( 866 ) 
data. To effect such caleulations KaAMBRLANGH Onnes') has given 
empirical equations of state, which, if specialised for the experimental 
gas, and, if necessary, between definite limits of temperature and 
pressure, represent the actual isotherms of the gas to the limits of 
accuracy of the observations, and in a form easy to manipulate. In 
this equation the product pv is expressed as a series of five powers 
of the density; thus 
B ae Ee Jl 
py=At+ Sik rn. eae 
where p is expressed in atmospheres, v in terms of the theoretical 
normal volume as unit, and the ‘‘virial-coefficients” A,5,C, etc, are 
calculated as functions of the temperature from the experimental 
isotherms of the gas in question, in conjunction with the isotherms 
of other substances which are brought into relation with the one 
investigated by means of the law of corresponding states. On this 
account the equation is usually given in the so-called reduced form : 
D g D g N 
F 
EEN 
5 
( 
v 
apo = U + 26 + EE Bal i gape? Se (2) 
Ty 
where 2 is equal to , vandv the reduced pressures and volumes 
PRVUr 
respectively, and 
Ree 
ern pple e= 73 bh > ele. 
$ 6. If the two following experimental conditions are fulfilled, viz. : 
1. that the difference between the kinetic energies of the gas 
before and after expansion is negligible; and 
2. that the conduction of heat from the apparatus to the expanding 
gas is also negligible; 
then the expansion process will be represented by the equation 
BOD Pals nh ON eee 
(where ¢ = internal energy of the gas, and the subscripts 1 and 2 
refer to the initial and final states respectively) quite independently 
of whether the expansion has taken place through a valve or 2 
plug”), or from a high or low initial pressure. Equation (3) repre- 
1) H. KAMERLINGH ONNES: These Proc. June 1901, and Arch. Néerl. S. Il, T. VI, 
1991. Comm. Phys. Lab. Leiden. No. 71 and 74. 
2) In expansion through a valve, since in parts of the jet the kinetic energy 
temporarily reaches values which are not negligible, intermediate stages of the 
process are not characterised by equal values of the enthalpy; in expansion 
through a plug the process, if it agrees with the theoretical suppositions, becomes 
wenthalpic. 
