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THERMO-ELECTRICITY), one of whose junctions is kept at a constant temperature, while the other is exposed to the temperature that is to be measured. Of these four general methods, the first two have been longest and most com monly employed; and the particular instru ments that have been most extensively used for putting them into practice are known respec tively as the "mercury-in-glass thermometer" and as the "gas thermometer." The mercury in-glass instrument is described under THER MOMETER, and the gas thermometer is described in the present article, below.

The gas thermometer was probably the first form of thermometer to be constructed. The mercury-in-glass instrument followed, and for many years was used almost exclusively for the measurement of temperatures, doubtless on ac count of its simplicity and the ease with which it can be used. But as the science of thermom etry developed, and increasing refinement in temperature determinations was demanded, it was found that the mercury-in-glass thermom eter is liable to serious errors on account of the anomalous expansions and contractions of the glass envelope; errors which were of little or no importance when a determination of tem perature to the nearest quarter of a degree or so was considered sufficiently accurate, but which were of paramount importance when it was proposed to determine a temperature to the hundredth or thousandth of a degree. The errors due to the cause in question can now be eliminated in large measure by making temper ature determinations by the "movable zero" method (see THEamobirrsa); but physicists nevertheless prefer to follow the lead of Reg nault, who, in his celebrated

The gas thermometer is made in two gen eral forms, according as it is desired to meas ure the temperature by the expansion of the gas at some constant pressure, or by the in crease in the pressure of the gas at some con stant volume. The latter plan being the one that is now by far the commoner in accurate work, we shall describe it first, and at some length.

The constant-volume gas thermometer is shown, in its essential features, in the accom panying illustration. It consists of a bulb, A, of considerable size, which is connected, by means of a capillary tube, with a mercury manometer, M. At a there is a mark upon the tube leading to the gas bulb, and care is taken, whenever an observation of any kind is made, to have the level of the mercury in the short arm of the manometer stand exactly at a, in order that the volume of the thermometric gas may always be rigorously the same. A movable reservoir of mercury, V, is connected with the column M for this purpose, by means of a flexible tube; so that by raising or lowering V the mercury in M may be brought to any desired level. Any gas that we please may be used in the bulb A, but hydrogen, nitrogen and air are the ones most commonly employed. In the filling of the bulb, the most elaborate precautions are taken, not only to have the gas that is used pure, but also, and more particularly, to have it per fectly dry. For this purpose the bulb is first exhausted by the aid of an air-pump, and is heated while in the exhausted condition, and allowed to stand for a time, so that any mois ture that may adhere to the walls of the bulb may be driven off and removed. The bulb is then filled with gas that has been carefully dried by calcium chloride or other drying agents, and is then exhausted again and heated; the operations of exhausting and refilling being repeated several times, until there can be no doubt about the dryness and purity of the gas which is finally allowed to remain. Temper

ature, according to this instrument, is defined as being rigorously proportional to the pressure that' prevails in the bulb A, so long as the volume of the gas in the bulb remains constant. It will be observed that there is here no as sumption that the thermometric gas obeys the laws of Boyle and Charles (see THERMOPY NAMICS) ; the relation which has just been as sumed being the definition of the term "tem perature," according to the constant-volume gas thermometer. If T be the temperature as thus defined, and P is the pressure prevailing within the bulb A, then 'we have, from the definition of temperature, T=CP, where C is a constant for the particular thermometer under consid eration. (It is to be observed that P is the total pressure to which the gas in A is sub jected. It includes not only the pressure that is read from the manometer M, but also that barometric pressure that prevails at the same time in the air of the laboratory; for this baro metric pressure acts upon the top of the mer cury column, and it is, therefore, to be added to the reading of the manometer M). To de duce the value of the constant C, we may sub ject the bulb A successively to the steam from boiling water, and to a mixture of ice and water, as described under THERMOMETER. The total pressure upon the gas in the bulb being noted in each case, let us suppose that it is P0 at the freezing point, and Pio. at the boiling point. Then the foregoing equation, when applied to these two cases, takes the following forms, respectively: To=CP0, CPloo; To being the temperature of the freezing point according to the scale of this thermometer, and noo being that of the boiling point. We may define either T. or T1.0 however we please, and then find the corresponding value of C; but it is desir able that the scale of the gas thermometer shall be as closely as possible like that of the ordi nary mercury-in-glass instrument; and in order to fulfil this condition it is found to be best to subject the gas thermometer scale to the condition that the difference between T0 and TIN, as determined by the gas thermometer, shall be numerically the same as the difference between the freezing and boiling points, on the ordinary mercury-in-glass scale. In other words, it is found to be best to have the aver age size of the degrees the same on the two instruments. In scientific work the Centigrade scale is used in practically every instance; and if we adopt it here, we shall have the relation T.— 100°, if the condition just men tioned is to be fulfilled. From this and the praqeding.ertuations we easily find that C(P1.. — 100 , or C=100/(P1ft —P.); so that when we know the values of Pm and Po by direct observation, we are prepared to deter mine C at once_, and hence to calculate the gas temperature, T, corresponding to any given pressure P, by means of the relation T =CP. It will be seen that the zero of the gas ther mometer scale does not coincide with the freez ing point of water, but that it is very much lower. The gas thermometer could not give T=0, for example, unless P=0; that is, not unless the temperature was so low as to cause the gaseous pressure to disappear altogether. The zero point from which the indications of the gas thermometer are counted, according to the formula given above, is called the ((natural zero" of the instrument; and in order to be able to compare the gas scale with the scale of the ordinary mercury-in-glass thermometer, it becomes necessary to know what the temper ature of freezing water is, as read from the gas scale. To determine this, we make use of the relation T.= CP.. Substituting in this the value of C as already found, we find that T.= 100Pd (Pio P.). Now the quantity (P10— Po)/Po is known as the "coefficient of expansion at constant volume" for the gas. (The name is somewhat absurd, it is true, be .

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