PROBLEMS ASSOCIATED WITH KHYTHM. 



249 



by parts of vortices A and B, and give attention 

 to the motions by which the water in the tract 

 is surrounded and influenced, taking care to re- 

 fer each motion to the middle of the tract itself. 

 Thus referred, the motion of the adjacent part 

 of the rear vortex A is to the left and down- 

 ward, that of the forward vortex B is to the 

 left and upward, and that of the bed is to the 

 left. The motions are indicated by arrows. 

 The influences of the vortices tend to make the 

 water about D rotate backward, while the influ- 

 ence of the bed tends to make it rotate forward. 

 The result is not a priori evident, but may be 

 assumed to be something different from simple 

 rotation. Its possibilities will again be re- 

 ferred to. 



Now consider the tract E, bounded below by 

 parts of A and B and above by the water 

 surface, and give attention to the motions by 

 which its water is affected. Motions being 

 referred as before to the tract itself, that of 

 vortex A is to the right and downward, and 

 that of vortex B is to the right and upward. 

 Above is the motion of the air, which, in the 

 absence of wind, is to the left, as indicated by 

 an arrow. The three influences to which the 

 tract of water is subject all tend to give a 

 backward rotation, as indicated in a similar 

 position at F. The vortex F is secondary to 

 the A, B, C system and rotates in the opposite 

 direction. If its motions be referred to the 

 fixed stream bed, it is evident that the water 

 in its upper part moves in the direction of the 

 current less rapidly than the water in its lower 

 part. The existence of such a vortex therefore 

 tends to reduce the average velocity at the 

 surface of the current and increase it at some 

 lower level. 



Abandoning now the specific and ideal case, 

 we may state the hypothesis in general terms. 

 Among the important causes of vortical motion 

 in a river or other stream is the mechanical 

 couple occasioned by the general forward 

 motion of the water in conjunction with the 

 resistance of the bed. This tends to form 

 vortices with horizontal axes and forward roll; 

 and the tendency is probably strongest in the 

 lower part of the stream. In a space adjacent 

 to two forward-rolling vortices there exists a 

 tendency toward the development of a second- 

 ary, backward-rolling vortex, but this tendency 

 is apt to be nullified by other and adverse 

 influences except in the upper part of the 



stream. The free surface of the water does 

 not oppose the development of such reversed 

 vortices. Wherever reversed vortices abound 

 the velocity at the surface (averaged with 

 respect to time) is less than at some level below 

 the surface. 



The hypothesis as stated has no stationary 

 element, but the phenomena of incipient dunes 

 show that in certain cases repetitive motions 

 are associated with stationary space divisions. 

 A supplementary suggestion assigns these 

 repetitive motions, or their initial phases, to 

 the triangular space D in the ideal diagram, 

 figure 83. The forces tending toward rotation 

 in that space are antagonistic; and the sugges- 

 tion is (1) that they produce some sort of 

 alternating movement with regular periodicity, 

 and (2) that the time interval of this move- 

 ment, in combination with the forward move- 

 ment of the major vortices A, B, C, yields a 

 stationary space interval. 



An investigation based on this line of sugges- 

 tion and designed to test it should lead also to 

 an explanation of the observed changes in the 

 method by which traction is accomplished. 

 The dune method is associated with a depth 

 which is large in relation to the mean velocity 

 and with a moderate bed resistance. It is 

 replaced by other methods in consequence of 

 (1) a reduction of depth, or (2) an increase of 

 velocity, or (3) an increase of resistance. 

 Reduction of depth diminishes the space for 

 development of the hypothetic vortices. In- 

 crease of velocity or of resistance tends to 

 enlarge their pattern. In either case the 

 coercion of the water surface restricts the 

 freedom of vortical movements and imposes 

 conditions tending to modify their system. 



THE MOVING FIELD. 



The competent investigator is resourceful in 

 the creation of new apparatus and methods as 

 the need for them arises. While fully conscious 

 of this fact, and of the further fact that no 

 device is of assured value till it has been tried, 

 I yet can not forbear to mention, for the benefit 

 of others, a method which the Berkeley experi- 

 ence leads me to think valuable for the study of 

 the internal details of a current of water. 



In a current limited by the sides of a narrow, 

 straight trough transverse movements are 

 largely suppressed, so that most of the action 

 can be learned from observation of what takes 



