Practical Remarks on Hydrometry. 



225 



There is little doubt but that Dubuat, with that yearning 

 for mathematical generalisations so characteristic of the 

 French philosophers, must, to a certain extent, have ignored 

 the results of experiment, in order to obtain the neat ex- 

 pression in the formula in question. 



De Prony's Eule, as expressed in metres, is 



_ / 2-372-f ^\ 



or, 



(7 71-}-^ \ ^^gj^ expressed in English, feet. 

 1U-254-W/ ' ^ 



It is far more accurate that Dubuat's, having been tested by 

 an immense number of observations, made not only in small 

 artificial channels, but alst) on the largest and deepest Euro- 

 pean rivers, with the aid of tachometers adapted for the 

 correct registration of velocities, at any depths below the 

 surface. 



For a surface velocity of fifteen English inches per second, 

 De Prony's rule gives the same mean velocity as Dubuat's 

 formula; but for surface velocities much less or much greater 

 than fifteen inches per second, the diversity between the 

 results is very great. 



For example, I will suppose that the observed surface 

 velocity of a stream is one inch per second. Then we should 

 have, 



1 f According to Duhuat's formula, \ « . . 



Corresponding mean velocity ^ ^^^Xyq^ to English inches, j " 



Ditto ditto According to Be Prony, ^ 0'75 inches. 



If, therefore, the sectional area of the imaginary stream be 

 such, that when multiphed by the mean velocity, as deter- 

 mined from Dubuat's formula, it would represent a water 

 supply for 100,000 persons, the more correct mean velocity, 

 according to De Prony, would represent a water supply for 

 150,000 persons! Whilst De Prony's formula thus gives 

 o-reater comparative mean velocities than Dubuat's, for sur- 

 face velocities less than fifteen inches per second, it gives less 

 mean velocities than Dubuat's for surface velocities exceeding 

 fifteen inches per second. 



The ratio of the mean velocity to the surface velocity 

 being mainly influenced by the rate of such velocity, and 

 being altogether independent of the depth or sectional area, 

 I cannot but think that tabulated quantities, for practical 

 c c • 



