B. A. Keen 409 



The values for the clay soil are, x = 5-18, c= 734 . lO"'-'^*. Hence 

 equation (5) becomes in the two cases, 



y^ = 10-3.366 y^^ . 3/^2.55^ ... (8) 



Y„ = 10-'-934 F34 . il./„5-18. ... (9) 



To test how accurately these equations fit the curve, it is simpler to 

 return to the logarithmic form, equation (7). This can be written: 



log ^21 or 34 - log c = a; log M„ - log/. . (10) 

 The left hand side of this equation is constant, hence the right hand 

 side should be constant also. In Table IV, the values of {x log M„ — log/) 

 are given for various values of M„ and/, taken from the curves. It will 

 be seen that excellent agreement holds over the whole range for both 

 soils. Hence the relation between free and total moisture content is 

 defined by the general equation (5), on the assumption that the freezing- 

 point depression is proj)ortional to the concentration of the soil solution. 



zlogM„-logf 

 3-37 

 3-37 

 3-38 

 3-37 

 3-36 

 3-37 



7-934 

 7-969 

 7-906 

 7-901 

 7-891 

 7-933 



If the approximate truth of this assumption be admitted, then we 

 have an important and very interesting insight into the general relations 

 existing between the soil and its moisture content. Of the total moisture 

 present at any time a certain part remains free, and the remainder 

 becomes unfree. The free water is related to the total moisture, and 

 therefore to the unfree water, by a definite mathematical relation over 

 the complete experimental range. We need not at present attempt to 

 define the exact meaning of "free" and "unfree"; indeed there is not, 

 as yet, nearly enough experimental evidence to enable definitions to be 

 made with any degree of accuracy. But it is difiicult to resist the con- 



