304 REPORTS ON THE STATE OF SCIENCE, ETC. 



empirically related by intercomparison of thermometers of the various types. 

 There is not, however, any a priori formal relation between the scales, and 

 it is necessary to make an arbitrary choice of some one of them as a standard 

 scale for defining the magnitude temperature. Unfortunately, no single 

 type of thermometer can be used over the whole range of temperature in 

 which physicists are interested, and the international temperature scale, 

 adopted in 1927, is a patchwork arrangement involving three essentially 

 different scales. From — 190° c. to 660° c. the standard scale is defined by 

 the variation of resistance of pure platinum wire ; from 660° c. to 1063° c. 

 by the variation of the e.m.f. of a thermocouple of platinum and a specified 

 alloy of platinum and rhodium ; and above 1063° c. by the variation in 

 intensity of monochromatic radiation emitted by a ' black body ' radiator. 



In each of these ranges the temperature scale is defined by postulating a 

 formal law relating the measurable variable (resistance of platinum thermo- 

 meter ; e.m.f. of platinum, platinum-rhodium thermocouple, or intensity 

 of monochromatic radiation) with temperature. The constants in these 

 laws are determined by means of appropriate ' fixed points,' e.g. the 

 temperatures of melting ice, boiling water, boiling sulphur, melting gold, 

 etc. In order to preserve the simplicity of thermodjTiamic equations and 

 the gas laws, the various scales are brought as closely into accordance with 

 the thermodynamic scale as possible by suitable choice of the values to be 

 assigned to the ' fixed point ' temperatures and by suitable choice of the law 

 of variation postulated for the standard type of thermometer applicable to 

 each range. This does not mean that we succeed in setting up a thermo- 

 dynamic scale. The scale is still in fact made up of several independent 

 parts, each of which is completely defined by the law of variation postulated 

 for the prescribed type of thermometer together with the values assigned to 

 those of the fixed points utilised in determining the constants of the law. 

 All we can succeed in doing by suitable choice of laws and constants is to 

 get a scale which is sufficiently close to the theoretical thermodynamic 

 scale that the laws of thermodynamics based on the theoretical scale are 

 approximately true for measurements made on the real scale. 



It is of great convenience to do this ; but it is not an essential require- 

 ment of measurement that it should be done, and the scale arrived at in this 

 way is not in any fundamental respect a ' truer ' scale of temperature than 

 one based on the postulation of simple proportionality of, say, the resistance 

 of a platinum thermometer and temperature. 



The fact that there is no operation of addition applicable to temperature 

 qua temperature, prevents it from being measurable in the true sense of 

 the term. All we are able to do, however we may disguise it by theoretical 

 considerations, is to assign numerals to temperatures in accordance with 

 an arbitrary postulated relation to some measurable property of some 

 specified substance or piece of apparatus. When once we have defined 

 some such scale of temperature, temperature becomes ' measurable ' in the 

 broad sense in which this word is generally used ; and the laws relating 

 other physical variables with temperature as so defined become open to 

 empirical investigation. 



It will be clear that the measurement of temperature is only possible 

 because the relations between temperature and those properties of sub- 

 stances or bodies which we utilise in defining the scale are constant. 



But how do we know they are constant ? It may be thought that con- 

 firmation of the constancy of the relations defining our scale is to be sought 

 in the constancy of the various other relations between phenomena and 

 temperature which we determine by means of our scale once we have 

 established it. This is not so, for such a principle is based on an a priori 



