Vol. G^.'j THE MOTION OF SUB-SURFACE WA.TBE. 87 



ISTearly all investigators of interstitial flow have considered it as 

 a motion through a series of capillaries of varying diameter, and of 

 a length much greater than the net thickness of the strata traversed. 

 Slichter (10) has assumed that rocks of varying degrees of porosity 

 can he represented by spheres packed in different orders of com- 

 pactness, having a maximum value of porosity ( = 0-4764) when the 

 hounding tangent-planes to the spheres form a cube, and the least 

 value ( = 0*2595) when the tangent-planes form a rhomboid with a 

 dihedral angle of 60°; and, in a neat mathematical analysis, he has 

 evaluated the diameter and length of the equivalent interstitial tube 

 for a given thickness of rock of given porosity. 



In the series of experiments which I conducted upon the influence 

 of pressure on interstitial flow, and recorded in tabular form in 

 the appendices to my former paper (24) previously mentioned, I 

 made no attempt at the determination of the length, or cross- 

 sectional area, of this ideal capillary tube, as it seemed to me to 

 be capable of almost infinite variation in these particulars, as well 

 as in the numerical frequency of such tubes per cubic foot of rock ; 

 but rather confined myself to a close investigation of the rate 

 of variation of discharge with pressure: and I found that, for 

 a wide range of pressure, the discharges were not strictly pro- 

 portional to the pressure. Thus, in the case of hard Daresbury 

 Sandstone, whilst the pressures varied in the ratios of 1, 2, 4, 8, 

 and 12, the corresponding discharges varied in the ratios 1, 2*4, 6*6, 

 10-7, and 14-1. 



The variations are still more apparent if one divides the dis- 

 charge from any test-piece by the pressure producing it, and 

 expresses the unit-discharge or discharge per unit-pressure in terms 

 of the volume of the pores of the test-piece, as in the appended 

 Table (IV, p. 88). 



From a study of this table, one sees that the unit-discharge 

 steadily increases throughout the whole range of pressure in the 

 case of the Oolites ; while, in the case of the other rocks tested, the 

 unit-discharge steadily increases until a certain pressure, which I 

 have called the critical pressure, is reached, and then falls off 

 with a steady decremental ratio. Thus, for instance, the hard 

 Daresbury Sandstone, 6 inches thick, has an unit-discharge or a 

 discharge per lb. of pressure at a pressure of 5 lbs. per square 

 inch that is only 0*61 of that at 20 lbs. per square inch, which 

 for this thickness of this stone is its pressure of maximum unit- 

 discharge, the rate of increase between 5 and 20 lbs. per square 

 inch being steady ; but thereafter the unit-discharge steadily 

 decreases until at a pressure of 70 lbs. per square inch the unit- 

 discharge is only 0-64 of that at a pressure of 20 lbs. per square 

 inch. 



For a thinner section of the same rock this phenomenon is 

 noticeable at a lower pressure. The maximum unit-discharge for 

 the 3-inch thickness of hard Daresbury Sandstone occurs at a 

 pressure of 15 lbs. per square inch, instead of at 20 lbs. per square 

 inch, which was the maximum for the 6-inch thickness, and the 



