16 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



ment more frequently encountered is to the 

 effect that the quantity varies with the sixth 

 power of the velocity; and the origin of this 

 assertion is not in doubt. It is an erroneous 

 version of a deductive law commonly attribu- 

 ted to Hopkins (1844) or Airy and Law (1885), 

 although announced as early as 1823 by Les- 

 lie. 1 The law, as formulated by Hopkins, is 

 that " the moving force of a current, estimated 

 by the volume or weight of the masses of any 

 proposed form which it is capable of moving, 

 varies as the sixth power of the velocity"; 

 and this law pertains not at all to the quantity 

 of material moved, but to the maximum size 

 of the grain or pebble or bowlder a given cur- 

 rent is competent to move. 



The subject of the competence of currents, 

 or the relation of velocities to the size of par- 

 ticles they can move, has also been treated 

 experimentally by several investigators, and 

 some account of their work will be given in 

 later chapters. 



About the year 1883 Deacon made, in Man- 

 chester, England, a notable series of experi- 

 ments in the field of stream traction. As a 

 result of definite measurements of quantities 

 of sand transported and of the velocities of the 

 transporting currents, he announced 2 that the 

 amount transported, instead of varying with 

 the sixth power of the velocity, as had been 

 supposed, actually varies with the fifth power. 



In the field of flume traction the work has 

 been somewhat more extensive, having as its 

 special incentive the needs arising in ore mills 

 for the conveyance of crushed rock; and a 

 resumS of results will be found in the chapter 

 on flume traction. 



A still greater body of investigation has been 

 conducted by German and French engineers 

 with the use of laboratory models of river chan- 

 nels. The French work was done largely for 

 the purpose of testing certain rules formulated 

 by Fargue 3 for the improvement of navigable 

 streams. The German experiments were and 

 still are addressed to the broader subject of 



i Sir John Leslie's analysis is to be found in his Elements of natural 

 philosophy, and in the edition of 1829 occurs at pages 426-427 of volume 1. 

 David Stevenson mentions 1823, which probably indicates the first 

 edition. William Hopkins gives a diflerent analysis with practically the 

 same result, and does not mention Leslie. The passage quoted occurs in 

 Cambridge Philcs. Sec. Trans., vol. 8, p. 233, 1844, and is probably from 

 his earliest discussion of the subject. Wilfred Airy's later but evidently 

 independent analysis appears in Inst. Civil Eng. Proc., vol. 82, pp. 25-26, 

 1885, with expansion by Henry Law on pp. 29-30. 



Deacon, G. F., Inst. Civil Eng. Proc., vol. 98, pp. 93-%, 1894. 



* Fargue, L., Annales des ponts et chauss&s, 1894. 



river engineering in general and include within 

 their scope the scientific study of the ways in 

 which rivers shape and reshape their channels. 

 The quantitative laws of stream traction, 

 which constitute the chief theme of the Berke- 

 ley work, thus fall within the province of the 

 German investigators, but their study has not 

 been taken up. There are three German labo- 

 ratories, all well equipped, located severally 

 at Dresden, Karlsruhe, and Berlin. 4 



The flow of a stream is a complex process, 

 involving interactions which have thus far 

 baffled mechanical analysis. Stream traction 

 is not only a function of stream flow but itself 

 adds a complication. Some realization of the 

 complexity may be achieved by considering 

 briefly certain of the conditions which modify 

 the capacity of a stream to transport debris 

 along its bed. Width is a factor; a broad 

 channel carries more than a narrow one. 

 Velocity is a factor; the quantity of debris 

 carried varies greatly for small changes in the 

 velocity along the bed. Bed velocity is affected 

 by slope and also by depth, increasing with each 

 factor; and depth is affected by discharge and 

 also by slope. If there is diversity of velocity 

 from place to place over the bed, more debris is 

 carried than if the average velocity everywhere 

 prevails, and the greater the diversity the 

 greater the carrying power of the stream. Size 

 of transported particles is a factor, a greater 

 weight of fine debris being carried than of 

 coarse. The density of debris is a factor, a 

 low specific gravity being favorable. The 

 shapes of particles affect traction, but the 

 nature of this influence is not well understood. 

 An important factor is found in form of chan- 

 nel, efficiency being affected by turns and curv- 

 ature and also by the relation of depth to 

 width. The friction between current and 

 banks is a factor and therefore likewise the 

 nature of the banks. So, too, is the viscosity 

 of the water, a property varying with tempera- 

 ture and also with impurities, whether dis- 

 solved or suspended. 



The enumeration might be extended, com- 

 plexity might be further illustrated by pointing 



< The equipment and work of the laboratory of river engineering of the 

 Technical High School of Dresden are discussed in the Zeitschrift fur 

 Bauwesen, vol. 50, pp. 343-300, 1900, and vol. 55, pp. 664-C80, 1905; the 

 equipment of the laboratory of the Technical High School "Frederici- 

 ana " of Karlsruhe in the same journal, vol. 53, pp. 103-136, 1903, and vol. 

 60, pp. 313-328, 1910; and the equipment and work of the Laboratory for 

 River Improvement and Naval Architecture, Berlin, in vol. 56, pp. 123- 

 151, 323-324, 1906. 



