262 A short Account of Horizontal Water-Wheels. 
by the radius, and then by the number and depth of the cuts, 
that is versed sine x radius x number x depth, it gives the 
area of a rectangular section equal to the area of the perpendi- 
cular sections of all the cuts. 
In the model the radius is six inches, the number of cuts 
twenty-four, and their depth one inch; the angle 15°, and its 
versed sine ‘034074 ; ; therefore 
*034074 x 6 x 24 x 1=4-906656 square inches, 
which, in consequence of the cuts having been made rather wider 
: . 5 5 
by dressing, is taken at five square inches or jaz Square feet, 
and the water being four feet deep, its velocity was 6./4=12 
feet per second ; 
5x19 5 
Hence, arr Tate cubic feet of water issue in a second, or 
5x60 z f : 5 
> = 25 cubic feet in a minute. 
Therefore for the power, we have 25 cubic feet, or 25 x 62°5 
- pounds of water descending through four feet in a minute ; hence 
The momentum of the power is 25 x 62°5 x 4=6250. 
Then to find the momentum of the effect, according to Mr. 
Smeaton’s method ;—when the wheel moved without water, a 
weight of ten ounces gave it a velocity of two revolutions per 
second. Therefore according to the third experiment, the 
weight raised was eight pounds ten ounces, or 8°625 pounds ; 
consequently, 
The momentum of the effect was 8625 x 210=1811°25 and 
as 6250: 1811:25.::1:°2398 the effect. But ifthe velocity of 
the water be found according te Mr. Banks’s mean of the ex- 
periments of six different authors, it will be 108 feet per se- 
cond, and the effect will be -522; and this makes the power of 
the horizontal wheel double to that of the undershot, according 
to the second example in Mr. Smeaton’s Table. 
Remark. 
Mr. Smeaton, at> page 12 of his Treatise on Mills, gives an 
account of an PapeTiment on the undershot wheel, where it ap- 
pears that his head, or fall, of water was thirty inches, and that 
264°7 pounds weight of-w ater was expended, or descended 
through thirty inches in a minute; hence, 
The momentum of the power was 264:7 x30=7941, that 
9-375 pounds weight of water was raised through 135 inches 
in a minute by the wheel ; hence, 
The momentum of the effect was 9°375 x 185= 1265-625, 
therefore as 7941 : 1265°625 :;1 ; +1594 the effect, and -1594 x 2 
=='3188= double the effect. 
But 
4 
