
" Parr IL. Secr. ii. §3.] FLOW OF RIVERS. — 363 
even in regard to their angle of slope. For example, two streams 
rising at a height of 1000 feet, and flowing 100 miles to the sea, would 
each have an average slope of 10 feet per mile; yet they might be 
wholly unlike each other, one making its descent almost entirely in 
the first or mountain part of its course, and lazily winding for most 
of its way through a vast low plain; the other toiling through the 
mountains, then keeping among hills and table-lands, so as to form 
on the whole a tolerably equable and rapid flow. The great rivers 
of the globe have probably a less average slope than 2 feet per mile. 
The Missouri has a descent of 28 inches per mile. The average 
slope of the channel of the Thames is 21 inches per mile; of the 
Shannon about 11 inches per mile, but between Killaloe and 
Limerick about 63 feet per mile; of the Nile, below Cairo, 3°25 to 
5-5 inches per mile; of the Doubs and Rhone, from Besangon to the 
_ Mediterranean, 24°18 inches per mile; of the Volga from its source 
to the sea, a little more than 3 inches per mile. Higher angles of 
descent are those of torrents, as the Arve, with a slope of 1 in 616 at 
Chamounix, and the Durance, whose angle varies from 1 in 467 to 1 
in 208. The slope of a navigable river ought hardly to exceed 
10 inches per mile, or 1 in 6336.7 
But not only does the rate of flow of a river vary at different 
parts of its course, it is not the same in every part of the cross- 
section of the river taken at any given point. The river channel 
(aa, Fig. 106) supports a succession of layers of water (0, c,d), moving 
with different velocities, the greatest : 
movement being at the centre (d), 3 
and the least in the layer which bietwest 
lies directly on the epee : At % Z) | y 
the same vertical depth, therefore, / yy yy GLE 
the velocity is greater in propor- MMT HH: iy 
tion as the point approaches the Fig. 106.—Cross Srction or A River. 
centre of the stream. The water 
next the sides and bottom being retarded by friction against the 
channel, moves less rapidly than the layers (b b, ¢ ¢) towards the 
centre (d). The central piers of a bridge have thus a greater velocity 
of river current to bear than those at the banks. It follows that 
whatever tends to diminish the friction of the moving current will 
increase its rate of flow. The same body of water, other conditions 
being equal, will move faster through a narrow gorge with steep 
smooth walls than over a broad rough rocky bed. For the same 
reason, when two streams join, their united current, having in many 
cases a channel not much larger than that of one of the single 
streams, flows faster, because the water encounters now the friction 
of only one channel. The average rate of flow is much less than 
might be supposed, even in what are termed swift rivers. <A 
moderate current is about 1} mile in the hour; even that of a 
torrent does not exceed 18 or 20 miles in the hour. Mr. D. Steven- 


1 D. Stevenson, “ Canal and River Engineering,” p, 224. 
