210 REPORT— 1897. 



APPENDIX I. 



Note on the Constant-volume Gas-thermometer. 

 By G. Carey Foster, F.B.S. 



The absolute thermodynamic scale of temperature introduced by Lord 

 Kelvin is connected with the properties of real fluids by the equation ' 



rfT_ dv 



T — T^ ^^> 



where dv is the infinitesimal increment which unit mass of a fluid occupying- 

 the volume v undergoes when it is heated, under constant pressure, from 

 the absolute temperature T to the infinitesimally higher absolute tempera- 

 ture T-f c^T, and ho is the amount of work required to restore the original 

 temperature of unit mass of the fluid when it has undergone a fall of 

 pressure, Sp, by passing through a porous plug, as in Joule and Thomson's 

 experiments, without loss or gain of heat. 



It follows that, if there is any fluid which does not undei'go a change 

 of temperature when forced through a porous plug, an infinitesimal change 

 of temperature is to the total temperature on the absolute scale as tlie 

 resulting change of volume of this fluid is to the total volume. Such a fluid 

 would be called a perfect gas. 



The following discussion of the bearing of the results of *\\q porous- 

 plug experiments on the indications of a constant-volume gas-thermometer 

 is taken from a copy which the writer made in January 1894 of a fuller 

 discussion of these experimen ' s communicated to him by his friend and 

 former pupil, Mr. John Rose-Tnnes. Mi-. Rose-Innes will shortly read a 

 paper on this question beforn the Physical Society of London. In the 

 meantime the writer has his permission to make the present use of his 

 hitherto'unpublished results. 



It will be remembered that Joule and Lord Kelvin found that all the 

 gases they experimented on were, with the exception of hydrogen, slightly 

 cooled by being forced through the plug. With hydrogen the eflect was 

 smaller than with other gases and was a rise of temperature. At a given 

 temperature the cooling eflect was, up to five or six atmospheres, propor- 

 tional to the diflerence of pressure on opposite sides of the plug. For a 

 given change of pressure the eflect decreased with rise of temperature, 

 and Joule and Lord Kelvin concluded that it was approximately propor- 

 tional to the inverse square of the temperature reckoned from — 273° C. 

 With hydrogen the variation with temperature was too small for them to 

 consider it as clearly established ; if anything the efiect became greater as 

 the temperature rose. 



Mr. Rose-Innes's discussion of these results is founded upon his 

 remark that an empirical formula with two constants, a and /3, namely 



^^^k+t + i'' 



' Compare equation (16) of Lord Kelvin's article ' Heat ' in the Encyclopedia 

 Britannica, vol. si. p. 571 ; Mathematical and Physical Papers, vol, iii. 



I 



