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XXI. Theory of the Constant-volume Gas-thermometer. 

 By J. Rose-Innes, M.A., B.Sc* 



fJ^HE importance which the constant-volume gas-ther- 

 JL mometer has assumed in practical physics justifies an 

 attempt to improve the theory of the instrument. 



Manipulation of tlie Fundamental Differential Equation. 

 In the customary theory of the constant-volume ther- 

 mometer we start with the differential equation 



{ft\- V = 



JK * 



op 



and after dividing by t 2 we integrate with respect to t. The 

 integration is of necessity along an isopiestic owing to the 



occurrence of the term ( -j- \ . The result of integration 



involves an arbitrary function of p, and in order to evaluate 

 this function we imagine the integration carried to infinite 

 values of v and t along the isopiestic. This plan has been 

 adopted by Lord Kelvin (Reprinted Papers, vol. i. pp. 429- 

 430) and by subsequent investigators ; it is also employed in 

 the paper published by me " On Lord Kelvin's Absolute 

 Method of Graduating a Thermometer " (Phil. Mag. xlv. 

 pp. 232-283). 



The weak point of this method is that we have to assume 



that JK^-is known at all temperatures, and that an empirical 



formula, which happens to fit the Joule-Thomson results 

 fairly well throughout the small range of their experiments, 

 necessarily holds at any temperature however high. An 

 extrapolation to infinity of the above kind must inevitably 

 introduce some uncertainty into the results obtained. But it 

 is possible to abolish this extrapolation by properly trans- 

 forming the differential equation before integration. 

 We start from the fundamental equation 



\dt Jp op 



In order to get rid of the isopiestic differential coefficient 

 we may employ the relation 



,dp_\ /dv\ /dt_\ ___ 1 



\dvjt\dt J p \dp)o 

 (See Baynes's Thermodynamics, p. 23.) 



* Communicated by the Author. 



