532 Mr. E. Buckingham on the Thermodynamic 
Plate XV. shows that the observations on carbonic acid 
indicate approach to an asymptote at about r* = 0*4 or 
t' = 0'5. Repeated trials have shown that the observations 
cannot be so well represented by any simple curve asymptotic 
to the vertical axis. If such a curve be made to fit the 
carbonic acid points at all well, the agreement is spoiled for 
the important group of points between t' = 2 and t' = 3, 
representing the observations on oxygen, air, and nitrogen. 
Nearly as good an agreement may be obtained by the 
more elementary method of plotting // = — . //, against r f . 
This is done in Plate XVI. Curve A has the equation 
10 9 ^./* = ^5!2-2-36(t'-0-42)-1o-9, ■ < 14 ) 
and is based on the assumption that the critical pressure of 
hydrogen is 19*4 atmospheres. Curve B, with the equation 
109 ^ =^ 2 -36-3, • • • • (15) 
assumes that p c = 13 atmospheres for hydrogen. Slight 
changes may, of course, be made in the constants of equa- 
tions (11), (14), and (15), but no great improvement is 
possible. 
4. Integration of the Constant-Pressure Equation. 
The various detached observations on the Joule-Thomson 
effect may thus be coordinated and made to support one 
another. It seems probable that any one of the three 
empirical equations, (11), (14), and (15), gives the true values 
quite as closely as the observations on any one gas separately, 
except perhaps in the case of carbonic acid. Moreover, the 
existence of a general curve which represents the observa- 
tions affords a very plausible means of computing the values 
of fi or of /LiGp for any one gas all the way from its critical 
temperature to some twelve times its critical temperature. 
Let us, for the present, confine our attention to equation 
(11). From this we may evidently obtain an unreduced 
equation of the form 
l*Cp=~i-c (16) 
for each gas. If we now integrate equation (4) on the 
assumption that /jlG p is correctly represented by equation (16) 
