zo4 A short Account of Horizontal Water-W heels. 
manner as in low falls, the height of the walls of the reservoir 
-would require to be equal to that of the fall. But, 
This however is not necessary, as both the reservoir and inner 
eylinder may be covered at any proper height, as denoted by the 
dotted line in the plate, but the reservoir must be made water- 
tight. 
A pipe may then be brought from the surface of the water ta 
the bottom of the reservoir, where it must be so fixed that the 
water may flow from it in the same direction as the wheel turns, 
which, in that respect, will augment the power. 
But as this supplying pipe will be in the place of a reservoir 
of water, the area of a section of it ought to be greater than the 
sum of the areas of the perpendicular sections of all the cuts, 
and it ought also to be constantly full up to the top, otherwise 
the water would not be supplied so fast as it could pass through 
the cuts, and a part of the power would be lost, unless there were 
a contrivance for covering or shutting up part of the cuts. 
Example.—Let the depth of the fall be 81 feet, diameter of 
the wheel 10 feet, number of cuts 30, arid their depth half a 
foot. 
Then, by the Table, the angle between two cuts will be 12°, 
and its versed sine -021552; therefore, 
(021852 x 5 x 30 x 1=1-6389 square feet, which is the area 
of a rectangular passage, equal to that of the perpendicular sec- 
tions of all the cuts, and the diameter of a circular pipe of equal 
area will be 17-3 inches, therefore the diameter of the supplying 
pipe must be greater than this. 
If the radius of the wheel and depth of the cuts remain the 
same, the greater the number is, the less will the area of the 
whole of their perpendicular sections be, and consequently, the 
less water will pass through them, but it will act nearer to the 
circumference ; and therefore, in proportion to its quantity, will 
produce a greater effect. 
Example.—Let the numbers be 12, 16, 30, 50, then these 
multiplied by their respective versed sines will be 
; 4 qn 2 ry r O07 which are the ratios of the sums of 
x 076120=1-21792 tl £ thei + ania 
30 x-021852=0°65556 he areas of their perpendicular 
50 x +007885 =0-39425 9 Sections. 
Hence, when the quantity, or supply of water is great, the 
number of cuts must be small, and, on the vontrary, when it is 
small,.the number of evts must be great in order to obtain the 
greatest effect, 
The 
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