148 On the Measure of 
to g*, (e—v)* and 39, h will be the height from 
which a body must fall to acquire the velocity 
c—v, and will be=“—**. Wherefore, by a 
proposition, well known in Hydraulics, the 
circumference of the wheel is urged by the 
weight of a column of water, of which the 
section is A, and the height on and of 
which the solidity is therefore Ax oon 
& 
Thus far the inyestigation is applicable to all 
undershot wheels, and to all hydraulic engines 
of a similar construction.” * 
Now, before we proceed to the remainder 
of this demonstration,t which is grounded 
upon the supposed certainty of this last con- 
clusion, let us see how far this theory agrees 
with the results of Mr. Smeaton’s experiments. 
Let w represent the weight of the column, 
the solidity of which is expressed by A x —?)® ee 
The value of w in Mr. Smeaton’s ee 
is easily found; and he has furnished data by 
which we can determine nearly the pressure 
by which the circumference of the wheel is 
urged. Let p represent that pressure; then, 
if the experiments agree with the theory, we 
* Edinb. Review, vol. 12, p. 124. 
+ Namely, that the maximum effect must be produced ; 
when v=3e, and that it is proportional to c?. 
a i a i i i li i) 
