366 LORD KAYLEIGH ON THE COMPRESSIBILITY OF GASPS 



where PV is the value of the product in a state of infinite rarefaction, then 



or 



J 



~ pv dp 



In applying a to correct the observed densities of gases at atmospheric pressure, 

 we are met with the consideration that a is itself a function of temperature, and that 

 the value of a really required for our purpose is that corresponding to C., at which 

 temperature the weighing vessels are charged with gas.* In the case of the principal 

 gases a is so small that its correction for temperature was not likely to be important 

 for the purpose in hand, but when we come to C0 2 and N 2 the situation might well 

 be altered. If we know the pressure-equation of the gas, there is no difficulty in 

 calculating a correction to a in terms of the critical constants. I had, in fact, 

 calculated such a correction for carbonic acid after VAN DER WAALS, when I became 

 acquainted with the memoir of D. BERTHELOT.! in which this and related questions 

 are admirably discussed. The "reduced" form of VAN DER WAALS' equation is 



+ 3\/ ix 80 



I 2 / \ o / O 



pressure, volume and temperature being expressed in terms of the critical values. 

 From this we find 



1 d(TT V ) _ J 



TTV dtr 8 



8 0J' 



and the effect of a change of temperature upon the value ot a is readily deduced. 

 Indeed, if the pressure-equation and the critical values could be thoroughly trusted, 

 there would be no need for experiments upon the value of a at all. The object of 

 such experiments is to test a proposed pressure-equation, or to find materials for a 

 new one ; but consistently with this we may use a form, known to represent the facts 

 approximately, to supply a subordinate correction. 



A careful discussion of the available data relating to various gases has led 

 D. BERTUELOT to the conclusion that the facts at low pressure are not to be 

 reconciled with VAN DEH WAALS' equation, either in its original form or as modified 

 by CLAUSIUS (i.e., with the insertion of the absolute temperature in the denominator 

 of the cohesive term). 



* Except in the comparison of hydrogen and oxygen. 



t " Sur les thermometres a gaz," ' Travaux et Me'moires du Bureau International,' tome XIII. I am 

 indebted to the Director for an early copy of this memoir, and of that of CHAPPUIS presently to be 

 referred to. 



