8& Prof. H. L. Callendar on the Thermodynamical 



employment o£ hydrogen, nitrogen, and air in gas-ther- 

 mometers. It also presents peculiar difficulties, as compared 

 with the case of a less perfect gas like C0 2 , because the 

 deviations to be measured and compared are so much smaller, 

 while the probable error of observation remains the same. 

 For instance, in the case of the three gases above mentioned, 

 the deviations from Boyle's law are of the order of one part 

 in a thousand only per atmosphere, and the order of accuracy 

 of measurements of the compressibility by the capillary- tube 

 method does not reach 1/1000 except under the best con- 

 ditions. The advantage of the porous-plug method is that 

 the cooling-effect represents the whole deviation sought, but 

 the order of accuracy of the individual observations of Joule 

 and Thomson did not exceed 5 or 10 per cent, at the higher 

 temperatures. One of the final series of observations on air 

 at 40° C. differs from the smoothed curve by more than 5 per 

 cent., and one of the observations on nitrogen at 92° (J. differs 

 from the other by about 20 per cent. The nitrogen was pre- 

 pared by burning phosphorus in air, and the values of the 

 cooling-effect exceeded those for air by about 20 per cent., 

 whereas the compressibility of nitrogen is decidedly less than 

 that of air. The formula of Rose-Innes, with three constants, 

 was designed to reconcile this apparent discrepancy, but if 

 we extrapolate it to lower temperatures we find that it makes 

 the compressibility of nitrogen much greater than that of air 

 at —100° C, which is certainly contrary to fact. In Tables 

 IV. & V., I have made a rough allowance for the fact that 

 the observed cooling-effect for nitrogen was greater than for 

 air, but little or no weight can be attached to this estimate. 

 Nor can we overlook the fact that Joule and Thomson con- 

 sidered their observations on nitrogen much less satisfactory 

 than those on air. 



Air. — In order to obtain a satisfactory measurement of 

 the constants c and b and of their rate of variation with 

 temperature, it is obviously necessary to make experiments 

 over a much wider range of temperature, and especially at 

 lower temperatures, where the deviations are much larger 

 and more easily measured. The observations of Witkowski 

 (Phil. Mag. xli. p. 288, 1896) on Air appear to be the only 

 ones available for the purpose. His method consisted in 

 filling two similar bulbs with air at the same pressure but at 

 different temperatures. The quantities of air in the two bulbs 

 were then compared by discharging them into eudiometers at 

 atmospheric pressure and temperature. From these data he 

 deduced the mean coefficient of expansion at the given 

 pressure, and all the data required for constructing a diagram 

 of the variations of pv w T ith p at constant temperature. The 



