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tional to each other when the density remains constant. Any one of these three elements being unchanged, the changes of the other two are proportional to each other; no one element of the three can be altered without altering one of the others, but it may be either one; and, when any two of them are constant, the third is also constant; so that, any two of them being given, the third is known.

Hence an increase of temperature does not necessarily cause bodies to expand, for this expansion may be restrained by the application of sufficient pressure; but this pressure is, in the case of solids and liquids, so great, or, in other words, their increase of elasticity is so great, for small increments of heat (supposing their bulk to remain constant), that probably no available amount of mechanical force could sensibly prevent their expansion. But the expansion of air is to some measurable extent impeded by the smallest measurable pressure; and even a change of pressure that would double its bulk may be prevented from causing any expansion, by inclosing the air in a vessel of moderate strength. But as air, however small in quantity, always fills the vessel in which it is inclosed, it is evident that no change of temperature can in this case alter its bulk except by bursting the vessel. If the vessel be strong enough to prevent this, the inclosed air, although its density be unaltered, must have the repulsive force of its particles, that is, its elasticity increased by increase of temperature; so that, if the elasticity of the external air remain unchanged, the vessel will have to bear a greater pressure on its inner than on its outer surface; and when the difference of these two pressures becomes greater than its cohesion, it will burst, as happens with an inflated bladder held near the fire. The warm air thus liberated suddenly expands, until its elasticity

EXPANSION OF AIRS.

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becomes equal to that of the surrounding cold air, although its density is less than that of the latter, so that it will ascend through it.

27. When, therefore, it is said that portions of air and of gas expand like other bodies by heat and contract by cold, it must always be remembered that this is true only when their elastic force remains unaltered. Otherwise, whatever change any degree of heating or of cooling may produce in their bulk when the elasticity is unaltered, the same change will it produce in their elasticity when their bulk is unaltered. To render the effect of expansion visible and measurable in these bodies, they must be confined in such a way that their elasticity may always balance a constant pressure, or a constant height of some liquid. To effect this requires much care and accuracy; but, from very exact experiments made in this way, the expansion of airs has been found to present the three following remarkable features:

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First. They are more expansible for a given increment of heat than either solids or liquids. For example, steel is increased in length only 15th, or in bulk only 35th, by being heated 180° from the temperature of melting ice to that of boiling water. But in the case of liquids mercury expands about th, water about and, and oil about th of its bulk by the same increase of heat. Air, however, is expanded by the same change (its elasticity remaining constant) no less than ths, so that 8 measures of air at the freezing temperature become 11 at the boiling point of water.

Secondly. That, although each solid and each liquid has its own peculiar rate of expansion, yet all gaseous bodies have the very same rate of expansion, namely, that above stated, which applies to all gases as well as to atmospheric air.

Thirdly. That, while all known solids and liquids expand in an increasing rate or with greater rapidity the more they are heated, airs on the contrary seem to preserve an equable rate of expansion at all temperatures, their increase of bulk, for example, being the same from 0° or zero to 100° as from 100° to 200°; and as their expansion from 32° to 212° Fahrenheit amounts to ths of their bulk at 32°, it follows that every degree on this scale corresponds to a change in their bulk amounting toth of the bulk at 32° (supposing their elasticity unchanged); but, if their density remain constant (as when they are confined in a given space), then each degree of Fahrenheit alters their elasticity byth of whatever the elasticity would be at 32o.

Hence, if the temperature of any gas be estimated from an imaginary zero 480° below the freezing point of water on Fahrenheit's scale, or 448° below Fahrenheit's zero, the temperature so reckoned will be directly proportional to the elasticity of the gas when its density is unchanged, or inversely proportional to the density when the elasticity is unchanged; or, when either of these two elements is constant, the other varies in the same ratio as the temperature on Fahrenheit's scale, augmented by the constant quantity 448°.

If we know the numerical measure of the density corresponding to a given elasticity at a given temperature, we can then find under any other circumstances the value of any one of these three elements when the others are given. In the case of common air these data have been measured most accurately by Dr. Prout, who found that when its temperature is 32°, and its elasticity balances the pressure of 30 inches of mercury, its density

* The reader will easily perceive that this number is obtained by dividing 180 (the number of degrees between 32° and 212° Fahr.) by . Recent experiments, however, assign the fraction or instead of

TEMPERATURE, ELASTICITY, AND DENSITY.

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is such that 100 cubic inches of space contain 32.7958 grains troy of it.

28. The relation of these data is different in different gases. Thus, when common air and chlorine have the same temperature and the same elasticity, the chlorine is two and a half times as dense as the air; while, on the other hand, air is more than fourteen times denser than hydrogen of the same temperature and elasticity. Hence the reason that a balloon ascends when filled with hydrogen, which is necessarily of the same elasticity as the air which presses on it. But in order to render the densities of these three gases equal, the hydrogen must have fourteen times the elasticity of the air, and this must have two and a half times the elasticity of the chlorine (supposing their temperatures equal). But in every gas the same simple relations subsist between these three properties; so that, when the temperature is reckoned from-448°, then any two of the three (temperature, elasticity, and density) are proportional, when the third is unchanged.

29. In order to gain clear ideas of the relations subsisting between the temperature, the elasticity, and the density of aeriform matter, it is necessary to limit our attention to a volume of air confined in a close vessel, or in a tube such as that by which the law of Mariotte was illustrated (9). It is obvious that these relations or laws could never have been discovered by studying the effects of heat on the atmosphere itself; but, having once established them by experiment, the natural philosopher knows by analogy that what is true on the small scale of experiment is equally true on the grand scale of nature. Experiments form a sort of index to the volume of creation; they guide us in our search by telling us what to look for; and, confiding in the constancy of nature's laws, the natural

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philosopher ascends from a few experiments with glass tubes and a little mercury to grand and comprehensive generalizations.

But, before we can understand the effects of heat upon the atmosphere, it is necessary to study another relation between heat and air.

30. All fluids are very bad conductors of heat, that is, the amount of heat which is capable of passing from particle to particle without disturbing their relative position is almost inappreciable. But the perfect fluidity and great expansive power of air renders it a most admirable conveyer of heat.

We may illustrate the difference between conduction and convection by comparing the action of heat on a solid with that on a liquid. If one end of an iron rod be placed in the fire, the heat will travel to the other end just as quickly whether the rod be inclined upwards or downwards. It will also travel very quickly upwards through a tube of water, but it will not travel downwards, or, if it does travel at all downwards, it will be so slowly, that a lump of ice sunk to the bottom of the tube will not be melted, although the water at the surface is boiling, as shown in Fig. 15. Hence water is

called a bad conductor of heat; but it is a good conveyer of heat, as may be proved by applying the heat below the tube. The particles of water at the bottom immediately expand by the heat, become lighter than the parts above them, and rise up to the surface, while the cooler and consequently heavier portions descend and occupy their place; they in their turn become heated and ascend, while another set of

cooler and heavier particles descend,

ICE

Fig. 15.

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