A NEW METHOD OF ESTIMATING STREAM-FLOW 219 
and 6.5 times the p.e. If N' be the total number of observations on a stream greater 
than its S c , then, on that stream, 0.0002 XiV'X 24.8 will be the probable number of 
stream-flows between 5.5 p.e.-f-*S e and 6.5 p.e.+^L Thus, on Stream A, 0.0002 
X 700X24.8 = 3.47, which is the probable number of flows out of every 700 greater 
than S c which is to be expected between a discharge of (5.5X.185+0.108 = )1.126, 
and (6.5X0.185+0.108 = ) 1.311 c.f.s. The actual number observed was 2. 
From the definitions of S c and the mode, one would expect them to have the 
same value or that the value of K t in (100) would be unity. The derived mode 
from the Type III Pearsonian curve, being negative in every case, has no meaning 
in this sense. The modes determined by inspection are shown in the lower left- 
hand corner of Plate 21 based upon the discharges for 1911-13, and in the lower 
right-hand corner of Plate 22 based upon the discharges for 1911-15. Compare 
first the modes based upon 1911-13 with the derived values of S e . For Stream B, 
the mode determined by inspection is 89. The value of S e is 96. This gives a 
value of K, of (96/89 = )1.08, which is 8 per cent larger than the value to be expected 
from theory. For Stream A, the value of K, based upon 1911-13 is( -tt7t= )l.26, 
or 26 per cent too large. Compare next the modes based upon the observed dis- 
charges for 1911-15 as determined by inspection. For Stream B, K t is (7^= ) 
1.26; and for Stream A,K t ia C^ = \.42. 
The proper interpretation of these discrepancies appears to be that the derived 
values of S c are too large in both cases. Note that the value of i£, for Stream B 
was nearer the value to be expected from theory than that of Stream A, correspond- 
ing to the known errors in the Stream A computations produced principally by the 
use of too large a value for M(=+8.39). Note that the values of K, for both 
streams were nearer the truth when based upon the data for 1911-13 than when 
based upon the data for 1911-15, corresponding also to the positive knowledge that 
M = +8.39 (used on Stream A) is too large, and with the suspicion that the final 
values of C, F and M used on Stream B give a computed net melting which is 
possibly too large. 
In the case of a frequency distribution of stream discharge which is skewed 
very little, from which the derived mode by Pearson's Type III curve would pre- 
sumably come out positive, the procedure would be to take i£ 3 = l in (100) in this 
case. For intermediate cases, in which the mode derived by Pearson's Type III 
curve would give absurd values of S c computed from K 3 = —0.48, the proper pro- 
cedure would be to reject such a value and base the S c upon the estimated mean 
and median, only. 
GENERAL RESUME OF THEORY 
In the preceding pages there has been presented in detail this method of esti- 
mating stream-flow. In the pages which follow it is proposed to give, first, at the 
expense of some repetition, a resume of the theory on which this method is based; 
second, to present certain conceptions which will aid one in applying this method 
to other streams; third, to state briefly some possible applications of this research; 
and fourth, to present a general summary of the conclusions reached. 
If one understood what happens to each portion of water in a drainage area 
between the time it falls as rain and the time it goes out of the drainage area as 
