146 A NEW METHOD OF ESTIMATING STREAM-FLOW 
between 40 and 50 per cent. Also according to figure 5, page 33, the maximum 
flow at various places in the Miami Valley during the 1913 flood was from 68 to 
571 c.f.s. per square mile, and for the whole drainage area it was 94 c.f.s. per square 
mile. 
The more than 40 or 50 to 1 ratio of the R"s and the 11 to 1, to 90 to 1, ratio 
of discharges in c.f.s. per square mile, show that the law of flood-flow is probably- 
different, to a decided degree, from the law of normal stream-flow. 
The meaning of the quantity "Maximum R' expressed as a percentage, etc.," 
as used in the second preceding paragraph has not yet been defined. The definition 
appears subsequently in the proper context. 1 
The form of observation equation for determining flood-flow is as follows: 
r, i R', i +r fl R' /1 +r /1 R' /3 +r, i R', l +r, i R' fi + . . . +F'=» (57) 
The r/s and the R'/s have already been defined in connection with equation 
(37). G for any day is that addition to storage for the day which is just sufficient to 
saturate the ground on that day. 
A least-square solution for determining the constants in equation (56) gives 
rise to a set of v's. Using normally only those which are negative and greater than 
the suspicion limit of the solution to which equation (56) pertains, there is obtained 
a set of absolute terms, the F"s, of equation (57), from which one can derive the 
flood coefficients R' fl , R' n , R' ft , . . . provided G is known for each day. Appar- 
ently the best criterion by which to determine G for any day, the size of the r, for 
that day required to glut the ground, is the size of the stream-flow the preceding 
day, when it was not appreciably affected by abnormal surface flow. An examina- 
tion of all the F"s of the solution to which equation (56) applies, in connection with 
the Z)"s of the preceding day, enables one to establish a curve from which any G 
can be taken for the corresponding D' on the preceding day. This enables one to 
compute (r x — G) or r fl , and thereafter, the other r/s, the r/s with subscripts larger 
than 1 being obtained from r n in the same manner as has been explained for the 
r's. Knowing the r/s, a set of observation equations in the form of equation (57) 
can be written, from which the R'/s can be determined from the least-square 
solutions. The v's, or right-hand members in equation (57), serve to indicate the 
over-all accuracy of the theory, and enable one to compute the individual probable 
errors of the unknowns. 
METHOD OF PROCEDURE ON STREAMS A AND B 
It is now proposed to state, in outline only, the method of procedure on Streams 
F 
A and B in establishing numerical values for the S c 's, the R"s, the R'/s, ~, 
E v 
C, F, M and T". A detailed exposition of these processes would be outside the 
limits of space and time justified for them. It is hoped that a sufficiently clear 
statement can be made to enable one to grasp the principles involved, so that he 
may apply them to any streams anywhere to which this method is at present 
limited. The method of procedure is that indicated in the following numbered 
steps: 
(1) Using, first, an observation equation of the form of equation (56), in which 
E 
— was assumed to be 0.62, approximate numerical expressions of the normal 
E v 
1 See page 163. 
