Rainfall and Flood Discharge. 151 



The next, and a difficult and serious matter in the estimate, 

 is the soakaofe. Durino- the averasfe time that the discharo^e 

 at any instant has been travelling, soakage has been taking 

 place, and the amount of soakage varies much more than the 

 rain. I have no doubt that parts of sandy areas, such as 

 Caulfield and Brighton, will absorb water faster than any 

 rain that ever fell. 



For the purpose of arriving at the form a simple formula 

 should take, it appears to me to be necessary to assume 

 quantities which cannot be fixed. The rainfall, for instance, 

 I assume to vary as the cube root of the time : — 1 inch in 

 :J hour, 2 inches in 2 hours, 4 inches in 16 hours, 8 inches 

 in 5 J days. The observed quantities I give at the end (A). 

 If the total maximum rain be assumed to vary as time", the 



TITYIP' I 



rate of fall will vary as r^ — = ,- Assume the watershed 



•^ time time^ 



a constant narrow width, and assume the water to flow at a 



constant rate, which though not true, the tendency is to 



equalise, as the grades near the extreme limits are generally 



steeper. The area will vary as the time the water has to 



, -| Til T'1 -n area area 



travel, and the discharge will vary as ,- — a = i rr-^ 



^ -^ time' length^ 



Then, if we assume length to vary as Varea, 1 = a*, as 

 for similar figures and substitute we obtain discharge varies 

 as areal This takes no account of soakage, or varying 

 inclinations. 



That is, that the maximum discharge will depend on the 

 area, and inversely on some power of the length, and this is 

 the form that I have adopted. 



For small areas of clay and rock, and tolerably impervious 

 surfaces in larger areas, I have for the present adopted the 

 following in the same form : — ' 



-r^. , 1 . p , 1 area sq. chains X 181 



Discharge cubic leet per second = ^ rr^ — • — to-, . -. o,^n. 



^ ^ length chains^ '^ + 1800 



The co-efficients for which I have obtained from the following 

 three recorded observations : — 



Maximum discharge 4 feet per second from 4 acres, 



length 7 chains. 

 Bendigo Creek 4100 feet per second from 10,000 acres, 



length 7J miles. 

 Coliban 10,000 feet per second from 64,000 acres, length 



22 miles. 



