Correction of the Gas- Thermometer. 73 



however, that it becomes u pluperfect " at a temperature 

 somewhere below 100° C. Here again the value of b is 

 undoubtedly in error. It may also be observed that the 

 error of the value of the absolute zero deduced in Table IV. 

 from Chappuis' pressure-coefficient for C0 2 , namely 274'0, is 

 to"o large to be attributed to errors of observation in the 

 coefficient or in the measurement of the cooling-effect. These 

 discrepancies suggest either that the type of formula is wrong 

 (i. e., that c does not vary inversely as the square of the 

 absolute temperature), or else that the variations of the 

 specific heat are too large to be neglected. 



13. Other Types of Formulae** 



Instead of attempting to readjust the values of the constants 

 in the original formula so as to obtain the best average 

 agreement with experimental data, wo might proceed, as 

 suggested by Joule and Thomson in 1854 (Phil. Trans, p. 360), 

 by the more usual method of introducing sufficient arbitrary 

 constants into the formula to enable it to reconcile all the 

 apparently discordant data. This method has recently been 

 applied by Rose-Innes (Phil. Mag. July 1901), who adopts a 

 formula with three constants, of the same type as that 

 employed by Joule and Thomson, No. (11) above, in the 

 calculation of their original table of corrections. But, in 

 place of Regnault's observations Rose-Innes adopts the later 

 observations of Joule and Thomson on the cooling-effect, in 

 conjunction with Amagat's values of d(pv)/dp. The values of 

 tn—h calculated by Ruse-Innes are given in Table VI. (p. 67) . 

 He does not apply his formula to the case of C0 2 . The 

 difference between the values of the absolute zero deduced 

 by Rose-Innes from ChappmV pressure-coefficients for H 2 

 and N 2 is rather larger than that given in Table IV., and 

 would make the value lie somewhere between 273*15 and 

 273*36, which appears hardly probable. 



To facilitate the comparison of the formulae and the calcu- 

 lation of the corrections, we may employ the notation already 

 explained in Section 8 above. The formula of Rose-Innes is 

 equivalent to the assumption 



e=pv/R+(c J + c"-b)p/R, . . . . (45) 



in which d and c" vary inversely as the first and second 

 powers of the temperature respectively. The corresponding 

 formulae for the corrections are: — 



* This section was added subsequently to the reading of the paper. 



