Limiting Width of Meander Belts 



377 



Calling the Tennessee comparable to 

 the first three rivers because of its mod- 

 erate descent, we may construct a curve 

 with discharges for ordinates and mean- 

 der belts for abscissas. The curve is, 

 however, determined at points too few 

 and badly placed to be of much value. 

 The following selected quantities indi- 

 cate well enouarh its character : 



md 



nib 



o 







500 



1,400 



1,000 



2,600 



5,000 



7,000 



10,000 



10,700 



50,000 



28,000 



100,000 



33-500 



500,000 



54,000 



That is, the larger the volume of 

 water discharged by a river, the wider 

 its meander belt, but the differences in 

 width are less as the rivers are greater 

 in volume. 



The data for incised rivers do not fall 

 into this curve. Such data do not suf- 

 fice to establish definite relations. 



SOME THEORETICAL CONSIDERA- 

 TIONS 



Stream volume is a function of width, 

 depth, and velocity. Maturely mean- 

 dering streams may be regarded as find- 

 ing their slope too steep. As this gave 

 them more energy than was needed to 

 carry their load of waste seaward, they 

 employed the excess in cutting sidewise, 

 forming meanders until their slope was 

 thus lengthened and flattened to their 

 taste. The Mississippi travels So miles 

 along its winding channel in flowing 

 from Greenville to a point 45 miles due 

 south. In so doing it reduces its 

 descent from 7 inches to 4 inches per 

 mile. When a cut-off thwarts further 

 lengthening of the course, we must 

 suppose that the proper slope has been 

 already reached. So maturely mean- 

 dering streams will have courses tend- 



ing to a minimum of inclination, differ- 

 ing with each other chiefly as they 

 carry more or less silt. It is probable 

 that meander-cutting, like all other 

 erosive work, is chiefly effected at re- 

 current moments of more intense activ- 

 ity. Perhaps there is never a cessation 

 of the cutting on the outer bluff ; yet 

 the greater part of the work will be 

 done at times of swollen waters. At 

 these moments the streams are bur- 

 dened with silt to their utmost capacity, 

 all of them alike and each of them in 

 its mean thread of flow. The swift 

 outer reaches are still eager to take 

 more earth from the bank, while every 

 check within a bend is the scene of act- 

 ive deposition. As the load of silt de- 

 termines the slope needed for its trans- 

 portation, here is another agency tend- 

 ing to uniformity of slope in all streams 

 with well-developed meander systems. 

 These considerations look to the elimi- 

 nation of velocity as a constant factor in 

 the volume of the stream ; there remain 

 as varying factors width and depth. 



We cannot assert that at the time of 

 most effective meander-making depth, 

 too,- is a constant, but there are consid- 

 erations which tend to show it has little 

 effect on the width of meander belts. 



The width of a meander belt depends 

 immediately upon the sharpness with 

 which a stream can turn a corner. Gen- 

 erally speaking, the longer the radius 

 of curvature, the wider the belt, and 

 the shorter the radius, the narrower the 

 belt. The stream's difficulties in turn- 

 ing increase with the stream's width 

 quite apart from its depth. 



Material cords and cables offer some 

 interesting analogies. A thread may be 

 doubled sharply on itself, a string less 

 sharply, while a large rope or cable can 

 only be bent in a wide, open turn. The 

 difficulty is with the inside strands. The 

 thicker the rope, the more there are of 

 them, and the more they insist on tak- 

 ing up room and holding the bend open. 

 If a board is to be bent sidewise, an in- 



