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strip experiences when it is heated. In Bréguet's instrument, three thin strips composed respectively of platinum, gold and silver are rolled together into the form of a single ribbon, the gold being in the centre. The ribbon is then coiled into a spiral, with the silver on the concave side. When one end of such a spiral is fixed, a rise of temperature causes the spiral to partially unwind, owing to the fact that the coefficient of expansion of silver is greater than that of gold, while the coefficient of gold is also greater than that of platinum. The free end of the spiral is caused to actuate a pointer, by which the temperature is indicated.

Platinum Resistance Thermometer.—An instrument for determining temperature, by noting the variation of the electrical resistance of a wire or strip of platinum. (See THERMOMETRY).

ALLAN D. RISTEEN, Director of Technical Research, The Travelers Insurance Company, Hartford, Conn. ANALYSIS. See

THERMOMETRIC CHEMICAL ANALYSIS.

THERMOMETRY, the art of measuring temperatures. The "measurement" of temperature is quite a different thing from the measurement of a time, or a length, or a mass, and it consists merely in assigning to each temperature that may come up for consideration a definite place upon some sort of a numerical scale. The scale itself may be perfectly arbitrary, so that an interval of temperature upon one part of the scale cannot be said to be "equal," in any physical sense, to an interval on some other part, even though the two are expressed by the same number of "degrees." The chief essentials of a practical thermemetric scale are (1) that it shall be perfectly definite, so that when the same temperature is "measured" on several different occasions, the same identical result will be obtained each time, at least to a degree of approximation sufficient for the purposes for which the temperature is being determined; and (2) that it shall be possible for two or more different observers, provided with distinct instruments of measurement, to measure the same temperature, and obtain results that are identical, at least to the same degree of approximation as noted above. So leng as these essential conditions are fulfilled, we may make use, for the purpose of establishing a thermometric scale, of any measurable property of matter, which varies in a determinate way with temperature; the "temperature," in any such case, being defined as proportional to the atttribute that is measured, or to any continuous function of that attribute. We may, therefore, have as many different "scales" of temperature as we please, and any one of these will be just as defensible, and just as "correct," as any other one, although no two of them will be in perfect agreement. In practice it is found that four particular kinds of thermometric scales are especially useful. These are based, respectively, upon (1) the expansion of some substance that is subjected to an unvarying pressure; (2) the increase in pressure of a gas which is kept rigorously constant in volume; (3) the variation of the electrical resistance of a conductor; and (4) the electromotive force of a thermo-electric couple (see

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 commonly employed; and the particular instruments 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 mercuryin-glass instrument is described under THER MOMETER, and the gas thermometer is described in the present article, below.

The gas thermometer was probably the firs form of thermometer to be constructed. Th mercury-in-glass instrument followed, and fo many years was used almost exclusively for th measurement of temperatures, doubtless on ac count of its simplicity and the ease with whic it can be used. But as the science of thermom etry developed, and increasing refinement i temperature determinations was demanded, was found that the mercury-in-glass thermom eter is liable to serious errors on account of th anomalous expansions and contractions of th glass envelope; errors which were of little c no importance when a determination of ten perature to the nearest quarter of a degree c SO was considered sufficiently accurate, bu which were of paramount importance when was proposed to determine a temperature the hundredth or thousandth of a degree. T errors due to the cause in question can now eliminated in large measure by making tempe ature determinations by the "movable zero method (see THERMOMETER); but physicis nevertheless prefer to follow the lead of Re nault, who, in his celebrated 'Fourth Memoi (1847), recommended the employment of th gas thermometer as the standard for the e tablishment of the temperature scale; and th gas thermometer is still the standard in a work of high precision. The great advantag of the gas thermometer consists in the fa that the coefficients of expansion of gases a many times greater than that of mercury, a the effects of anomalous changes of size in th glass bulb are of correspondingly less impor

ance.

The gas thermometer is made in two ge eral forms, according as it is desired to mea ure the temperature by the expansion of th gas at some constant pressure, or by the i crease in the pressure of the gas at some co stant volume. The latter plan being the of that is now by far the commoner in accura work, we shall describe it first, and at son length.

The constant-volume gas thermometer shown, in its essential features, in the accor panying illustration. It consists of a bulb, A, considerable size, which is connected, by mea of a capillary tube, with a mercury manomet M. At a there is a mark upon the tube leadi to the gas bulb, and care is taken, whenev an observation of any kind is made, to ha the level of the mercury in the short arm of t manometer stand exactly at a, in order that t volume of the thermometric gas may always rigorously the same. A movable reservoir mercury, V, is connected with the column for this purpose, by means of a flexible tub so that by raising or lowering V the mercu

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 perfectly 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 moisture 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. Temperature, according to this instrument, is defined as being rigorously proportional to the pressure that prevails in the bulb A, so long as the

M

a

A

the bulb A, then we have, from the definition of temperature, TCP, where C is a constant for the particular thermometer under consideration. (It is to be observed that P is the total pressure to which the gas in A is subjected. 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 barometric pressure acts upon the top of the mercury column, and it is, therefore, to be added to the reading of the manometer M). To deduce the value of the constant C, we may subject 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 P. at the freezing point, and P100 at the boiling point. Then the foregoing equation, when applied to these two cases, takes the following forms, respectively To CP, T100-CP100; To being the temperature of the freezing point according to the scale of this thermometer, and T100 being that of the boiling point. We may define either To or T100 however we please, and then find the corresponding value of C; but it is desirable that the scale of the gas thermometer shall be as closely as possible like that of the ordinary 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 T. and T100, 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 average 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 T100-To-100°, if the condition just mentioned is to be fulfilled. From this and the preceding equations we easily find that C(P100 - P.) 100°, or C=100/(P100-Po); so that when we know the values of P100 and P. by direct observation, we are prepared to determine C at once, and hence to calculate the gastemperature, T, corresponding to any given pressure P, by means of the relation TCP. It will be seen that the zero of the gas thermometer scale does not coincide with the freezing 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 temperature of freezing water is, as read from the gas scale. To determine this, we make use of the relation To CPo. Substituting in this the value of C as already found, we find that To 100P/ (P100-Po). Now the quantity (P100-Po)/Po is known as the "coefficient of expansion at constant volume" for the gas. (The name is somewhat absurd, it is true, be

volume of the gas in the bulb remains constant. It will be observed that there is here no assumption that the thermometric gas obeys the laws of Boyle and Charles (see THERMODYNAMICS); the relation which has just been assumed being the definition of the term "temperature," according to the constant-volume gas thermometer. If I be the temperature as thus defined, and P is the pressure prevailing within

cause there is no expansion at all, if there is no change of volume; and it would be more accurate to designate this fraction as the "coefficient of increase of pressure" at constant volume). It appears, therefore, that the temperature of melting ice, on the scale of the constant-volume gas thermometer, is numerically equal to 100 times the reciprocal of the coefficient of expansion of the gas at constant volume. Having found To, we have only to subtract it from every reading of the gas thermometer, in order to reduce that reading to its corresponding value as reckoned from the freezing point of water. If we call the values of T-To, as computed for any given gas thermometer, the "reduced readings" of that thermometer, then we find that the reduced readings of the nitrogen, hydrogen, air and carbon dioxide constantvolume thermometers are all nearly identical, and that they are all closely comparable with the readings of the ordinary mercury-in-glass thermometer. If two constant-volume gas thermometers be filled with the same gas in different states of density, then the reduced readings of the two are very nearly equal, but yet not necessarily identical.

The coefficients of expansion at constant volume of certain of the more important thermometric gases are given in Table 1, as deduced from a careful analysis of the data given by Chappuis, Regnault and numerous other experimenters of high standing. The "initial pressure signifies the pressure on the gas in the thermometric bulb, when the bulb is surrounded by ice and water; this pressure being given as the most convenient way of fixing the density for which the coefficients were determined. Two coefficients are given for air at each initial pressure, because it appears to be 1.- COEFFICIENTS OF EXPANSION AT CONSTANT VOLUME.

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impossible to decide, from the observations thus far made, which one of these values is most likely to be correct, the available measures falling into two general groups, one of which favors one of the foregoing values, while the second favors the other one. In Table 1 the values of To are also given, for convenience of reference.

The International Committee of Weights and Measures, in consideration of the differences that exist even between the reduced readings of constant-volume gas thermometers, adopted the following standard scale for the measurement of temperature, calling it their "normal thermometric scale." The scale adopted is the Centigrade scale of the constant-volume hydrogen thermometer, in which the hydrogen has a density such that its

pressure, at the freezing point of water, is equal to that due to a column of ice-cold mercury, one metre (1,000 mm.) high. The temperatures are understood to be "reduced," as described above, so that the thermometer reads 0° at the freezing point and 100° at the boiling point. The ideal scale would of course be the absolute thermodynamic scale (see THERMODYNAMICS); but the corrections that are required in order to reduce gas thermometer readings to this scale are still too uncertain to be definitely adopted in precise thermometry.

2. COMPARATIVE READINGS OF CONSTANTVOLUME GAS THERMOMETERS AND THE MERCURY-VERRE DUR SCALE ("REDUCED TEMPERATURES).

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In Table 2 comparative readings are given, of the mercury-in-glass ("verre dur"; see THERMOMETER) scale, and the scales of the constant-volume hydrogen, nitrogen and carbon dioxide thermometers, in which the "initial pressures are 1,000 millimetres of mercury. significance of the table will be made plain by the following example: If all of these thermometers were exposed to a temperature at which the "reduced" reading of the hydrogen instrument was 30° C., then the nitrogen thermometer would read 30.011°, the carbon dioxide thermometer would read 30.054° and mercuryin-glass thermometer would read 30.102°. The readings given in the second column were obtained from experiments made upon the nitrogen thermometer; but Chappuis states that the reduced readings of the air thermometer and of the nitrogen thermometer are practically indistinguishable; and hence this column will serve for each of them.

In the constant-pressure gas thermometer, temperature is defined as proportional to the volume of a fixed mass of gas which is allowed to expand in such a manner that its pressure remains constant. Regnault experimented with thermometers of this class, and considered them to be distinctly inferior in accuracy to those in which the volume is constant, and which we have already described. This judgment pronounced by Regnault has met with the approval of nearly every subsequent authority upon experimental physics, and hence the constantpressure gas thermometer has not been at all extensively used in practical work. Professor H. L. Callendar, in fact, is almost the only prominent advocate of the constant-pressure instrument at the present time. He claims that the constant-pressure gas thermometer is capable of yielding results even superior to those of the constant-volume thermometer; and

he has devised a very ingenious form of the constant-pressure instrument, which certainly appears to overcome most of the objections that have been urged against it in the past. (Consult his paper entitled 'On a Practical Thermometric Standard,' in the Philosophical Magazine, for 1899, Vol. 48, page 519. Consult also, Proceedings of the Royal Society,' Vol. 50, 1892, page 247, and Preston, Theory of Heat'). To facilitate computations connected with the constant-pressure gas thermometer, we present, in Table 3, the coefficients of expansion of the principal thermometric gases at the constant pressure of 1,000 millimeters of mercury and also at 760 millimeters. These are obtained by a careful comparison of the best determinations that have yet been made.

3.- COEFFICIENTS OF EXPANSION AT CONSTANT PRESSURE.

OF GASES

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The coefficient of expansion of carbon dioxid at a constant pressure of 760 millimeters of mercury must be considered as still somewhat uncertain, though the value given in the table appears to be the best now attainable. The "natural zero" of the constant-pressure thermometer lies in about the same general region as the natural zero of the constant-volume instrument. The temperature of melting ice, as referred to the "natural zero" of the scales of the several constant-pressure gas thermometers, is given in Table 3, in the columns headed "T.." No extensive and accurate comparisons have yet been made between the constant-pressure and constant-volume thermometers, either for the same gas or for different ones.

In the platinum-resistance thermometer, temperature is defined as proportional to the electrical resistance of a coil of pure, annealed platinum wire. The "thermometer" itself consists of a coil of the wire, wound upon a sheet or strip of mica, and placed in one of the arms of a Wheatstone's bridge, so that its resistance may be accurately determined. It is usual to denote a temperature as defined by the platinum-resistance thermometer by the symbol "pt" ("platinum temperature"). We have, therefore, pt CR, where R is the observed resistance of the coil at the temperature denoted by pt and Cis a constant whose value is to be determined. If R. and pt. and R100 and pt100 are the respective resistances and platinum-resistance temperatures at the freezing and boiling points of water, then we have, precisely as in the case of the constant-volume gas thermometer, pt= 100 R/(R100-R), as the platinum-resistance temperature, as reckoned from the "natural zero" of the platinum-resistance thermometer. The "reduced platinum temperature," obtained by subtracting pto from the temperature pt as

VOL. 26-35

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A being a constant whose value is to be determined experimentally. Callendar and Griffiths, for the purpose of determining A, recommend that the resistance of the platinum coil of the thermometer be observed at the temperature of boiling sulphur; the "reduced temperature" of this boiling point being, according to their experiments with the constant-pressure air thermometer, 444.53° C. (Eumorfopoulos states that the boiling point of sulphur on this scale is between 443.58° and 443.62° C. See 'Proceedings of the Royal Society, 1908 A, 81, p. 339. Compare, also, Callendar and Moss, in the same publication, 1909 A, 83, p. 106). The platinumresistance thermometer gives great promise of being a highly valuable instrument in the future. Indeed, it is so already; but it does not yet appear to be capable of determining the absolute values of temperatures closer than to 0.01° C. It may be used as a differential thermometer, however, so as to give results of a far higher order of accuracy. For this purpose two similar coils or strips of platinum are used, these being placed in two of the arms of a Wheatstone's bridge, so that the smallest departure from equality in their resistances can be observed. (See RESISTANCE, ELECTRICAL). Langley's bolometer is an instrument of this sort. It is used to explore the solar spectrum, and consists of two strips of platinum foil, which are placed across the spectrum to be examined, with their edges toward the source of the light. The two strips are placed in the two arms of a sensitive Wheatstone's bridge, and so long as both the strips are exposed to radiation of the same intensity, the balance of the bridge is preserved. When one of the strips coincides with a Fraunhofer line, however, while the other is still exposed to the full radiative power of the source of light, the balance is destroyed, and the existence of the line is thereby demonstrated, even though the line be in the infra-red, where it is not visible to the eye.

Thermo-electric couples have been used to a considerable extent for the measurement of temperature, and Regnault experimented with them somewhat, but showed that they are distinctly inferior in accuracy to the other known methods of determining temperature. At exceedingly low temperatures, however, they are often of great value. Wroblewski, for example, made use of thermo-couples quite extensively for temperature measurements in his researches on the critical points of the gases which are liquefiable only at extremely low temperatures. The platinum resistance thermometer is more generally favored, however, for this purpose; though it cannot be used for temperatures too close to the absolute zero on account of the anomalous and sudden changes of resistance that occur in that region. (See RESISTANCE, ELECTRICAL). At these extremely low tempera

tures the helium thermometer is still useful, however.

Consult Guillaume, Thermometrie de Précision, and Preston, 'Theory of Heat. See, also, the numerous scientific papers of Kamerlingh-Onnes relating to low-temperature research.

ALLAN D. RISTEEN, Director Technical Research, The Travelers Insurance Company, Hartford, Conn.

THERMOPHONE, a resistance thermometer (see THERMOMETRY), in which the galvanometer that is most commonly employed is replaced by a telephone. Two coils of platinum wire, which are exposed to the respective temperatures that are to be compared, are introduced into two of the arms of a Wheatstone's bridge whose remaining arms contain known resistances. The telephone is placed in the cross-arm of the bridge. An alternating or pulsating current of low frequency is used in making the observation, and when the bridge is in balance, this fact is indicated by the silence of the telephone. See Warren and Whipple, "The Thermophone,' in The Technology Quarterly, Vol. VIII, page 125.

THERMOPOLIS, Wyo., town and countyseat of Hot Springs County, on the Chicago, Burlington and Quincy Railroad, and on the west bank of the Bighorn River. It is noted for the large hot springs which issue along the river bank at this place. These springs are considered curative for rheumatism and similar ailments. They are protected as a State reservation. Pop. (1920) 2,095.

hot

THERMOPYLE (Gk. Оεрμovλαι gates), in classical geography, a pass on the southeastern frontier of Æniania, Greece, leading from Thessaly into Locris, and on the route of the only good road from Thessaly to central Greece. It was situated between the range of Mount Œta and an inaccessible morass which bordered the Maliac Gulf; and in breadth it was a narrow tract of perhaps some 50 feet. Its name was derived from the presence of thermal springs. As the only means by which a hostile army_might penetrate from northern into southern Greece, it held a peculiar strategic value in Grecian history. It is celebrated as the scene of the defense by Leonidas (q.v.) and the 300 Spartans against the vast host of Xerxes (q.v.) in August 480 B.C. The account of this battle given by Herodotus has been generally followed. Xerxes, ridiculing the numbers of the Hellenic defenders (5,200, not counting the Locrians, whose numbers are not known), sent against them the Medes and Cissians with instructions to take them prisoners and bring them before him. When, after a day's fighting, these were unsuccessful, the picked 10,000, called the "Immortals," were sent forward; but, handicapped by the shortness of their spears, they were no match for the Hellenes, of whom few fell, while the Persian loss was on both days excessive. Xerxes was now in great perplexity, when Ephialtes, a Malian, came "to tell him of the pathway which led across the mountain to Thermopyla." This path ascended the gorge of the river Asopus, and the hill Anopæ; then passed over the crest of Eta and to the rear of Thermopylæ. The Persians arrived in the rear

of Thermopyla soon after mid-day of the third day. Tidings of their coming had already been brought to the Greeks by scouts and Persian deserters. Most of the Greeks withdrew, but the Spartans and the Thespians (700) remained, and the Thebans (400) were compelled to stay. Of the Spartans and Thespians, all fell; and of the Thebans, few escaped. To the complaint that the Persian arrows darkened the sky the Spartan Dieneces is said to have answered, "Good; then we shall fight in the shade."

Through deposits from the Spercheius and other streams, great alterations have taken

place at Thermopylæ, so that it is not now a pass but a swampy plain. Consult Schliemann, Untersuchungen der Thermopylen' (1883) and various standard histories of Greece. See also GREECE, ANCIENT - History.

THERMOPYLE OF AMERICA, a title applied to Fort Alamo, Texas. See Alamo, THE.

THERMOSCOPE (Greek, "to show heat"), any instrument for indicating temperature. The term is commonly applied, however, to such instruments as indicate one temperature only, or a very limited number of temperatures; or to those which are used for indicating changes or difference of temperature, without giving the magnitude of these changes or differences. The forms that have been given to instruments of this kind are so manifold as to be almost past numeration. As a single illustration, the instrument may be cited, whose indications depend upon the melting points of alloys. An instrument or device of this sort contains buttons or wires of a number of alloys, whose several melting points are known; and in the observation of temperature by this method, the instrument is exposed to the temperature under examination, and a note is made of which of the alloys melt, and of which remain unmelted. If T1 is the melting point of the least fusible of the alloys that have melted, and T, is the melting point of the most fusible of the alloys that have not melted, we can then assert that the temperature under consideration is higher than T1, but lower than T2. For many purposes in the arts, it is quite sufficient to know, in this manner, that a temperature is between certain limits. A thermoscope which can only indicate certain limits between which a temperature lies is called a "discontinuous thermoscope." Continuous thermoscopes, which are capable of affording an actual measurement of any temperature within their range, are now commonly called "thermometers," whether they resemble the ordinary mercury-in-glass thermometer or not. A thermoscope in which temperature is inferred by noting the electrical resistance of a coil of platinum wire, for example, is called a "platinum resistance thermometer." See PYROMETER; THERMOMETER; and THERMOMETRY.

THERMOSTAT, a device in which the variation of heat is utilized to expand and contract a long strip of metal, so that its motion can be utilized to regulate a damper or to maintain approximately uniform steam pressure.

THERMOTAXIS, the regulation of the temperature of the body. The principal sources of animal heat are muscular exercise and the combustion of food, involving absorption of

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