8 H. J. Harman—Operations for obtaining [No. 1, 
There is a clumsiness in the formula, but no alteration has been made, 
because I set up all the quantities for giving the discharges before it was 
noticed. The values of the discharges are not affected, but I may as well 
note how the formula took its shape. 
Let M N O P (Fig. 6) be an open channel of considerable length 
the flow of water uniform, the section of the channel rectangular, 
Let ed and ef be two lines parallel to each other, at a perpendicular 
distance apart equal to gh. ab is a section at right angles to length of 
tube and to the direction of flow of water. 
Let the angle cgi = 90° + 6, and v be the depth. 
Let ¢ be the time in seconds taken by a particle of water to move 
from g to K. 
Then the Discharge through the section ed = EE EA 
The Discharge through ab = ed x cos 6 x v x gh — 0 oe cd Xv xX gh 
t 
It is this formula (1) which has been employed. 
Fig. 6. 
(a) The line of maximum velocity of a river is found at a short dis- 
tance below the surface. The velocity at the bottom of a river is less than 
the surface velocity ; the retardation is great if there are many weeds. 
The bottoms of all the rivers measured were of coarse heavy sand, 
excepting a short stretch of big pebbles in the bed of the combined Dihang 
and Dibang rivers. 
Professor Rankine assumes that the mean velocity on a vertical line, 
is to the greatest velocity on the same line, as 3 to 4 for slow rivers and 4 
to 5 in rapid streams. 
The velocity of a rod extending to nearly the bed of the stream is ap- 
proximately the mean velocity of the water in the vertical plane traversed 
by the rod. In assigning a mean velocity for computation to the several 
portions of the sections of the rivers, all the above facts were kept in view. 
At some sections of observation for determining velocity, many differ- 
ent instruments were used and many passages made; at other sections only 
a few observations were made. 
