OBSERVATIONS ON DETERMINATIONS OF DROUGHT-INTENSITY. 75 



duration of the rainfall — t say. If we divide the total fall into 

 two portions, z x and z 2 , denoting respectively 'surface-flow' and 

 'permeable-flow,' then dzjdt will be zero for all values of dz/dt 

 below the critical value. And always, if we neglect losses by 

 evaporation — de/dt say — while rain is actually falling, we should 

 have the total rate of fall equal to the sum of the rates of 'run-off' 

 and saturation : that is 



dz _ dz x dz 2 ,o\ 



~dt~~dt ~dt ^ ' 



To recapitulate : — Both elements of flow are functions of the 

 duration and rate of fall, the permeability, the temperature of the 

 soil (6 say) and the slope and roughness of the surface ; and may 

 be symbolically represented by 



V dt 



-t( t~.B.0.s.n) 

 dt r \ dt J 



-^^(t.^.B.O.s.n) 

 dt \ dt / /a\ 



dz 2 , i A dz 



the functions <j> and \p being however by no means easy to deter- 

 mine. One necessary element in the solution, viz., the law of flow 

 of a thin stratum of liquid over a rough inclined surface, has not 

 as yet been satisfactorily solved, though roughly approximate 

 solutions are available. The matter however is actually not as 

 simple as indicated by these equations, which represent the solu- 

 tion for an extremely elementary case. This will more fully 

 appear latter. 



10. Percolation into or through permeable strata when the inter- 

 stices are full. — When a permeable stratum is covered by a liquid, 

 the flow thereinto is, for cases naturally occurring, always irro- 

 tational. 1 Hence, for a stratum whose interstices are uniform in 

 size, the resistance to flow — due to the total shear or distortion of 

 the fluid in translational motion only — will vary as the square of 

 their linear dimensions (as E 2 say); and for a stratum whose inter- 



1 In a thin stratum of say pebbles, rotational flow would be developed, 

 in which case the potential is exhausted not only by translational, but 

 also by the rotational motion. 



