20 
Arterial Drainage 
and direction for the carrier which shall convey away the water 
as rapidly as possible in times of excess, and yet not suddenly 
exhaust the country, but leave a supply for the droughts of summer 
and early autumn. 
The power which moves the rainfall from the pores of the 
earth to the river, and thence to the ocean, is that due to gravity, 
or the attraction which the earth exercises upon all bodies in a 
direction perpendicular to the surface of the sea. Every particle 
of a fluid being equally attracted in the same direction, the 
surface always has a tendency to become level, and water, if left 
free to act, continues in motion until all its particles attain the 
same level. Hence the particles of water at the upper end of 
a stream are always in motion towards the lower level, and the 
whole mass moves downwards until the lowest level attainable is 
reached. The vertical space through which the water moves in 
its course is termed the " fall," and the length of the stream 
divided by the fall, gives the rate of fall, inclination, or gradient. 
This motion is checked by the retarding force due to the friction 
which the particles of water meet with from the sides and bottom 
of the channel, and from weeds, and other impediments. The net 
result attained from the operation of the two forces is termed 
the velocity of the stream, generally reckoned at so many feet per 
minute or miles per hour. The greater the length, therefore, in 
proportion to the fall, the greater the friction, the slower the 
current, and the smaller the quantity moved in a given time. 
Water rubbing against water meets with less friction than when 
rubbing against earth, consequently the smaller the surface of 
earth which the water touches in the channel the less the friction. 
Water in a deep narrow channel will move more rapidly than 
in a broad shallow one, because it encounters less friction. And 
so also a straight stream will, cceteris paribus, discharge more 
water than a crooked one, because the proportion of length to 
fall is less, the friction is less, and the space travelled 'over is 
less. Engineers use the term " hydraulic mean depth " to 
represent the proportion of rubbing surface in a stream to the 
volume of water passing along it. The figure representing 
this is found by dividing the sectional area of the channel 
l)y the length of the border touched by the water, and forms an 
important clement in all calculations for the discharge of water- 
courses. 
In order to find the size of a stream adequate to convey a 
given quantity of water in a given time, it is necessary to fix its 
area, contour, rate of fall, and mean frictional resistance. For 
tliis tliere are several different lormuhr ; but that adopted in 
Beardmore's ' Manual of Hydrology,' I'or finding the velocity ia 
feet per minute (v) is to multiply the square root of the hydraulic 
