414 Soil, Soil Solution and Freezing -Point Determinations 



the freezing-point depression varying as the concentration, or in the 

 present case, inversely as the moisture content. In other words 



3I„D„ = K, 



where £^ is a constant, andZ)„is the freezing-point depression, at a moisture 

 content of M„. Soils do not obey this law, the freezing-point depression 

 rapidly increasing as the moisture content decreases. 



Bouyoucos qualitatively reconciles this difference in behaviour by 

 the assumption that some of the water is rendered unfree, in the sense 

 that it does not take part in the depression of the freezing-point. 



The hypothesis is quantitatively examined in the present paper, and 

 assuming its truth, it has been shown that : 



(1) The water rendered unfree is not a constant amount, but varies 

 with the total moisture content; 



(2) A definite relation exists between the free, unfree and total 

 moisture, expressed by the equations: 



Y„ = cM„, 



1 i 

 7 — -Z. V '^ — V 



where c and x are constants for any one soil, 



M„ = total moisture content, 

 Y„ = free water, 

 Z„ = unfree water. 



(3) The proportion of free to total water continually decreases and 

 that of unfree to total continually increases as the total moisture 

 diminishes in amount, over the experimental range. 



(4) The actual amount of free water continually decreases as the 

 total moisture diminishes, but it cannot be definitely stated at present 

 how the actual amount of unfree water changes as total moisture 

 diminishes. The uncertainty is due to the presence of an unknown (but 

 constant) factor in the constant "c" of the equation, viz. the quantity 

 of free water present at the highest amount of total water used in the 

 experiments of Bouyoucos. According to the value arbitrarily assigned 

 to this quantity, so the amount of unfree water may continually de- 

 crease with decrease of total moisture over the experimental range, or 

 may increase to a maximum and then decrease. It is probable that the 

 former is more truly representative of the actual condition in soil, 

 although the possibility of a maximum occurring in the amount of un- 



