Vol. 63.] 



THE MOTION" OF SUB-SURFACE WATEE. 



95 



This table affords an interesting study of the increased rate of 

 flow induced by a difference of pressure. At the outset, the inflow 

 to the well being at normal velocity is not equal to the volume 

 abstracted by the pumps, and a considerable central depression is 

 produced. As the difference, however, in the volume of successive 

 hourly cones is not a constant quantity, but the differences are 

 related one to the other in a decremental ratio, it follows that the 

 rate of inflow must steadily increase, since the quantity abstracted 

 is fairly constant. 



Hoadley has also devised a neat piece of apparatus for experi- 

 mentally determining in the laboratory the outline of the cone of 

 depletion in sands of varying degrees of coarseness. 



Slichter assumes that the circumferences of concentric circles are 

 crossed by equal amounts of water in the same time, and that 

 therefore the velocity varies inversely as the distance from the axis 

 of disturbance ; and he deduces a mathematical expression for the 

 pressure at any point, at any distance from the well. He also 

 evaluates the drop in pressure in a sandstone under a head of 10 feet 

 at various distances from the well, somewhat as shown in the 

 following Table (IX) :— 



Table IX. 



Distance from centre of well, 



Drop in pressure, 



in feet. 



in lbs. 



0-25 



10 



0-54 



9 



1-19 



8 



2-58 



7 



5-62 



6 



1225 



5 



2667 



4 



57-52 



3 



126-50 



2 



275-50 



1 



I endeavoured to solve the question, upon the assumption that 

 the outline of a transverse vertical section of the cone of depletion 

 would be a curve, the coordinates of which would vary directly as 

 the distance from the centre of disturbance, and as the rate of loss 

 of unit-pressure at the several distances from that centre : the value 

 for the basal radius of the cone of depletion being that distance from 

 the centre of disturbance in the plane of the water-surface at which 

 the loss of unit-pressure is zero, or at which the velocity of flow i& 

 normal. I therefore made an experimental determination of the 

 loss of pressure at each inch of depth below the surface of a cylinder 

 of rock of certain thickness, when subjected to a considerable 

 difference of pressure on its two surfaces : the upper surface being- 

 subjected to various constant hydrostatic pressures, and the pressure 

 on the lower side being atmospheric. The internal pressures were 



