Correction of the Gas-Thermometer. 59 



Thomson experiment must be to a first approximation 

 proportional ito the fall o£ pressure, or the ratio Q inde- 

 pendent of p. The expression which he gave for the 

 cooling effect is equivalent to the following : 



SQ=2a/R0-6 (24) 



As applied to the constant-volume thermometer, the equation 

 gives very simple results, since p is accurately a linear 

 function of 6, so that the scale-correction is identically zero. 

 The absolute zero correction is given by the formula 



d o -T o =alRv=ap o /R 2 o . . . . (25) 



Yan der Waals himself observed that the values of a and b 

 which he adopted for C0 2 to represent the experiments of 

 Regnault and Andrews did not satisfy the results of Joule 

 and Thomson on the cooling-effect. Rose-Innes, however, 

 has shown (Phil. Mag. March 1898, p. 227) that a formula 

 of the type Q = A/T— B (which is the same as that given by 

 van der Waals) represents the cooling-effect much better 

 than that of Raukine, including the case ' of hydrogen, 

 and has calculated the appropriate values of the constants. 

 Adopting his values of the coefficients A and B, and taking 

 S = 8'4xl0 6 , we find for C0 2 



«/R0 o =ll-9c.c, />=12-3c.c. . . (26) 



Rose-Innes applied this formula to calculate the absolute 

 zero from Regnault's expansion-coefficients, and obtained 

 results practically identical with Lord Kelvin's ; but he did 

 not apply it to calculate the absolute zero from the pressure- 

 coetlicient. If we take, as before, UhappmV pressure- 

 coefficient for C0 2 at ^ = 100 cms., namely, '003725, 

 T Q = 268°-45, the correction is 8°'4, which gives <9 = 276°-9, 

 a result which is obviously much too large. 



This discrepancy is partly due to the fact that the type of 

 formula assumed to represent the variation of Q with tem- 

 perature is wrong, although it represents the observations 

 perfectly over the experimental range. It shows very clearly 

 that the method previously given, which does not assume any 

 particular type of formula, but deduces the zero correction 

 directly from the observations, is much to be preferred, 

 although it may appear less rigorous at first sight. More- 

 over, it is evident that the values of a and b deduced from 

 the cooling-effect in this manner would not satisfy the 

 observations of Regnault or Amajrat en the isothermal 

 compressibility, since they would make d{pv)jdp at I'. 



