SMITH. — EXPANSION OF ETHER AND ALCOHOL. 459 



exact course of the Thomsou isothermal where it cuts the saturation 

 curve. It is seen that the present investigation has been able to 

 supply some information on this point. 



2. From the data given in Tables II, III, IV, V, VI, and VII, values 

 of the van der Waals a have been calculated, for the two liquids in 

 the various states examined, by the method used by Professor Hall in 

 his paper in the Boltzmann Festschrift, that is, by use of the formula 



a=fy7^ — 7^1 c\ which assumes, tentatively, that the energy per mole- 

 cule, aside from the potential energy due to the attraction ~^, is a func- 

 tion of the temperature only, so that it remains constant during any 

 isothermal change of state. (But see footnote to p. 447.) 



3. The values of a thus found prove in the case of ether to be 

 almost exactly those which would be obtained by extrapolation from 

 the values calculated by Professor Hall from the data of Amagat. 

 There is, therefore, no indication of any significant change of the in- 

 ternal state of ether as it approaches and enters the superheated 

 condition. 



A like conclusion is probably to be drawn in the case of alcohol, 

 though the evidence against such a change of internal state upon 

 entering the superheated condition is less satisfactory in the case of 

 alcohol than in the case of ether. 



4. From the data of Ramsay and Young on the vaporization of 

 ether the value which Professor Hall calls a' has been calculated for 

 this substance at various temperatures, ranging from 40° C. to 193° C, 



by means of the formula a' =p-^ { ), in which 



p = the internal latent heat of vaporization, 



t'o = the specific volume of the liquid state, 



Vi = the specific volume of the saturated vapor state. 



These values are smaller than those which Professor Hall found for a' 

 from the Regnault vaporization data for ether, and these latter were 

 smaller than the values found for a at corresponding temperatures. We 

 should expect a and a' to approach the same limit at the critical tem- 

 perature and pressure. The lack of satisfactory data for determining 

 a in the immediate neighborhood of this condition makes it impossible 

 at present to put this expectation to the proof The last stage of 

 approach reached in the calculations leaves 



