76 G. H. KNIBBS. 



stices vary in size, as the mean of the squares of their linear 

 dimensions (as E^ say). Thus it is easy to determine by a single 

 experiment, the constant for any kind of stratum considered ; as 

 we proceed to shew. 



Let q be the efflux per unit of time from a cylinder of soil of 

 sectional area A, in which the rate of fall of pressure along the 

 axis of the cylinder is /. Then if a = cA, be the efficient inter- 

 stitial area on the surface through which the efflux takes place, 

 so that c is always and necessarily a proper faction, we have 

 from (1) 



q =Ua = cA RP-IR* (5) 



rj 



In an experiment it is not possible to discriminate between c, K, 



and B 2 , so that we may practically include all these under the 



symbol k, and shall then have 



q=kA^I (6) 



r; 



Since the value of p/rj for any definite liquid depends solely on 

 temperature, it may be denoted by/' and obtained from tables 

 with that argument. The constant k which varies only with 

 different soils may then be formed from the equation 



*-74r-£ (7) 



V denoting not actual, but average mean velocity of flow for the 

 whole area A. Since for water p does not differ sensibly from 

 unity — in regard to the general precision possible in the question 

 under consideration — -f is sensibly equal to/ in §7. 1 Thus a series 

 of simple experiments will determine the values of the constants 

 k for any classes of soil. 



It may here be noticed that since the velocity of the permeable 

 flow is also dz^/dt we have from (6) 



~1 =± = Zr = kLl (8) 



dt A rj v ' 



1 For a table of accurate values of/ see " On the steady flow of water 

 etc."— Journ. Roy. Soc, xxxi., pp. 318 - 319, 1897 j a paper by the author. 



