Correction of the Gas-Thermometer. 87 



0*86 c. c. respectively, which are evidently quantities of the 

 same order of magnitude as the volumes of the liquids. The 

 difficulty in the determination of b from experiments at 

 moderate pressures lies in the fact that it is of the order of 

 a tenth of one per cent, of the volume of the gas at atmo- 

 spheric pressure, that it cannot be determined independently 

 of c, and that the values of both b and c depend on small 

 differences between larger quantities in which the errors of 

 observation are often of the same order as b itself. Boltzmaun 

 (Gas-Theorie) and van der Waals [Arch. Neer. iv. p. 299, 

 and vi. p. 47, 1901) have recently given formulae for the 

 variation of b with pressure, which might theoretically be 

 applied to correct the values of b obtained from observations 

 at higher pressures so as to deduce the values at atmospheric 

 pressure required for the correction of the gas thermometer 

 or for the behaviour of gases at moderate pressures. Bat 

 the development of these formulse rests on assumptions even 

 more uncertain than the discordant estimates of Meyer and 

 van der Waals, and the range of variation indicated (Boltz- 

 niann says it is probably not greater than 1 to 10), would 

 make the extrapolation of such formulae very doubtful. It 

 seems better to adopt a formula of the type already quoted, 

 and to determine c and b from observations of the com- 

 pressibility or the cooling-effect on the assumption that b is 

 constant. The application of this method appears to lead to 

 the conclusion that the value of b at moderate pressures 

 does not differ greatly, if at all, from the volume of the liquid 

 at or below its boiling-point. In applying the equation to 

 calculate the properties of steam, in which case b is so small 

 compared with c that it cannot be determined with any 

 accuracy, I have for this reason simply assumed b equal to 

 the volume of the liquid, and then calculated the values of 

 n and c from the observations on the cooling-effect. The 

 error involved is necessarily small since the value of (n + l)c 

 at the boiling-point in this case is more than a hundred times 

 the assumed value of b. 



With regard to the variation of b with temperature, we 

 can learn nothing from theory, and the indications of experi- 

 ment cannot be interpreted with certainty. From an empirical 

 point of view the assumption /> = constant is the simplest, and 

 since; it appears to satisfy the observations better than any 

 other simple assumption, it should be retained unless it is 

 decisively disproved. 



20. Application to Diatomic Gases. 



The application of the theory to diatomic gases is of par- 

 ticular interest and importance on account of the general 



