37 2 Dr. Young's Hydraulic Investigations. 
by determining v according to this method ; then, taking 
b = - — ■— — - or rather, as Langsdorf makes it, b = 
b —V , Af"Jo rJ — V t 4.02 
to proceed in calculating v by the formula v ■= 148.5 
{s/d- . 2 ) . ( v/i ,_ H . L ' v . (t+ ,. 6) - .001 ) , since this determi- 
nation of b will, in general, be far more accurate than the 
simple expression b = and the continued repetition of 
the calculation, with approximate values of v, may thus be 
avoided. Sometimes, indeed, the values of v found by this 
repetition, will constitute a diverging instead of a converging 
series, and in such cases, we can only employ a conjectural 
value of v, intermediate between the two preceding ones. 
Having sufficiently examined the accuracy of my formula, 
I shall now reduce it into English inches, and shall add a se- 
cond table of the coefficients, for assisting the calculation. In 
1440 
1 8c 
this case, a becomes .0000001 ( 41 q + ^ „ — , , 
5 V ^ o 1 d d 128 ^ + -355 
9 °° M +^(1085 + ^ + ^i). and 6 = 
: .OOOOOOl ( 
(Id -J- II 36 
t 
al : d + .0017 1 
, e being 
b cl , 
— , and v 
= = y/{bh - f e 4 ) 
— e, or = 
v/( ~ J r~) ~~ ~ , as before; and in either case the superficial 
velocity of a river may be found, very nearly, by adding to the 
mean velocity v its square root, and the velocity at the bottom 
by subtracting it. 
