Practical* Remarks on Hydrometry. 995 
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 Rule, as expressed in metres, is 
Tie 2:372 Lv 
= (3153-0) 3 
or, 
771-Lv , 
Gees v; when expressed in English feet, 
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 also 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 pier 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, 
: 0 According to Dubuat’s formula. 
Corresponding mean velocity { coulis Pa eee ae ie, z } 0:50 inches. 
Ditto ditto According to De Prony, . 0°75 inches. 
Tf, therefore, the sectional area of the imaginary stream be 
such, that when multiplied 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, 
greater 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 
Cc Cc 
