Correction of the Gas- Thermometer, 



55 



which may also be obtained by substituting pr = R0 in the small 

 term of Rankine's. They found, however, that the heating- 

 effect in the case o£ hydrogen increased slightly with rise of 

 temperature, and could not be represented by the formula. 

 Assuming Rankin e's formula, it would evidently be easy to 

 calculate the value of the absolute zero, and to deduce tables 

 of corrections for the gas-thermometer. But as the formula 

 did not represent the case of hydrogen, which was the most 

 important for thermometric purposes, they did not publish 

 any further tables of corrections, and the absolute zero was 

 still taken at — 273°'7 C, as calculated in their previous 

 paper from Regnault/s limiting value for the pressure- 

 coefficient in the case of air. 



5. Estimation of the Absolute Zero. 



The problem of the thermodynamical correction of the 

 gas-thermometer is naturally divided into two parts : (1) the 

 determination of the value of the freezing-point of water on 

 the absolute scale in terms of the fundamental interval, which 

 may be called the value of the Absolute Zero ; (2) the de- 

 termination of the correction to be applied at other points of 

 the scale to reduce an interval of temperature measured on 

 the scale of the gas-thermometer to the corresponding value 

 measured on the absolute scale, which may be called the 

 Scale-Correction. The latter depends essentially on the type 

 of empirical formula assumed to represent the mode of 

 variation of Q with temperature, whereas the former may be 

 approximately estimated without any such assumptions. 

 Moreover, the scale-correction is necessarily small for gases 

 at ordinary temperatures, whereas the absolute zero correction 

 may be considerable, and is required for determining the 

 variations of the pressure- and expansion-coefficients. 



A simple and accurate method of determining the value of 

 the absolute zero from observations of the cooling-effect 

 alone, was given by Sir Win. Thomson in his article " Heat " 

 in the Encyclopaedia Britannica (vol. xi. p. 554, 1880). 

 The differential equation (4) may be written in the form 



d0/0=jv/(v+m), .... (15) 



in which, if we require only to make an approximate estimate 



of the absolute zero correction, we may put SQ constant and 

 equal to its average value between 0° and 100° C. Integrating 

 this at constant pressure p between limits 0° and 100°, ana 

 writing T for the expression 100?\,/(r 10 o — <\,) (the reciprocal of 



