BASELEVEL, GRADE AND PENEPLAIN 93 
in one does not necessarily call for a change in the other. 
But when all falls and rapids are worn down, and all lakes 
ane sullled? up, and the entire: mver system is joraded,))as 1s 
characteristically the case in the late-mature stage of a cycle, 
the organization of the system is so complete that all its parts 
are correlated. A change at any one point then involves a 
change, of infinitesimal amount perhaps, all through the system. 
It is this condition of organization that Gilbert alluded to in 
describing the “interdependence” that comes to be developed 
among the different lines of a river system, as a result of which 
‘“‘a disturbance upon any line is communicated through it to 
the main line and thence to every tributary” —( 1877, 124). 
The actual slopes of the different parts of a graded river sys- 
tem vary from a faintest declivity in the lower course of the 
trunk river to decidedly steeper declivities in the uppermost 
courses of the headwater streams. If any stream line is followed 
from head to mouth its profile will show a curve, approximating 
theoretically to the flatter part of one wing of a parabola ;* but 
when studied in detail, the normally continuous decrease of slope 
down stream is found to be seldom realized. The entrance of a 
tributary is usually accompanied by a decrease of slope up- 
stream and an increase of slope down-stream from the tributary 
mouth; the spasmodic action of floods introduces some faint 
symptoms of disorder in otherwise simple slopes; and in this 
connection the inequalities due to what McGee has called “ vari- 
gradation” are to be considered (1891, 269; see also Oldham, 
1888). All these complications in the slopes of a graded river 
system make it extremely difficult to conceive of a surface which 
d 
shall generalize the river slopes. Indeed, it is hardly worth while 
to attempt this conception, for the reason that all the value of the 
imaginary surface is to be found in the actual slope lines of the 
graded river systems by which the surface is guided. It is with 
respect to the sloping course of a graded stream that the valley 
*It is evidently only under the assumption that the baselevel is not a convex 
level surface, but a plane that the profile of a river can be described as a parabola. 
The actual profile of a large river, such as the Mississippi, is convex to the sky. 
