TEMPERATURE AND THE PROPERTIES OF GASES 53 



not only does the proportional error become of more importance, 

 but at the same time the difficulties become greater. It may 

 hence be said that an accuracy of o*i per cent, is about the limit of 

 usefulness in isothermal determinations even at very low tem- 

 peratures. Such accuracies can now be attained at the tempera- 

 ture of boiling hydrogen and should be attainable even in 

 boiling helium, so that the properties of helium as a gas and 

 everything else as a solid can be investigated at very nearly the 

 absolute zero, that is, at and about 5 K. 



At any temperature where the system of isotherms is ac- 

 curately known it should not be difficult to determine experi- 

 mentally both BCv/8v and hCpjhp by enclosing the gas in a 

 comparatively athermanous envelope and causing a small change 

 of temperature by electrical means in the gas, keeping this at 

 one time at constant volume and at another at constant 

 pressure. The energy, and therefore heat, absorbed would be 

 known, so that all the data would be present to calculate the 

 above values by starting with volumes or pressures which 

 were increased by a small proportion. The isothermals would 

 only be required for correction to standard value and the 

 results would be much more accurate than any deductions 

 from the isotherms themselves, as these involve the second 

 differential coefficients with the temperature (see 15). It 

 would be necessary to have the thermometer in the gas, which 

 might introduce some difficulty in the construction ; or, if the 

 isothermals were sufficiently accurately known, the temperature 

 change could be deduced from the changes in p or v when the 

 other variable was kept constant. 



From what has been said it will be seen that the subject has 

 reached a stage at which it is clear that much new light cannot 

 be obtained without either many accurate data or some unlooked- 

 for discovery. To obtain the former, lengthy experiments with 

 complicated apparatus are necessary, but the results would well 

 repay the labour, if such labour were possible. However, in 

 spite of the growing importance of the subject from every point 

 of view, it is strictly true that there is only one place in this 

 country where such measurements are at all possible, although 

 they form the only real foundation of a kinetic theor}' of matter 

 and its connection with practical thermodynamics. 



