302 REPORTS ON THE STATE OF SCIENCE, ETC. 



The foregoing considerations obviously apply to the majority of the 

 magnitudes measured by physicists. There are some cases in which the 

 application is less obvious, for example the measurement of intervals of 

 time and the measurement of temperature. To discuss satisfactorily the 

 measurement of time would, at the present stage in the development of 

 physical theory, involve a long excursion into Relativity problems ; so as no 

 one has tried to base sensory measurements on any analogy with time measure- 

 ments, there is no justification for devoting space to it here. Suffice it to 

 say that there is no method of measuring time which is not in accordance 

 with the general .principles already laid down. More consideration must 

 be given to the measurement of temperature, for attempts are frequently 

 made to justify the use of certain so-called scales of sensation intensity by 

 analogy with arbitrary scales of temperature. There is no real analogy ; 

 but before this can be demonstrated we must examine the case of temperature. 



When we observe physical objects by the sense of touch the sensations 

 produced contain various constituents which we interpret as indicating 

 distinctive properties of the objects. Objects may be rough or smooth, 

 hard or soft, hot or cold, etc. The condition of an object in virtue of which 

 it may feel hot or cold to the touch is called its temperature. Experiment 

 has shown many observable relations of a general kind between the tempera- 

 tures of bodies and their measuable properties. The length and electrical 

 resistance of a given rod, for example, are usually greater when the rod 

 feels hot than when it feels cold. In fact, nearly all the properties of a sample 

 of any substance are appreciably different in these two conditions, and in 

 particular, what is called the amount of heat in the sample, which has been 

 identified with the energy of the relative movements of the ultra-microscopic 

 particles of which bodies are known to be composed, is greater when the 

 body feels hot than when it feels cold. When two bodies, of which one is 

 hotter than the other, are brought into close contact, there is a transfer of 

 energy from the hotter body to the cooler, which goes on until the molecular 

 movements in each body are (on the average) equally energetic. We are 

 entitled to use the term ' equally energetic ' here, because kinetic energy is 

 measurable quite apart from this property of hotness or coldness of bodies, 

 so that equality, as applied to quantities of energy, has a definite significance. 

 When the transfer is complete, the hotter body has been cooled and the 

 cooler body warmed until neither is hotter than the other. The bodies are 

 then said to be in thermal equilibrium. This is a symnnetrical transitive 

 relation between bodies, and so provides a practical criterion of equality for 

 the condition called temperature. But there is no practical operation 

 similar to addition which can be applied to temperature. Obviously there 

 is no method of combining bodies of equal temperature which will provide 

 a series of different temperatures. In this respect temperature is analogous 

 to density : any combination of bodies of equal density results in no change 

 in the value of density. Similarly, any combination of bodies of equal 

 temperature results in no change of temperature. Temperature must 

 therefore be treated as a B magnitude. Our scale of temperature must 

 depend on the measurement of something else for which a scale of measure- 

 ment is already established. Since the temperature of a body depends on 

 the energy of molecular movement, we may produce our arbitrary association 

 between a series of temperatures and the series of numbers by considering 

 the temperature of a body to increase by equal amounts for equal increments 

 of the energy of molecular movement. If we assume a scale of temperature 

 to be established on this basis it can be shown theoretically that certain 

 physical relations — called thermodynamical relations — are of a very simple 

 form. This is of great convenience to the mathematician, but is of no 



