STREAM VALLEYS AND THEIR MEANING 



479 



of the bank at ^ . If only inertia were acting, the meanders would 

 be enlarged symmetrically; but there are two other factors to be 

 taken into account. These are the down-stream component of 

 gravity and the tendency of the thread of the current to follow the 

 shortest course round the insides of the bends/ The former of 

 these acting on a particle of water at any point, X, would tend to 

 make the particle move in a direction 

 X-Y , parallel to the median Hne of 

 the stream at that point. The latter 

 would tend to lead the current along 

 the inner bank, A-C. The resultant 

 course of the thread of fastest current 

 would be along some line such as 

 A-D, intermediate between A-B and 

 A-C, giving greatest erosion at and 

 below D rather than at B . The cur- 

 rent, on account of a combination of 

 the two latter forces, would hug the 

 down- valley bank A-C more closely 

 than would otherwise be the case, 

 while it would draw away from 

 the up-valley bank near B. Thus 

 would the meander migrate down- 

 valley. 



It is at once evident that an in- 

 crease in gradient of the stream would 

 increase this tendency to down-valley 

 migration because it would increase 

 the down-valley component of grav- 

 ity at a greater rate than it would in- 

 crease the force due to inertia, since 



the latter, dependent as it is on velocity, would be cut down by 

 friction. 



Increase in volume without change in gradient would tend 

 toward greater symmetry and relatively slower down- valley migra- 

 tion, for greater velocity, due to lessened frictional resistance, 



^ J. Thompson, Proceedings of the Royal Society of London, XXV (1876), 5-8. 



Fig. 5. — Diagram of a stream 

 meander to show the explanation 

 of the down-valley migration or 

 sweep of meanders and the effects 

 of gradient on the forces con- 

 cerned. The dashed line repre- 

 sents the thread of fastest current; 

 the dotted lines the courses this 

 thread of fastest current would 

 take if the various forces were act- 

 ing alone. The line from A to B 

 represents its course if inertia alone 

 were active; ^ to C that if inertia 

 were inoperative. 



