MATHEMATICAL FORMULAE 81 



multiplied by some constant, depending mainly on the char- 

 acter of the surface, the substitution of this gives 



A 3 

 D 10 = o.oooioigr 3 , 



with c=J, and r = i; but 



and 



assuming the constant 100: R is the hydraulic radius and s 

 is the slope; but R for a circular pipe flowing full = Z>/4. There- 

 fore 



Q=Av=-, 



4 



Q =~5 V#3 = 39- 



whence 



or 



Equating this value of D 10 with that from the formula 

 given above, 



/ Q V I 



() - = o.< 

 \39- 2 7/ s 2 



= O.OOOIOI< 



\39- 2 7/ 

 or 



which is a modified form of the Hawksley formula. 



Adams, on the ground that experience showed that, while 

 this formula was sufficiently satisfactory for small districts, 

 it gave sewers of inadequate dimensions in the case of larger 

 areas, proposed a modification of the ordinary formula for 



