256 Mr. J. Rose-Innes on the Theory of 



of mercury. The value of M may be fairly taken as "000765, 

 the arithmetic mean between '000505 and '001025. 



For the purpose of calculating N we may employ the 

 results of M. Amagat, who examined the relation of the pres- 

 sure to the volume of various gases when the temperature is 

 kept constant. In the case of hydrogen, the range of tem- 

 perature of his experiments was from 17°'7 C. to 100°'l C. 

 He plotted the values of pv against p, and found that within 

 the limits of temperature of his experiments the isothermals 

 could be treated as a set of parallel straight lines. It is not 

 possible to accept this conclusion as absolutely correct. For 

 if the isothermals at all temperatures were taken as repre- 

 sented by a set of parallel straight lines, there would be no 

 critical state, liquefaction would be impossible ; and we should 

 never have pv decreasing as p increases. We may therefore 

 infer that M. Amagat's law is only an approximation, and 

 that at higher temperatures pv really increases rather more 

 rapidly with p than at lower temperatures. M. Amagat con- 

 siders that the value of (-—) is 00078 when the unit of 



\dpJt 

 volume is the volume occupied by the gas under standard 

 conditions. It is perhaps safest to attach this number to the 



isothermal of 50° C.; we then obtain for {^\ at 50° C. the 



value of —'001215 of a metre of mercury, which pressure 

 may also be taken as equal to N. 



The resulting value of M + N is —'000450 of a metre of 

 mercury; and the corresponding correction for t is 0°'123. 

 This yields as the final value of t the figure 273°'157, which 

 is very close to the estimate derived by Lord Kelvin from 

 the constant-pressure air-thermometer (Reprinted Papers, 

 vol. iii. p. 177). 



The Characteristic Equation of a nearly Perfect Gas. 



We have already seen that for substances like hydrogen 

 and air the equation 



reduces to 





and we remarked that the condition necessary and sufficient 

 to make t a linear function of p when v is kept constant is 



