156 
A NEW METHOD OF ESTIMATING STREAM-FLOW 
was about May 8. It is apparent, then, that every r for June 1, 1913, which reached 
back beyond May 8 was made up in part of net melting, which was, for Solution M , 
computed by equation (64). In order to apply equation (64) to any winter season 
to compute the net melting, it is necessary to know the limits of the freezing-melting 
period, and the law of decreased rate of melting. 
FREEZING-MELTING PERIOD 
When the temperature, t, of the air over a watershed begins to lower with the 
approach of the winter season, there is a tendency for some of the stored water (in 
the lakes and ponds, if any, and streams and ground) on the watershed to freeze. 
When it reaches the temperature T' , there is no net change in storage on a day, due 
to freezing and melting, but as it goes below T", some of the water is held back from 
storage by freezing. As the spring season approaches, the temperature begins to 
rise and when it becomes greater than T' the storage in the watershed is augmented 
by the melting of the stored snow and ice on and in the ground. The "freezing- 
melting period," as used in this investigation, is defined as having its beginning 
when the temperature t first becomes and tends to remain continuously smaller 
than T' in the fall, and its ending when the last trace of snow has disappeared from 
the watershed. During the freezing-melting period, t may, and often does, rise 
above T' for short or long intervals. Throughout the freezing-melting period, with 
the exception to be stated in the following paragraph, that part of the change in 
storage due to melting or freezing is computed from the general expression, equation 
(36). In Solution M, the specific expression, equation (64), was used, as already 
mentioned. It is understood, from the definition of the r's, that if rain should fall 
during the freezing-melting period, it is added to the computed net melting to get 
the total addition to the storage for the day. 
DECREASE IN RATE OF MELTING 
The exception mentioned in the third preceding sentence is now to be stated. 
In the spring, toward the end of the freezing-melting period, the ground area, which 
might have been completely covered with snow several feet deep during the winter, 
becomes bare of it, rather rapidly at first, then more slowly, since the deep drifts 
offer more resistance to the melting influences than the lighter snows which cover 
most of the surface at a relatively uniform depth. After a while nothing remains 
but the scattered relics of the deep drifts, which yield smaller and smaller amounts 
of water to the underground storage by melting mainly around their fringes. From 
the definitions given after equation (36), in assumption No. (12), and elsewhere, 
and from the nature of the derivation of C, F and M as given later, the net melting 
can not be computed by equation (36) clear to the end of the freezing-melting 
period. After a certain part of the ground surface becomes bare, the decrease in 
rate of melting has been found to be approximated by the following expression: 
Decreased rate net melting of = 
-{T"-t)F 
or 
+ (t-T")M 
A-A, 
(67) 
In this expression A is the total water equivalent of the snow on the ground at 
the beginning of the period during which melting is taking place at a decreased rate, 
and A i is the total computed amount of melting which has taken place, commencing 
the day before the beginning day of the period and up to, but not including, the 
