Vol.63.] THE M0TI0X OF SUB-SURFACE WATER. 89 



correspou cling ratios are 0*68 and 0*72, at pressures of 5 and 70 lbs. 

 per square inch respectively. 



Similar phenomena were exhibited by the specimens of Millstone 

 Grit, the pressures of maximum unit-discharge being 60 and 35 lbs. 

 per square inch, for thicknesses of 6 and 3 inches respectively ; and 

 the ratios of the unit-discharge at pressures of 5 and 70 lbs. per 

 square inch to the respective maxima being 0*19 and 0*97, and 0*97 

 and 0-73. 



The Chalk exhibits still more irregular variations : the Mottis- 

 font Chalk having a maximum unit-discharge at a pressure of 5 lbs. 

 per square inch, which decreases steadily to a minimum value = O'SO 

 of the maximum at a pressure of 20 lbs. per square inch, and then 

 steadily increases to an unit-discharge =0'96 of the maximum 

 at a pressure of 35 lbs. per square inch, which is the highest recorded 

 pressure for the chalk from this locality, as a little above the 

 pressure of 40 lbs. per square inch the stone ruptured. The Michel- 

 dever Chalk exhibited a more variable unit-discharge, first increasing 

 with the pressure to a maximum unit-discharge at a pressure of 

 10 lbs. per square inch, then decreasing at a pressure of 15 lbs. per 

 square inch to an unit-discharge =0*98 of that at the maximum, a 

 value only slightly less than that observed at a pressure of 5 lbs. 

 per square inch ; thereafter the unit-discharge increases to a value 

 = 0*99 of the maximum at a pressure of 20 lbs. per square inch, 

 and then it steadily decreases to 0*92 of the maximum unit-discharge 

 at a pressure of 40 lbs. per square inch, above which stress the 

 stone ruptured. 



From a general consideration of the previous table, we see that 

 there is no simple direct connexion between porosity and discharge, 

 and we must seek for some other explanation of the extreme 

 variability of the discharge of the several rocks. Keeping to the 

 assumption that the flow is analogous to that through capillaries, 

 and that the phenomena of capillary flow are comparable with 

 those of ordinary pipe-flow, then the extreme variability of flow 

 may be due to the greater or less sinuosity of the interstitial 

 tube, or to the extreme variability of its cross-section from 

 point to point, giving rise to losses of energy such as eddies, etc., 

 which always result from unsteady fluid-motion, or to the magni- 

 tude of the coefficients of friction of the various rocks, or to a 

 combination of these causes. Further, as in ordinary pipe-flow, 

 an increase of pressure up to a certain pressure will be productive 

 of an increased flow, but when that pressure is exceeded the 

 excess of pressure is expended only in the production of eddies and 

 excessive friction, and the discharge per unit of pressure more or 

 less rapidly diminishes with increase of pressure, so also these 

 phenomena may hold for the interstitial tube. This critical pressure 

 varies for different rocks, and for different thicknesses of the same 

 rock. Thus, for instance, for the slowly-percolating water in the 

 interstices of the Oolites, there was no critical pressure within the 

 range of the pressures in the experiments, but in the more numerous 

 and finer capillaries of the Chalk the flow was relatively faster, 



