108 E. F. PITTMAN. 



Gregory argues that inasmuch as the loss of head in pipes 

 increases, owing to friction, as the diameter of the pipes 

 decreases, in porous rocks the loss of head rises to a maxi- 

 mum, because the interstitial spaces represent pipes of 

 exceedingly small diameter. The answer to this is that the 

 loss of head also increases approximately as the square of the 

 velocity, 1 and that therefore velocity is a much greater 

 factor in determining loss of head than is either the dis- 

 tance travelled or the diminution of the diameter of the 

 tubes: and the head is therefore maintained in artesian 

 basins owing to the extremely slow rate of flow of the 

 water in the porous beds. Kuibbs has shown 2 that in a 

 uniform stratum the velocity diminishes, as the distance 

 from the bore is increased, in the ratio -J- , where r is the 



iv 



radius of the bore and R the distance of the point con- 

 sidered : that is to say, putting v for the velocity at the 

 bore of radius r, and V for that at the distance B from its 

 centre, V = — . Consequently if a 6 inch bore discharges 



with a velocity of oh feet per second from a porous bed of 

 uniform thickness, the velocity of the water in the porous 

 bed at a distance of one mile from the bore would be sio inch 

 per second, or 2'2£ feet per day : if the distance be increased 

 to five miles, the velocity of the water in the porous bed 

 would be reduced to 4J feet per day. In short we may 

 conceive that, in the first instance, the water in an artesian 

 basin would, unless there were a natural outlet, be practi- 

 cally without motion: in this case the pressure would be 

 hydrostatic; then the putting down of bores would induce 

 a flow, with high velocity in their immediate vicinity, but 

 decreasing gradually to an infinitesimal rate of movement 

 as the distance from the bores increased. The pressure 

 would thus become hydraulic. 



1 The Dead Heart of Australia, p. 302. 



8 G. H. Knibbs, The Hydraulic aspect of the Artesian problem. This 

 Journal xxxvu., 1903. p. xxx. 



