266 <A short Account of Horizontal Water-Wheels. 
in a minute = 138, then 18388+60=2:5=7, and 
AW 30--'5236 x 2:3=4°55 feet, the diameter required. 
It may be proper here to observe, that when the quantity of 
water is not too great, nor the fall too high nor too low for the 
overshot wheel; its power will exceed that of the horizontal ; 
yet, in general practice the horizontal will certainly be superior, 
for the following reasons : 
1. Because the horizontal will act in any fall, its friction will 
not increase by the increase of water, and as it receives the wa- 
ter quite round the circumference, it will (when the supply is 
sufficient) work with a quantity greater than can be applied to 
the overshot without great loss of power. 
2. In the horizontal, while the depth from the surface of the 
water to the centre of force in the cuts remains the same, the 
power will increase with the quantity of water acting against the 
floats, or as the depth of the cuts; and since the quantity of 
water increases also with the circumference, or the radius of the 
wheel: Therefore 
The power will be as the product of the radius and depth of 
the cuts. 
Thus, if the depth of the cuts be made three times as great, 
and the radius twice as great, the power will be 3 x 2=6 times 
as great. Tlence 
If, in the model, the depth of the cuts be made 10 inches, 
and the radins 60 inches, or ten times as great, the power will 
be 10x 10=100 times as great, though the depth of the fall 
would be increased only 4} inches. 
. 8. When the depth of the fall is given, the size of the over- 
shot, as also its velocity, is fixed ; for if its diameter be 16 feet, 
its velocity, to produce the greatest effect must be five feet per 
second; but the velocity of the horizontal wheel, with a fall of 
16 feet, must be 12 feet per second. Again, an overshot of 
36 feet diameter must move 5°33 feet per second; but a hori- 
zontal with a fall of 36 feet must move with a velocity of 18 feet 
per second, to produce the greatest effect. 
4, The overshot must have a wheel fixed on its axis, and con- 
nected with other wheels or machinery before any effect can be 
produced ; but in the horizontal this is sometimes not necessary, 
as a mill-stone may be fixed on the top of the axis, and made to 
revolve with a proper velocity, without any connexion with other 
wheels, 
TABLE 
