A short Account of Horizontal Water-W heels. 263 
But it appears that Mr. Smeaton has inserted °32 in his 
Table as the true effect in this case, on a supposition that the 
same effect may be obtained irom half the power; and he there- 
fore multiplies the weight of the water expended in a minute by 
15, or half the depth, instead of 50, which was the depth through 
which the water, that turned the wheel, actually descended in a 
minute. 
Had he made such a discovery as this, he ought to have given 
a demonstration, or a clear proof of its truth; for his argument 
about a virtual head, certainly gives no such proof: on the con- 
trary, he says that he has obtained more than double of what is 
assigned by theory; and that this is very different from the opi- 
nions and calculations of authors of the first reputation. 
The reason of making this remark is, that it is probable the 
power of the horizontal wheel will be compared with that of the 
undershot, according to Mr. Smeaton’s Table, where he has in- 
serted double the power of the undershot wheel (or very near it) 
according to his own experiments. 
The horizontal wheel may be used in any fall however high or 
low. 
In low Falls. 
Example.—Let the depth of the fall be two feet, diameter of 
the wheel twenty feet, number of cuts twenty-four, and their 
depth four inches ; 
Then, by the Table, the angle between two cuts is 15°, and 
its versed sine ‘034074 ; therefore, 
034074 x 10 x 24 x +=2°72592 square feet, or the area of a 
rectangular passage equal to that of the perpendicular sections 
of all the cuts. 
This may therefore be considered as the base of a column of 
water, the height of which is the perpendicular distance from the 
surface to the centre of pressure or the middle point of the cut, 
which in this case is 22 inches, or |! feet; hence we have 
2°7592 x ‘3 =5 cubic feet, nearly =5 x 62°5=312°5 pounds 
weight constantly impelling the water through the cuts against 
the floats quite round the wheel, and 312-5 divided by 24, gives 
13 pounds for each cut or passage. ‘The greatest velocity of 
the wheel will be 6/11 = V 66=8'124, or about eight feet per 
second; and therefore when it works to the greatest advantage 
will be four feet per second. Then 
as 4:1°;;20x3'1416; 157 time of a revolution, 
In high Falls, 
In order to obtain the full force of the water here in the same 
manner 
