A short Account of Horizontal Water-Wheels. 261 
velocity of the wheel, therefore 6 x square root of the depth = 
velocity of the wheel, and this may also, in practice, be taken 
for the velocity of the water without any material error, though 
its velocity will always be something greater than that of the 
wheel when moving without resistance. 
On these principles a small wheel with a high fall will move 
with a velocity amazingly great. Thus, let the diameter of the 
wheel be one foot, and the height of the fall eighty-nine feet, then 
5 Vv 89=56-60388 feet, the velocity per second; and as the cir- 
cumference of the wheel is 3:1416 feet; therefore 
As 3°1416:1::56°60388 : 18 revolutions per second, 
or 18 x 60 = 1080 revolutions in a minute. 
Power. 
In the specification, the power of the horizontal wheel was 
compared to that of the overshot, on a supposition that the force 
of a stream of water acting against a perpendicular plane near 
the orifice from which it flows, is nearly equal to the weight of 
the column which impels it, as Mr, Banks has proved by experi- 
ment. 
But in making some experiments for the purpose of ascer- 
taining the manner in which the water acts against the floats of 
the horizontal wheel, it appeared, 
_ That if a stream of water from a horizontal pipe, act against 
a perpendicular plane near the orifice with any considerable force, 
it will spread quite round in a thin sheet parallel to the plane, 
and leave it on all sides in that direction; and So til 
That if the edge of the stream be brought a little beyond the 
edge of the plane, so that part of it may pass by, it will form an 
angle with it; and that as the further side of the stream ap- 
proaches the edge of the plane, the angle will increase until they 
coincide, when it will become a right angle. 
Hence it is evident, that there is a reaction in this machine 
against the water coming in, which it is impossible to avoid, and 
that this is what reduces its power below that of the overshot 
wheel ; but that this reaction is very different from the centri- 
fugal force. 
Before we proceed to compute the power of the wheel, it is 
necessary to observe, that when the radius is one, the width of a 
cut is equal to the natural versed sine of the angle between two 
of them, taken at the centre, aud therefore, 
If the versed sine of the angle between two cuts be multiplied 
by any given radius, the product will be the width of a cut to 
that radius; and siuce all the cuts, in any cylinder, are equal in 
width, as they are also in depth; therefore, 
If the versed sine of the angle between two cuts be multiplied 
R 3 by 
