302 Mr. J. Rose-Innes on the Practical Attainment of 
the results obtained by Joule and Kelvin ; we can form a 
consistent theory if we accept the Joule-Thomson figures as 
giving us simply the relative values of the cooling-effect for 
various temperatures and pressures of the streaming gas, and 
if we use these relative values in conjunction with other 
experimental data. Proceeding in this way, I have succeeded 
in diminishing some of the difficulties which were encountered 
in the first part of the paper. 
Integration of the fundamental Differential Equation. 
The differential equation for a gas streaming through a 
porous plug is 
'&).—■ *i 
¥ 
(See Kelvin's Reprinted Papers, vol. i. p. 248 ; see also 
vol. iii. p. 179.) 
The notion underlying the present plan is that in certain 
cases the Joule-Thomson measurements might be, as regards 
their absolute value, less trustworthy than observations made 
on some other physical quantity, and yet might be trusted to 
give us the relative values of the Joule-Thomson effect with 
sufficient accuracy; that is to say, the ratio of the values of the 
Joule-Thomson effect for two different sets of conditions might 
be given sufficiently well by means of the measurements. We 
may express this algebraically by supposing that the Joule- 
Thomson effect is equal to the experimentally determined 
valae multiplied by A, where X is a constant factor, which 
must subsequently be either calculated or eliminated from 
the equations. 
But even though complete confidence is not placed in the 
Joule-Thomson measurements as regards their absolute value, 
they may be supposed sufficiently accurate to tell us ihe 
Pit 
order of magnitude of JK ^- ; for such gases as are actually 
used for thermometric purposes JK~- is always small, and 
will be treated as such in what follows. Further, the experi- 
ments of Joule and Kelvin show us that JK^- may be 
treated as a function of the temperature only, if we are 
neglecting squares of small quantities. 
Let us denote by the letter v the experimentally deter- 
&t 
mined values of ^— ; then the above differential equation 
