rapidly than the pendulum-rod, and produces the same effect as the zinc in the gridiron pendulum. Both pendula are called, for obvious reasons, "compensating." Chronometers differ from watches in having similar arrangements applied to their balancewheels.

§ 38. The different rates of the expansion of iron and zinc may be shown by riveting two equal lengths together. When such a compound bar is heated, the zinc expanding most forces the bar to bend (fig. 15) in such a way that the zinc forms the convex side of the arch.

§ 39. The different linear expansions of different solids for the same increase, or those of the same solid for different increases of temperature, are shown in "Fergusson's Pyrometer" (fig. 16). A rod (A) of the solid, of known length, passes watertight through the end walls of a trough, T. One end, B of A, rests against the end of the screw S, working through a support. The other end, C of A, works upon the lever of the third order, DCE, of which the fulcrum is D; the other end of this lever works at E upon a second lever, F G, of the third order. The lower end of G, which is free to move, is before a graduated arc, H. It is clear that if

DE

C advances a distance, X, E will advance a distance, X

and G

DC'

DE FG

will advance, X X (see Mechanics). Thus, if D E=10 DC, DC FE

and FG-10 FE, then, for every advance of C, the advance of G will be 100 times as great. The instrument is used by screwing up S until G is opposite a fixed point on the scale, the rod being kept cold by filling the trough T with melting ice. If the ice be then exchanged for boiling water, the rod A expands. The end B cannot recede; the end C advances, and the index end G moves with exaggerated motion.

§ 40. The following are some of the more common consequences of the expansion of solids.

The equality in the expansions of platinum and glass make it possible to fuse glass upon platinum, without danger of subsequent separation on cooling. If glass be softened, a platinum wire may be thrust through it in such a manner as to form airtight contact when cold. If an iron or copper wire be treated in the same way, it will shrink more rapidly than the glass, and crack away on cooling.

Allowance must be made for the expansion of the iron of bridges and similar structures, lest by alternation of temperature it may injure the masonry, which is not so affected by temperature.

Nails driven into bricks or mortar become loosened in cold weather, and gradually work themselves out.

The official standard of length (the yard) varies with the tem

perature. In order that its length may be the same, it must be brought to the same temperature-say, that of melting ice.

The force exerted by solids on expansion by heat and the equal force which they exercise on contraction by loss of heat, is enormous. But the amount of movement is so small, that this force can only be applied in the arts in a few cases.

The rivets used in joining boiler-plates are used red-hot, partly for the sake of convenience in hammering out their heads, but partly because on cooling they drag the plates together by their contraction with immense force.

The tire of carriage-wheel is made a little smaller than the wheel. On making it hot it passes over the wheel; on cooling, it contracts and binds the wheel together. Metallic collars are in the same way "shrunk" on to bodies.

§ 41. Many solids, at the moment of becoming so from the liquid state, expand considerably, and also with great force. Thus ice, as it is formed, swells very considerably and with such force as to burst water-pipes, and even bomb-shells.

Type-metal, a mixture of lead and antimony, also swells at the moment of solidification from the melted state, and, in doing so, forces itself into the type-mould so perfectly as to produce a sharp and clean casting, which is necessary for clear printing.

§ 42. Many crystalline solids expand unequally in different. directions, so that a change of temperature produces change of shape.

§ 43. Expansion of solids by volume.-If a solid rod of length

1

L expands th of its length for a given rise of temperature,

n

or

If, as is always the case with solids, n is a very large number,

1

n

very small, the third and fourth terms of this value may be

neglected, and we have very nearly

or the cubic increase of size is three times the linear.

CHAPTER IV.

THERMOMETERS.

§ 44. Instruments for measuring the temperature of bodies are called Thermometers (heat-measurers) or Pyrometers (fire-measurers). The latter are employed for determining very high temperatures, as those of furnaces, the temperatures of melting metals, &c.; the former are used for the measurement of the lower ranges of temperature.

§ 45. Since all bodies* expand by heat, it is clear that if we take a fixed quantity of any substance at any temperature, and accurately measure its size, we are sure that whenever it has the

* Excepting water at a certain temperature (§ 31), and an alloy of bismuth, tin, and lead (§ 35, note).

same size it will have the same temperature*. When it has a larger size it must have a higher, and when a smaller, a lower temperature.

§ 46. Since (for the same increase of temperature) gases, as a rule, expand more than liquids, and liquids more than solids, it follows that a mass of gas of a given size will, by its change of size, form a more accurate and sensitive index of temperature than a mass of liquid or solid of the same size.

§ 47. Air-thermometers are used for determining sudden and slight changes of temperature. The arrangement of an airthermometer has been described (§ 20, fig. 4). It is essential to the action of such a thermometer, that the surface of the liquid in the vessel A (see fig. 4) should be exposed to the air. The pressure of the atmosphere, however, is continually varying, both at the same place at different times and at different places at the same time. (See Natural Philosophy, Pneumatics.)

Consequently, even when the temperature remains the same, a diminution of the atmospheric pressure will cause a descent of the liquid in the stem of the instrument, by relieving the air in B of a part of the pressure which is compressing it; that is, such a diminution will produce the same effect as though the air in the upper bulb had undergone expansion by heat. For this reason such a thermometer cannot be used for comparing temperatures at different times or places, unless the variation in the atmospheric pressure, as measured by the barometer, be ascertained and allowed for.

§ 48. Leslie's" differential thermometer " consists of two glass bulbs, A and B (fig. 18), containing air, and connected together by a narrow tube, C, bent twice at right angles, containing mercury or some coloured liquid. The upright proportions of C carry scales. The whole being closed, the changes of barometric pressure are without influence upon the volume of air in either of the bulbs. But if one of the bulbs only, as A, be warmed, the air in it expands, forces down the liquid in the corresponding limb of C, and forces the liquid to rise in the opposite stem, thereby In the case of gases, provided that the pressure upon it is the same.