1887.] for the Change of State from Liquid to Gas. 217 



late the values of certain rather complicated exponential functions, and 

 has published tables of their values which greatly facilitate the work 

 of comparing his formula with observations of vapour-pressures at 

 different temperatures. He has compared his formula with deter- 

 minations of vapour-pressure, &c, by Andrews and Regnault of carbon 

 dioxide, and by Regnault and Sajotschewsky of ether, and with 

 Regnault's experiments on water, and has shown that they agree very 

 well. He has also, by help of his formula, calculated the critical 

 temperature for water, and finds it to be about 332° C, and the 

 critical pressure to be 134 atmospheres. 



Professor Ramsay has kindly furnished me with his and Mr. 

 Young's observations on alcohol, and I have compared them with 

 Clausius's formula, with which they agree very well. 



The formula Clausius has given may be described as follows : — ■ 

 The relation connecting the volume, pressure, and temperature of 

 a substance can be expressed by the formula — 



p 1 1_ 



RT v-cc e(v + (3) 2 ' 



In this R, x, and /3 are constants for each substance, p is the 

 pressure, v the specific volume, T the absolute temperature, and is a 

 function of the temperature which vanishes with T, and for which 

 Clausius has given the formula — 



in which b and n are constants for any one substance, and T c and Q c 

 the values of T and at the critical temperature. 



From a consideration of the isothermals represented by Clausius's 

 formula it is easy to show that the critical isothermal, for which two 

 of the tangents parallel to the axis from which pressures are measured 

 coincide, gives — 



ec = 27(« + P)' 



As the combination a + (3 occurs frequently, Clausius denotes it 

 by 7. He expresses the specific volumes of the saturated liquid and 

 gas by a and s, and uses w and W for a — a. and s — a. respectively. 

 He also uses the symbol II = P/(RT) where P is the saturated 

 vapour-pressure, and subscribes c, thus II C , to express the value of any 

 of these quantities at the critical point. Hence we get — 







* There is a misprint of — for — on the last line of the text, formula 7, of 



©c 



p. 135 of Clausius's second paper in the ' Phil. Mag.,' vol. 13. 



