14 JOHN' JOHNSTON AND L. H. ADAMS 



balance is about 1600 meters; and this depth varies inversely as 

 the pore diameter.^ 



It is evident therefore that capillarity plays a minor role unless 

 the pores are very small; and this minuteness of the pores leads 

 us to inquire what amount of water could actually flow through 

 them. This quantity can be calculated by application of the well- 

 known Poiseuille formula, by means of which the rate of flow can 

 be calculated if the radius of the tube, the pressure gradient, and 

 the viscosity of the liquid are known. Hence, assuming the mean 

 viscosity of the water to be 0.005 (its value at a temperature of 

 30°), the amount of water flowing through a pore of diameter i ix 

 (i.e., Yj'h^'o inch) would be about 15X10"^ c.c. per year; a value 

 which will tend to be too high, since the Poiseuille formula applies 

 to straight pores of uniform circular cross-section, whereas those 

 in the rocks are zig-zag and altogether irregular in shape. 



Now if we make the very generous estimate that 10 per cent 

 of the volume occupied by the rock consists of pore-spaces, there 

 will be one million (10^) pores of i ]u diameter in each square centi- 

 meter. On these assumptions, therefore, the quantity of water 

 flowing would be only 15 c.c. per sq. cm. of surface per year; and 

 the assumptions are such as to tend apparently to make this result 

 too large, rather than too small. But from Table II it is evident 

 that capillarity is quantitatively negligible at any considerable 

 depth in pores of i ju diameter; in finer pores, on the other hand, 

 where the pressure producible by capillarity is relatively important, 

 the quantity of water in flow is absolutely insignificant. Thus, 

 if the diameter of the pores is {a) o.i /x (b) o.oi fx, and on the 

 assumption again that the proportion of total pore space is 10 

 per cent,^ the amount of water flowing would be (a) o. 15 (b) 0.0015 

 c.c. per sq. cm. of surface per year. In the latter case, in other 

 words, a period of 1,000 years would be required for a quantity of 

 water equivalent to i . 5 cm. (about one-half inch) of rain to flow 

 past a given horizontal plane; moreover, the adoption of any reason- 

 able assumptions other than those used above would not, we feel 

 sure, increase these calculated values more than tenfold. In con- 

 nection with this, we would remark only that water percolating 



' At least, this is true with suii&cient approximation for the present purposes. 

 ^ This corresponds to (a) 10^ (b) 10" pores per sq. cm. of surface. 



