Gases and the Equation of Virial. 



505 



we see from (18) that for any part of the virial which is 

 independent of v, the function F must be constant, so that 

 the virial is proportional to T and independent of fi. 



To return to the question with which we started, there 

 seems good reason to doubt that the relation of pressure to 

 temperature with volume constant is accurately linear, even 

 at high rarefactions. On the other hand, it is clear that 

 this relation is approximately satisfied; and the natural 

 course would be to take it as a foundation, determining 

 the functions ^ and i/r in (2), as well as the function 

 of v and T jointly which may be required in supplement. 

 As regards the latter part of the question, a differential 

 arrangement in which two gases, say C0 2 and H 2 , are 

 balanced against one another at the same temperature, 

 would appear to offer advantages. This is shown diagram- 

 matically in fig. 2. where the two gas-reservoirs are connected 



Fi£. 2. 



by a U-tube containing mercury. According to Boyle's 

 law, even as modified by the introduction of a co-volume, 

 the mercury may stand in the U-tube at fixed marks at the 

 same level, in spite of variations of temperature affecting both 

 bulbs alike. And under the more general law (2) the same 

 fixity of the mercury thread can be attained, though now 

 with the extremities at different levels. With such an 

 arrangement the departure from (2) becomes a matter of 

 direct observation, and so long as uniformity of temperature 

 is secured, a precise measurement of it, or of the total 

 pressure, is of secondary importance. Useful results would 

 probably require a total pressure of four or five atmospheres. 

 Phil. Mag. S. 6. Yol. 9. No. r o2. April 1905. 2 L 



