96 SLODIES FOR SEODENTS 
erosion and deposition its slope thenceforward remains constant. 
The beginner would gather this understanding of the question 
from several of the definitions of ‘ baselevel”’ above quoted, 
but such is evidently not the case. When a stream is first 
graded, its channel is not level, and it has not reached the base 
of its erosive work. In virtue of the continual, though slow, 
variations of stream volume and load through the normal cycle, 
the balanced condition of any stream can be maintained only by 
an equally continuous, though small, change of river slope, 
whereby capacity to do work and work to be done shall always 
be kept equal. It might at first be thought that changes of this 
kind would be perceptible, and that there would be occasional 
departures of a river from the graded condition ; but such is not 
the case, because the change in the value of any variable in a 
unit of time is only by a quantity of the second order, by a dif- 
ferential of its total value. Once graded, a river will never 
depart perceptibly from the graded condition as long as the 
normal advance of the cycle is undisturbed. The slope of a 
river must necessarily be steeper on the first attainment of grade 
in early maturity, when an abundant load is received from the 
steep valley sides and the active headwater, than in late old age, 
when the valley sides have been worn down almost level, and 
when the even headwater streams are weak and sluggish. 
Hence, just as a graded river has slopes of varying declivities in 
its different parts at any one time, so the slope at any one part 
of the river must vary at different times in the successive stages 
Of thereyele: 
Not only so: it is eminently possible that the slope of a 
graded stream may have to be increased for a time after it has 
been first attained, for there is no necessity that the load should 
cease increasing just when its value has risen to equality with 
that which the stream can transport. There is much probability 
that, after grade is reached in a normal, undisturbed cycle, a 
river may have for a time to aggrade its valley floor until the 
time of maximum load is reached: and only after the maxi- 
mum gives way to a decrease of load can there be a beginning 
