Theory of Heat (Maxwell, 4th edition)/Chapter 2

by James Clerk Maxwell

CHAPTER II.

ON THERMOMETRY, OR THE THEORY OF TEMPERATURE.

Definition of Temperature.—The temperature of a body is its thermal state considered with reference to its power of communicating heat to other bodies.

Definition of Higher and Lower Temperature.—If when two bodies are placed in thermal communication, one of the bodies loses heat, and the other gains heat, that body which gives out heat is said to have a higher temperature than that which receives heat from it.

Cor. If when two bodies are placed in thermal communication neither of them loses or gains heat, the two bodies are said to have equal temperatures or the same temperature. The. two bodies are then said to be in thermal equilibrium. We have here a means of comparing the temperature of any two bodies, so as to determine which has the higher temperature, and a test of the equality of temperature which is independent of the nature of the bodies tested. But we have no means of estimating numerically the difference between two temperatures, so as to be able to assert that a certain temperature is exactly halfway between two other temperatures.

Law of Equal Temperatures.—Bodies whose temperatures are equal to that of the same body have themselves equal temperatures. This law is not a truism, but expresses the fact that if a piece of iron when plunged into a vessel of water is in thermal equilibrium with the water, and if the same piece of iron, without altering its temperature, is transferred to a vessel of oil, and is found to be also in thermal equilibrium with the oil, then if the oil and water were put into the same vessel they would themselves be in thermal equilibrium, and the same would be true of any other three substances.

This law, therefore, expresses much more than Euclid's axiom that 'Things which are equal to the same thing are equal to one another,' and is the foundation of the whole science of thermometry. For if we take a thermometer, such as we have already described, and bring it into intimate contact with different bodies, by plunging it into liquids, or inserting it into holes made in solid bodies, we find that the mercury in the tube rises or falls till it has reached a certain point at which it remains stationary. We then know that the thermometer is neither becoming hotter nor colder, but is in thermal equilibrium with the surrounding body. It follows from this, by the law of equal temperatures, that the temperature of the body is the same as that of the thermometer, and the temperature of the thermometer itself is known from the height at which the mercury stands in the tube.

Hence the reading, as it is called, of the thermometer—that is, the number of degrees indicated on the scale by the top of the mercury in the tube—informs us of the temperature of the surrounding substance, as well as of that of the mercury in the thermometer. In this way the thermometer may be used to compare the temperature of any two bodies at the same time or at different times, so as to ascertain whether the temperature of one of them is higher or lower than that of the other. We may compare in this way the temperatures of the air on different days; we may ascertain that water boils at a lower temperature at the top of a mountain than it does at the sea-shore, and that ice melts at the same temperature in all parts of the world.

For this purpose it would be necessary to carry the same thermometer to different places, and to preserve it with great care, for if it were destroyed and a new one made, we should have no certainty that the same temperature is indicated by the same reading in the two thermometers.

Thus the observations of temperature recorded during sixteen years by Rinieri^[1] at Florence lost their scientific value after the suppression of the Accademia del Cimento, and the supposed destruction of the thermometers with which the observations were made. But when Antinori in 1829 discovered a number of the very thermometers used in the ancient observations, Libri^[2] was able to compare them with Réaumur's scale, and thus to show that the climate of Florence has not been rendered sensibly colder in winter by the clearing of the woods of the Apennines.

In the construction of artificial standards for the measurement of quantities of any kind it is desirable to have the means of comparing the standards together, either directly, or by means of some natural object or phenomenon which is easily accessible and not liable to change. Both methods. are used in the preparation of thermometers.

We have already noticed two natural phenomena which take place at definite temperatures—the melting of ice and the boiling of water. The advantage of employing these temperatures to determine two points on the scale of the thermometer was pointed out by Sir Isaac Newton ('Scala Graduum Caloris,' Phil. Trans. 1701).

The first of these points of reference is commonly called the Freezing Point. To determine it, the thermometer is placed in a vessel filled with pounded ice or snow thoroughly moistened with water. If the atmospheric temperature be above the freezing point, the melting of the ice will ensure the presence of water in the vessel. As long as every part of the vessel contains a mixture of water and ice its temperature remains uniform, for if heat enters the vessel it can only melt some of the ice, and if heat escapes from the vessel some of the water will freeze, but the mixture can be made neither hotter nor colder till all the ice is melted or all the water frozen.

The thermometer is completely immersed in the mixture of ice and water for a sufficient time, so that the mercury has time to reach its stationary point.
Fig. 2.The position of the top of the mercury in the tube is then recorded by making a scratch on the glass tube.. We shall call this mark the Freezing Point. It may be determined in this way with extreme accuracy, for, as we shall see afterwards, the temperature of melting ice is very nearly the same under very different pressures.

The other point of reference is called the Boiling Point. The temperature at which water boils depends on the pressure of the atmosphere. The greater the pressure of the air on the surface of the water, the higher is the temperature to which the water must be raised before it begins to boil.

To determine the Boiling Point, the stem of the thermometer is passed through a hole in the lid of a tall vessel, in the lower part of which water is made to boil briskly, so that the whole of the upper part, where the thermometer is placed, is filled with steam. When the thermometer has acquired the temperature of the current of steam the stem is drawn up through the hole in the lid of the vessel till the top of the column of mercury becomes visible. A scratch is then made on the tube to indicate the boiling point.

In careful determinations of the boiling point no part of the thermometer is allowed to dip into the boiling water, because it has been found by Gay-Lussac that the temperature of the water is not always the same, but that it boils at different temperatures in different kinds of vessels. It has been shown, however, by Rudberg that the temperature of the steam which escapes from boiling water is the same in every kind of vessel, and depends only on the pressure at the surface of the water. Hence the thermometer is not dipped in the water, but suspended in the issuing steam. To ensure that the temperature of the steam shall be the same when it reaches the thermometer as when it issues from the boiling water, the sides of the vessel are sometimes protected by what is called a steam-jacket.
Fig. 3.A current of steam is made to play over the outside of the sides of the vessel. The vessel is thus raised to the same temperature as the steam itself, so that the steam cannot be. cooled during its passage from the boiling water to the thermometer.

For instance, if we take any tall narrow vessel, as a coffee-pot, and cover its mouth and part of its sides with a wider vessel turned upside down, taking care that there shall be plenty of room for the steam to escape, then if we boil a small quantity of water in the coffee-pot, a thermometer placed in the steam above will be raised to the exact temperature of the boiling point of water corresponding to the state of the barometer at the time.

To mark the level of the mercury on the tube of the thermometer without cooling it, we must draw it up through a cork or a plug of india-rubber in the steam-jacket through which the steam passes till we can just see the top of the column of mercury. A mark must then be scratched on the glass to register the boiling point. This experiment of exposing a thermometer to the steam of boiling water is an important one, for it not only supplies a means of graduating thermometers, and testing them when they have been graduated, but, since the temperature at which water boils depends on the pressure of the air, we may determine the pressure of the air by boiling water when we are not able to measure it by means of the appropriate instrument, the barometer.

We have now obtained two points of reference marked by scratches on the tube of the thermometer-the freezing point and the boiling point. We shall suppose for the present that when the boiling point was marked the barometer happened to indicate the standard pressure of 29.905 inches of mercury at 0° C. at the level of the sea in the latitude of London. In this case the boiling point is the standard boiling point. In any other case it must be corrected.

Our thermometer will now agree with any other properly constructed thermometer at these two temperatures.

In order to indicate other temperatures, we must construct a scale—that is, a series of marks—either on the tube itself or on a convenient part of the apparatus close to the tube and well fastened to it.

For this purpose, having settled what values we are to give to the freezing and the boiling points, we divide the space between those points into as many equal parts as there are degrees between them, and continue the series of equal divisions up and down the scale as far as the tube of the thermometer extends.

Three different ways of doing this are still in use, and, as we often find temperatures stated according to a different scale from that which we adopt ourselves, it is necessary to know the principles on which these scales are formed.

The Centigrade scale was introduced by Celsius.^[3] In it the freezing point is marked 0° and called zero, and the boiling point is marked 100°.

The obvious simplicity of this mode of dividing the space between the points of reference into 100 equal parts and calling each of these a degree, and reckoning all temperatures in degrees from the freezing point, caused it to be very generally adopted, along with the French decimal system of measurement, by scientific men, especially on the Continent of Europe. It is true that the advantage of the decimal system is not so great in the measurement of temperatures as in other cases, as it merely makes it easier to remember the freezing and boiling temperatures, but the graduation is not too fine for the roughest purposes, while for accurate measurements the degrees may be subdivided into tenths and hundredths.

The other two scales are called by the names of those who introduced them.

Fahrenheit, of Dantzig, about 1714, first constructed thermometers comparable with each other. In Fahrenheit's scale the freezing point is marked 32°, and the boiling point 212°, the space between being divided into 180 equal parts, and the graduation extended above and below the points of reference. A point 32 degrees below the freezing point is called zero, or 0°, and temperatures below this are indicated by the number of degrees below zero.

This scale is very generally used in English-speaking countries for purposes of ordinary life, and also for those of science, though the Centigrade scale is coming into use among those who wish their results to be readily followed by foreigners.

The only advantages which can be ascribed to Fahrenheit's scale, besides its early introduction, its general diffusion, and its actual employment by so many of our countrymen, are that mercury expands almost exactly one ten-thousandth of its volume at 142° F. for every degree of Fahrenheit's scale, and that the coldest temperature which we can get by mixing snow and salt is near the zero of Fahrenheit's scale.

To compare temperatures given in Fahrenheit's scale with temperatures given in the Centigrade scale we have only to remember that 0° Centigrade is 32° Fahrenheit, and that five degrees Centigrade are equal to nine of Fahrenheit.

The third thermometric scale is that of Réaumur. In this scale the freezing point is marked 0° and the boiling point 80°. I am not aware of any advantage of this scale. It is used to some extent on the Continent of Europe for medical and domestic purposes. Four degrees of Réaumur correspond to five Centigrade and to nine of Fahrenheit.

The existence of these three thermometric scales furnishes an example of the inconvenience of the want of uniformity in systems of measurement. The whole of what we have said about the comparison of the different scales might have been omitted if any one of these scales had been adopted by all who use thermometers. Instead of spending our time in describing the arbitrary proposals of different men, we should have gone on to investigate the laws of heat and the properties of bodies.

We shall afterwards have occasion to use a scale differing in its zero-point from any of those we have considered, but when we do so we shall bring forward reasons for its adoption depending on the nature of things and not on the predilections of men.

If two thermometers are constructed of the same kind of glass, with tubes of uniform bore, and are filled with the same liquid and then graduated in the same way, they may be considered for ordinary purposes as comparable instruments; so that though they may never have been actually compared together, yet in ascertaining the temperature of anything there will be very little difference whether we use the one thermometer or the other.

But if we desire great accuracy in the measurement of temperature, so that the observations made by different observers with different instruments may be strictly comparable, the only satisfactory method is by agreeing to choose one thermometer as a standard and comparing all the others with it.

All thermometers ought to be made with tubes of as uniform bore as can be found; but for a standard thermometer the bore should be calibrated—that is to say, its size should be measured at short intervals all along its length.

For this purpose, before the bulb is blown, a small quantity of mercury is introduced into the tube and moved along the tube by forcing air into the tube behind it. This is done by squeezing the air out of a small india-rubber ball which is fastened to the end of the tube.

If the length of the column of mercury remains exactly the same as it passes along the tube, the bore of the tube must be uniform; but even in the best tubes there is always some want of uniformity.

But if we introduce a short column of mercury into the tube, then mark both ends of the column, and move it on its own length, till one end comes exactly to the mark where the other end was originally, then mark the other end, and move it on again, we shall have a series of marks on the tube such that the capacity of the tube between any two consecutive marks will be the same, being equal to that of the column of mercury.

By this method, which was invented by Gay-Lussac, a number of divisions may be marked on the tube, each of which contains the same volume, and though they will probably not correspond to degrees when the tube is made up into a thermometer, it will be easy to convert the reading of this instrument into degrees by multiplying it by a proper factor, and in the use of a standard instrument this trouble is readily undertaken for the sake of accuracy.

The tube having been prepared in this way, one end is. heated till it is melted, and it is blown into a bulb by forcing air in at the other end of the tube. In order to avoid introducing moisture into the tube, this is done, not by the mouth, but by means of a hollow india-rubber ball, which is fastened to the end of the tube.

The tube of a thermometer is generally so narrow that mercury will not enter it, for a reason which we shall explain when we come to the properties of liquids. Hence the following method is adopted to fill the thermometer. By rolling paper round the open end of the tube, and making the tube thus formed project a little beyond the glass tube, a cavity is formed, into which a little mercury is poured. The mercury, however, will not run down the tube of the thermometer, partly because the bulb and tube are already full of air, and partly because the mercury requires a certain pressure from without to enter so narrow a tube. The bulb is therefore gently heated so as to cause the air to expand, and some of the air escapes through the mercury. When the bulb cools, the pressure of the air in the bulb becomes less than the pressure of the air outside, and the difference of these pressures is sufficient to make the mercury enter the tube, when it runs down and partially fills the bulb.

In order to get rid of the remainder of the air, and of any moisture in the thermometer, the bulb is gradually heated till the mercury boils. The air and steam escape along with the vapour of mercury, and as the boiling continues the last remains of air are expelled through the mercury at the top of the tube. When the boiling ceases, the mercury runs back into the tube, which is thus perfectly filled with mercury.

While the thermometer is still hotter than any temperature at which it will afterwards be used, and while the mercury or its vapour completely fills it, a blowpipe flame is made to play on the top of the tube, so as to melt it and close the end of the tube. The tube, thus closed with its own substance, is said to be 'hermetically sealed.'^[4]

There is now nothing in the tube but mercury, and when the mercury contracts so as to leave a space above it, this space is either empty of all gross matter, or contains only the vapour of mercury. If, in spite of all our precautions, there is still some air in the tube, this can easily be ascertained by inverting the thermometer and letting some of the mercury glide towards the end of the tube. If the instrument is perfect, it will reach the end of the tube and completely fill it. If there is air in the tube the air will form an elastic cushion, which will prevent the mercury from reaching the end of the tube, and will be seen in the form of a small bubble. We have next to determine the freezing and boiling points, as has been already described, but certain precautions have still to be observed. In the first place, glass is a substance in which internal changes go on for some time after it has been strongly heated, or exposed to intense forces. In fact, glass is in some degree a plastic body. It is found that after a thermometer has been filled and sealed the capacity of the bulb diminishes slightly, and that this change is comparatively rapid at first, and only gradually becomes insensible as the bulb approaches its ultimate condition. It causes the freezing point to rise in the tube to 0°.3 or 0°.5, and if, after the displacement of the zero, the mercury be again boiled, the zero returns to its old place and gradually rises again.

This change of the zero-point was discovered by M. Flaugergues.^[5] It may be considered complete in from four to six months.^[6] In order to avoid the error which it would introduce into the scale, the instrument should, if possible, have its zero determined some months after it has been filled, and since even the determination of the boiling point of water produces a slight depression of the freezing point (that is, an expansion of the bulb), the freezing point should not be determined after the boiling point, but rather before it.

When the boiling point is determined, the barometer is probably not at the standard height. The mark made on the thermometer must, in graduating it, be considered to represent, not the standard boiling point, but the boiling point corresponding to the observed height of the barometer, which may be found from the tables.

To construct a thermometer in this elaborate way is by no means an easy task, and even when two thermometers have been constructed with the utmost care, their readings at points distant from the freezing and boiling points may not agree, on account of differences in the law of expansion of the glass of the two thermometers. These differences, however, are small, for all thermometers are made of the same description of glass.

But since the main object of thermometry is that all thermometers shall be strictly comparable, and since thermometers are easily carried from one place to another, the best method of obtaining this object is by comparing all thermometers either directly or indirectly with a single standard thermometer. For this purpose, the thermometers, after being properly graduated, are all placed along with the standard thermometer in a vessel, the temperature of which can be maintained uniform for a considerable time. Each thermometer is then compared with the standard thermometer. A table of corrections is made for each thermometer by entering the reading of that thermometer, along with the correction which must be applied to that reading to reduce it to the reading of the standard thermometer. This is called the proper correction for that reading. If it is positive it must be added to the reading, and if negative it must be subtracted from it.

By bringing the vessel to various temperatures, the corrections at these temperatures for each thermometer are ascertained, and the series of corrections belonging to each thermometer is made out and preserved along with that thermometer.

Any thermometer may be sent to the Observatory at Kew, and will be returned with a list of corrections, by the application of which, observations made with that thermometer become strictly comparable with those made by the standard thermometer at Kew, or with any other thermometer similarly corrected. The charge for making the comparison is very small compared with the expense of making an original standard thermometer, and the scientific value of observations made with a thermometer thus compared is greater than that of observations made with the most elaborately prepared thermometer which has not been compared with some existing and known standard instrument.

I have described at considerable length the processes by which the thermometric scale is constructed, and those by which copies of it are multiplied, because the practical establishment of such a scale is an admirable instance of the method by which we must proceed in the scientific observation of a phenomenon such as temperature, which, for the present, we regard rather as a quality, capable of greater or less intensity, than as a quantity which may be added to or subtracted from other quantities of the same kind.

A temperature, so far as we have yet gone in the science of heat, is not considered as capable of being added to another temperature so as to form a temperature which is Digitized by Google the sum of its components. When we are able to attach a distinct meaning to such an operation, and determine its result, our conception of temperature will be raised to the rank of a quantity. For the present, however, we must be content to regard temperature as a quality of bodies, and be satisfied to know that the temperatures of all bodies can be referred to their proper places in the same scale.

For instance, we have a right to say that the temperatures of freezing and boiling differ by 180° Fahrenheit; but we have as yet no right to say that this difference is the same as that between the temperatures 300° and 480° on the same scale. Still less can we assert that a temperature of

244° F. = 32° + 212°

is equal to the sum of the temperatures of freezing and boiling. In the same way, if we had nothing by which to measure time except the succession of our own thoughts, we might be able to refer each event within our own experience to its proper chronological place in a series, but we should have no means of comparing the interval of time between one pair of events with that between another pair, unless it happened that one of these pairs was included within the other pair, in which case the interval between the first pair must be the smallest. It is only by observation of the uniform or periodic motions of bodies, and by ascertaining the conditions under which certain motions are always accomplished in the same time, that we have been enabled to measure time, first by days and years, as indicated by the heavenly motions, and then by hours, minutes, and seconds, as indicated by the pendulums of our clocks, till we are now able, not only to calculate the time of vibration of different kinds of light, but to compare the time of vibration of a molecule of hydrogen set in motion by an electric discharge through a glass tube, with the time of vibration of another molecule of hydrogen in the sun, forming part of some great eruption of rosy clouds, and with the time of vibration of another molecule in Sirius which has not transmitted its vibrations to our earth, but has simply prevented vibrations arising in the body of that star from reaching us.

In a subsequent chapter we shall consider the further progress of our knowledge of Temperature as a Quantity.

 

ON THE AIR THERMOMETER.

The original thermometer invented by Galileo was an air thermometer. It consisted of a glass bulb with a long neck. The air in the bulb was heated, and then the neck was plunged into a coloured liquid. As the air in the bulb cooled, the liquid rose in the neck, and the higher the liquid the lower the temperature of the air in the bulb. By putting the bulb into the mouth of a patient, and noting the point to which the liquid was driven down in the tube, a physician might estimate whether the ailment was of the nature of a fever or not. Such a thermometer has several obvious merits. It is easily constructed, and gives larger indications for the same change of temperature than a thermometer containing any liquid as the thermometric substance. Besides this, the air requires less heat to warm it than an equal bulk of any liquid, so that the air thermometer is very rapid in its indications. The great inconvenience of the instrument as a means of measuring temperature is, that the height of the liquid in the tube depends on the pressure of the atmosphere as well as on the temperature of the air in the bulb. The air thermometer cannot therefore of itself tell us anything about temperature. We must consult the barometer at the same time, in order to correct the reading of the air thermometer. Hence the air thermometer, to be of any scientific value, must be used along with the barometer, and its readings are of no use till after a process of calculation has been gone through. This puts it at a great disadvantage compared with the mercurial thermometer as a means of ascertaining temperatures. But if the researches on which we are engaged are of so important a nature that we are willing to undergo the labour of double observations and numerous calculations, then the advantages of the air thermometer may again preponderate.

We have seen that in fixing a scale of temperature after marking on our thermometer two temperatures of reference and filling up the interval with equal divisions, two thermometers containing different liquids will not in general agree except at the temperatures of reference.

If, on the other hand, we could secure a constant pressure in the air thermometer, then if we exchange the air for any other gas, all the readings will be exactly the same provided the reading at one of the temperatures of reference is the same. It appears, therefore, that the scale of temperatures as indicated by an air thermometer has this advantage over the scale indicated by mercury or any other liquid or solid, that whereas no two liquid or solid substances can be made to agree in their expansion throughout the scale, all the gases agree with one another. In the absence of any better reasons for choosing a scale, the agreement of so many substances is a reason why the scale of temperatures furnished by the expansion of gases should be considered as of great scientific value. In the course of our study we shall find that there are scientific reasons of a much higher order which enable us to fix on a scale of temperature, based not on a probability of this kind, but on a more intimate knowledge of the properties of heat. This scale, so far as it has been investigated, is found to agree very closely with that of the air thermometer.

There is another reason, of a practical kind, in favour of the use of air as a thermometric substance, namely, that air remains in the gaseous state at the lowest as well as the highest temperatures which we can produce, and there are no indications in either case of its approaching to a change of state. Hence air, or one of the permanent gases, is of the greatest use in estimating temperatures lying far outside of the temperatures of reference, such, for instance, as the freezing point of mercury or the melting point of silver.

We shall consider the practical method of using air as a thermometric substance when we come to Gasometry. In the meantime let us consider the air thermometer in its simplest form, that of a long tube of uniform bore closed at one end, and containing air or some other gas which is separated from the outer air by a short column of mercury,

Fig. 5 Air Thermometer.

oil, or some other liquid which is capable of moving freely along the tube, while at the same time it prevents all communication between the confined air and the atmosphere. We shall also suppose that the pressure acting on the confined air is in some way maintained constant during the course of the experiments we are going to describe.

The air thermometer is first surrounded with ice and ice-cold water. Let us suppose that the upper surface of the air now stands at the point marked 'Freezing.' The thermometer is then surrounded with the steam rising from water boiling under an atmospheric pressure of 29.905 inches of mercury. Let the surface of the enclosed air now stand at the point marked 'Boiling.' In this way, the two temperatures of reference are to be marked on the tube.

To complete the scale of the thermometer we must divide the distance between boiling and freezing into a selected number of equal parts, and carry this graduation up and down the tube beyond the freezing and boiling points with degrees of the same length.

Of course, if we carry the graduation far enough down the tube, we shall at last come to the bottom of the tube. What will be the reading at that point? and what is meant by it?

To determine the reading at the bottom of the tube is a very simple matter. We know that the distance of the freezing point from the bottom of the tube is to the distance of the boiling point from the bottom in the proportion of 1 to 1.3665, since this is the dilatation of air between the freezing and the boiling temperatures. Hence it follows, by an easy arithmetical calculation, that if, as in Fahrenheit's scale, the freezing point is marked 32°, and the boiling point 212°, the bottom of the tube must be marked –459°.13. If, as in the Centigrade scale, the freezing point is marked 0°, and the boiling point 100°, the bottom of the tube will be marked –272°.85. This, then, is the reading at the bottom of the scale.

The other question, What is meant by this reading? requires a more careful consideration. We have begun by defining the measure of the temperature as the reading of the scale of our thermometer when it is exposed to that temperature. Now if the reading could be observed at the bottom of the tube, it would imply that the volume of the air had been reduced to nothing. It is hardly necessary to say that we have no expectation of ever observing such a reading. If it were possible to abstract from a substance all the heat it contains, it would probably still remain an extended substance, and would occupy a certain volume. Such an abstraction of all its heat from a body has never been effected, so that we know nothing about the temperature which would be indicated by an air thermometer placed in contact with a body absolutely devoid of heat. This much we are sure of, however, that the reading would be above –459°.13 F.

It is exceedingly convenient, especially in dealing with questions relating to gases, to reckon temperatures, not from the freezing point, or from Fahrenheit's zero, but from the bottom of the tube of the air thermometer.

This point is then called the absolute zero of the air thermometer, and temperatures reckoned from it are called absolute temperatures. It is probable that the dilatation of a perfect gas is a little less than 1.3665. If we suppose it 1.366, then absolute zero will be –460° on Fahrenheit's scale, or –273°⁠1/3⁠ Centigrade.

If we add 460° to the ordinary reading on Fahrenheit's scale, we shall obtain the absolute temperature in Fahrenheit's degrees.

If we add 273°⁠1/3⁠ to the Centigrade reading, we shall obtain the absolute temperature in Centigrade degrees.

We shall often have occasion to speak of absolute temperature by the air thermometer. When we do so we mean nothing more than what we have just said—namely, temperature reckoned from the bottom of the tube of the air thermometer. We assert nothing as to the state of a body deprived of all its heat, about which we have no experimental knowledge.

One of the most important applications of the conception of absolute temperature is to simplify the expression of the two laws discovered respectively by Boyle and by Charles. The laws may be combined into the statement that the product of the volume and pressure of any gas is proportional to the absolute temperature.

For instance, if we have to measure quantities of a gas by their volumes under various conditions as to temperature and pressure, we can reduce these volumes to what they would be at some standard temperature and pressure.

Thus if V, P, T be the actual volume, pressure, and absolute temperature, and V₀ the volume at the standard pressure P₀, and the standard temperature T₀, then $vpt=vpt$ or $v=vptpt$

If we have only to compare the relative quantities of the gas in different measurements in the same series of experiments, we may suppose P₀ and T₀ both unity, and use the

quantity VP/T without always multiplying it by To, which is a constant quantity.1

The great scientific importance of the scale of temperature as determined by means of the air or gas thermometer arises from the fact, established by the experiments of Joule and Thomson, that the scale of temperature derived from the expansion of the more permanent gases is almost exactly the same as that founded upon purely thermodynamic considerations, which are independent of the peculiar properties of the thermometric body. This agreement has been experimentally verified only within a range of temperature between 0° C. and 100° C. If, however, we accept the molecular theory of gases, the volume of a perfect gas ought to be exactly proportional to the absolute temperature on the thermodynamic scale, and it is probable that as the temperature rises the properties of real gases approximate to those of the theoretically perfect gas.

All the thermometers which we have considered have been constructed on the principle of measuring the expansion of a substance as the temperature rises. In certain cases it is convenient to estimate the temperature of a substance by the heat which it gives out as it cools to a standard temperature. Thus if a piece of platinum heated in a furnace is dropped into water, we may form an estimate of the temperature of the furnace by the amount of heat communicated to the water. Some have supposed that this method of estimating temperatures is more scientific than that founded on expansion. It would be so if the same quantity of heat always caused the same rise of temperature, whatever the original

^[7] temperature of the body. But the specific heat of most substances increases as the temperature rises, and it increases in different degrees for different substances, so that this method cannot furnish an absolute scale of temperature. It is only in the case of gases that the specific heat of a given mass of the substance remains the same at all temperatures.

There are two methods of estimating temperature which are founded on the electrical properties of bodies. We cannot, within the limits of this treatise, enter into the theory of these methods, but must refer the student to works on electricity. One of these methods depends on the fact that in a conducting circuit formed of two different metals, if one of the junctions be warmer than the other, there will be an electromotive force which will produce a current of electricity in the circuit, and this may be measured by means of a galvanometer. In this way very minute differences of temperature between the ends of a piece of metal may be detected. Thus if a piece of iron wire is soldered at both ends to a copper wire, and if one of the junctions is at a place where we cannot introduce an ordinary thermometer, we may ascertain its temperature by placing the other junction in a vessel of water and adjusting the temperature of the water till no current passes. The temperature of the water will then be equal to that of the inaccessible junction.

Electric currents excited by differences of temperature in different parts of a metallic circuit are called thermo-electric currents. An arrangement by which the electromotive forces arising from a number of junctions may be added together is called a thermopile, and is used in experiments on the heating effect of radiation, because it is more sensitive to changes of temperature caused by small quantities of heat than any other instrument.

Professor Tait^[8] has found that if $t_{1}$ and $t_{2}$ to denote the temperatures of the hot and cold junction of two metals, the electromotive force of the circuit formed by these two metals is

${\mbox{A}}\left(t_{1}-t\right)\lbrack {\mbox{T}}-{\frac {1}{2}}\left(t_{1}+t_{2}\right)\rbrack$,

where A is a constant depending on the nature of the metals, and T is a temperature also depending on the metals, such that when one junction is as much hotter than T as the other is colder, no current is produced. T may be called the neutral temperature for the two metals. For copper and iron it is about 284° C.

The other method of estimating the temperature of a place at which we cannot set a thermometer is founded on the increase of the electric resistance of metals as the temperature rises. This method has been successfully employed by Mr. Siemens.^[9] Two coils of the same kind of fine platinum wire are prepared so as to have equal resistance. Their ends are connected with long thick copper wires, so that the coils may be placed if necessary a long way from the galvanometer. These copper terminals are also adjusted so as to be of the same resistance for both coils. The resistance of the terminals should be small as compared with that of the coils. One of the coils is then sunk, say to the bottom of the sea, and the other is placed in a vessel of water, the temperature of which is adjusted till the resistance of both coils is the same. By ascertaining with a thermometer the temperature of the vessel of water, that of the bottom of the sea may be deduced.

Mr. Siemens has found that the resistance of the metals may be expressed by a formula of the form

${\mbox{R}}=\alpha {\sqrt {\mbox{T}}}+\beta {\mbox{T}}+\gamma ,$

where R is the resistance, T the absolute temperature, and $\alpha \,\beta \,\gamma ,$ coefficients. Of these α is the largest, and the resistance depending on it increases as the square root of the absolute temperature, so that the resistance increases more slowly as the temperature rises. The second term, β T, is proportional to the temperature and may be attributed to the expansion of the substance. The third term is constant.

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1. Pupil of Galileo; died 1647.
2. Annales de Chimie et de Physique, xlv. (1830).
3. Professor of Astronomy in the University of Upsala.
4. 'From Hermes or Mercury, the imagined inventor of chemistry.'—Johnson's Dict.
5. Ann. de Chimie et de Physique, xxi. p. 333 (1822).
6. Dr. Joule, however, finds that the rise of the freezing point of a delicate thermometer has been going on for twenty-six years, though the changes are now exceedingly minute.—Phil. Soc. Manchester, Feb. 22, 1870.
7. For a full account of the methods of measuring gases the student is referred to Bunsen's Gasometry, translated by Roscoe.
8. Proceedings of the Royal Society of Edinburgh, 1870-71.
9. Proceedings of the Royal Society, April 27, 1871.