36 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



relation of depth to width. The relation is a 

 simple ratio, and either of the two terms 

 might be made the divisor. The width has 

 been chosen because, as in the case of fineness 

 its selection conduces to symmetry in formula- 



tion. The ratio will be called 



form ratio. Its symbol is R. 



Duty and efficiency. Capacity varies with 

 discharge, but is not proportional to it. The 

 load which may be borne by a unit of dis- 

 charge varies with the discharge and also with 

 the other conditions. It is the capacity per 

 unit discharge, or the quotient of capacity by 

 discharge, and will be called the duty. The 

 symbol is U. 



Capacity varies also with slope but is not 

 proportional to it. As the product of discharge 

 by slope (by the acceleration of gravity) 

 measures the stream's potential energy per 

 unit time per unit distance, capacity also varies 

 with the energy but is not proportional to it. 

 The load which may be borne by a unit of dis- 

 charge on a unit slope varies with all the con- 

 ditions of transportation. It is the capacity 

 per unit discharge and unit slope, or the quo- 

 tient of capacity by the product of discharge 

 and slope, and will be called the efficiency. 

 It is a measure of the stream's potential work 

 of transportation in relation to its potential 

 energy. Its symbol is E. 



The primary definition of efficiency in me- 

 chanics is the ratio of work done to energy ex- 

 pended; it implies that the work may be ex- 

 pressed in the same unit as energy. The ratio 

 is always less than unity. But there is an 

 important secondary use of the term, applied 

 to cases in which the result accomplished can 

 not be expressed in terms of energy. In such 

 cases the ratio may have any magnitude, as it 

 arises from the comparison of incongruous 

 quantities. It does not measure economy of 

 energy but relative accomplishment in respect 

 to any condition selected for comparison. As 

 capacity for transportation is not statable in 

 units of energy, the use of the term efficiency 

 in this connection falls under the second defini- 

 tion. 



Symbols. An index of symbols, with brief 

 definitions and references to pages for fuller 

 definition, may be found on page 13. 



TABLE OF OBSERVATIONS ON STREAM 

 TRACTION. 



The observations on stream traction &re 

 presented in Table 4. As the original notes 

 are voluminous, certain combinations and re- 

 ductions were made before tabulation. The 

 reduction of the slope observations involved 

 discrimination, and the mode of reduction is 

 therefore described below. Each horizontal 

 line of the table contains the record of a single 

 experiment. 



The observations are arranged according to 

 (1) fineness of dfibris, (2) width of channel, 

 (3) discharge, (4) load and slope. The cate- 

 gories of fineness begin with single sizes, 

 taken in order from fine to coarse, and follow 

 with mixtures; they constitute subtables, each 

 designated by a letter in parentheses. The 

 arrangement by load and slope is approximate 

 only. In a general way the sequences of load 

 and slope are parallel, each increasing as the 

 other increases, but the data are not per- 

 fectly harmonious, and where the two se- 

 quences differ the arrangement is somewhat 

 irregular. 



The first column, for all divisions of the 

 table except (J), gives width of trough; the 

 second, discharge. The third, fourth, and 

 fifth pertain to load and give, respectively, 

 the load as measured by debris fed at the 

 head of the trough, the load as measured by 

 debris caught at the outfall end, and the 

 period, in minutes, during which debris was 

 collected at the outfall end. The precision of 

 measurement is probably somewhat higher 

 where the period is relatively long. 



The next three columns pertain to slope. 

 The sixth contains the slope, in per cent, of 

 the water surface; the seventh, the slope of 

 the bed of debris as shaped by the current; 

 and the eighth, the extreme distance between 

 points at which were made observations used 

 in computing the slope or slopes. Nearly all 

 the experiments for which the recorded dis- 

 tance is 16 feet or less were made in the 

 shorter trough, of which the gross length was 

 31.5 feet, the distance between the debris- 

 feeding apparatus and the debris-arresting ap- 

 paratus being 24.5 feet. The experiments for 

 which the recorded distance exceeds 16 feet 

 were made in the longer trough, the distance 



