KEVIEW OF CONTROLS OF CAPACITY. 



195 



In the first sentence of the passage (pp. 193- 

 194) which has been inclosed in quotation marks 

 to indicate its literal translation, Lechalas ap- 

 pears to equate the velocity of a particle of the 

 load with the difference between the forward 

 pressure of the current and the resistance given 

 by the particle. Hooker 1 suggests that the ac- 

 celeration of the particle instead of its velocity is 

 intended ; but with or without such emendation 

 the author's reasoning is obscure to me, for I 

 see no necessary physical relation between the 

 number or mass of debris particles moved and 

 the pressure of the current. The load may be 

 defined as the product of the mass of particles 

 by their average speed; and their speed, being 

 produced by the pressure of the current, may 

 be simply related to it, but any relation of the 

 mass to the pressure is necessarily indirect and 

 presumably involved. 



Whatever the strength or weakness of the 

 postulates on which the formula is based, the 

 manner in which it incorporates the principle 

 of competence gives it a rough resemblance to 

 those we have developed, while the char- 

 acterization of its constant m gives to it a 

 large empiric factor; and it is- in order to 

 inquire whether, as an empiric formula, it 

 finds support in the Berkeley data. As the 

 Berkeley observations do not include bed 

 velocities, the most direct comparison is 

 impracticable; but an indirect relation may 

 readily be established. 



The difficulty we have found in defining bed 

 velocity may be avoided, for the purpose of 



1 Hooker, E. H., Am. Soc. Civil Eng. Trans., vol. 36, p. 256, 1896. 



the present comparison, by accepting the 

 definition used by Lechalas in 



- (3) 



and by assuming depth to be constant. Ac- 

 cording to the Chezy formula this assumption 

 makes V m approximately proportional to 

 T/S~, so that loads', in (3), is proportional to 

 V m . It follows that V b is proportional to V m , 

 and this permits us to substitute V m for F 6 in 

 equation (4) by changing the constants: 



-l<) __________ (6) 



This expression implies that capacity for trac- 

 tion varies with mean velocity at a rate which 

 diminishes as mean velocity increases but is 

 never so low as that of the second power of 

 mean velocity. The corresponding data from 

 our experiments, namely, the data for capacity 

 in relation to mean velocity under the condi- 

 tion of constant depth, are in accord with this, 

 except that they indicate a limiting index of 

 relative variation somewhat less than 2. In 

 Table 51 the values of the synthetic index, Ir d , 

 range from 2.03 to 7.86; and a value of 2.03 

 for the synthetic index implies smaller values 

 of the instantaneous index. This discrepancy 

 is not important, and the formula of Lechalas, 

 regarded as empirical, is probably adequate 

 for the discussion of a body of observations 

 on capacity and velocity. It could not, how- 

 ever, be used in connection with the Berkeley 

 data unless both K and Tc (or m and 0.06 in 

 equation (4)) were permitted to vary with 

 conditions. 



