74 G. H. KNIBBS. 



the soil is capable of taking up, the total quantity goes directly 

 into the soil and is efficient in helping to saturate it. But for 

 rates of fall greater than that, more or less of the rain will run 

 off, and only part will be efficient in respect of saturation. Hence 

 clearly there is, for any given set of circumstances, some critical 

 value of dz/dt, changing however with the circumstances, above 

 which it becomes necessary to consider how much is lost by flow- 

 ing away. (See the point t x in Fig. 1, § 21 hereinafter). The 

 quantity efficient in producing saturation is obviously not only a 

 function of the permeability and temperature, it is also, even in 

 dry soil, a function of the slope (s say) of the surface; for the rate, 

 at which flow will take place over the surface, increases with the 

 slope. In other words in the case of falls of rain which are not 

 entirely absorbed by the soil, for a given quantity falling in a 

 given time, less enters the ground in a steep slope than in a slight 

 one ; and for the same soil and the same degree of saturation, 

 somewhat less enters in winter than in summer. 



9. Effect of slope of surface. — The effect of slope demands further 

 consideration. For any definite rate of rainfall on an impermeable 

 surface — let us suppose of uniform slope — the rate of run-off will 

 finally equal that of fall, and the depth to which the surface will 

 be covered will depend on its rugosity — n say — and the slope ; 

 that is to say the depth will increase until the velocity depending 

 on that depth and on the roughness, is sufficiently developed to 

 carry off the entire amount of rain falling. A similar, but not 

 identical thing happens, when the surface is permeable, provided 

 that more rain falls than can be simultaneously absorbed. The 

 rapidity of the flow into the permeable stratum, also increases with 

 increase of the depth to which the surface is covered, and is more- 

 over affected by the depth in the stratum to which the flow has 

 reached, so that the rate of surface-flow, or 'run-off' is not only 

 dependent on the intensity of rainfall and on the character and 

 slope of the surface, it too is similarly dependent on the depth to 

 which flow into the soil has attained. It is thus evident that both 

 'surface-flow' and 'permeable-flow' are definite functions 1 of the 

 1 Not necessarily discoverable functions. 



