62 PHYSICS. 
can be easily calculated when the lever, fay, becomes elevated. The weight, 
p, maust be so regulated as to admit of the raising of the valve only when 
the pressure has reached a certain limit. PJ. 18, fig. 70, represents the 
part through which the piston, s, passes, constructed so as to prevent the 
escape of any fluid. fig. 71 is an ingenious contrivance of Bramah, 
intended to supply the place of a water-tight end of the piston, p. It 
consists of a bent leather, laid in an annular channel of the piston, and 
against whose walls, as well as against the piston, it is pressed the tighter 
with an increased pressure from below. 
It has been before mentioned that the force increases with the atio of 
the sectional surfaces of the pistons. When the smaller piston, s, is 
depressed, every part of the inclosing walls, equal in area to the bottom of 
the piston, experiences the same pressure as that with which the piston s 
is depressed. The lower surface of the piston p is, however, a part of 
these inclosing walls, and every part of the surface, equal in area to the 
bottom of the piston s, must experience the same pressure, and the sum of 
all these pressures will represent the force with which the piston p is 
elevated. Thus, if the small piston have an area of one square inch, and 
that of the larger 100 square inches, the force on s will be multiplied a 
hundred fold on p. By means of the lever, J, a pressure of 600 pounds can 
easily be exerted by one man on s, and the piston, p, must therefore be 
raised with a force of 600 x 100 = 60,000 pounds, and the same pressure 
exerted upon any body between p' and e. From this some deduction must 
be made for friction, é&ec. 
A proof that the law of Archimedes, established for liquid bodies, applies 
also to gaseous, is furnished by the Azr Balloon or Aerostat. very body 
surrounded by, or‘immersed in the air, loses an amount of weight equal to 
that of the air displaced, and must therefore ascend in the atmosphere 
whenever its weight is less than that of an equal volume of air. Owing to 
the great lightness of the air, this can only be attained when a hollow body 
is filled with some very rare matter. These conditions may be fulfilled by 
.making a bag of paper, gold-beaters’ skin, or oiled silk, and filling it with 
rarefied air, or with a gas lighter than the atmosphere. Vacuum balloons, 
whose contents would be certainly of least possible weight, are not feasible, 
as independently of the great difiiculty of exhausting air on so large a scale, 
they would be immediately compressed by the external air, unless made of 
some very strong material, as metal, in which, to compensate for the great 
weight, the size must be enormously large to produce an ascent. 
Independently of the material, there are two principal kinds of air-balloons 
characterized by the mode of filling: 1, Montgolfier, open below and filled 
with heated, and consequently rarefied air. The source of heat must be at 
some distance below the lc wer opening, and must accompany the balloon in 
its ascent, to continue th: rarefaction, which would otherwise be of short 
duration. This balloon derives its name from the inventors, the brothers 
Montgolfier, who caused the ascent of the first balloons at Annonay in 
France, June 5, 1783. The second kind of balloon is the Charliére, filled 
with hydrogen gas, which, when perfectly pure, is fourteen times lighter 
236 
