APPLICATION TO NATURAL STREAMS. 



233 



The dune movement, the migrations of 

 greater bars, and the transfers of debris from 

 deep to shoal and shoal to deep are all compe- 

 tent to give information as to tractional load, 

 but the estimates they give are minimum 

 estimates, to be supplemented by estimates of 

 the material which at flood stages is swept 

 steadily along without contributing to any of 

 the temporary deposits in such way as to be 

 accessible to measurement. 



AVAILABILITY OP LABORATORY RESULTS. 



THE SLOPE FACTOR. 



Wo are now ready to inquire whether, in 

 view of the diversities and complexities affect- 

 ing traction by natural streams, the formula 

 for tractional capacity derived under the 

 comparatively simple conditions of the labora- 

 tory is of practical value in connection with 

 natural streams. The four factors of the 

 formula may first be considered separately. 



The general slope of a stream is the quotient 

 of fall by distance, the distance being taken 

 along the stream's course. It is best measured 

 at high stage, because the chief work of grading 

 the channel is accomplished by floods. 



With reference to variations in capacity at a 

 single locality, slope does not enter, the varia- 

 tions being referred to discharge; but account 

 must be taken of slope in comparing different 

 divisions of the same stream and in comparing 

 one stream with another. 



In all such cases the stream's slope is as 

 definite a quantity and is susceptible of as 

 precise measurement as is the slope of the 

 laboratory channel. It differs as to its repre- 

 sentative character. The laboratory slope is 

 connected with a single discharge and a single 

 grade of debris of determinable fineness. The 

 slope of the natural stream does not represent 

 the adjusting work of a determinable discharge 

 but is a compromise product of the work of 

 many discharges, and it is usually true that 

 the velocities associated with these discharges 

 have determined equally diverse mean fine- 

 nesses of debris. The work of the natural 

 stream, moreover, has been characterized by 

 greater diversity, from point to point, of the 

 bed velocities, and its system of velocities has 

 been regulated in part by suspended load. 



These difficulties would prove insuperable if 

 attempt were made to infer the capacity of a 

 natural stream from that of a laboratory 



stream, but they are not necessarily important 

 in transferring a law of variation from a group 

 of laboratory streams to an equally harmonious 

 group of naturalstreams. If the diversification 

 of discharges and finenesses is of the same type 

 for the examples of natural streams between 

 which comparison is made, it may well be that 

 the slopes are comparable, one with another, 

 in the same sense in which they are comparable 

 in laboratory work, and that their relations to 

 capacity should follow the same law. 



THE DISCHARGE FACTOR. 



Discharge differences must be considered 

 when the tractional capacities of different 

 streams are to be compared, and also in com- 

 paring the capacities of the same stream at 

 different tunes. 



In making comparison between different 

 streams it is important that the discharges used 

 be coordinate that is, that they represent 

 equivalent phases of stream work. If co- 

 ordination be not secured, allowance must be 

 made in one stream or the other for the varia- 

 tion of capacity with stage. In case the prob- 

 lem is such that the choice of phase is optional, 

 preference should be given to flood phases, 

 because the general slope and the details of 

 channel shape are approximately adjusted to 

 such phases. The greatest known discharge is 

 probably less representative of the channel 

 conditions than is the mean of annual maxima 

 of discharge. It is believed that with use of 

 discharges that are both representative and co- 

 ordinate the discharge factor of the empiric 

 formula may be applied. The result of such 

 application will be the more satisfactory in 

 proportion as the streams compared are allied 

 in type and will be relatively unsatisfactory for 

 streams in different climatic provinces or for 

 comparison of a direct alluvial stream with 

 one which meanders. 



It is to be observed that in ah 1 studies of allu- 

 vial streams the discharge of which account 

 should be taken in connection with traction is 

 the discharge flowing in the channel proper. 

 That which passes the banks ceases to con- 

 tribute of its energy to the work of traction, 

 and the portion of load diverted with it is not 

 tractional. 



The case of variation of discharge in the 

 same stream is complicated by simultaneous 

 variations of fineness and competence. In the 



