70 Prof. H; L. Callendar on the TJiermodynamical 



produced in a mercury thermometer by exposure to a low 

 temperature (corresponding to the temporary depression pro- 

 duced by exposure to a high temperature), was discovered 

 for the first time in the course of this series of observations. 

 Taking these facts into consideration, we may conclude that 

 the difference of the scales between 0° and 50° is probablv 

 less than that given by Chappuis' formula, and that the 

 Joule-Thomson curve is more nearly correct, though, as we 

 shall see, there is other evidence tending to show that even 

 the latter is too high. 



11. Extrapolation to Higher and Lower- Temperatures. 



Since the observations of Joule and Thomson were confined 

 to the range 0° to 100° C, the estimates of the corrections 

 given in Table V. (p. 66) are liable to much greater uncertaintv 

 beyond this range, since they depend on the validity of the 

 type of equation (39) assumed. According to the table, the 

 difference between the scales of the constant-volume and the 

 constant-pressure hydrogen thermometers would be about 

 half a degree at the temperature of liquid air. This has been 

 recently confirmed by Travers (B. A. Rep. 1901), and may be 

 taken as an indication that the divergence indicated in the 

 table is at least of the right order of magnitude, even in the 

 case of hydrogen. Similarly the corrected value of the 

 boiling-point of sulphur given by Chappuis (Phil. Mag. 

 1902), namely 444°'7, obtained with a constant-volume 

 nitrogen thermometer at 56 cms. initial pressure, when com- 

 pared with the value 444°'5 obtained with a constant-pressure 

 air thermometer (Phil. Trans. 1891) agrees in sign and 

 order of magnitude with the difference of the scales (0°'2) at 

 this point indicated in the table. Chappuis has recentlv 

 proposed an empirical method of estimating the correction, 

 which leads to a much smaller result. His original formula 

 (44) is evidently of a type unsuitable for extrapolation ; but 

 if we employ it to calculate the true coefficient of expansion 

 of nitrogen at t, assuming hydrogen to be an ideal gas, we 

 find that the coefficient diminishes from '00367698 at 0° C. 

 to -00367378 at 80° C, and then increases to '00367393 

 at 100° C. Chappuis sivnposes that this increase is illusory, 

 and that the coefficient really diminishes to a minimum value, 

 namely '00367378. and then remains constant at all higher 

 temperatures. This assumption would make the scale-differ- 

 ence linear above 100° C, increasing by '017° for each 100°, 

 and amounting to '076° at the boiling-point of sulphur 

 for a constant-volume thermometer at 100 cms. initial 



