the Thermodynamic Scale of Temperature. 131 



not involve an extrapolation to infinity ; but they laboured 

 under the disadvantage of requiring us to know the isothermal 

 compressibility for the same range of temperature as that for 

 which the Joule-Thomson effect is known. Such knowledge 

 is not at present in our possession, and we are not likely to 

 obtain it for some time, as experiments on compressibility are 

 exceedingly difficult to carry out at temperatures even mode- 

 rately high. 



I have accordingly devised a method of treating the dif- 

 ferential equations which necessitates our knowledge of the 

 Joule-Thomson effect as before, and of the isothermal com- 

 pressibility at one temperature only. For this method of 

 treating the equations the experimental data at present 

 available are sufficient, and yet the extrapolation to infinity 

 is avoided. 



Integration of the Fundamental Differential Equation. 



It was first shown by Lord Kelvin that for a gas streaming 

 through a porous plug we must have the equation 



(' Reprinted Papers/ vol. i. p. ±'2S; see also ' Reprinted Papers,' 

 vol. iii. p. 179). The right-hand side of this equation was 

 found by experiment to be very small for such gases as 

 hydrogen, oxygen, nitrogen, air, and carbonic acid. It was 

 also found that the difference of temperature was propor- 

 tional to the fall of pressure to a considerable degree of 



accuracy: and we may therefore treat JK ' as a function 



dp 

 of the temperature only if we are neglecting squares of small 

 quantities. 



Assume that for our present purpose JK ^ may be siiffi- 



ciently well represented by an ascending series of powers 



of -; thus -. 



where n may be zero or positive, but not negative. 

 Then • 



\dt), *-*«•' 

 1/d 



/ \dt% & ~ r + -' 



K2 



