702 MECHANICS. 
the times of emptying veffeis are founded, entirely from 
experiment. He was too cautious to truft to theory alone, 
under all the uncertainties to which he appears to have 
been fenfible it mult be fubjeft. He had, in a preceding 
part of that great work, deduced the general principles of 
motion, and applied them to the folution of problems 
which had never before been attempted ; but, when he 
came to treat of fluids, he faw it was neceffary to eftablifh 
his principles upon experiments ; principles, not indeed 
mathematically true, like his general principles of motion 
before delivered, but, under certain limitations, Suffici- 
ently accurate for practical purpofes. The principles 
therefore upon which we reafon in this branch of philo¬ 
sophy, mult be confidered as depending upon direft ex¬ 
periments adapted to the particular cafes, rather than upon 
the general principles of equilibrium and motion, as ap¬ 
plied in Mechanics. 
Of the WEIGHT and PRESSURE of FLUIDS. 
Prop. I. The weight of fluids is as their quantities of 
matter.— Since each particle of any fluid gravitates towards 
the earth, the greater is the number of particles, that is, 
the quantity of matter in any mafs of fluid, the greater 
will be the weight of that mafs. 
1. The different preffures of different columns of fluid 
in the fame veffel at different depths, appear from the dif¬ 
ferent quantities of fluid difcharged, at different depths, 
in the fame time, from orifices of the fame bore. 
2. If the air be exhaufled from a tube in part filled 
with water, and the tube be clofed up, the folidity of the 
particles of water will be perceived from the found pro¬ 
duced by Suddenly lifting up the tube. 
Cor. Fluids gravitate in fluids of the fame kind. For 
they cannot lofe the property of gravity which belongs to 
all bodies by fuch a change of fituation. 
Sufpend a flopped phial from one arm of a balance, in 
•a veffel of water, and balance it by weights from the op- 
pofite arm of the balance: upon unftopping the phial un¬ 
der water, a quantity of water will rufh into it, by which 
the weight will be increafed as much as the weight of the 
water in the phial. 
Prop. II. When the flurface of a fluid is level, the whole 
'mafs will be at reft. —Let A B C D, Plate XVIII. fig. i. be 
a veflel containing water, the level furface of which is EF. 
Conceive the whole mafs of fluid in the veflel to be di¬ 
vided into thin ftrata, or plates, RS, T V, XY, &c. lying 
horizontally one above another ; and into Small perpen¬ 
dicular columns G H, IK, LM, &c. contiguous to each 
ether. In the Stratum XY, and the columns IK, let 
? h , n, be two adjacent drops. Neither of thefe drops can 
move towards the column in which the other is, without 
driving the other out of its pla^e, becaufe the fluid i3 
fuppoled incoinpreflible. But, with whatever force the 
particle m endeavours to difplace the particle n, this force 
is counterbalanced by an equal and contrary effort on the 
part of n ; becaufe (Prop. I.) they are equally prefled by 
the equal columns above them : confequently the particles 
will be at reft. 
Prop. III. Any part of a fluid at reft prejfes, and is prejftd, 
equally in all direElions. —For each particle is difpofed to 
give way on the flighteft difference of preifure: and, by 
fuppofition, each particle is prefled by the contiguous 
particles in Such a manner as to be kept at reft in its 
place: it is therefore prefled with an equal degree of force 
on all fidesj and, consequently, it prefles equally in all 
direftions. 
Cor. Hence the lateral preflure of a fluid is equal to the 
perpendicular prefTure. This is one of the molt extraor¬ 
dinary properties of fluids, and can be conceived to arife 
only from the extreme facility with which the component 
particles move upon each other. 
i. Into feveral tubes, bent near their lower ends in 
various angles, pour a fuffieient quantity of mercury to 
fill the lower parts of their orifices} then dip them into a 
deep glafs veflel filled with water, keeping the orifice of 
the longer legs above the Surface: whilft the tubes are 
defeending, the mercury will be gradually prefled upwards 
in the tubes, and the preflure will be equal at any given 
depth, whatever be the direction of the prefting column 
of fluid in the ftiorter leg of the tube. Oil may be ufed 
inftead of mercury. 
2. Dip an open end of a tube, having a very narrow 
bore, into a veflel of quickfilver: then, flopping the up¬ 
per orifice with the finger, lift up the tube out of the 
veflel : a fhort column of quickfilver will hang in the 
lower end, which, when dipped in water lower than 14 
times its own length, will, upon removing the finger, be 
fufpended, and prefled upwards. 
3. Let a large open tube be covered at one end with a 
piece of bladder drawn tight: pour into the tube a quan¬ 
tity of coloured water fuffieient to prefs the bladder into 
a convex form ; then, dip the covered end of the tube 
Slowly into a deep veflel of water ; the bladder, by the up¬ 
ward preflure, will become firft lefs convex, then plane, 
and at laft concave. 
4. If the like be done with feveral tubes, whofe covered 
orifices are cut obliquely at different angles, the lateral 
preflure will be Seen to increaSe with the depths to which 
the tubes are immerSed. 
5. Let a circular piece of brafs, whofe upper Surface is 
covered with wet leather, be held clofe to one orifice of 
a clofe open tube, by means of a cord or wire faftened to 
the middle of the plate, and pafling through the tube: 
let the plate, thus kept clofe to the orifice of the tube, be 
immerfed with the tube into a large veffel of water: when 
the plate is at a greater depth than 8 times its thicknefs 
in the water, the cord or wire may be left at liberty, and 
the upward preflure of the fluid will keep the plate clofe 
to the tube. 
6. Let a Small bladder, tied cloSely about one end of 
an open tube having a large bore, be filled with coloured 
water till the water riSes above the neck of the bladder} 
upon immerfing the bladder into a veffel of water, the 
bladder will be compreffed on all Sides, and the coloured 
water will be raiSed up in the tube in proportion to the 
depth to which the bladder is Sunk. 
Prop. IV. Let the bottom of the veflel B C, fig. 2, be oblique 
to the ftdes, and alfo [0 final/, that the whole may be conceived 
to be of the fame depth ; then the preflure perpendicular to B C 
will be as BC yi depth. —For the number of particles in 
contact with BC is as B C. Alf’o, fluids prefs equally in 
all direftions, and in proportion to their depths, and the 
whole preflure on BC mult be as the number of par¬ 
ticles X the preflure of each ; hence, the preflure perpen¬ 
dicular to B C is as B C X depth. 
Prop. V. The preflure exerted upon BC downwards, or 
in the direElion of gravity , is equal to the weight of the fluid .—> 
Draw CE perpendicular to B C, BE to BA, and C F to 
BE. Now let CE reprefent the preflure (P) perpendi¬ 
cular to B C, which refolve into CF, FE; then C F is 
that part which afts downwards; alio, letreprefent the 
preflure down wards, it the preflure which would aft upon 
BF, as the bottom, or the weight of the fluid. Hence, 
p : P :: CF : CE:: (by fun.trian.) B F : B C, 
P : 7T :: BCXdepth : BFxdepth :: BC : BF, 
p : m :: BFxBC : B CXBF} ' 
hence, p = ir. 
Prop. VI. The preflure of a fluid againfl. any furface, in 
a direElion perpendicular to it, varies as the area of the fur~ 
face multiplied into the depth of its centre of gravity below tha 
furface of the fluid. —Let ABC, fig. 3. be a veflel} AB 
the lurface of the fluid, A C B the furface prefled, G its 
centre of gravity ; and divide ACB into an indefinite 
number of parts m, n, 0, See. and draw G Q, mx, ny, oz, 
Sec. perpendicular to A B. Now every part of the inde¬ 
finitely Small Surface m may be conceived to be at the 
fame perpendicular depth m x ; alfo, the preflure at 711 is 
in proportion to its depth, and that preflure is exerted 
equally in all direftions} hence, the preflure on m per- 
a pendiqular 
