258 PRINCIPLES OF STRATIGRAPHY 



especially the size of the grains. The following formula of Allen 

 Hazen (32:57/) takes more factors into consideration and serves 



for experimental purposes, v^=c d~ - (0.704-0.03^), v being the 



velocity of the water in meters per day in a solid column of the same 

 area as that of the sand, c a constant factor found empirically to 

 approximate 1,000; d is the "effective size""' of sand grains in 

 mm., which is such that 10 per cent, of the material is of smaller 

 grains and go per cent, of larger grains than the size given ; h is 

 the loss of head; / is. the thickness of sand through which water 

 passes, and t is the temperature on the centigrade scale. The loss 

 of head is measured from points just inside the ends of the column 

 of sand or soil. (See, further, King-4i:5p; and Slichter-64 :5i'^, 

 329; 65:79, 22.) 



The quantity of water transmitted by a column of sand depends 

 upon the length of the column and the head of water, and further- 

 more varies with the effective size of the soil grain, the tempera- 

 ture of the water and with the porosity of the soil. The flow varies 

 as the square of the size of the soil grain, and doubling the size of 

 the grain will quadruple the flow of water. Thus the flow through a 

 soil whose effective size of grain is i mm. is 10,000 times the flow 

 through a soil whose effective size of grain is o.oi mm. The flow 

 at 70° F. is about double that at 32° F. 



The. Underflozv. This is the moving sheet of water beneath the 

 bed and banks of a stream through the porous medium. This may 

 be so concentrated as to produce a subterranean stream, scores of 

 feet in depth and miles in breadth. It naturally follows a line of 

 depression in the surface of the sustaining impervious layer — the 

 Thahi'eg — and the rapidity of flow will depend in a very large 

 measure upon the texture of the material forming the river bed. 

 Where this is fine the water will be stored, but a considerable un- 

 derflow is impossible. Where the 'material is coarse sand and 

 gravel, however, as near the mountains, the water will readily flow 

 through it. In arid regions, the lower reaches of the surface 

 streams often disappear altogether, by sinking into the ground. 

 They are then continued by the underflow, and only occasionally 

 after a heavy storm are the "dry washes" filled again by a rushing 

 surface torrent. In general, the underflow follows the trend indi- 

 cated by the surface branches, which may extend as dry washes 



* Determined by experiment to be the mean diameter of the grains, or the 

 one which, if all the grains corresponded to that size, would give the soil the 

 porosity it actually has. 



