342 



The Windings of Rivers 



Tracing B represents the part of the Mississippi between 

 the mouth of the Arkansas River and that of the Red River. 

 Tracing A represents the Devon Water, a tributary of the 

 Forth, and tracing C represents a quite insignificant brook 

 called the Catter Burn, a tributary of the Endrick, one of 

 the principal affluents of Loch Lomond. These tracings, and 

 indeed the maps of all countries, show clearly the great family 

 likeness exhibited by rivers in all parts of the world. This 

 likeness rests on the fact that in all rivers the relation between 

 the length of an arc or bow and that of its chord is nearly 

 the same. It is a racial rather than a family likeness, and 

 resembles that which exists between dogs of different breeds 

 or builds. 



The following table shows, for a selection of well-known 

 rivers, the degree in which the above relation holds good: 



From the table it will be seen that over a length of nearly 

 one thousand miles of the Mississippi the average length of 



