762 
MECHANIC S. 
afcend full of water till they reach the top K, where they 
{bike again(t the extremity n of the fixed refervoir M, and, 
being overfet, di (charge their contents into that refervoir. 
As toon as the bucket quits the refervoir, it relumes its 
perpendicular pofition by its own weight, and defcends as 
before. On each bucket is fixed a fpring r, which moves 
over the top of the bar m, fattened to the refervoir. By 
this means the bottom of the bucket is raifed above the 
level of its mouth, and its contents completely difcliarged. 
On fofne occaiions, the Perfian wheel is made to raife 
water only to the height of its axle. In this cafe, ir.ffead 
of buckets, its fpokes c, d, e, f g, h, are made of a fpifal 
form, and hollow- within, fo that their inner extremities 
all terminate in the box N on the axle, and their outer ex¬ 
tremities in the circumference of the wheel. When the 
rim CDEF, therefore, is immerfed in the itream, the wa¬ 
ter'runs into the tubes C, D, E, F, &c. rifes in thefpiral 
fpokes c, d, &c. and is dilcli3rged from the orifices at O 
into the refervoir P, from which it may be conveyed in 
pipes. 
Of WATER-MILLS. Plate XXVII. and XXVIII. 
At p. 620, ive have fpoken of the antiquity and im¬ 
portance of water-mills ; and, at p. 685, have fully de- 
feribed the exterior and interior of a wind-mill ; but, as 
corn-mills are very frequently impelled by water, it re¬ 
mains to complete the (ubjeft by deferibing the modes in 
which this is effected. 
In water-mills, then, the momentum of the water is the 
moving power, and the attrition of the two ftones in grind¬ 
ing is the force to be overcome. Of thefe there are three 
kinds ; viz. thofe where the force of the water is applied 
above the wheel, called overfhot-mills ; thofe where the 
water (bikes againft the middle of the wheel, called brealt- 
mills; and thofe where the water is applied below the 
■wheel, which laft are called under/hot-mills. Before we 
{how the application of thefe wheels with the interior ma¬ 
chinery, we mutt fir ft clear the way by deferibing the mode 
of aftion of each of the three fpecies of water-wheel in 
particular. 
i. An overjhot-wheel is a wheel driven by the weight of 
water conveyed into buckets difpofed on its circumfer¬ 
ence. It is reprefented at fig. 97. where A B P C is the 
circumference of the wheel, furniftied with a number of 
buckets. The canal M N conveys the water into the fe- 
cond bucket from the top A a. The equilibrium of the 
wheel is therefore deftroyed ; and the power of the buc¬ 
ket A a, to turn the wheel round its centre of motion O, 
is the fame as if the weight of the water in the bucket 
were fufpended at m, the extremity of the lever O m, c 
being the centre of gravity of the bucket, and Own per¬ 
pendicular let fall from the fulcrum O to the direction cm, 
in which the force is exerted. In confequence of this 
deftruefion of equilibrium, the wheel will move round in 
the direftion A B, the bucket A a will be at d, and the 
empty bucket b will take the place of A a, and receive 
water from the fpout N. The force afting on the wheel 
is now the water in the bucket d afting with a lever n O, 
and the water in the bucket A a afting with a lever m O. 
The velocity of the wheel will therefore increafe with the 
number of loaded buckets, and with their dittance from 
the vertex of the wheel ; for the lever by which they tend 
to turn the wheel about its axis, increases as the buckets 
approach to c, where their power, reprefented by eO, is a 
maximum. After the buckets have patted e, the lever by 
which they aft gradually diminifbes, they lofe by degrees 
a fmall portion of their water; and, as foon as they 
reach B, it is completely difcliarged. When the wheel 
begins to move, its velocity will increafe rapidly till the 
quadrant of buckets be is completely filled. While thefe 
buckets are defeending through the inferior quadrant eP, 
and the buckets on the left hand of b are receiving water 
from the fpout, the velocity of the wheel will (till increafe ; 
but the increments of velocity will be fmaller and fmaller, 
fincc the levers by which the inferior buckets aft are gra¬ 
4 
dually djminilhing. As foon as the hjgheft bucket Ac 
has reached the point B where it is emptied, the whole fe- 
inicircumference nearly of the wheel is loaded with water ; 
and, when the bucket at B is difcharging its.contents, the 
bucket at A is filling, fo that the load in the buckets, by 
which the wheel is impelled, will he always the fame and 
the velocity of the wheel will become uniform. 
In order to find the power of the loaded arch to turn the 
wheel, or, which is the fame thing, to find a weight which, 
fufpended at the oppofite extremity C, will balance the 
loaded arch or keep it in equilibrio, we mutt multiply the 
weight of water in each bucket by the length of the vir¬ 
tual lever by which it afts, and take the Cum of all thefe 
momenta for the momentum of the loaded arch. It will 
be much eafter, however, and the refult will he the fame, 
if we multiply the weight of all the water on the arc A B 
by the dittance of its centre of gravity G from the ful¬ 
crum or centre of motion O. Now, by the property of 
the centre of gravity, the dittance .of the centre of gravity 
of a circular arc from its centre, is a fourth proportional 
to half the arc, the radius, and the fine of half the arc. 
Since the vertical bucket b has no power to turn the 
wheel if it were filled, and fince two or three buckets be¬ 
tween B and P are always empty, we may fafely fuppofe 
that the loaded arc never exceeds 160 0 ; fo that, if R ~ r3 _ 
dius of the wheel in feet, we ttiall have the length of half 
the loaded arc, or 8o c =iR X 3-1416 x^ 5 =SX 1396 ; and 
the dittance of the centre of gravity trom the fulcrum O, 
_RXttn.8o° 
—G u — ~yr~-—• Now, if N be the number of buc- 
K X i ’396 
1 • , , , 160 N 4 N 
kets in the wheel, —-—, or-will be the number of 
360 9 
buckets in the loaded arc ; and, if G be the number of ale- 
gallons contained in each bucket, the weight of the water 
in each bucket will he iouxG pounds avoirdupois. The 
weight of the water, therefore, in the loaded arc, will be 
4N 
-—X io*2 G; and confequently the momentum of the 
4 N 
R x fin. 8o° 
4N 
9 
loaded arc will be =-x io’sG X- 1 - 
9 Rxi'396 
_ „ 4N 
X i°'2 G X o , 6338=—- x (>'465 G pounds avoirdupois. 
Hence, we have the following rule ; Multiply theconttant 
number 6'4.65 by § of the number of buckets in the wheel, 
and this produft by the number of ale-gallons in each buc¬ 
ket; and the refult will he the effective weight, or mo¬ 
mentum of the water in the loaded arc. 
2. A breajl-wheel partakes of the nature both of an over- 
fliot and an underihot wheel ; and is driven partly by the 
impulfe, but chiefly by the weight, of the water. A water¬ 
wheel of this kind is reprefented at fig. 98. where M C is 
the flream of water falling on the floatboard 0, with a ve¬ 
locity correfponding to the altitude mn, and afterwards 
afting by its weight on the floatboards between 0 and B. 
The mill-courfe cB is made concentric with the wheel, 
which is fitted to it in fitch a manner that very little water 
is allowed to efcape at the fides and extremities of the 
floatboards. According to Mr. Smeaton; the effeft of a 
wheel driven in this manner is equal “to the effeft of an 
underfhot-wheel vvhofe head of water is equal to the diffe¬ 
rence of level between the furface of water in the refer¬ 
voir, and the point where it (trikes the wheel, added to 
that of an overfhot whole height is equal to the difference 
of level between the point where it Ittilies the wheel and 
the level of the tail-water.” That is, the effeft of the 
wheel A is equal to that of an underffiot-wheel driven by 
a fall of water equal to inn, added to that of an over.'hot- 
wheel whofe height is equal to »D. 
Mr. Lambert of the Academy of Sciences at Berlin, has 
ffiown that, when the floatboards arrive at the pofition op, 
they ought to be horizontal; the point p fitoukl be lower 
than 0, in order that the whole (pace between any two ad¬ 
jacent floatboards may be filled with water; and that Cm 
ffiould 
