G. K. Gilbert—The Oolorado Plateau Province. 95 
fine detritus, its velocity will be less than when carrying its 
maximum load of coarse detritus; and the greater load corre- 
sponds to the less velocity. 
It follows also thata stream which is supplied with heterogene- 
ous debris will select the finest. If the finest is sufficient in quan- 
tity, the current will be so checked by it, that the coarser cannot 
be moved. If the finest is not sufficient, the next grade will 
be taken, and so on. 
_ Transportation and Dectivity—To consider now the relation 
of declivity to transportation we will assume all other conditions 
to be constant. Let us suppose that two streams have the same 
length, the same quantity of water, flow over beds of the same 
character, and are supplied to their full capacities with detritus 
of the same kind; but differ in the total amount of fall. Their 
declivities, or rates of fall, are proportional to their falls. Since 
the energy of a stream is measured by the product of its vol- 
ume and its fall, the relative energies of the two streams are 
proportional to their falls, and hence, proportional to their de- 
clivities. The velocities of the two streams, depending as we 
ave seen above, on the character of the detritus which loads 
them, are the same; and hence the same amount of energy 1s 
consumed by each in friction on its bed. And since the energy 
which each stream expends in transportation is the residual 
after deducting what it spends in friction from its total energy, 
it is evident that the stream with the greater declivity will not 
merely have the greater energy, but will expend a less per cent 
of it in friction and a greater per cent in transportation. : 
Hence declivity favors transportation in a degree that is 
greater than its simple ratio. 
[There are two elements of which no account is taken In the 
preceding discussion, but which need to be mentioned to pre- 
vent misapprehension, although they detract in no way from 
the conclusions. 
The first is the addition which the transported detritus makes 
to the energy of the stream. A stream of water charged with 
detritus is ai once a compound and an unstable fluid. It has 
iring a constant 
Water alone, in the precise ratio of the mass of the mixture to 
the mass of the simple water. 
