commonly cited as Boyle's Law, or Mariotte's Law. It supposes that the temperature of the air is the same in all the experiments.

11. The Height of homogeneous Atmosphere, with given Temperature, is independent of its Density.

One consequence of Law (I) is, that the element which we have called "the height of a homogeneous atmosphere" is independent of the density of the air. For, the element in question is that height of a column of air, of the same density, whose weight would produce the observed pressure; but, by this Law (I), when the density is increased or diminished, the observed pressure is found to be increased or diminished in the same proportion; and therefore the height of a column of air of this altered density, whose weight will produce this altered pressure, will be the same as before.

12. Symbols, and Units of Measure.

It may now be convenient to introduce symbols. Let D be the density of air under some normal circumstances. By D we mean the mass of the air contained in a cubic unit; the mass being measured by its equality with multiples of the unit of mass described as a weight, as ascertained by weighing. (Though gravity enters into the operation of weighing, its power or change of power affects the two subjects equally, and therefore this definition is independent of the measure of gravity at the locality

of any experiment.) The unit of weight may be the grain, the pound, the gramme, &c., and the unit of measure may be the foot, the inch, the centimetre, &c. And let P be the pressure of air under the same circumstances. By P we mean the pressure which the air exerts upon a unit of surface, estimated not as a mass but as a weight; the weight being defined by the number of units of weight. (This definition does depend on the measure of gravity at the locality of the experiment; the greater is the gravity, the smaller will be the number of units of weight required to produce the observed pressure.) Now a column of the height H (expressed by the number of units of length) will contain # cubic units, each of which has the mass D and is weighed at the locality as D; and the whole column will weigh HD. This, when H means the height of a homogeneous atmosphere, is supported by the pressure which is measured by weight P. Therefore P=H.D..

13. Algebraical expression for Pressure in terms of Density.

If the space occupied by the air is changed without changing its temperature, and if P becomes II, and

D becomes A, then Law (I) asserts that

bining this equation with the last,

II A

Com

P D'

II=H.A....

14. Dependence of Elastic Force of Air and of Height of Homogeneous Atmosphere on Temperature.

We may now proceed with Law (II); but it requires no details, because the experiments are precisely the same in form as those for Law (I), the only difference being that the air is used at various temperatures, and the inferences from the various experiments are compared. And the result may be stated thus with sufficient accuracy. The effect of increasing the temperature of air is, to increase its elastic force if its volume is not altered, or to increase its volume if the compressive force answering to its elastic force is not altered; and the law, as depending on temperature, is, that the elastic pressure (in one case) or the volume (in the other case) may be represented by 450+ the degrees of Fahrenheit's scale. Thus the pressure with given quantity in a given space at the temperature 32° Fahrenheit will be to that with the same quantity in the same space at 50° Fahrenheit as 482 to 500. It is easily seen from this that if the symbol H be confined to the meaning "height of homogeneous atmosphere at the freezing point of water," then the corresponding height II', for

the temperature 50° Fahrenheit, will be

500

482

x H.

15. Rise or Fall of Atmospheric Temperature, produced by sudden Contraction or Expansion.

Law (III) applies to a very remarkable property of air, which is not recognized, we believe, as affecting

с

any other theories of natural philosophy connected with the atmosphere, but which is of the utmost importance in relation to the theory of Sound. In the experiments described in Articles 9 and 10 the operations are not. rapid, and great pains have been taken to make the temperatures perfectly uniform, through the changes of pressure in each experiment. And the Law (I), or Boyle's or Mariotte's Law, holds true only on the supposition that the temperature of the air is the same with air much compressed and with air little compressed. But when the changes of volume and pressure are very rapid, the changes of temperature of the air are very great. Upon suddenly condensing air it becomes very hot. We have verified the experiment that; if inflammable tinder is placed in the bottom of a cylinder in which a piston fits tightly and slides easily; when the piston is driven rapidly down so as to condense the air very much before it has had time to impart the whole of its caloric to the surrounding metal, the air will inflame the tinder. And we have remarked, in the powerful air-pumps (driven by large steam-engines) which were used to exhaust the air-tubes upon the Atmospheric Railway, that when the attenuated air in the tube, having acquired the temperature of the ground, was compressed by the operation of pumping so as to be able to open the last valve in opposition to the pressure of atmospheric air, the emergent air was so hot as to be unbearable to the hand. If the heated air, without having lost caloric, be allowed to expand to its former dimensions, it exhibits its former temperature: that is, it cools by sudden expansion. And

this is so well known that it has been proposed to supply apartments in hot climates with cool air, by compressing air in a close vessel, allowing the increased heat to escape by contact of the vessel with the external air or neighbouring substances, and then permitting the condensed air (at the atmospheric temperature) to expand into the apartments, when it would have a much lower temperature.

16. Alteration of the law connecting Elastic Force or Pressure with Density, by the circumstance last mentioned.

It follows that when the changes of volume of the air are rapid (and in the theory of Sound we shall have to treat of changes which are never so slow as 30 in a second of time, and sometimes as quick as 4000 in a cannot hold. For, sup

second), the equation II = P. pose that the air is suddenly compressed, or that ▲ is greater than D, then the heat is increased above that which is supposed in the equation; the elasticity is increased (by Law (II)); and II>P. On the contrary, when the air is suddenly expanded it is cooled ; the heat and elasticity are less than the equation contemplates; and II<P. In both cases the pressure may be represented, at least approximately, by the for