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evidently greater in proportion as the wax has fused to a greater distance. The experiment is sometimes modified by attaching glass balls or marbles to the ends of the rods by means of wax. As the wax melts, the balls drop off, and this in the order of their respective conductivities. By these and other experiments it has been ascertained that metals are the best conductors, then marble, porcelain, brick, wood, glass.
208. Conducting power of liquids. Manner in which they are beated.-Liquids, with the exception of mercury, which is a metal, are all bad conductors of heat. They conduct so imperfectly that Rumford assumed water to be entirely destitute of conducting power. But its conductivity, though small, has been established beyond doubt, as well as that of other liquids, by the most accurate experiments.
From their small conducting power, liquids are not heated in the same manner as solids. If heat be applied to a solid, whether on the top, the bottom, or the sides, it is transmitted from layer to layer, and the whole mass becomes heated. This is not the case
with a liquid ; if it is heated at the top, the heat is only propagated with extreme slowness, and it cannot be completely heated. But if it be heated at the bottom, the temperature of the liquid rapidly rises. This, however, is not in virtue of conductivity, but by ascending and descending currents, which, in virtue of the mobility of the molecules, are produced throughout the whole mass of liquid.
The existence of these cur
rents may be demonstrated by Fig. 176.
placing in the water a powder
of approximately the same density, for instance, oak sawdust, and then gently heating this at the bottom. As the lower layers become heated they expand, while the upper layers, which are colder and therefore denser, sink and take the place of the first ; these in their turn become heated, rise, and so on, until the entire mass is heated. These
currents are evident from the shavings which are seen to rise slowly in the centre, and to redescend near the edges.
209. Conductivity of gases. — Gases are extremely bad conductors of heat; but this cannot be easily demonstrated by experiment, owing to the extreme mobility of their particles. For so soon as they are heated in any part of their mass, expansions and currents are produced, in virtue of which the heated parts mingle with the cold ones; hence a general elevation of temperature, which we might be tempted to consider as due to conductivity. When, however, gases are hindered in their motion, their conductivity seems extremely small, as the following examples show.
210. Applications.— The greater or less conductivity of bodies meets with numerous applications. If a liquid is to be kept warm for a long time, it is placed in a vessel and packed round with nonconducting substances, such as shavings, straw, bruised charcoal. For this purpose water pipes and pumps are wrapped in straw at the approach of frost. The same means are used to hinder a body from becoming heated. Ice is transported in summer by packing it in bran, or folding it in flannel.
Double walls constructed of thick planks having between them any finely divided materials such as shavings, sawdust, dry leaves, etc., retain heat extremely well; and are likewise advantageous in hot countries, for they prevent its access. During the night the windows are opened, while during the day they are kept close. If a layer of asbestos, a very fibrous substance, is placed on the hand, a red-hot iron ball can be held without inconvenience. Red-hot cannon balls can be wheeled to the gun's mouth in wooden barrows partially filled with sand. Lava has been known to flow over a layer of ashes underneath which was a bed of ice, and the non-conducting power of the ashes has prevented the ice from fusion.
The clothes which we wear are not warm in themselves ; they only hinder the body from losing heat, in consequence of their spongy texture and the air they enclose. The warmth of bed-covers and of counterpanes is explained in a similar manner. Double windows are frequently used in cold climates to keep a room warm --they do this by the non-conducting layer of air interposed between them. It is for the same reason that two shirts are warmer than one of the same material, but of double the thickness. Hence too the warmth of furs, eider down, etc.
That water boils more rapidly in a metallic vessel than in one of porcelain of the same thickness; that a burning piece of wood can
be held close to the burning part with the naked hand, while a piece of iron heated at one end can only be held at a great distance, are easily explained by reference to their various conductivities.
The sensation of heat or cold which we feel when in contact with certain bodies is materially influenced by their conductivity. If their temperature is lower than ours, they appear colder than they really are, because from their conductivity heat passes away from us. If, on the contrary, their temperature is higher than that of our body, they appear warmer from the heat which they give up at different parts of their mass. Hence it is clear why carpets, for example, are warmer than wooden floors, and why the latter are warmer than stone floors.
CHAPTER V. MEASUREMENT OF THE EXPANSION OF SOLIDS, LIQUIDS, AND
211. Espansion of solids.-The expansion of bodies by heat being a general effect which exerts its influence on all bodies, and is continually changing their volume, it will be readily understood that the determination of the amount of this expansion is a problem of great importance, both in its purely scientific, as well as in its practical, aspects. We shall first describe the method of determining the expansion of solids. We have already seen that the expansion of solids may be either as regards the length or the volume. Hence the investigation of the expansion of solids may be divided into two parts, the first relating to linear, and the second to cubical expansion.
Linear expansion. In order to compare with each other the expansion of bodies, the elongation is taken which the unit of length undergoes when it is heated from zero to i degree, and this elongation is called the coefficient of linear expansions. The coefficients of a great number of substances were accurately determined towards the end of the last century by Lavoisier and Laplace. They took a bar of the substance to be determined, placed it in melting ice, and then accurately determined its length. Having placed it then in a bath of boiling water, they again measured its length. They then observed an elongation, which represented the total expansion for an increase of temperature of 100 degrees. This, divided by
-212] Applications of the Expansion of Solids. 207 100, gave the coefficient of linear expansion for one degree. In this manner the following numbers have been obtained.
Coefficients of linear expansion for 1° between oo and 100°C. White glass : 0'00000861 Bronze . . 0'000018167 Platinum . . 0'00000884 Brass . . . '000018782 Steel . . . 0'00001079 Silver
. 0'0000 19097 Iron . . . 0'00001220 Tin . . . 0'00002 1 730 Gold . . . 0'00001466 Lead . . . O'000028575 Copper . . O'00001718 Zinc . . . O'000029417
It will be seen from this table, that the coefficients of expansion are in all cases very small. Thus, when we say, that the coefficient of expansion of copper is about o'000017, we mean that a rod of this metal when heated through i degree, will expand by 17 millionths of its length; that is to say, a rod of copper a million feet in length would be longer by 17 feet under these circumstances.
Cubical expansion. The coefficient of cubical expansion is the increase in volume for a temperature of one degree. Calculation shows that the coefficient of cubical expansion is three times its coefficient of linear expansion ; and the coefficients may therefore be obtained by multiplying the above numbers by three.
212. Applications of the expansion of solids.- In the arts we meet with numerous examples of the influence of expansion. (i.) The bars of furnaces must not be fitted tightly at their extremities, but must, at least, be free at one end, otherwise, in expanding, they would exert sufficient force to split the masonry. (ii.) In making railways a small space is left between the successive rails, for, if they touched, the force of expansion would cause them to curve or would break the chairs. (iii.) Water pipes are fitted to one another by means of telescopic joints, which allow room for expansion. (iv.) If a glass is heated or cooled too rapidly it cracks; this arises from the fact that glass being a bad conductor of heat, the sides become unequally heated, and consequently unequally expanded, and the strain thereby produced is sufficient to cause a fracture.
When bodies have been heated to a high temperature, the force produced by their contraction on cooling is very considerable ; it is equal to the force which is needed to compress or expand the material to the same extent by mechanical means. According to Barlow a bar of malleable iron a square inch in section is stretched joooo of its length by a weight of a ton; the same increase is ex
perienced by about 9° C. A difference of 45° C. between the cold of winter and the heat of summer is not unfrequently experienced in this country. In that range a wrought iron bar, ten inches long, will vary in length by 1 of an inch, and will exert a strain, if its ends are securely fastened, of fifty tons.
An application of this contractile force is seen in the mode of securing the tires on wheels. The tire being made red hot, and thus considerably expanded, is placed on the circumference of the wheel, and then cooled. The tire, when cold, embraces the wheel with such force as not only to secure itself on the rim, but also to press home the joints of the spokes into the felloes and naves. Another interesting application was made in the case of a gallery at the Conservatoire des Arts et Métiers in Paris, the walls of which had begun to bulge outwards. Iron bars were passed across the building, and screwed into plates on the outside of the walls. Each alternate bar was then heated by means of lamps, and when the bar had expanded, it was screwed up. The bars being then allowed to cool contracted, and in so doing drew the walls together. The same operation was performed on the other bars.
213. Compensation pendulum.—An important application of the expansions of metals has been made in the compensation pendulum. To understand the utility of such an arrangement, we must call to mind what has been said about pendulums ; namely, that their oscillations are isochronous, that is, are made in equal times, and that their application to the regulation of clocks depends upon this property. But we have also seen that the duration of an oscillation depends on the length of the pendulum ; the longer the pendulum the more slowly it oscillates, and, therefore, the shorter it is, the more rapidly does it oscillate. Hence a pendulum formed of a single rod terminated by a metal bob, c, as represented in fig. 52, could not be an exact regulator; for, as the temperature rises, it would elongate, and the clock would go slower : the exact opposite would take place when it contracted by cooling. These inconveniences have been remedied by taking the remedy from the cause of the evil.
For this purpose the pendulum rod consists of several metal bars arranged as represented in fig. 177. The rods, a, b, c, d, are of steel, and all expand on a downward direction when the temperature rises, thus making the bob sink. The rod, d, supporting the bob is fixed to a cross-piece mn, which in turn is fastened to two rods, k and h, which are connected to the piece or, and therefore cannot expand downwards, but only in an upward direction ; they raise the