provided with a suitable scale for measuring the altitude of the column, is a complete barometer. The height of the barometric column fluctuates somewhat, even at the same place, on account of changes of temperature, and other causes yet to be considered.

Observation has shown, that the average height of the barometric column at the level of the sea, is a trifle less than 30 inches.

The weight of a column of mercury 30 inches in height, having a cross section of one square inch, is nearly 15 pounds. Hence, the unit of atmospheric pressure at the level of the sea, is 15 pounds.

This unit is called an atmosphere, and is often employed in estimating the pressure of elastic fluids, particularly in the case of steam. Hence, to say that the pressure of steam in a boiler is two atmospheres, is equivalent to saying, that there is a pressure of 30 pounds upon each square inch of the interior of the boiler. In general, when we say that the tension of a gas or vapor is n atmospheres, we mean that each square inch is pressed by a force of n times 15 pounds.

Mariotte's Law.

189. When a given mass of any gas or vapor is compressed so as to occupy a smaller space, other things being equal, its elastic force is increased; on the contrary, if its volume is increased, its elastic force is diminished.

The law of increase and diminution of elastic force, first discovered by MARIOTTE, and bearing his name, may be enunciated as follows:

The elastic force of a given mass of any gas, whose temperature remains the same, varies inversely as the volume which it occupies.

As long as the mass remains the same, the density must vary inversely as the volume occupied. Hence, from MARIOTTE'S Law, it follows, that,

The elastic force of any gas, whose temperature remains the same, varies as its density, and conversely, the density varies as the elastic force.

D

MARIOTTE'S law may be verified in the case of atmospheric air, by the aid of an instrument called MARIOTTE'S Tube. This instrument consists of a tube ABCD, of uniform bore, bent so that its two branches are parallel to each other. The shorter branch AB, is closed at its upper extremity, whilst the longer one remains open for the reception of mercury. Between the two branches of the tube, and attached to the same frame with it, is a scale of equal parts for measuring distances.

PP

To use the instrument, place it in a vertical position, and pour mercury into the tube, until it just cuts off the communication between the two branches. The mercury will then stand at the Fig. 168 same level BC, in both branches, and the tension of the confined air in AB, will be exactly equal to that of the external atmosphere. If an additional quantity of mercury be poured into the longer branch, the confined air in the shorter branch will be compressed, and the mercury will rise in both branches, but higher in the longer, than in the shorter one. Suppose the mercury to have risen in theshorter branch, to K, and in the longer one, to P. There will be an equilibrium in the mercury lying below the horizontal plane KK; there will also be an equilibrium between the tension of the air in AK, and the forces which give rise to that tension. These forces are the pressure of the external atmosphere transmitted through the mercury, and the weight of a column of mercury whose base is the cross-section of the tube, and whose altitude is PK. If we denote the height of the column of mercury which will be sustained by the pressure of the external atmosphere, by h, the tension of the air in AK, will be measured by the weight of a column of mercury, whose base is the cross-section of the tube, and whose height is h + PK. Since the weight is proportional to the height, the tension of the confined air will be proportional to h+ PK.

Now, whatever may be the value of PK, it is found that,

If PK = h, we shall have, AK = AB; if PK = 2h, we shall have, AK = {AB; in general, if PK = nh, n being any positive number, either entire or fractional, we AB

shall have, AK

to n =

MARIOTTE'S Law was verified

in this manner by DULONG and ARAGO for all values of n, up 27. The law may also be verified when the pressure is less than an atmosphere, by means of the following apparatus.

ARK

AK represents a straight tube of uniform bore, closed at its upper and open at its lower extremity: CD is a long cistern of mercury. The tube AK is either graduated into equal parts, commencing at A, or it has attached to it a scale of brass or ivory.

Fig. 164.

To use the instrument, pour mercury into the tube till it is nearly full; place the finger over the open end, and invert it in the cistern of mercury, and depress it till the mercury stands at the same level without, as within the tube, and suppose the surface of the mercury in this case to cut the tube at B. Then will the tension of the confined air in AB, be equal to that of the external atmosphere. If now the tube be raised vertically, the air in AB will expand, its tension will diminish and the mercury will fall in the tube, to maintain the equlibrium. Suppose the level of the mercury in the tube to have reached the point K. In this position of the instrument the tension of the air in AK, added to the weight of the column of mercury, KE will be equal to the tension of the external air. Now, it is found, whatever may be the value of KE, that

If EK = }h, we have, AK = 2AB; if EK = th, we

have, AK 3AB; in general, if EK:

AK =

=

AB n+ 1

=

h, we have, n+1

MARIOTTE'S law has been verified in this manner, for all values of n, up to n = 111.

It is a law of Physics that, when a gas is suddenly compressed, heat is evolved, and when a gas is suddenly expanded, heat is absorbed; hence, in making the experiment, care must be taken to have the temperature kept uniform.

Gay Lussac's Law.

190. If, whilst the volume of any gas or vapor remains the same, its temperature be increased, its tension is increased also. If the pressure remain the same, the volume of the gas will increase as the temperature is raised. The law of increase and diminution, as deduced by Gay Lussac, whose name it bears, may be enunciated as follows:

In a given mass of any gas, or vapor, if the volume remains the same, the tension varies as the temperature; if the tension remains the same, the volume varies as the temperature.

According to REGNAULT, if a given mass of atmospheric air be heated from 32° Fahrenheit to 212°, the tension, or pressure remaining constant, its volume will be increased by the .3665th part of the volume at 32°. Hence, the increase of volume for each degree of temperature is the .00204th part of the volume at 32°. If we denote the volume at 32° by ", and the volume at the temperature t', by v', we shall therefore have,

v' = v[1 + .00204(ť' — 32)]

Solving with reference to v, we have,

(152.)

v'

v =

1+.00204(t'- 32)

( 153.)

Formula (153) enables us to coinpute the volume of any

mass of air at 32°, knowing its volume at the temperature t', the pressure remaining constant.

To find the volume at the temperature t", we have simply to substitute t'' for t'in (152.) Denoting this volume by v', we have,

v''= v[1 + .00204(ť" — 32)].

Substituting for v its value from (153), we get,

This formula enables us to compute the volume of any mass of air, at a temperature t', when we know its volume at the temperature t'; and, since the density varies inversely as the volume, we may also, by means of the same formula, find the density of any mass of air, at the temperature t', when we have given its density at the tempera

ture t'.

Manometers.

191. A MANOMETER is an instrument used for measuring the tension of gases and vapors, and particularly of steam. Two principle varieties of manometers are used for measuring the tension of steam, the open manometer, and the closed manometer.

The open Manometer.

192. The open manometer consists, essentially, of an open glass tube AB, terminating below,

nearly at the bottom of a cistern EF. The cistern is of wrought iron, steam tight, and filled with mercury. Its dimensions are such, that the upper surface of the mercury will not be materially lowered, when a portion of the mercury is forced up the tube. ED is a tube, by means of which, steam may be admitted from the boiler to the surface of the mercury in the cistern. This tube is sometimes filled with

E

B

Fig. 165,