528 Mr. E. Buckingham on the Thermodynamic 
is plausible for the diatomic gases and air, while we know by 
experiment * that the isothermals of air and carbonic acid 
are congruent when drawn to the proper scales. Admitting 
this assumption, we conclude that in corresponding states, 
the reduced value of fiQ p per gram-molecule, or 
y=-z--^ (6) 
' c 
is the same for all the gases, M being the molecular weight. 
But since the value of /jl is, for such pressures as are used in 
gas-thermometry, independent of the pressure, and therefore, 
at any given temperature, independent of the volume, we 
may, in considering the Joule-Thomson effect, regard two 
gases as being in corresponding states if only they are at 
corresponding temperatures. It follows that there must be 
a single equation, 
^•*Ma co 
or 
y-#(*0, (8) 
which is satisfied by the experimental values for all the 
gases. To discover the form of this general reduced equation 
for /jlC p , we plot the value of y as ordinate against the reduced 
temperature r' as abscissa ; draw a smooth curve to represent 
the distribution of the points as nearly as possible ; decide by 
inspection upon the general type of equation to be adopted ; 
and, finally, adjust the constants by trial. If our use of the 
law of corresponding states is permissible, the points should 
all lie close to a single smooth curve ; if they do not, the 
assumptions are faulty or the experimental data erroneous. 
A similar process may be pursued with fx alone, instead of 
fiCp, We may plot the values of 
*'=-£#• 0) 
against t', and attempt to determine a curve 
/*'=tO') (io) 
Since we know that we are dealing with approximations 
and that the reasoning is not rigorous, the justification of our 
procedure depends in either case upon its success. 
* Amagat, Journ. Phys. (3) vi. p. o (1897), 
