in relation to Pressure, Volume, and Temperature. 405 



For all these reasons it must be concluded that some un- 

 certainty still attaches to the highest observed values of p ; 

 and consequently accordance between the calculated and the 

 observed values must not be too strictly insisted on. I there- 

 fore abandoned the above-mentioned complicating alteration 

 of the formula, and reverted to its original and most simple 

 form, which seems to me, not only in respect of practice, but 

 of theory also, to deserve preference. 



By rather laborious calculations I so determined the con- 

 stants of the formula that the resulting values of p agreed as 

 well as possible with both the newer and the older results of 

 observation obtained by Andrews, and that, of the differences 

 remaining at high densities of the carbonic acid, about as 

 many are positive as negative. With these values of the con- 

 stants there is also a satisfactory accordance with Regnault's 

 results of observation, which in regard to the condensation of 

 carbonic acid do not extend so far, by a long way, as those of 

 Andrews. I therefore think that these values of the constants 

 correspond with sufficient accuracy to the stock of observa- 

 tions at present existing, which is more complete as regards 

 carbonic acid than with respect to any other gas. 



To the other gases the general equation (7) can, in my 

 opinion, be applied ; but of course the constants must be de- 

 termined for each gas. 



In connexion with the foregoing another question must be 

 discussed, which forces itself upon us in the consideration of 

 the curves drawn by Andrews and completed by James 

 Thomson. 



When a gas, e. g. carbonic acid, is compressed at a tempe- 

 rature below the critical temperature, at a certain volume 

 condensation begins ; and therewith a state enters in which 

 one portion of the substance is liquid and the other gaseous. 

 As long as this state continues, with the further diminution 

 of the volume the pressure remains constant, and the corre- 

 sponding part of the isothermal pressure-curve is consequently 

 a horizontal straight line. Beside this straight line, one can 

 imagine, as was discussed above, according to James Thomson, 

 another isothermal pressure-curve, representing that pressure 

 which would take place at the same change of volume if this 

 proceeded in such wise that constantly the entire quantity of 

 the substance was in the same state. Although this latter 

 kind of change of volume does not really take place, because 

 the states of equilibrium occurring in it are in part unstable, 

 yet it must be regarded as theoretically possible ; and, in fact, 

 the latter pressure-curve represents the pressure determined 

 by our formula. 



