A NEW METHOD OF ESTIMATING STREAM-FLOW 165 
hundred and fifty-sixth days, inclusive, after the change occurred. The probable 
errors of these quantities are those of equation (71) reduced to percentages. The 
product of each quantity in column 4 by the time interval involved in the compu- 
tation of the r's (shown in column 5) gives the total percentage of the change in 
storage on the current day which is delivered to the stream during the time 
interval in question. Thus, during the ninth to the sixteenth days, inclusive, after 
the change in storage occurs, a total of 0.088 per cent of it is delivered to the 
stream (shown inline 6, column 6). Evidently, totaling all the quantities in 
column 6 gives the total percentage of the change in storage, on the current or 
specific day, which is delivered to Stream A during a period of 257 days thereafter 
(including the current day). This is shown to be 13.G08 per cent. In other words, 
according to Solution M, only 13.6 per cent of any change in storage in the drainage 
area of Stream A on a day is delivered to the stream after a lapse of 8.4 months by 
travel through the ground to the stream, if, after the current or 0th day, the stor- 
age is assumed constant ; that is, if it is assumed that after the 0th day the evapora- 
tion and run-off are just equal to the rainfall plus net-melting on each day of the 
8.4-month period. If the change in storage is great enough to cause surface travel 
also, it will be shown subsequently that somewhat more of it than the above will be 
delivered in 32 days, by surface travel alone. * 
SMOOTHING THE R's 
In column 4 of the preceding tabulation, for any time interval involving more 
than one day, the percentage of the change in storage on a day which reaches the 
stream subsequently is written as if it were a constant amount throughout the 
time interval involved, as it necessarily must from the nature of the definitions of 
the r's and the manner of derivation of the R"s. As a matter of fact this is probably 
not the case. Presumably there must be a gradual rise in the R"s expressed as 
percentages, from the beginning of the current day until a peak is reached, after 
which there must be a gradual decline. The values in column 4 are represented as 
having a peak on the current day, a subsequent decline to the end of the 16th day, 
a rise from then to the end of the 96th day, followed by a final decline to the end of 
the 257th day. These fluctuations are probably not real. The increase in storage 
on a specific day must certainly decrease continuously along a smooth curve after 
the maximum rate of delivery is reached, which for this case was on the current day. 
The fluctuations in column 4 are probably due, in the main, to errors in the com- 
puted net melting computed from equation (64). They may be due, also, in part, 
to approximations in the assumptions and to using too small a number of observa- 
tions in their derivation. Whatever the causes, it was assumed in this investigation 
that the R"s expressed as percentages (column 4) should decrease along a smooth 
curve. Accordingly, column 4 and similar values for Stream B were smoothed off 
by taking successive means of three. The numerical work of that smoothing-off 
process for Stream A is shown in Table 44. 
In Table 44, column 2 is copied from column 4, Table 43. It was assumed 
that R\, R's and R\ should remain unchanged as they are apparently fairly well 
determined and fall on a smooth curve. It was assumed at this point also that R'i 
should remain unchanged as it appeared to fall in a probable position, and that 
r'u, 2 the next value after R' 1B , should be zero. With these assumptions, the 
1 See page 178. 
2 R'u was not evaluated in this investigation. 
