46 HEAT. 



We may use either the values of a previously found, or, since 

 a only appears in small terms, we may put it equal to /3 without 

 sensible error. 



Regnault found for air at atmospheric pressure . a = -0036706 

 and at ...... = -003665 



From his other results we select those for hydrogen 



For hydrogen at atmospheric pressure . a = -0036613 

 atO ..... /? = -0036678 



The value of a is not quite independent of the pressure, nor is 

 that of /3 quite the same for different values of the initial pressure at 

 C., but the variations for small changes of pressure are inconsider- 

 able. Thus for hydrogen even when reduced to i atmosphere he found 

 a = -0036616 ; while for air at atmosphere a = -0036954. 



Gas Thermometry. The researches just described showed that the 

 relation between pressure, volume, and temperature on the mercury-glass 

 scale, for the less easily condensed gases such as oxygen, nitrogen, air, 

 and hydrogen, may, without great error, be represented for ordinary 

 temperatures by 



where K is a constant for a given portion of gas and a = -00366 = 1/273 

 approximately. If we date the temperature from - 273 0. as a new 

 zero and write 6 for 273 + 1 and R for KCL we have 



For the same kind of gas R is proportional to the mass dealt with, and 

 if we deal with equal masses of different gases R is inversely as their 

 molecular weights. 



If Boyle's Law were exactly true, R would be constant for a given 

 portion of gas at a given temperature, and though it would not be quite 

 constant for different temperatures on the mercury-glass scale, we might 

 arrange a new temperature scale so that R should be constant. 



But as Boyle's Law is not a quite correct expression of the relation 

 between pressure and volume for any gas, we cannot give such a simple 

 definition for a gas scale of temperature. We must specify the way in 

 which the pressure or the volume is allowed to vary. 



Two methods have been used in practice, corresponding to the two 

 kinds of research described above. In the one the pressure of the gas is 

 kept constant, say at 1 atmosphere, and equal degrees of temperature 

 are defined by equal increments of volume of the gas. In the other the 

 volume of the gas is kept constant and equal degrees of temperature are 

 defined by equal increments of pressure, starting, say, from 1 atmosphere 

 at 0. In each there are 100 degrees between C. and 100 C. 



In the first case, if a is |y, f the expansion between 0. and 



100 C. of a volume which is 1 at 0., the temperature t, measured from 

 C. is given by 



