HEAT. It Heat is known only by its effects on matter. makes water boil, iron by its means becomes redhot, and so on. In ordinary language the term heat is used to express the sensation of warmth, and absence of heat constitutes cold. Two theories have been advanced to explain the phenomena of heat. The first theory supposes heat to be an elastic fluid without weight, enveloping and permeating all bodies, and capable of passing freely from one body to another. The particles of this fluid repel each other, and are attracted by the particles of other bodies. This is called the emission theory. According to the second theory, heat consists of the vibratory motion of the particles of bodies, which motion is transmitted from one body to another through an elastic fluid, called ether, in a manner precisely the same as sound is transmitted through the air. The warmest bodies are those in which the vibrations are most rapid. This is the undulatory theory of heat. According to the first theory, a body cools by losing a portion of the fluid; according to the second theory, in cooling, its vibratory motion becomes less rapid. All bodies expand by heat. In a solid body there is expansion on the application of heat. The heat is converted into motion, the solid particles may be looked upon as endeavouring to overcome external pressure, and the force of cohesion which holds them together. The result of the continued application of heat is expansion, which goes on until the solid is converted into a liquid; now the force of cohesion is slight, and the application of heat will have a greater effect in expanding the liquid, for there is only external pressure of the atmosphere to overcome. The gaseous state will follow, where cohesion is almost nil, and pressure alone the counteracting force. In short, then, solids expand with heat slightly, liquids to a much greater degree; gases are extremely dilat able. There are three kinds of expansion,-linear expansion or dilatation, superficial expansion, and cubical expansion or increase of volume. Linear and Superficial Expansion.-Expansion of Volume.-If we wish to compare the rate of linear dilatation of different bodies, we must take for a term of comparison the expansion experienced by a unit of length of each body when heated from 32° to 33° F., and this is called the co-efficient of linear expansion. The co-efficients of linear expansion on many bodies were determined by Lavoisier in the following way :-The substance to be experimented on was reduced to the form of a uniform bar. It was then exposed for some time to the temperature of melting ice, and its exact length measured. The bar was then exposed to boiling water, and its exact length again measured. The increased length, divided by 180°, gave the increase in length of the whole bar for 1°F. This result, divided by the length of the bar at 32° F., gave the linear expansion of a unit of length for an increase of temperature of 1° F., that is the co-efficient of linear expansion. The co-efficient of superficial expansion is, as the term implies, the increase in surface of a square unit, for a rise of 1° F. in temperature. It may be obtained by doubling the co-efficient of linear expansion, The reason of this is explained in the next paragraph. The co-efficient of expansion in volume is the increase which a cubic unit of the substance undergoes when its temperature is raised 1° F. This co-efficient may be found experimentally, or by multiplying its co-efficient of linear dilatation by 3. For although the co-efficients vary with different bodies, for the same body the co-efficient of cubical expansion is three times that of linear expansion. Suppose a rectangular bar, whose length, breadth, and thickness are a bc, its contents will bear a certain ratio to a3. If it be expanded it will bear the same ratio to a cube of the side corresponding to a, for all parts expand proportionally. Hence, if h be the linear dilatation of a, the new length will be a + h, and the ratio of the contents or volume will be a3 (a+h)3. The measure of linear dilatation is then (a + h)-a and of cubical expansion (a + h)3 — a3 a h a' 3h 3h2 ; a3 3a2h+3ah2 + h3 a3 + In all cases of solid expansion, a a2 a3. the linear dilatation, is a very small fraction. Thus, for Falmouth tin, heated from 32° F. to 212° F., it is only. The ratio of cubical expansion to linear 3h 3/2 h3 α + a2 2). + 3, little from very h = or a' and we may safely take this rule, when not requiring an exactness within of the whole quantity measured, that the cubical expansion may be found by trebling the linear dilatation. The co-efficients of linear expansion, as given by Professor Tyndall, are for Platinum Inches. 0'0000088 Mercury. 0'00116 0'000154 For the surperficial expansion multiply by 2; for the. cubical, by 3. Note carefully the co-efficients of platinum and glass. They are nearly alike. Many instruments used in physical science require platinum wire to be fused into glass. This may be done, because they expand and contract alike; therefore, in contracting, the glass does not leave the platinum. The co-efficients of expansion of gases are given as follows: Hydrogen Air Carbonic oxide Sulphurous acid 0.00366 0'00365 0*00367 0'00371 0*00390 From consulting this table, the student will notice that carbonic acid, and more notably sulphurous acid, differ from the other gases in their co-efficients. They are, in fact, imperfect gases; they are in an intermediate state between gases and liquids, and are with comparative ease compressed into liquids. Gaseous bodies expand equally for equal increments of temperature, with slight exceptions. 1,000 parts of air at 32° F. become 1,375 at 212° F., and the same expansion is experienced by other aëriform bodies. The ratio of the expansion of gases has recently been corrected by Rudberg, and, according to his investigation, one volume of gas at 32° F. becomes 1365 at 212° F. To find the increment of volume for 1 F., we have only to divide the fraction 365 by 180, which gives 365 or 3. 1800009 1000 The increase of volume, therefore, which any gas or vapour undergoes when the temperature is raised one degree is the 493rd of the volume which it would have if reduced to the temperature of 32°. It follows from this that if air be raised from the freezing point to 493°, it will double its volume. (Exercise V.) Experiments and Examples of Expansion. Solids.—A pyrometer is an instrument for showing the expansion of metal bars. In Fig. 76 a rod, B, is Fig. 76. subjected to heat from burning alcohol in a vessel, C, and at the end of the rod is an arrangement by which, on a graduated quadrant, D, the dilatation is shown. A Gravesande ring is of exactly sufficient size to allow a cold brass ball to pass through it. When the ball is heated it will not pass through the ring. The pyro |