MILL. 
adequate size can be applied, water becomes 
the momentum ; but where neither of the 
foregoing can be found under suitable cir- 
cumstances, a well-exposed spot is ordina- 
rily selected for the erection of a wind- 
mill. We shall shew the quantity of water 
necessary to work a wheel of certain di- 
ameters; observing that eighteen feet has 
been found from experience to be the most 
commodious measurement, as well as suf- 
ficiently Dowerful for any overshot- mill : in- 
deed for breast-mills, that diameter may be 
considered as capable of giving motion to 
all the ordinary systems of machinery. It 
should be observed, that the breadth of the 
water wheel ought to correspond with the 
power necessary on the occasion ; supposing 
that a proportionate volume of water is at 
command ; fora wheel of two feet in breadth 
will be more than doubly as powerful as one 
of only a foot in breadth; there being a 
double volume of water acting upon it, 
while the friction of the axis is by no means 
doubled by the added breadth. 
Water is generally made to act upon ma- 
chines, particularly water-wheels, by means 
of its momentum when in motion. We 
have already shewn, under the heads of 
Hydraulics and Hydrostatics, how wa- 
ter derives force from its depth, or gravity. 
The effect of water in motion will depend 
manifestly upon the quantity of fluid and its 
velocity jointly. Desaguliers, in his Experi- 
mental Philosophy, vol. ii. p. 419, gives the 
following easy mode of ascertaining these 
data. “ Observe a place where the banks 
of the river are steep, and nearly parallel, 
so as to make a kind of trough for the water 
to run through ; then by taking the depth 
in various parts of the stream’s breadth, ob- 
tain a correct section of the river. Stretch 
one line over it at right angles, and another 
at a small cjistance above or below, but per- 
fectly parallel. Now throw in some buoy- 
ant body (such as an apple, which will not 
float so high as to be affected by the wind) 
immediately above the upper line : observe 
the time it occupies in passing from one to 
the other string. Thus you ascertain how 
many feet the current runs in a second, or 
in a minute. Then having the two sec- 
tions, i. e. one at each line, reduce them to 
a mean depth, and compute the area of the 
mean section, which being multiplied by the 
distance between the lines will give the so- 
lid contents of the intermediate volume of 
fluid, which in the noted time passed from 
one string to the other. Now this way, by 
the rule of three, is adapted to any portion 
of time; the question being merely if the 
velocity be such in such an area, or trough, 
what would be the velocity in another of 
less size. It is -obvious, that if the area give 
twelve solid feet, and that water passed 
at the rate of four feet in a second, through 
a conduit of one foot square; if the conduit 
were only six inches square, the velocity 
would be as 16 to 4; or in other words 
quadrupled. The arch of a bridge is an 
excellent station for observing the force of 
a stream ; because the sides are there regu- 
lar, and the intermediate space may be cor- 
rectly ascertained. But the depth is not 
always to be ascertained in such places 
without the aid of a boat, or of two intelli- 
gent assistants, who should be very correct 
in their observations.” 
The late Mr. John Smeaton made a va- 
riety of experiments on the powers, velo- 
cities, and friction attendant upon water 
wheels, of various sizes, and under different 
influences. He observed, that, in regard to 
power, it is most accurately measured by 
the raising of a weight to any given height 
in a given time : according to the weight 
raised, the height, and the time, so is the 
product to tlie power by which it is effected. 
For a power that can raise ten pounds to 
the height of ten feet in one second will 
correspond with that power which in the 
same period can raise flve pounds to twenty 
feet in height; it being evident that the 
products must be the same. But in such 
case the power is supposed to be equable, 
without the least acceleration or diminution 
of velocity ; and even then we are rather to 
consider this as a popular and simple mode 
of estimation ; for the quantity of motion 
extinguished, or produced, and not the pro- 
duct of the weight and height, is the true, 
unequivocal, and perfect measure of me- 
chanical power really expended, or the me- 
chanical effect actually produced: tliese 
two are always equal and opposite. Yet it 
is true that Mr. Sraeaton’s mode is most 
applicable to the cases in which he adopts it. 
To compute the effects of water-wheels 
with precision, it is necessary to ascertain, 
1. The real velocity of the water which in- 
fringes or acts upon the wheel ; 2. the quan- 
tity of water expended in a given time; and, 
3. how much of the power is counterba- 
lanced, or lost, by the friction of the machi- 
nery. Mr. Smeaton established, after a 
variety of experiments, that the mean power 
of a volume of water inches in height 
gave 8.96 feet of velocity in each minute to 
a wheel on which it impinged. The com- 
