ADJUSTMENT OF OBSERVATIONS. 



95 



was made on logarithmic section paper. By 

 way of illustration the plot for grade (B), 

 width 1.96 feet and discharge 1.119 ft. 3 /sec. is 

 reproduced in figure 28, the finer lines of the 

 logarithmic net being omitted. The vertical 

 lines represent values of slope; the horizontal 

 lines, capacity, depth, mean velocity, and form 



-C- 



100 V m 



.1.0 



I 



-.2 



.3 



R, 



.4 .6 



SJope 



.8 1.0 



2.0 



FIGUKE 28. Logarithmic computation sheet, combining relations of 

 capacity, mean velocity, form ratio, and slope. 



ratio. For the convenience of having the 

 graphs close together their scales are made to 

 differ, the ratio of one to another being 10, 100, 

 or 1,000. In the particular instance shown in 

 figure 28 the same line represents C= 100, 

 d = 0.1, V m = 1.0, and 5 = 0.1. With use of this 

 notation were plotted the equations for C, d, 



V m , and R, as functions of . In their loga- 

 rithmic forms these are 



log d = log &' ttj log $ 



log F m =log ^-log <Z=log log I' + n, log 8 

 log R = log d log w = log ! log $ 



log (7= log & t + log (S-ff) 



Their loci are the straight lines marked d, V m , 

 and R and the curve marked C. 



After the preparation of these constructions 

 the values of d, V m , and R, corresponding to the 

 selected series of values of 8, were read from the 

 sheets, affording the data of Table 14. The 

 sheets had also many other uses, for in record- 

 ing the relations of four interdependent varia- 

 bles to slope they also recorded their relations 

 to one another. The points of the four loci 

 which lie in the same vertical represent corre- 

 sponding values of the several variables, and 

 this property made it possible to read from the 

 plot the value of a variable corresponding to a 

 particular value of one of the others. For 

 example, if it is desired to learn the capacity 

 corresponding to a mean velocity of 2 ft./sec., 

 the intersection of the velocity line with the 

 line representing 2 on the scale of velocities is 

 first found. From that intersection a vertical 

 is followed or drawn to the capacity line and 

 the position of the second intersection is read on 

 the capacity scale. 



A large part of the numerical data cited in 

 the following discussions were either taken 

 directly from the computation sheets or based 

 upon them. 



The accuracy of the computations by loga- 

 rithmic graph may be characterized by saying 

 that it is slightly below that by slide rule. The 

 theoretic accuracy is the same, but tests of uhe 

 logarithmic paper employed showed it to be a 

 less perfect instrument than the slide rule, 

 which was used for a large body of routine 

 computations. 



