*)49 
pordoual to the areas of the apertures, or to 
the squares of their diameters. 
Secondly, that the quantities of water 
discharged through additional pipes of the 
same diameter, under different altitudes of 
water in the reservoir, are proportional to the 
square root of the altitude. 
1 hirdiv, '{ hat in general the quantities of 
water discharged in the same space of time 
through different additional pipes, under dif- 
ferent heights of water in the reservoir, are 
to each other nearly as the product of the 
square of the diameters of the pipes by the 
square root ot the altitude of the reservoirs. 
I he efflux ot water, therefore, through ad- 
ditional pipes, tollows the same laws as water 
when discharged through apertures made in 
thin substances. 
It the vessel AB (Plate Hydrostatics, &c. 
fig. 1.) is full of water, and the horizontal pipe 
U f 11 the middle ot its side, and the semicircle 
NEC described upon D, as a centre, with 
tire radius, or semidiameter DC, or DN, the 
perpendicular DE to the diameter CDN, is 
the longest that can be drawn from any part of 
the diameter to the circumference: and if the 
vessel be kept full, the jet will spout from the 
pipe D to the horizontal distance MN, which 
is double the length of the perpendicular DE, 
If two other pipes, as F and G, be fixed into 
the side of the vessel, at equal distances above 
and below the pipe D, the perpendiculars 
I' ll and GI, from these pipes to the semi- 
circle will be equal; and the jets spouting 
from them, will each go to the horizontal 
distance NR, which is double the length of 
either of the perpendiculars FH or GI. 
Ftyids, by their pressure, may be convey- 
ed over hills and valleys, in bended pipes, to 
any height not greater than the level of the 
springs whence they flow. This the antients 
were ignorant of; and therefore they usually 
built aqueducts (vast rows of arches, one 
above another, between two hills, at an im- 
mense expence of money, time, and labour) 
in order to convey water over them, across 
the valley. 
I Ijis is now done to equal advantage, and 
at much less expence, bv a range of pipes laid 
down one hill and up the other. If water is 
poured into one of the legs of the bended 
pipe ACB (lig. 2.) it will rise exactly to the 
same level in the other. The reason is ob- 
vious: in the leg A there are, suppose, two 
ounces of water, endeavouring by the force 
of gravity to descend with the force of two; 
this will thrust forward, buoy up and support 
an equal quantity of a like fluid in B; and the 
bottom of the machine C, against which both 
sides equally bear, will of consequence sus- 
tain a double pressure, or that of four ounces ; 
and in the present case, will pretty well re- 
present the prop, or fixed point, of a balance- 
beam; as the equal fluid columns AC and 
BC, may be admitted to denote equal 
weights, suspended on the balance-arms, 
counterpoising each other: so that the rise of 
fluids to their first level, thus considered, is a 
case truly statical; and all their other mo- 
tions proceed only from weight added. 
We have seen, that water will rise through 
bended- pipes to the same level as the reser- 
voir from which it proceeds. Upon the same 
principle, jets, or fountains, are formed ; for 
if near the bottom of the vessel AB (tig. 1.) 
you fasten a small pipe m, bending upwards, 
the water will spout out through the pipe, 
HYDRAULICS. 
and vise nearly as high as the surface of the 
water in the vessel. It will not rise quite so 
high, because it is somewhat impeded by the 
resistance of the air, and the friction against 
the opening of the pipe, or adjutage. 
It is always found necessary to increase 
the bore of tin* adjutage, or spouting-pipe, 
with the height of the reservoir; for if it is too 
small, the rising stream will want sufficient 
weight and power to divide the air, which 
being densest near the earth, a small stream 
of water, endeavouring to mount to a great 
height, will be dashed against it with so much 
violence, as to fall away in a mist, and be 
wholly lost. 
There is a certain and fit proportion to be 
observed between the adjutage by which the 
jet is delivered, and the- pipe conducting it 
from the head. In general, about five times 
the diameter of the adjutage, for jets under 
half an inch, and six or seven times for all 
above, will give the size of pipes of conduct 
pretty well ; tlmugh it will always be an error 
on the right side, to have them rather larger 
than in strictness they ought to be, that the 
jet may always be freely supplied with water, 
and in. due time. 
For a like reason, if there is occasion for a 
cock to be placed in any part of the pipe of 
conduct, particular care must be taken that 
it should be there bigger in proportion, that 
the water may not be pinched, but that the 
cavity be left at least equal to the bore of the 
rest of the pipe. 
The bore of an adjutage cannot be too 
smooth, or true. Those that are cylindrical 
are best; those that are bored conical, worst ; 
because of the reflections of the water from 
the inclined sides of the machine, which, in 
the hurry of the issuing stream, will in them 
unavoidably be made. 
Archimedes’ screw (fig, 7.) deserves consi- 
deration, not only for its antiquity, but its 
usefulness in raising water. It consists of a 
long cylinder, with a hollow pipe-tube, or 
groove, coiled about it, as represented in the 
figure. It is placed in a position oblique to 
the horizon, with the lower end in the water, 
the other being supported on the lower part 
of the winch I, by which the screw and cy- 
linder are turned round. As soon as the screw 
is immersed in water, it immediately rises in 
the machine by the orifice C, to the level of 
the surface of the water E; and if the point 
of the helix, or spiral, which in the beginning 
of the motion is coincident with the surface 
of the water, happens not to be on the lower 
side of the cylinder, the water will, upon the 
motion of the screw, move on in the helix, 
until it comes to the point which is on the 
under side, and coincident with the watery 
surface: when it is arrived at that point, it 
cannot afterwards possess any other part of the 
spiral, than that which is upon the lowest part 
of the cylinder, for it cannot move towards H, 
because H is situated higher; and since this 
will ever be the case, after the surface of the 
water in the helix has attained the point E, it 
is plain that it must always be on the under 
side of the cy linder. But since the cylinder is 
in motion, every part of the spiral screw from 
EF, will by degrees succeed to the under 
part of the cylinder; the water- therefore in 
the helix must succeed to every part from F, 
to F, as it comes to the lower side; that 
is, it must ascend on the lower part of the 
cylinder through all the length of the pipe, 
until it comes to the orifice at top, where it 
will run out. 
Of all the machines the antients invented 
to raise water, it appears that though Archi- 
medes’ screw was the most curious, the tym- 
panum, mentioned by T Vitruvius, elevated 
the greatest quantity at once pa brief descrip- 
tion of this may suffice, as preparatory to the I 
account of machines made in imitation of it, 
but more ingenious and more perfect 
Thu tympantnn is a great hollow wheel, 
forming a kind of barrel or drum (as its name 
imports) composed of several planks joined 
together, we:l calked and pitched^and having 
a horizontal axle on which it turns: the in- 
terior of this drum is divided into eight equal 
spaces by as many partitions placed in the di- 
rections ol the radii ; each space or cell has 
an orifice ot about half a foot in the rim of 
the drum or wheel, so shaped as to facilitate ~ 
the admission of the water; moreover, there 
are eight hollow channels running contiguous 
to each other, and parallel to the axle of the 
wheel, each corresponding to one of the eight 
large cells; into these channels the water: 
passes out of the cells just mentioned, and 
after running along the channels to a conve- 
nient distance, it escapes through orifices into 
a reservoir placed just under the axle. Thus, 
the water is elevated through a vertical space 
equal to the radius of the hollow wheel. 
When the tympanum is used to raise water ’ - 
from a running stream, it is moved by means- 
of float boards which are impelled by the- 
stream ; but when it is employed to rai5e- 
stagnant water, there is commonly a smaller 
wheel on the same shaft, which is turned by' 
men walking in it, as in the old walking 
crane. '1 lie chief defect of this machine is 
that it raises the water in the most disadvan- 
tageous situation possible; for the load being 
found always towards the extremity of a ra- 
dius ot the wheel, the arm of the effective 
lever which answers to its increases through, 
the whole quadrant the water describes hi 
passing from the bottom of the wheel to the 
altitude ot its centre; so that the power must; ; 
act as it it was applied at a winch handle, 
and cannot therefore act uniformly. 
Mr. II. Sarjeant, ot Whitehaven, contrived! 
a very cheap engine for raising water, for: 
which the Society for the Encouragement of 
Arts awarded him a silver medal in the yearr 
1801. A sketch ot this- simple invention is 
given in fig. 8. 
This 1 engine was -erected at Irton-hall, which . 
is situated on an ascent of CIO or til feet per- 
pendicular height: at the foot of this elevation, 
about 1.40 yards distant from the offices, there 
runs a small stream of water, and in order to 
procure a constant supply of that necessary 
fluid, the object was to raise such stream to 
the house lor culinary and domestic uses. 
With .this view, a dam was formed at a short; 
distance above the current, so as to cause a 
fall' of about four feet : the water was then 
conducted through a wooden trough, inta- 
whioh a piece of leaden pipe, two inches in 
diameter, was inserted, and part of which is- 
delineated at- A. 
'I ’fie stream, of this pipe is directed in such 
a manner as to run into the bucket B, when 
the latter is elevated ;. but as soon as it be- 
gins to descend, the stream passes over it,, 
and flows progressively to supply the woodeh 
trough or well, at the toot of wlncl/stands the 
