82 G. H. KNIBBS. 



uncertainty as to the laws governing this depth, very much 

 increases the complexity of the problem. 1 



21. Graphs representing natural phenomena. — The absolute 

 necessity for considering the rate of rainfall in attempting to 

 ascertain what proportion is taken up by the soil, and how much 

 runs away, has already been adverted to. It may incidentally be 

 remarked, that the "run-off" from given areas, due to certain 

 types and quantities of rainfall, is an unsolved problem of great 

 practical importance, as civil engineers well know. In order to 

 deduce these two elements, the ' intensity curve ' of the rainfall, 

 as it may be called, is as we have already said, required. Graphi- 

 cally this may be shewn by ordinates (OY) giving the values dz/dt, 

 i.e., rate of fall, with the abscissae (OX) representing time, L 

 See Fig. 1 . Thus in the illustrative figure the curve (1) represents 



Fur. i. 

 a fall, at first gradually and then more rapidly increasing its 

 intensity, reaching a maximum, then somewhat rapidly diminishing, 

 afterwards very slowly, and finally ending rather abruptly. In 



curves of this type, where 



dz 



y — — , so that dz = y dt (12) 



we obtain the total fall in the unit of z — inches practically — by 

 integration. Thus from (12) we have on integrating 



z= p ydt=A (13) 



that is, the area A between the abscissa and the curve is the total 

 fall. Similarly if the ordinates of curve (2), shewn by the broken 



l In the paper previously referred to it is shewn that plants root more 

 deeply in arid climates. 



