139.]

INCREASE OF MEAN DILATATION BY HEAT.

299

external bulb merely diminishes the space occupied by the alcohol vapour, and is not communicated to the interior bulb. When submitted to hydraulic pressure of three tons on the square inch, the index of one of these protected thermometers was raised 15 F., due to the heat produced by the compression of the water, while an unprotected thermometer indicated a rise of 11°5 F. (W. A. Miller, Proc. Roy. Soc. 1869, xvii. 482).

(139) Increase of the Rate of Dilatation with Rise of Temperature. A scale divided upon the principles already described evidently depends for accuracy on the supposition that equal increments of heat produce equal amounts of expansion. With due precautions, a pound of water, at o° C., mixed with a pound of water at 100°, should yield a mixture in which the thermometer should stand at 50°, the exact mean. Yet it is not true that even in the same substance equal increments of heat at different temperatures produce an equal amount of expansion:for example, the expansion of mercury for the 10° between o° and 10°, is less than its expansion for the 10° between 90° and 100°. In the mercurial thermometer, for temperatures between freezing and boiling water, it may nevertheless be assumed, without sensible error, that equal increments of heat raise the thermometer through an equal number of degrees. The increase in the capacity of the glass bulb, especially if the thermometer be made of crown glass, almost exactly compensates for the increasing rate of the expansion of mercury; though for temperatures above 100° the compensation is not so exact. The general result is, that for all bodies, in proportion as the temperature rises, the expansion increases; the distance between the particles augments with the heat, and consequently their mutual cohesion is more readily overcome. The expansion of mercury, for example, for three progressive intervals of 100° C., according to Regnault, is the following: between 。° C. and 100° it is I part in 55'09; between 100° C. and 200° it is 1 in 54'57; and between 200° and 300° C. 1 in 54'11. Platinum is more equable in its expansion than any other of the metals, though it also exhibits a similar increase in the rate of its expansion as the heat riscs.

The following table embodies some experimental results obtained upon this point by Dulong and Petit:

The temperature of 572° (300° C.), as measured by an air thermometer, if measured by the expansion of mercury, in an ordinary thermometer, would be indicated as 586° (307°.7 C.), because the apparent dilatation of the mercury increases as the temperature rises.*

In consequence of this expansion of all vessels employed to contain the mercury, there is considerable difficulty in measuring the absolute expansion of mercury; but the difficulty was ingeniously overcome by Dulong and Petit in the following manner (Ann. Chim. Phys. 1817 [2], vii. 124):-Two long vertical tubes of glass, open at the upper extremities to the air, were connected below by a capillary tube, and the apparatus was filled with mercury. The mercury in both limbs stood at the same level so long as the temperature of both was equal. One limb of the apparatus was now enclosed in melting ice, whilst the other limb was surrounded by a hot bath, the temperature of which could be regulated at pleasure the mercury in the heated limb of course expanded with the heat, consequently a longer column of the hot mercury was required to balance a corresponding column of the cold mercury. By means of a cathetometer (note, p. 60), the difference in height of the two columns was read off, and the length of each column being known, it was easy to calculate the density of the mercury for any given temperature above the freezing point.

These experiments have been repeated by Regnault on a larger scale, and

* If the specific expansion of each solid and liquid were equal for that substance for equal increments of temperature, the volume of the body might be calculated for any given temperature by the formula V = 1 + at, in which V is the required volume, I the volume at o° C., t the temperature in degrees C., and a the coefficient of expansion ascertained by experiment. Thus the volume of mercury for any temperature between o° C. and 100° C. may be approximately determined by the formula, V = I +000018153 t; but, generally speaking, it becomes necessary to take other terms of the series into the account, so that the formula becomes

V = I + at + bť2 + ct3,

a, b, and c, being coefficients calculated from the experimental numbers.

In the case of permanent gases, the simple formula, V = 1+at gives the true result for the expansion, the coefficient a being taken = 0.002036 for each 1° F., or = 0·003665 for each 1o C.

140.]

BREGUET'S AND DANIELL'S PYROMETERS.

301

with additional precautions: he obtained as the result numbers slightly lower than those of Dulong and Petit.

(140) Pyrometers. Since the expansions of dissimilar metals for equal increments of temperature are unequal, it is evident that if a compound bar, consisting of two such metals as brass and steel, be formed by riveting equal plates of each metal together, the application of heat would occasion curvature of the bar; the concavity being upon the side of the steel, the metal which expands least. On this principle, a very delicate solid thermometer has been constructed by Breguet. It consists of a compound ribbon of three metals, platinum, gold, and silver, which are rolled out into a very thin lamina and coiled into a cylindrical spiral, to the lower extremity of which an index is attached, the upper end of the spiral being fixed. The silver expands much more than the platinum, so that the coil twists and untwists as the temperature rises and falls. The value of the degrees is ascertained by comparison with a standard thermometer.

For the estimation of high degrees of temperature, such as the heat of furnaces and the fusing points of many metals, instruments of a different description, usually termed pyrometers (from Tup, fire), are required.

120.

The most manageable of these is Daniell's register pyrometer, which is shown in fig. It consists of two parts, the register, I, and the scale, 2. The register is a solid bar of black-lead earthenware, A, highly baked. In the axis of this a hole is drilled, reaching from one end of the bar to within

half an inch of the other extremity. In this cylindrical cavity a rod of platinura or of iron, a, a, 6 inches long, is placed. Upon the top of the bar rests a cylin

302

DANIELL'S PYROMETER.

[140.

drical piece of porcelain, c c, sufficiently long to project a short distance beyond the extremity of the black-lead bar, so as to serve as an index. It is confined in its position by a ring or strap of platinum, d, passing round the top of the blacklead tube, which is partly cut away at the top; the ring is tightened by a wedge of porcelain, e. When exposed to a high temperature, the expansion of the metallic rod, a a, forces the index forward to a distance equal to the difference in the amount of expansion between the metallic rod and the black-lead bar, and when cool, it will remain protruded to the same distance, which will be greater or less according to the temperature: the exact measurement of this distance is effected by the scale,' 2. This scale is independent of the register, and consists of two rules of brass, f, g, joined together by their edges accurately at a right angle, and fitting square upon the two sides of the black-lead bar. Near one end of this double rule a small brass plate, h, projects at a right angle, which, when the instrument is used, is brought down upon the shoulder of the register, formed by the notch cut away for the platinum strap. To the extremity of the rule nearest this brass plate, is attached a moveable arm, D, turning at its fixed extremity upon a centre, i, and at the other end carrying an arc of a circle, E, the radius of which is exactly 5 inches, accurately divided into degrees and thirds of a degree. Upon this arm, at the centre, k, another lighter arm, c, is made to turn, carrying upon the extremity of its longer limb a vernier, H, which moves on the face of the arc, and subdivides the graduation into minutes. The shorter arm, which is half an inch in length, crosses the centre, and terminates in an obtuse steel point, m, turned inwards at a right angle.

To use the instrument, the metallic rod is placed in the register, the index is pressed firmly down upon its extremity, and secured tightly by the platinum strap and the wedge. The position of the index is then read off on the scale, by placing the register in the re-entering angle for its reception, with the cross-piece firmly held against the shoulder, and the steel point, m, resting on the top of the index, in a notch cut for it, which coincides with the axis of the rod. A similar observation, made after the instrument has been heated and allowed to cool, gives the value of the expansion. The scale of the pyrometer is compared with that of the mercurial thermometer, by observing the amount of expansion between two fixed points, such as the freezing of water and the boiling of mercury.

(141) A combination of the thermometer with the pyrometer gives a range of temperature extending through wide limits. The means of attaining very elevated temperatures are much more under command than those of procuring great degrees of cold.

The following table gives, in degrees both of Fahrenheit's and of the Centigrade scale, some remarkable points of temperature:

(142) Pressure Exerted by Expansion.-The amount of pressure exerted by a bar when heated or cooled, if its expansion or contraction is prevented, is enormous; for it is equal to that which would be required to elongate or compress a cold bar by mechanical means, by an amount equal to the expansion or contraction which would have occurred if the bar had been free. According to the experiments of Barlow, a bar of malleable iron of a square inch (25.4mm.) in section, is stretched T of its length by a ton weight (about 1016 kilos.); the same elongation is produced by about 9° C. In this climate a variation of 45° C. between the cold of winter and the heat of summer is frequently experienced. With that range, a wrought iron bar would be elongated Too of its length if it is free to expand, or would exert a stress of 5 tons per square inch of section if the expansion is prevented. Calculating upon Joule's data, it may be estimated that the work done by heat in producing the expansion of 1 lb. of iron between 0° and 100° C., during which it would increase about of its volume, would be adequate to lift a weight of 7 tons to the height of 1 foot-that is to say, that in order to drive asunder the particles to an extent sufficient to cause a pound of iron to increase of its volume, an expenditure of work of this enormous amount would be required.

In many instances in the arts this effect is turned to useful account With this view the wheelwright makes the iron tire of his wheels a little smaller in diameter than the rim of the wheel, and applies the tire in a heated state; on cooling, it contracts, and binds the parts firmly together. In rivetting steamboilers, the rivets are clenched whilst red-hot, in cooling they contract and draw the plates closely together. But, on the other hand, this expansion requires often to be carefully guarded against. Iron clamps built into furnaces frequently destroy, by their expansion and contraction, the masonry which they are intended to support. In long lengths of steam pipe an expansion joint is provided which permits alteration of length. For the same reason, a small interval is left between the ends of the iron bars in laying down a line of rails. Each tube of the Britannia Bridge, across the Menai Straits, is liable, from