Correction of the Gas-Thermometer. 49 



The earliest work of any value was that of Regnault 

 {Me moires de VInstitut, Paris, 1847) (I) on the deviations of 

 gases from Boyle's law ; (2) on the pressure- and expansion- 

 coefficients at various pressures; (3) on the comparison of 

 the thermometric scales of different oases over the range 0° 

 to 300° 0. These experiments established the suitability of 

 the gas-thermometer as a standard, but the order of accuracy 

 attained in the comparisons did not suffice to detect any differ- 

 ence between the scales of the more permanent gases. 



The Absolute or Thermodynamic scale of temperature was 

 invented shortly afterwards by Lord Kelvin, who devised a 

 very delicate method of detecting the deviations of actual 

 gases from the ideal state (Trans. Roy. Soc. Edinb. vol. xx. 

 p. 289, April 1851 ; Phil. Mag. [4] 1852, p. 481), and 

 explained how to reduce the indications of the gas-thermo- 

 meter to the absolute scale. The experimental measurements 

 were carried out shortly afterwards in conjunction with 

 Joule (Phil. Trans. 1854, p. 321), and still remain among 

 the most important data for the determination of the thermo- 

 dynamical correction. The history of this investigation is 

 contained in Sir Wm. Thomson's Mathematical and Physical 

 Papers, vol. i. pp. 333-455, and need not be considered in 

 detail ; but it will be necessary to give a brief account of the 

 method for the elucidation of the notation adopted and the 

 method of calculation proposed in the present paper. 



2. Tlieory of the Porous-Plug Experiment *. 

 The notation adopted is as follows : — 



E-~ intrinsic energy of fluid per unit mass. 



p = pressure; v= volume of unit mass. 



F ==E +pv = total heat of fluid per unit mass. 



H = heat supplied per unit mass from external sources. 



Q = [dOjdp) F = " Cooling Effect," or fall of temperature 



per unit fall of pressure in adiathermal expansion at 



constant F. 

 S = (dH/rf0) p = specific heat of fluid at constant pressure. 

 T={pv/R) = temperature by gas-thermometer. 

 = temperature on the thermodynamic scale. 



We have the following relations between the different 

 quantities : — 



By the first law of thermodynamics, 



( m=dR-pdr (1) 



* For practical details see Preston. ' Theory of Heat,' p. TOi 1 (1894) ; 

 Edser, ' Heat for Advanced Students,' p. 384. 



Phil. Mag. S. 6. Vol. 5. No. 25. Jan. 1903. E 



