130 Mr. J. Rose-Innes on the Practical Attainment of 



We are yet, it is true, far from able to prophesy as to 

 coming years of plenty and of famine, but it is hardly too 

 much to say that recent studies of others as well as of the 

 writer strongly point in the direction of some such future 

 power of prediction. 



VII. On the Practical Attainment of the Thermodynamic Scale 

 of Temperature. By J. Rose-Innes, M.A., JB.Sc* 



IN this paper I hope to develop the theory of the gas- 

 thermometer in such a way as to make the readings of 

 that instrument readily reducible lo the thermodynamic scale. 

 As I have already written two papers on tins subject, it might 

 be as well to indicate briefly wherein this paper differs from 

 my earlier ones. 



The subject of gas-therm ometry has been often investigated, 

 but the first theoretical treatment which need be seriously 

 considered is that given by Joule and Kelvin in 1862 (see 

 Kelvin's Reprinted Papers, vol. i. pp. 429-431). They 

 assumed that the Joule-Thomson effect for air varied as the 

 inverse square of the temperature at all temperatures, and 

 from this assumption obtamed the characteristic equation of 

 the gas (loc. cit.). The correction for the constant- volume 

 air-thermometer obtained from ibis equation was first given 

 by Rowland (Amer. Acad. Arts & Sciences, xv.). 



In my first paper on this subject (Phil. Mag. xlv. pp. 227- 

 234) ; I suggested the use of a different empirical formula for 

 the Joule-Thomson effect; this formula suited the experi- 

 mental results rather better than Lord Kelvin's ; and it led 

 to the conclusion that there is no thermodynamic correction 

 for the constant-volume air-thermometer of the kind calcu- 

 lated by Rowland. Both Rowland's result and my own 

 suffered from a defect, inasmuch as they assumed that an 

 empirical formula which had been found to hold over a 

 limited range of temperature necessarily held at any tempe- 

 rature however high. But the mere fact that two contra- 

 dictory results could be reached from the same data seemed 

 to show that the Joule-Thomson results by themselves were 

 not capable of leading to the proper correction for the 

 constant-volume thermometer. 



In order to avoid the difficulties occasioned by the extra- 

 polation to infinity, I proposed in my second paper (Phil. 

 Mag. 1. pp. 251-260) to change the independent variable. 

 The end aimed at was attained, as the resulting formulas did 



* Communicated by the Author. 



