8. Height of Homogeneous Atmosphere, dry or humid.

The authors cited above have given the weight of one cubic centimetre of dry air (found by exhausting. the air from a bottle, and weighing the bottle empty of air and full of air) as 0·00129954 gramme, the air having been weighed when the height of the barometer was 0.76 metre, and the temperature of the air 0° Centigrade; and this gives us the means of determining the' value of one very important constant. The weight of one cubic centimetre of mercury was found (see last page) to be 13.5962 grammes; and therefore the weight 13.5962 of mercury is x the weight of air such as we 0.00129954

have at the earth's surface under these circumstances; and therefore the pressure of air (with the barometric height and temperature mentioned above) is equal to the weight of a sea of air whose depth is

provided that air were like water, an incompressible and homogeneous fluid; the weight being considered as produced by the action of gravity at that place (Paris) at which the experiments were made. This is usually called "the height of a homogeneous atmosphere." It' will enter as a constant into every part of the investigations which follow. Taken in connexion with the value of the gravity under whose action it is estimated, it represents a fundamental element in the constitution

of air. The numerical value formed from the numbers above is 7951-36 metres or 26087-6 English feet. We shall always use the symbol H for this element.. It will appear shortly that the height of the homogeneous atmosphere is not invariable, but that it depends on the temperature of the air: for that variable height we shall use the symbol H'.

.

In this calculation we have omitted the consideration of the moisture in the atmosphere. It is to be understood that we possess means in ordinary use for ascertaining the amount of moisture in the air (usually based on the principle of observing how much the air must be cooled in order to make it deposit dew), and that, having examined the properties of vapour at various temperatures nearly as we have examined those of air, we know what is the elastic force of the vapour in the air. Also that we know the weight of vapour which exercises a given elastic force, and that it is about g of the weight of dry air which exercises the same force. With this we must make use of "Dalton's Law," based on experiments which shew that, when dry air and vapour (or any other gases) are inclosed together in the same space, the elastic force which the mixture exerts is the sum of the elastic forces due separately to each. Suppose then that, with barometer and thermometer as above mentioned, we find that the elastic force of the vapour

1

is of that of the dry air: (n in these countries is

n

seldom less than 30). We now have a mixture of dry air producing a pressure, on the square centimetre, of

n

x076 x 13.5962 grammes, and of vapour pro

ducing a pressure of

1
n+1

× 0.76 × 13·5962 grammes:

total 0.76 x 13:5962 grammes. And the weight of a

Hence, the height of the homogeneous atmosphere will be

{1

When n=30, the fraction increases the height of the homogeneous atmosphere by part (which, as we shall shortly see, increases the velocity of sound by part). We shall usually omit all mention of this.

9. Measure of Elastic Force of Air under different

circumstances.

We are now in a state to consider the investiga tion of law (I) regarding the relation between the elastic force of air and the space which it occupies. We premise that in a glass tube, though we cannot everywhere measure the section, we can with great accuracy

measure the capacity of the tube from a closed end to various points of the tube, by successively pouring in small quantities of mercury whose weights are known. Suppose then that in Figures 4 and 5 we have tubes of the siphon form, each containing air above the mercury in the closed leg. The quantity of that inclosed air will be known with accuracy by varying the quantity of mercury in the open leg till the mercury stands at the same height in the two legs: for then it is evident that the pressure of air on every unit of surface of the mercury in the closed leg is equal to the pressure similarly measured in the open leg, and the elastic state of the air in the closed leg is the same as that of the open air. Suppose now, that to produce the state of things in Figure 4, some quicksilver is withdrawn, or that to produce the state of things in Figure 5 some quicksilver is added. Then the equilibrium at the lower of the two surfaces is thus to be estimated. In Figure 4 a unit of the surface in the closed tube is pressed down by the elastic force of the inclosed air: to this is to be added the weight of the column of mercury whose height is the excess of height in the closed leg above height in the open. leg; and thus is found the pressure upon a unit in the horizontal section of the mercury in the closed leg at the height of the surface in the open leg. This must be balanced by the pressure upon a unit in the surface in the open leg; which pressure is merely the atmospheric pressure; that is, it is the pressure of a column of mercury whose height is the length of the

barometric column found by the operations in Article 7. Hence the pressure of the inclosed air upon a unit of surface plus the pressure of the column of mercury whose length is the difference of heights of the two surfaces of mercury must equal the pressure of the barometric column. In the case of Figure 5, it will: be found in the same way that the pressure of the inclosed air is equal to the pressure of the column whose length is the difference of heights of the two surfaces plus the pressure of the barometric column. By these operations we have obtained measures of the volume occupied by a given quantity of air, and of the corresponding pressure upon a unit of surface estimated by the height of a column of mercury.

10. With given temperature: Elastic Force of Air is proportional to its Density.

These experiments have been made frequently, and to great extents of compression and of expansion of the air inclosed in the tube. And the result, or Law (I) is the very simple one-"The pressure which a given quantity of air produces on a unit of surface is inversely proportional to the space occupied by that air." Or, since the diminution or increase of the space occupied necessarily increases or diminishes in the same proportion the density of the given quantity of air occupying that space, the Law: (I) may be stated, "The pressure which air exerts upon a unit of surface: is proportional to the density. of the air." This is