25.0 
30.0 
.0 
25.4 
1,101 
43.4 
173.5 
C_ 
.0 
.0 
.3 
13.3 
71.0 
1 
| 15.4 
23.8 
1,690 
71.0 
284.0 
It is natural to assume that the binding power is influenced by the amount of 
surface of the sand. The surface area of material of this character is very difficult 
to estimate accurately, but for purposes of comparison the particles were assumed 
to be cubes and the average diameter of the particles was assumed to be the 
longest diagonal of a cube. Then if D is the average diagonal measured in cen¬ 
timeters, and S is the total surface area of 1 gm. of material (specific gravity 
2.65) measured in square centimeters 
cr— 3.92 s 
6 - D 
The surface of 1 gm. of each of the sands in Table V and the mixtures of sands 
in Table VI was calculated by this formula. The relation between the load and 
the surface was assumed to be of the form 
L—kS n 
where L is the load per gram of briquette, and S is the surface area of 1 gm. of 
sand. For the sands separately the values of k and n which most nearly satisfied 
all of the equations were 0.42 and 0.52 respectively, while for the mixtures of 
sands they were 1.66 and 0.47 respectively. Substituting these values in the 
above equation, the loads were calculated for purposes of comparison with the 
observed loads. The results of these calculations are shown in Table VII and 
figure 6. It will be noted that the value of n is approximately the same in each 
case, the variation in strength under the two different conditions being indicated 
largely by the value of k. 
5 This equation is derived as follows: 
The side of a cube in terms of the longest diagonal *= — 
V 3 
The surface area of a cube in terms of the longest diagonal= 2D 2 . 
The volume of a cube in terms of the longest diagonal** 
The volume of 1 gram of sand= 2 ^* 
1 
2)3 
3 
The number of particles in 1 gram of sand** 
2.65 _3V3 
J>3 2.652)3* 
3/3 
The total surface is equal to the number of particles multiplied by the surface area of 1 particle. 
~ lVs_ 
* 2.652)3 
X2D*= 
3.92 
2 ) 
