MILL. 
\Q2 
its impulse to the float, has room on all sides 
to escape, as the theory supposes, but in a 
conduit, to which the Uoat being adapted, the 
water cannot otherwise escape than by mov- 
ing along with the wheel, it is observable, 
that a wheel working in this manner, as soon 
as the water meets the float, receiving a sud- 
den check, it rises up against the float like a 
wave against a lixed object ; insomuch that, 
when the sheet of water is not a quarter of an 
inch thick before the float, yet this sheet will 
act upon the whole surface of a float whose 
height is three inches ; and, consequently, 
was the float no higher than the thickness of 
the sheet of water, as the theory also sup- 
poses, a great part of the force would have 
been lost by the water dashing over the float. 
Mr. Sim eat on next proceeds to give tables 
of the velocities of wheels with different 
heights of water; and from the whole de- 
duces the following conclusions : 1. The vir- 
tual or effective head being the same, the ef- 
fect will be nearly as tlxe quantity of water 
expended. 2. The expence of water being 
the same, the effect will be nearly as the 
height of the virtual, or effective head. 3. 
The quantity of water expended being the 
same, die effect is nearly as the square of the 
velocity. 4. The aperture being the same, 
the effect will be nearly as the cube of the 
velocity of the water. Hence, if water passes 
out of an aperture in the same section, but 
with different velocities, the expence will be 
proportional to the velocity ; and therefore, 
if the expence is not proportional to the ve- 
locity, the section of the water is not the 
same. 5. The virtual head, or that from 
which we are to calculate the power, bears no 
proportion to the head-water ; but when the 
aperture is larger, or the velocity of the wa- 
ter less, they approach nearer to a coinci- 
dence ; and consequently, in the large open- 
ings of mills and sluices, where great quan- 
tities of water are discharged from moderate 
heads, the head of w ater, and virtual head 
determined from the velocity, will nearly 
agree: which is also confirmed by expe- 
rience. 6. The most general proportion be- 
twixt the power and effect is that of 10 to ,3 ; 
the extremes 10 to 3.2, and 10 to 2.8. But 
it is observable, that where the power is 
greatest, the second term of the ratio is 
greatest also : hence we may allow the pro- 
portion subsisting in great w r orks to be as 
three to one. 7. The proportion of velocity 
between the water and w'heel is, in general, 
about live to two. 8. There is no certain 
ratio between the load that the wheel will 
carry at its proper maximum, and what wiil 
totally stop it ; though the proportions are 
contained within the limits of 20 to 19, and 
20 to 15 : but as the effect approaches nearest 
to the ratio of 20 to 1 5, or of 4 to 3, when 
the power is greatest, either by increase of ve- 
locity, or quantity of water, this seems lo be 
the most applicable to large works; but as 
the load that a wheel ought to have, in order 
to work to the best advantage, can be assign- 
ed by knowing the effect that it ought to 
produce, and the velocity it ought to have in 
producing it, the exact knowledge of the 
greatest load it wiil bear is of the least conse- 
quence in practice. 
Mr. Smeaton, after having finished his ex- 
periments on the undershot-mills, reduced the 
number of floats, which were originally 24, to 
12 \ which caused a diminution in the effect, 
by reason that a greater quantity of water 
escaped between the floats and the floor than 
before : but on adapting to it a circular sweep 
of such a length, that one float entered into 
the curve before the other left it, the effect 
came so near that of the former, as not to 
give any hopes ol advancing it by increasing 
the number of floats beyond 24 in this parti- 
cular wheel. 
Our author next proceeds to examine the 
power of water when acting by its own gra- 
vity, in turning an overshot-wheel : “In rea- 
soning without experiment,” says he, “ one 
might be led to imagine, that however dif- 
ferent the mode of application is, yet that, 
whenever the same quantity of water de- 
scends through the same perpendicular space, 
the natural effective power would be equal, 
supposing the machinery free from friction, 
equally calculated to receive the full effect- of 
the power, and to make the most of it: for, 
if we suppose the height of a column of wa- 
ter to be 30 inches, and resting upon a base 
or aperture of one inch square, every cubic 
inch of water that departs therefrom will ac- 
quire the same velocity or momentum from 
the uniform pressure ot 30 cubic inches above 
it, that one cubic inch let fall from the top 
wili acquire in falling down to the level of the 
aperture : one would therefore suppose that 
a cubic inch of water let fall through a space 
of 30 inches, and there impinging upon an- 
other body, would be capable of producing 
an equal effect by collision, as if the same 
cubic inch had descended through the- same 
space with a slower motion, and produced its 
effects gradually. But, however conclusive 
this reasoning may seem, it will appear in the 
course of the following deductions, that the 
effect ot the gravity of descending bodies is 
very different from the effect of the stroke of 
such as are non-elastic, though generated by 
an equal mechanical power.” 
Having made such alterations in his ma- 
chinery as were necessary for overshot- 
wheels, our author next gives a table of ex- 
periments with the apparatus so altered. In 
these the head was six inches, and the height 
ot the wheel 24 inches, so that the whole de- 
scent was 30 inches ; the quantity of water 
expended in a minute was 9d-| pounds ; 
which, multiplied by 30 inches,' gives the 
power = 2900 : and’, after making the pro- 
per calculations, the effect was computed at 
1914; whence the ratio of the power to it 
comes to be nearly as 3 to 2. If, however, 
we compute the power from the height, of the 
wheel only, the power will be to the effect 
nearly as 5 to 4. 
From another set of experiments the fol- 
lowing conclusions were deduced : 
1 . I he effective power of the water must be 
reckoned upon the whole descent ; because 
it must be raised to that height, in order to be 
able to produce the same effect a second 
time. 1 lie ratios between the powers so esti- 
mated, and the effects at a maximum, differ 
nearly from 4 to 3, and from 4 to 2. Where 
the heads of water and quantities of it ex- 
pended are the least, the proportion is nearly 
from 4 to 3 ; but where the heads and quan- 
tities are greatest, it comes nearer to that of 
4 to 2 ; so that by a medium of the whole the 
ratio is nearly as 3 lo 2. Hence it appears 
that the effect of overshot-wheels is nearly 
double to that of undershot ones : the conse- 
quence of which is, that non-elastic bodies., 
when acting by their impulse or collision, 
communicate only a part of their original im- 
pulse, the remainder being spent in changing 
I their figure in consequence of the stroke. 
The ultimate conclusion is, that the effects as 
well as the powers are as the quantities of 
water and perpendicular heights multiplied 
together respectively. 
2. By increasing the head, it does- not ap- 
pear that the effects are at all augmented in 
proportion ; for, by raising it from 3 to 1 1 
inches, the effect was augmented by less than 
one-seventh of the increase of perpendicular j 
height. Hence it follows, that the higher th<^ 
wheel is in proportion to the whole descent, i 
the greater will be the effect ; because it de- 1 
pends less upon the impulse of the head, and I 
more upon the gravity of the water in the j 
buckets : and if we consider how obliquely 
the water issuing from the head must strike 
the buckets, we shall not be at a loss to ac- ; 
count tor the little advantage that arises from j 
the impulse thereof, and shall immediately I 
see of how little consequence this is to the 1 
effect of an overshot-wheel. This, however, 
as well as other things, must be subject to li-i 
inflation ; for it is necessary that the velocity 
of the water should be somewhat greater than 
the wheel, otherwise the latter will not only 
be retarded by the striking of the buckets j 
against the water, but some of the power will • 
be lost by the dashing of the water ever tiie ’ 
buckets. 
3. To determine the velocity which tiie 1 
circumference of the wheel ought to have, in j 
order to produce the greatest effect, Mr. j 
Smeaton observes, that the more slowly any 
body' descends by the force of gravity, when 
acting upon any piece of machinery, thei 
more that force will be spent upon it; and 
consequently the effect will be greater. If a 
stream of water falls into the bucket of an 
overshot-wheel, it will be there retained (ill ' 
the wheel discharges it by moving round ; I 
and of consequence, the "slower the wheel 
moves, the more Water will it receive : so that 
what is lost in velocity is gained by the greater 1 
pressure of water upon the buckets. From 
the experiments, however, it appears, that j 
when the wheel made about 20 turns in a 
minute the effect was greatest ; when it made j 
only ISJthe motion was irregular ; and when 1 
loaded so as not to admit its turning 18 times, ’ 
the wheel was overpowered with the load. 
When it made 30 turns, the power was di- ] 
minished by about one-twentieth ; and when 
the number of turns was increased to 40, it I 
was diminished by one-fourth. Hence we 
see that, in practice, the velocity of the wheel 
should not be diminished farther than what 
will procure some solid advantage in point of j 
power ; because, caeteris paribus, the buckets j 
must be larger as the motion is slower; and 
the wheel being more loaded with water, the I 
stress will be proportionably increased upon 
every part of the work. The best velocity 
for practice, therefore, will be that when the | 
wheel makes 30 turns in a minute, which is j 
little more than three feet in a second. This ] 
velocity is applicable to the highest overshot- 
wheels as well as the lowest. ’ Experience i 
however determines, that high wheels may ; 
deviate farther from this rule before they will 
lose their power by a given aliquot part of ■ 
the whole, than low ones can be permitted to 1 
do ; for a wheel of 24 feet high may move at 
