A NEW METHOD OF ESTIMATING STREAM-FLOW 223 
SLOPE TRAVEL 
Slope travel is uniformly distributed over a large area in such manner that the 
rate of travel is most increased at first at the lower end of such travel, and becomes 
a progressively smaller increase. As a consequence it follows that the maximum 
R' (expressed as a percentage) tends to be greater the smaller the average slope 
travel for a stream, and to be greater the more rapid the slope travel. For any 
given line of slope travel there is a normal profile for the water surface. S c is the 
discharge corresponding to the normal profile. This normal profile will be ap- 
proached by a stable profile whenever the r,, r 2 , r,, . . . r„ for a given day are all 
zero, and will be reached if at that time the total storage in the drainage area is 
equal to the average storage of a long period. All profiles are nearly coincident 
at their lower ends with the normal profile, and the discharge corresponding to a 
stable profile is a close approach to S c . 
When a stable profile is reached, for any short section of the profile, the flow 
at the lower end of the section will equal the flow along the profile at the upper end 
of the section, plus the total amount of water received vertically from above. The 
changes in the water received vertically from above tend to be the same simultane- 
ously over the whole drainage area, and hence tend to raise (or lower) all parts of 
all profiles by the same amount simultaneously. After the period necessary to 
establish a stable profile the remaining R"s tend to be more nearly alike; that is, 
the discharge expressed by these R"s is merely a function of the total storage and 
not of the time when that storage was accumulated or reduced. 
Whenever any part of a profile is changed, the rate of flow at that part changes 
in proportion to the quantity h/p, in which h is the head (or vertical travel) and p 
is the corresponding length along the profile. (Note that the maximum value of 
h/p is 1.0.) It follows that in any given section the rate of flow may, as a first 
approximation, be taken proportional to h in that section. Under all steep slopes 
the percentage variation in h tends to be small, because h is large in proportion to 
the change of level of the water surface. Consider the cross-sections of divides as 
shown in the upper right-hand corner of Plate 21. The percentage variation in h 
will be smaller in (a) than in (6) if the variation of the water level at the upper end 
of the slope is less in (a) than in (b). It will be smaller in (6) than in (c) if the 
variation in water level at the lower end of the slope is less in (6) than in (c). Under 
all flat slopes, the percentage variation in h tends to be large. It tends to be 
especially large and prompt at and near the lower end of such slopes. It 
follows then that the rate of flow under steep slopes tends to be relatively con- 
stant; and that the rate of flow under flat slopes tends to be relatively variable. 
The greater the percentage of slope travel w T hichis above the point of steepest 
slope, the steadier will be the flow and the longer the change of flow due to a given 
r, will last. Also the greater the height, h, involved in the steep slope, the steadier 
the flow. 
Of the five cases shown on Plate 21, the order of steadiness of flow would 
probably be, steadiest first, (c), (d), (b), (a), (e). 
The preceding remarks apply to slope travel alone. To estimate the relations 
of the various R"s one must also take thalweg and stream travel into account. 
THALWEG TRAVEL 
Thalweg travel is much more rapid than stream travel, because under a well- 
defined thalweg at the depth of rapid travel of water the soil or rock is more porous 
