164 
BIOVINC FORCE. 
Cases of diffi- square of the velocity of the water. Tliis conclusion seems, 
docm'nes'of quite in favour of the theory of mechanical 
Moving force, force, as laid down by our author, and the other supporters of 
the vis viva ; and yet we shall presently find, that it is perfectly 
conformable to the other theory, and to those reasonings of 
Desaguliers and Maclaurin, which Mr. Smeaton has censured 
as leading to conclusions altogether wide of the truth.” 
“ Let c be the velocity of the stream, v that of the wheel, 
A the area of the part of the float-board immersed in the 
water, g the velocity which a heavy body acquires in one se- 
cond when falling freely. Then c — v will be the relative velo- 
city of the stream and the wheel, or the velocity with which 
the water strikes the wheel ; and if we take h, a fourth pro- 
portional tog*, (c — v)* and h will be the height from 
which a body must tall to acquire the velocity c— v, and will be 
(c — n)® 
= , Wherefore, by a proposition, well known in Hj- 
draulics, the circumference of the wheel is urged by the weight 
of a column of water, of which the section is A, and the 
{c—v)*, (c— v)® 
height and of which the solidity is therefore A X . 
Thus far the investigation is applicable to all undershot wheels, 
and to all hydraulic engines of a similar construction*.” 
Now, before we proceed to the remainder of this demon- 
strationf, which is grounded on the supposed certainty of this 
last conclusion, let us see how far this theory agrees with the 
results of Mr. Smeaton’s experiments. 
I 
Let w represent the weight of the column, the solidity of 
(c—v)* 
which is expressed by A X . The value of tv in Mr. 
^g . 
Smeaton’s experiments, is easily found, and he has furnished 
t 
* Edinburgh Review, vol. 12, p. 124. H 
f Namely, tliat tlic iiiaximiiiu etfect niutt be produced when f* ".c, ( 
and that it i« proportional to c^- 
data 
