308 Mr. J. Rose-Innes on the Practical Attainment of 
expansion at constant pressures p and p is given by 
a '" a= ipt \vj ~ r ) l 2 '/^l(^^' if*) 
This equation may be considered as fixing the value of k ; 
c -\~ tc e 
once a: is known we know also the series X-^—z, — -, which 
t n 
fulfils the three conditions laid down at the end of last 
section. It is clear that l + # is equivalent to the X of last 
section. 
Application of the above Theory to Hydrogen and to JSitroyen. 
We have next to consider the application of the above 
theory to the gases actually used for thermometric purposes. 
It. is found that for hydrogen and for nitrogen we can fulfil 
the three conditions, specified at the end of the first section, 
with sufficient accuracy by putting 
* t» o+ t + r 
It is worth remarking that the precise algebraic form 
which we choose for the series does not perceptibly affect 
the final numerical results for the thermodynamic correc- 
tions, so long as we employ the same experimental data to 
calculate the constants, and so long as we keep within the 
limits of temperature and pressure over which the Joule- 
Thomson effect has been observed. We may express this by 
saying that the ihree conditions determine the thermo- 
dynamic corrections with arithmetical uniqueness within the 
field of observation over which they hold good. Hence, if 
we do not attempt to extrapolate, we may choose the form of 
our series solely with a view to ease in arithmetical calcula- 
tion, and the form suggested above is on the whole the most 
convenient for such a purpose. 
The experimental data relating to hydrogen and to nitrogen 
Will be considered separatelv. 
Hydrogen — This gas was subjected to the porous-plug 
experiment by Joule and Kelvin ; the results are given in 
Kelvin's Reprinted Papers, vol. iii. p. 176. There was a 
heating effect which amounted, per 100 inches of mercury 
