548 PROCEEDINGS OF THE AJVIERICAN ACADEMY. 



constants as possible which should accurately represent the behavior 

 of as many liquids as possible under changes of temperature and 

 pressure. 



The bearing of these data for water on the theory of liquids as de- 

 veloped in this way may be best shown by testing how well the equa- 

 tions already proposed are applicable by extrapolation over this wider 

 pressure range. For this purpose we may choose the equation given 

 by Tumlirz ^^ as perhaps the best. Tumlirz has applied his formula to 

 the data of all the liquids studied by Amagat over a pressure range of 

 3000 kgm. and a temperature range of 40^" or 50°, with really remark- 

 able agreement. Tumlirz's formula has the form 



{p -f P)(y -a) = RT, 



where a and R are constants for any given substance, and P is a 

 function of the temperature only, to be determined by experiment. 

 The significance of the assumption evidently is that the covolume 

 (proportional to the total volume of the molecules) is independent of 

 pressure and temperature, and that the internal pressure P is not 

 affected by changes of volume at constant temperature. The re- 

 sults calculated by Tumlirz's formula, and the actual experimental 

 results are shown in Table XXXII. The constants used at 0° in the 

 calculation are those given by Tumhrz. At 22°, P was found by in- 

 terpolation from Tumlirz's values above and below to be 7152. At 0°, 

 the agreement is fairly satisfactory, and the discrepancies are of the 

 same order throughout the entire pressure range. The discrepancies 

 are greatest at the low pressures, corresponding to the abnormal be- 

 havior of water here. At 22°, for the lower pressures, the discrepancy 

 is about the same as at 0°, but the most interesting thing about these 

 values at 22° is the very evident failure of the formula at high pres- 

 sures. The values given by the formula for the compressibility 

 become small too rapidly at the high pressures. 



This question as to the behavior of the compressibility at high 

 pressures is the first one that would occur to one as of significance 

 for the theory of liquids at high pressures. That is, does the 

 volume shrink toward a limiting value in the way indicated at low 

 pressures, or is there some other effect introduced by the high pressure? 

 The physical picture of the mechanism of the liquid suggesting this 

 question is that of an assemblage of molecules with intervening spaces. 

 Is the change of volume of the molecules themselves under pressure 

 sufficient to produce an appreciable effect after the intervening spaces 



» TumUrz, Sitzber. Wien, Bd. CXVIII, Abt. Ila (Feb., 1909), pp. 1-39. 



