Contents xlvii 



PAGE 



by every stream of water that flows over it, and to 

 show that the message of all of them is identical. 



Impossibility of determining the magnitude of a 



from the study of a tracing of its course alone . 341 

 Illustrated by tracings of three streams of very 

 different magnitudes in Fig. i . 



The great family likeness exhibited by rivers is due 

 to the fact that the relation between the arc and the 

 chord of their sinuosities is nearly the same for streams 

 ot all magnitudes ....... 342 



Table showing this in the case of well-known rivers. 

 On the Thames the distance along the windings from 

 Teddington to the Isle of Dogs is exactly equal to the 

 length of the semicircle described on the shortest dis- 

 tance between these two points as base. 



Considering rivers flowing through plains consist- 

 ing of alluvial matter in which the river carves out 

 and maintains its own bed, the distance along the 

 windings from one point on its course to another is 

 between 60 and 70 per cent, greater than the shortest 



i nee between these two points .... 343 



1 1 is the flood waters which determine the bed of a 

 cessity of transverse oscillations in every 

 im. 



A stream following a straight course is unstable, 

 attempt made to arrive a priori at the laws of 



s of streams. 



The old method of trial by error has been used. 

 Curves have been traced according to different 

 >nic specifications until a family <>f curves was 

 1 at \\hich offered a good resemblance to. the 

 s of actual n 



2 is an example of one of th< . . . 344 



It ia n < 1 1 linear and a reciprocating 



Hi* linn ot tin- general How of the rivn 



motion ;i ' - to it. Th<> 



itnm motion is double 



itiiiK motion. 



Geomrtii. allv. it is a I .minis. .id. that is a o>m- 

 tilmrar motion with motion Kuind a 



i sea te or figure of < 345 



hrs and thrir imp 



