on Rivers and Canals. 569 
17. The velocity of each particle of water in a regu- 
lar channel, that is, where the bed is a regularly inclined 
plane, may be determined by drawing a perpendicular 
from the particle propofed to the horizontal curve which 
paiTes through the fpring, or that point of the river 
where the particle in queftion begins to acquire its velo- 
city. For the velocity which this particle would acquire,, 
in falling freely along the faid perpendicular, is the fame 
as that which it has acquired in its defcent along the in- 
clined plane of its bed. 
18. So long as a river perfeveres in the fame fate 
(N° 5.) there flows an equal quantity of water in equal 
times, how unequal foever the fedtions be througli 
which they flow ; and, confequently, where the fedtion 
of the river is greater,, the velocity of the flowing water 
is lefs; and where the fedtion is lefs, the velocity is 
greater; always in an inverfe proportion. From hence 
may be deduced the following and other limilar propo- 
fitions. 
1 ft, Through equal fedtions, in equal times, and with 
equal velocity, there muft flow equal quantities of water. 
adly, Through equal fedtions, in equal times, but 
with unequal velocities, the quantities of water which 
flow, are in a diredt ratio of the refpedtive velocities. 
3dly, Through 
