# Thermometry

## temperature, scale, zero, absolute, fundamental, interval and arbitrary

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THERMOMETRY, the art of measuring temperature or degree of heat (Gr. 0Eppin warm; i.Arpov, a measure). The instruments used for this purpose are known as thermometers, or sometimes, when the temperatures to be measured are high, as pyrometers.

A brief sketch of the evolution of the thermometer is included in the article HEAT. The object of the present article is to discuss the general principles on which the accurate measurement of temperature depends, and to describe the application of these principles to the construction and use of the most important types of thermometer. Special attention will be devoted to more recent advances in scientific methods of testing thermometers and to the application of electrical and optical methods to the difficult prob lem of measuring high temperatures.

Zero : Fundamental Interval.—In all systems of measuring temperature it is necessary (I) to choose a zero or starting-point from which to reckon, (2) to determine the size of the degree by subdividing the interval between two selected fixed points of the scale (called the "fundamental interval") into a given number of equal parts. The fundamental interval selected is that between the temperature of melting ice and the temperature of condensing steam, under standard atmospheric pressure. On the Centigrade system the fundamental interval is divided into zoo parts, and the melting-point of ice is taken as the zero of the scale. We shall denote temperature reckoned on this system by the letter t, or by affixing the letter C. It is often convenient to reckon tem perature, not from the melting-point of ice, but from a theo retical or absolute zero representing the lowest conceivable tem perature. We shall denote temperature reckoned in this manner by the letter T, or 0, or by affixing the letters Abs. In practice, since the absolute zero is unattainable, the absolute temperature is deduced from the Centigrade temperature by adding a constant quantity, T., representing the interval between the absolute zero and the melting-point of ice; thus T= t+T..

Arbitrary Scales.—An arbitrary scale can be constructed by selecting any physical property of a substance which varies regu larly with the temperature, such as the volume of a liquid, or the pressure or density of a gas, or the electrical-resistance of a metal.

Thus if V denote the volume of a given mass at the temperature t, and if V., represent the volumes of the same mass at the temperatures o° and ioo° C, the size of I° C on the scale of this arbitrary thermometer is one hundredth part of the fundamental interval, namely (V1—V.)/Ioo, and the temperature t at volume V is the number of these degrees contained in the expansion *V —V. between o° and t° C. We thus arrive at the formula t= ioo(V—V0)/(Vi—V.) (I) which is the general expression for the temperature Centigrade on any such arbitrary scale, provided that we substitute for V the particular physical property selected as the basis of the scale. If we prefer to reckon temperature from an arbitrary zero de fined by the vanishing of V, which may conveniently be called the fundamental zero of the scale considered, we have, putting V=o in equation (I), the numerical values of the fundamental zero T., and of the temperature T reckoned from this zero It is frequently convenient to measure temperature in this man ner when dealing with gases.

Absolute Scale.—It is necessary for theoretical purposes to reduce all experimental results as far as possible to the absolute scale, defined as explained in HEAT, on the basis of Carnot's prin ciple, which is independent of the properties of any particular substance. This scale can be most nearly realized in practice by observing the temperature on the scale of a gas-thermometer, and making special experiments on the gas to determine how far its scale deviates from that of the thermodynamical engine. In the case of the gases hydrogen and helium, which can exist in the liquid state only at very low temperatures, the deviations from the absolute scale at ordinary temperatures are so small that they cannot be determined with certainty. Thermometers con taining these gases are generally taken as the ultimate standards of reference in practical thermometry.

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