224 A NEW METHOD OF ESTIMATING STREAM-FLOW 
than under the slopes, chemical and mechanical erosion having developed porosity- 
there. Thalweg travel affects the time of delivery at the maximum rate at the stream- 
flow measuring station very decidedly, but influences the rate of that maximum 
(maximum R') but little, that little being, however, in the direction of a reduction. 
Closely related to thalwegs are underground paths of small resistance to flow. 
In the formation of such paths, the mechanical erosion produces extension of such 
paths from the downstream end upward, since the rate of such erosion is apt to be 
greater the more rapid the movement of the water and the greater the total amount 
of water involved, and, since the erosion of this character may be negative, a plug- 
ging up in regions where the rate of movement is small. 
The chemical erosion tends to be greatest where there is water which has been 
in contact with the earth but a short time; that is, near the beginning of the under- 
ground travel, and at and near streams where there is the most active flow of 
underground water, i.e., near and at underground paths of small resistance to flow. 
The chemical erosion at a given point will tend to be proportional to the departure 
from chemical saturation of the water at that point, and the total amount of water 
per year departing from that point. Chemical erosion may in some cases cause a 
progressive extension of paths of small resistance to flow from the upstream end 
downward. 
The existence of thalwegs favors the development of underground paths of 
small resistance to flow by concentrating underground flow in certain paths under 
the thalwegs, and by producing locally large differences of head underground. 
Conversely, the existence of underground paths of small resistance to flow favors 
the development of thalwegs by favoring rapid local underground chemical and 
mechanical erosion, which in time produces a local lowering of the surface and 
thereby starts a thalweg, which tends to accentuate itself by surface erosion; and 
by favoring a concentration of underground flow to the point at which it produces 
surface flow, intermittent and steady, which in turn tends to produce surface 
erosion which favors a gradual upstream extension of a thalweg from the temporary 
or permanent headwaters of the stream. 
It follows that close dissection of the topography of a region by streams and 
thalwegs is strong presumptive evidence of close dissection of that region by under- 
ground paths of small resistence to flow, and vice versa. 
STREAM TRAVEL 
Stream travel predominates in the control of the lag of the maximum R' behind 
the corresponding rainfall, and reduces the size of the maximum R'. The rate of 
travel of the crest of a flood wave is not fixed by accelerations, except in great 
expansions of the river — lakes — in which there is a negligible current. The aver- 
age rate of travel of the crest of flood waves was found statistically to be 44 miles 
per day, or 1.8 miles per hour, or 33 minutes to the mile. The wave controlled by 
accelerations, the tidal wave, would move at double this speed even though the 
depth were only one foot, or at that rate if the depth were 0.25 foot. The average 
rate of travel of the crest of a flood-wave throughout its trip downstream is sub- 
stantially a constant for all streams. It is fixed in some way by the Chezy formula 
expressing the relation between slope of surface, hydraulic radius or resistance and 
velocity of flow. In other words it is fixed primarily by the internal and boundary 
resistance of the water. 
