322 The Shrinkage of Soils 



In any particular case the point at which the internal forces 

 opposed to the pull of the contracting gel begin to make themselves 

 felt must depend in large measure on the aggregate thickness of the 

 colloidal film, that is to say on the amount of colloids present in the 

 sample, and this will also govern the total contraction recorded. 



Up to the present the relationship between contraction and water 

 loss has been considered purely in respect of the linear contraction. 

 It is now convenient to discuss the connection between linear and 

 cubical contraction and the corresponding water loss. 



The cubical contraction can be calculated from the observed hnear 

 contraction by means of the formula 



where C = the cubical contraction per cent., 



a = the Hnear contraction per cent. 

 It is to be observed that with quantities of the order of magnitude 



in question the terms — -~^ + fm ^^'® ^^°* sufficiently small as to be 



negUgible in comparison with the term 3a, so that the relationship 



between hnear and cubical contraction is not the simple hnear function 



which with sufficient accuracy is usually assumed to exist in the case 



of hnear and cubical expansion of sohds under the influence of heat. 



In point of fact so soon as the value of a reaches appreciable propor- 



,, ,. Cubical contraction ,. . . , . ,, .^, . 



tions the ratio -r-. . — diminishes rapidly with increases 



Linear contraction 



in the value of a. 



On the other hand in the earlier stages when the value of a is small 

 the relationship does not depart very greatly from constancy. 



If we examine the figures obtained in the case of Example A (in 

 which the linear relationship between hnear contraction and water 

 loss has been shown to persist to the furthest point) and calculate 

 the cubical contraction corresponding to the hnear shrinkage up to a 

 value of 9 per cent, for the hnear shrinkage (at which point departure 

 from the linear relationship becomes evident owing to causes already 

 discussed), we obtain the following values: 



