Page:Encyclopædia Britannica, Ninth Edition, v. 11.djvu/600

566 HEAT metric assvmi} tions. mometry by mixtures. Liquid mercury might be used with the advantage of being available for both higher and lower temperatures than water, through a much wider whole range indeed than either water or oil. For use as thermometric substance for the method of mixtures both water and mercury, in the conditions of approximate purity in which they are easily obtained in abundance, have a paramount advantage over all other liquids, in near enough approxima tion to perfect definiteness and constancy of constitution to give practically perfect thermometric results. Different 33. In 12, 24, 25, 30, 31, 32, several distinct equally definitions of numerical reckoning of temperature have sible U ~ keen gi veu - I n eacu f these the differences of tempera- thermo- ture which are to be called equal are defined specially, and this is the essence of the thermometric scale in each case (the marking of and 100 for the "freezing" and "boiling" points being common to all as a matter of practical usage and not an essential of the thermometric principle in any case). Thus in 12, 31, and 32 differences of tempera ture are called equal which are produced by the com munication of equal quantities of heat to a given quantity of the particular thermometric substance chosen water, for example, or mercury; in other words ( 68 below), this thermometric system is chosen so as to make the specific heat of a particular thermometric substance the same for all temperatures. Again in 24 differences of temperature are called equal for which the differences of pressure are equal in air of the particular density which air has if its pressure is one atmo when its tempera ture is " freezing." This is Regnault s " normal thermo metry." lu 25 (1), (2), (3), (4), other reckonings of Each temperature differing essentially from this, though, as founded Regnault s experiments proved, by but very small differ ences, are given simply by the substitution of air of on a par ticular property ther than Regnault s normal density, and of other gases of a par- than air, for the air of Regnault s normal thermometer. In ticular 25 (5) a thermometry founded on a complex coefficiency of change of pressure and volume of a gas and change of volume of some one particular glass vessel is defined and compared with Regnault s normal thermometry; and in 25 (6) and (7) the same is done for the ordinary mercury- in-glass thermometer, which depends on a coefficiency of glass and mercury leading to the reckoning of temperature defined in 30. Again in 26 and 24 (I.) is indi cated a system of thermometry founded on the absolute dilatation of some fluid, such as mercury or alcohol or buty- rate of oxide of methyl or other permanent liquid or air, at some constant .pressure, such as one atmo, with equal differences of temperature defined as those which give equal dilatations of the particular substance chosen as the thermo metric fluid. 34. Each of all these different definitions of tempera ture is founded on some particular property of a particular substance. A thermometer graduated to fulfil one of the definitions for one particular substance would not agree with another thermometer graduated according to the same definition for another substance, or according to some of Prelim- the other definitions. A much more satisfactory foundation inary for f or thermometry is afforded by thermodynamic science, draaniic w ^ cn ( see THERMODYNAMICS) gives us a definition of defini- temperature depending on certain thermodynamic pro- tion of perties of matter in such a manner that if a thermometer is graduated according to it from observation of one class of thermal effects in one particular substance, it will agree with a thermometer graduated according to the same thermodynamic law from the same class of effects in any other substance, or from the same or from some other class of effects in another substance. Thus we have what is called the absolute thermodynamic scale. This scale is now in modern thermal science the ultimate tempera ture. scale of reference for all thermometers of whatever kind ( 67). It is defined in 35 and 37 after the following preliminary. A piece of matter which we shall call the "thermometric body" or "thermometric substance" must be given, and at each instant it must be throughout at one temperature, whatever operations we perform upon it. For simplicity we shall suppose it to be of one substance throughout. It may be all solid, or it may be partly solid and the- remainder gaseous (as the contents of a wholly frozen cryophorus l or any other form of closed vessel full of ice and vapour of water, but with no air) ; or it may at one particular temperature in the course of its use be partly solid and partly liquid and partly gaseous (as the contents of a partially frozen cryophorus) ; or it may be partially liquid and partially gaseous (as the contents of an unfrozen cryophorus or of a "philosopher s hammer") ;- or it may be all liquid ; or it may be all gas ; or it may be all fluid at a temperature above the Andrews " critical temperature." 3 If it be all solid it may be under any homogeneous stress (ELASTICITY, Mathematical Theory, part i., chap, i.) ; but in any case we suppose for simplicity the stress to be homogeneous throughout, and therefore if the thermometric body be partly solid and partly fluid, the stress in the solid as well as in the fluid must be uniform pressure in all directions. To avoid excluding the case of all solid from our statements, we shall use generally the word stress, which will mean normal pressure reckoned in number of units of force per unit of area in every case in which the whole or any part of the thermometric body is fluid, and will denote this or any other possible stress when the thermometric body is all solid. 35. (1) Alter the bulk or shape of the thermometric substance till it becomes warmer to any desired degree. (2) Keeping it now at this higher temperature, alter bulk or shape farther, and generate the heat which the substance takes to keep its temperature constant, by stirring water, or a portion of the substance itself, if it is partly fluid, and measure the quantity of work spent in this stirring. (3) Bring it back towards its original bulk and shape till it becomes cooled to its original temperature. (4) Keeping it at this temperature, reduce it to its original bulk and shape, carrying off, by a large quantity of water, the heat which it must part with to prevent it from becoming warmed. Find by a special experiment how much work must be done to give an equal amount of heat to an equal amount of water by stirring. Then the ratio of the first measured quantity of work to the second is the ratio of the higher temperature to the lower on the absolute ther modynamic scale. 36. The following is equivalent to 35, and is more convenient for analytical use, It is derived from 35 by supposing the first and third operations to be so small that the ratio defined as the ratio of the two temperatures is infinitely nearly unity, and conversely 35 our first form of definition of absolute temperature may be derived from the second, which is to be now given, by passing through a finite range of temperature by successive infini tesimal steps, and applying the second definition to each step. 37. Let the thermometric body be infinitesimally warmed by stirring a portion or the whole of itself if it be partially or wholly fluid, or by stirring a quantity of fluid in space around it if it be all solid ; and during the process let the stress upon the body be kept unchanged. The body expanding or contracting or changing its shape with the heat, as the case may be, does work upon the surrounding material by which its stress is maintained. 1 See articles LIQUID, MATTER (PROPERTIES OF), and STEAM.

2 Ibid. 3 Ibice.