QUANTITATIVE ESTIMATES OF SENSORY EVENTS 303 



special importance to anybody else. We must not make the mistake of 

 assuming that the simplicity of thermodynamic fornnulae on this scale of 

 temperature indicates that we have hit upon a ' true ' measure of tempera- 

 ture. The thermodynamic relations v/ill obviously be simple since nothing 

 but dynamical quantities are taken into account in establishing our scale of 

 temperature, which is purely conventional and made to give the simplest 

 possible relation between temperature and energy. Unfortunately this 

 scale is of little use to the practical physicist as there is no practicable method 

 of measuring molecular energies, which have to be deduced from measure- 

 ments of still other things, such, for example, as the properties which would 

 be exhibited by a so-called perfect gas or an ideally perfect heat engine. 

 But as there is no perfect gas and no ideally perfect heat engine practical 

 measurements can only be made with imperfect gases or imperfect heat 

 engines, and corrections which are difficult to determine and in some cases 

 involve assumptions of doubtful validity have to be made. The thermo- 

 dynamic basis does not, therefore, afford a practical means of measuring 

 temperature. It cannot be over-emphasised that measurement is a practical 

 process for obtaining experimental information, and it is not sufficient to 

 be able to formulate the necessary kind of association between a series of 

 magnitudes and numbers ; it must also be possible to carry out all the 

 operations involved in defining the basis of the association. Otherwise we 

 have a theoretical scale of measurement with which we cannot measure 

 anything. The thermodynamic scale of temperature is in this category. 

 For the practical measurement of temperature we must seek some other 

 basis. We seek it in some measurable physical property of substances or 

 bodies which varies continuously with temperature. We have an em- 

 barrassing choice of such properties : the length of a rod, the volume of a 

 given mass of a gas or liquid, the electrical resistance of a wire, the e.m.f. 

 of a 'thermocouple' of two wires of dissimilar metals, the intensity of 

 radiation from a ' black body,' etc., etc. All these are measurable by 

 practical processes and all vary with temperature. We may choose any one 

 of them to provide a scale of temperature by deeming to be equal those steps 

 in temperature which accompany equal increments in the measurable pro- 

 perty, or by postulating any other convenient law relating the property with 

 temperature. The mercury thermometer scale is based on this principle, 

 the practically measurable property utilised being the apparent volume of 

 mercury in a glass container. It is as ' true ' a scale of temperature as any 

 other, that is to say, there is nothing either true or false about it. Physicists, 

 however, soon wanted to pursue their investigations of thermal phenomena 

 to temperatures both higher and lower than those for which mercury 

 thermometers can be used, and various forms of gas thermometer were 

 evolved. Each of these involves a new definition of a temperature scale 

 based on deeming to be equal the increments of temperature associated with 

 equal increments in the pressure, at constant volume, or the volume at 

 constant pressure, of a constant mass of whichever gas is used, usually 

 hydrogen or nitrogen. When the pressure is low, and the temperature 

 high, the properties of hydrogen approximate very closely to those of the 

 mathematician's idea of a perfect gas. The scale of the hydrogen thermo- 

 meter, except at low temperatures, therefore agrees closely with the thermo- 

 dynamic scale. 



But there are disadvantages in using a gas thermometer for everyday 

 thermometry, and in practice other types of thermometer are used. Con- 

 spicuous among these are the platinum resistance thermometer and various 

 types of thermocouple. All of these provide scales of temperature which 

 are essentially independent of each other, though they may, of course, be 



