54 BULLETIN 1017, XJ. S. DEPARTMENT OP AGRICULTURE. 
a continuous increase in size of channel of the Red Eiver and a de- 
crease in the general slope of the channel, broken by short stretches j 
of greater fall (see fig. 2). 
"When the water in the river reaches a stage of 23 feet on the gauge 
maintained by the United States Weather Bureau at Moorhead, 
Minn., the water starts to overflow the inner banks and reaches some 
of the lower lying road grades, buildings, and bridges — the channel 
between the mouth of the Dakota Wild Eice Eiver and the mouth of 
the Sheyenne Eiver will easily carry 6,000 second-feet. A rise above 
23 feet causes the overflow of low areas within loops of the river and 
parts of the city of Fargo which lie but slightly above the banks of 
the lower-water channel. Even at stages as high as 35 feet at Fargo 
no extensive areas of land are flooded. Below the mouth of the Shey- 
enne Eiver the channel of the Eed Eiver will carry 12,000 second- 
feet, and from the mouth of the Buffalo to Grand Forks 15,000 sec- 
ond-feet can be passed without overflow. Below the mouth of the 
Eed Lake Eiver at Grand Forks the channel is considerably larger 
than above, and in the stretch between that point and the interna- 
tional boundary, along which the slope constantly diminishes, are 
found the sections of maximum area (see figs. 2 and 4). This part 
of the channel will carry a volume of 25.000 second-feet without top- 
ping the outer bank. 
It should not be presumed that the river when flowing at these 
maximum rates will entirely fill the channel for its whole length, or 
that greater volumes can not be carried at some points without over- 
flow. The figures given refer to the approximate maximum volumes 
that can be passed through the various sections of the channel with- 
out overflow at any point along the river. Greater volumes can be 
carried at certain points, but even though the river remains within 
the banks at these points it will overflow either above or below. When 
flowing bank- full, on the other hand, the smaller sections pass more 
water than their size and the slope of the stream as a whole would 
indicate. This is due to the heading up of the water above the sec- 
tions of small area, and the ability of the larger sections below to 
carry the same volume at lower stages, which gives an increased 
water-surface slope through the restricted portions. The capacity 
.as calculated by Kutter's formula agrees very closely with actual 
discharge as indicated by stream-gauging records. 
TRIBUTARY STREAMS. 
In some respects the tributary streams are much like the Eed Eiver, 
the fall being slight in the lower parts of the channels. However, in 
their upper reaches the fall in most cases is much greater than in the 
Eed. These streams rise outside the old lake boundary and flow 
from the east and west through the old beaches across the flat lake 
