Encyclopaedia Britannica; or, A dictionary of arts and sciences, compiled upon a new plan … > Volume 2, C-L

HYDROS
In the fame figure, let the tube be re-cutved from the
bottom at O into the (hape DE, and the hole at C be
ftopt with a cork. Then pour water into the tube to
any height, as Ag, and it will fpout up in a jet EFG,
nearly as high as it is kept in the tube AB, by continuing
to pour in as much there as runs through the hole E;
which, will be the cafe whilft the furface Ag keeps at the
fame height. And if a little ball of cor^k G be laid upon
the top of the jet, it will be fupported thereby, and
dance upon it. The reafon why the jet rifes not quite
fo high as the furface of the water Ag, is owing to the
refiftance it meets with in the open air : for if a tube, ei¬
ther greater fmall, was ferewed upon the pipe at E, the
water would rife in it until the furfaces of the water in
both tubes were on the fame level; as will be ftrewn by
the next experiment.
The hydrojlatic paradox.
Any quantity of a fluid, how fmall foever, may be
made to balance and fupport any quantity, how great fo¬
ever. This is defervedly termed the hydrojlatical para¬
dox, which we ftiall firft flrew by an experiment, and
then account for it upon the principle above-mentioned,
namely, that the prejfure offluids is direftly as their per¬
pendicular height, •without any regard to their quantity.
Let a fmall glafs tube DCG, (fig. 4.) open at both
ends, and bended at B, be joined to the end of a great
one AI at cd, where the great one is alfo open ; fo that
thefe tubes in their openings may freely communicate
with each other. Then pour water through a fmall-
necked funnel into the fmall tube at H ; this water will
run through the joining of the tubes at cd, and rife up
into the great tube : and if you continue pouring until
the furface of the water comes to any part, as A, in the
greattube, and then leave off, you will fee that the furface
of the water in the fmall tube will be juft as high at D;
fo that the perpendicular altitude of the water will be the
fame in both tubes, however fmall the one be in propor¬
tion to the other. This fhews, that the fmall column
DCG balances and fupports the great column Acd;
which it could not do if their prefiures were not equal a-
gainft one another in the recurved bottom at B.—If the
fmall tube be made longer, and inclined in the fituation
GEF, the furface of the water in it will ftand at F, on
the fame level with the furface A in the great tube ; that
is, the water will have the fame perpendicular height in
both tubes, although the column in the fmall tube is long¬
er than that in the great one ; the former being oblique,
and the latter perpendicular.
Since then the preflure of fluids is diretfly as their per¬
pendicular heights, without any regard to their quantities,
it appears that whatever the figure or fize of vefiels be,
if they are of equal heights, and if the areas of their
bottoms are equal, the preffures of equal heights of water
are equal upon the bottoms of thefe veflels ; even though
the one fltould hold a thoufand or ten thoufand times as
much water as would fill the other. To confirm this
part of- the hydroftatical paradox by an experiment, let
two veflels be prepared of equal heights, but very une¬
qual contents, fuch as AB in fig. 5. and AB in fig. 6.
Vo-L. II. No. do. 1
T A T I C S. 805
Let each veflel be open at both ends, and their bottoms
Y)d Y)d be of equal widths. Let a brafs bottom CC
be exadUy fitted to each veflel, not to go into it, but for
it to ftand upon ; and let a piece of wet leather be put
between each veflel and its brafs bottom, for the fake of
clofenefs. Join each bottom to its veflel by a hinge D,
fo that it may open like the lid of a box ; and let each
bottom be kept up to its veflel by equal weights E and E,
hung to lines which go over the pulleys F and F (whole
blocks are fixed to the Tides of the veflels at f') and the
lines tied to hooks at d and d, fixed in the brafs bottoms
oppofite to the hinges D and D. Things being thus
prepared and fitted, hold the veflel AB (fig. j.) upright
in your hands over a bafon on a table, and caufe water
to be poured into the veflel flowly, till the preflure of the
water bears down its bottom at the fide d, and raifes the
' weight E ; and then part of the water will run out at d.
Mark tlffe height at which the furface H of the water
flood in the veflel, when the bottom began to give way
at d ; and then, holding up the other veffel AB (fig. 4.)
in the fame manner, caufe water to be poured into it at
H ; and you will fee that when the water rifes to A in
this veflel, juft as high as it did in the former, its bot¬
tom will alfo give way at d, and it will lofe part of the
water.
The natural reafon of this furprifing phenomenon is,
that fince all parts of a fluid at equal depths below the
furface are equally prefled in all manner of direftions,
the water immediately below the fixed part B/(fig. 4 )
'dll be prefled as much upward againft its lower furface
within the veflel, by the aflion of the column Ag, as it
would be by a column of the fame height, and of any
diameter whatever ; (as was evident by the experiment
with the tube, fig. 3.) and therefore, fince aftion and
reaction are equal and contrary to each other, the water
immediately below the furface By will be prefled as much
downward by it, as if it was immediately touched and
prefled by a column of the height ^A, and of the diame¬
ter By: and therefore, the water in the cavity BD^//*
will be prefled as much downward upon its bottom CC,
as the bottom of the other veflel (fig. 5.) is prefled by all
the water above it.
To illuftrate this a little farther, let a hole be made
aty(fig. 5.) in the fixed top By, and let a tube G be
put into it ; then, if water be poured into the tube A,
it will (after filling the cavity B</) rife up into the tube
G, until it comes to a level with that in the tube A ;
which is manifeftly owing to the preffiire of the water in
the tube A, upon that in the cavity of the veflel below it.
Confequently, that part of the top By, in which the hole
is now made, would, if corked up, be prefled upward
with a force equal to the weight of all the water which
is fupported in the tube G : and the fame thing would
hold at g, if a hole were made there. And fo if the
whole cover or top By were full of holes, and had tubes
as high as the middle one Ag put into them, the water
in each tube would rife to the fame height as it is kept
into the tube A, by pouring more into it, to make up
the deficiency that it fuftains by fupplying the others,
until they were all full: and then the water in the tube
A would fupport equal heights of water in all the reft of
8 II the