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piece mn, and with it the bob. In order, therefore, that this latter shall neither raise nor sink, it is necessary that the upward expansion of the rods, k and h, shall exactly compensate the downward expansion of the rods, a, b, c, d.

Brass being more expansible than steel, compensation is effected by taking the first metal for the rods, h and k, and the second for the rods, a, b, c, and d. The only condition necessary for compensation is that the lengths of the two metals must be inversely as their coefficients of expansion. That is to say, that if brass is two or three times as expansible as steel, its length must be one-half or one-third as much.

In fig. 177 the pendulum has been represented with a single frame of steel and one of brass; but in order to reduce the length, there are always at least two rows of steel and brass.

EXPANSION OF LIQUIDS.

214. Absolute and apparent expansions.-We have already seen that liquids are more expansible than solids (188), which is a consequence of their feeble cohesion; but their expansibility is far less regular, and the less so the nearer their temperature approaches that of their boiling point.

Fig. 177.

In solids two kinds of expansion have to be considered, the longitudinal and the cubical. Now it is clear that the latter is the only kind of expansion which can be observed in the case of liquids. The expansion may be either real or apparent. The former is the real increase in volume which a liquid assumes when it is heated; while the latter is that which the eye actually observes, that produced in the vessel containing the liquid. Thus in thermometers, when the liquid expands and rises in the stem, the apparent expansion is observed, which is less than the real or absolute expansion. For, while the mercury expands, the bulb of the thermometer does so too; its volume is greater, and hence the liquid does not rise so high in the stem as it would if the volume of the bulb were unaltered. If a flask of thin glass, provided with a capillary stem, the flask and part of the stem being filled with

P

some coloured liquid, be immersed in hot water, the column of liquid in the stem at first sinks, but then immediately after rises, and continues to do so until the liquid inside has the same temperature as the hot water. This first sinking of the liquid is not due to its contraction; it arises from the expansion of the glass, which becomes heated before the heat can reach the liquid; but the expansion of the liquid soon exceeds that of the glass, and the liquid ascends.

Hence since, whatever be the nature of the material in which a liquid is contained, it has some expansibility, and always expands with the liquid, the apparent expansion is the only one directly ob served in liquids.

The coefficient of expansion of a liquid is the increase which the unit of volume experiences for a rise in temperature of one degree. These coefficients greatly vary. In a glass vessel the apparent expansion of mercury is 15 parts in ten thousands; that of water is 4.6 parts, that is, three times as great; alcohol is still more expansible, for its coefficient is 116 parts in ten thousands. 215. Maximum density of water.-Water presents the remark

Fig. 178.

able phenomenon, that when its temperature sinks it contracts up to 4°; but from that point, although the cooling continues, it expands up to the freezing point, so that 4° represent the point of greatest contraction of water, or, what is called, its point of maximum density.

This phenomenon may be observed by comparing a water thermometer, one, that is to say, filled with water, with one of mercury; both being exposed to gradually diminishing tempe

rature.

Hope used the following method to determine the maximum density of water. He took

a deep vessel, perforated by two lateral apertures, in which he fixed thermometers (fig. 178), and having filled the vessel with water at 0°, he placed it in a room at a temperature of 15o. As the layers of liquid at the sides of the vessel became heated they sank to the

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Expansion of Gases.

211

bottom, and the lower thermometer marked 4°, while that of the upper one was still at zero. Hope then made the inverse experiment; having filled the vessel with water at 15°, he placed it in a room at zero. The lower thermometer having sunk to 4°, remained stationary for some time, while the upper one cooled down until it reached zero. Both these experiments prove that water is heavier at 4° than at o°, for in both cases it sinks to the lower part of the vessel. This phenomenon is of great importance in the economy of nature. In winter the temperature of lakes and rivers falls, from being in contact with the cold air, and from other causes, such as radiation. The colder water sinks to the bottom, and a continual series of currents goes on until the whole has a temperature of 4°. The cooling on the surface still continues, but the cooled layers being lighter remain on the surface, and ultimately freeze. The ice formed thus protects the water below, which remains at a temperature of 4°, even in the most severe winters, a temperature at which fishes and other inhabitants of the waters are not destroyed.

EXPANSION OF GASES.

216. Value of the expansion of gases.--Not merely are gases the most expansible of all bodies, but their expansion is the most regular. It was originally assumed, on the basis of Gay Lussac's experiments, that all gases expanded to the same extent for the same increase of temperature, that is, that they had all the same coefficient of expansion. It has, however, been established, that the coefficients of various gases do present slight differences. They are, however, so slight, that for all practical purposes they may be assumed to be the same; that is to say, 367 parts in a hundred thousand, or, in other words, that 100,000 volumes of air, or any other gas, when heated through 1 degree Centigrade, would become 100,367 volumes, or I volume in 273. This expansibility is about 13 times as great as that of water.

217. Effects of the expansion of gases.—The expansion of gases affords us numerous important applications, not merely in domestic economy, but also in atmospheric phenomena. Thus in our dwellings, when the air is heated and vitiated by the presence of a great number of persons, it expands and rises in virtue of its diminished density to the highest parts of rooms; and to allow this to escape, apertures are made in the cornice, while fresh and pure air enters by the joints of the doors and of the windows.

In theatres the spectators in the galleries are exposed to the highest temperature and the most impure air, while those near the orchestra respire in a purer air.

Draughts in chimneys are due to the expansion of air. Heated by the fire in the grate, the air rises in the chimney with a velocity which is greater the more it is expanded. Hence results a rapid current of air, which supports and quickens the combustion by constantly renewing the oxygen absorbed.

The expansion and contraction of air have a fortunate influence on the temperature of that part of the atmosphere in which we live. For when the ground is strongly heated by the sun's ardent rays, the layers of air in immediate contact with it tend to acquire the same temperature and to form a stifling atmosphere; but these layers, gradually expanding, rise in virtue of their diminished density; while the higher layers, which are colder and denser, gradually replace them. Thus the high temperature which would otherwise be produced in the lower regions is moderated, and never exceeds the limits which plants and animals can support.

The expansion and contraction produced in the atmosphere over a large tract of country are the cause of all winds, from the lightest zephyr to the most violent hurricane. These winds, which at times are so destructive, so capricious in their direction, and so variable in their intensity, not merely have the effect of mixing the heated and the cooler parts of the atmosphere, and of thus moderating extremes of temperature, but by driving away the vitiated atmosphere of our towns, and replacing it by pure air, they are one of the principal causes of salubrity; without them our cities would be centres of infection, where epidemics of all kinds would be permanent. Without winds clouds would remain motionless over the country where they were formed, the greater part of the globe would be condemned to absolute aridity, and neither rivers nor brooks would moisten the soil. But carried by the winds the clouds formed above the seas are transported to the centres of continents, where they fall as rain; and this having fertilised the soil, gives rise to the numerous rivers which fall into the ocean, thus establishing a continuous circulation from the seas towards the continents and from continents towards seas.

218. Density of gases.-The densities of solids and of liquids have been determined in reference to water (100); those of gases by comparison with air; that is, having taken as term of comparison, or unity, the weight of a certain volume of air, the weight

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Fusion.

213

of the same volume of other gases is determined. But as gases are very compressible and very expansible, and as therefore their densities may greatly vary, they must be reduced to definite pressure and temperature. This is why the temperature of zero and the pressure 30 inches have been chosen.

Hence the relative density of a gas, or its specific gravity, is the relation of the weight of a certain volume of the gas to that of the same volume of air; both the gas and the air being at zero and at a pressure of 30 inches.

In order, therefore, to find the specific gravity of a gas, oxygen for instance, it is necessary to determine the weight of a certain volume of this gas, at a pressure of 30 inches, and a temperature of zero, and then the weight of the same volume of air under the same conditions. For this purpose a large globe of about two gallons capacity is used, like that represented in fig. 88, the neck of which is provided with a stopcock, which can be screwed to the air-pump. The globe is first weighed empty, and then full of air, and afterwards full of the gas in question. The weights of the gas and of the air are obtained by subtracting the weight of the exhausted globe from the weight of the globes filled, respectively, with air and gas. The quotient, obtained by dividing the latter by the former, gives the specific gravity of the gas. It is difficult to make these determinations at the same temperature and pressure, and therefore all the weights are reduced by calculation to zero, and the normal pressure of 30 inches.

In this manner the following densities have been found:

From these numbers the lightest of gases, and therefore of all bodies, is hydrogen, whose density is less than 1th of air.

CHAPTER VI.

CHANGES OF STATE OF BODIES BY THE ACTION OF HEAT.

219. Fusion. In treating of the general effects of heat, we have seen that its action is not only to expand them, but to cause them to pass from the solid to the liquid state;`or from the latter state