HYGROMETRICAL TABLES. llll 



themselves. This is particularly the case with the more recent data over 

 the whole range of temperature from o° to the critical temperature at about 

 374 Centigrade. Two remedies have been utilized to overcome this diffi- 

 culty. First, the employment of separate equations of interpolation ad- 

 justed to fit the observations accurately over a short range of temperature, 

 o° to ioo° for example, as in the case of Broch's computations. (It has al- 

 ready been mentioned that theory requires the function for vapor pressures 

 over ice to differ from the one for pressures over water, so that the values 

 for ice offer no difficulty.) The second remedy sometimes employed con- 

 sists in fitting any reasonably accurate equation as closely as possible to 

 the observations. The differences between the observed and computed 

 values are then charted and a smooth curve drawn by hand through the 

 points thus located. This method has been employed notably by Henning 1 

 and others, using an empirical equation proposed by Thiesen. 



For the purpose of these tables Marvin has found it possible from 

 among a multitude of equations to develop a modification of the theo- 

 retical equation of Van der Waals which fits the whole range of observa- 

 tions much better than any hitherto offered and with an order of preci- 

 sion quite comparable to the data itself. In fact, the equation serves to 

 disclose inconsistencies in the observations, more particularly between 50 

 and 8o° C, which seem to suggest the need for further experimental de- 

 termination of values possibly over the range between o° and ioo°. 



Although it is not difficult to show, as Cederberg 2 has done, tnat the 

 simple form of general theoretical equation for all vapors developed by 

 Van der Waals is inadequate to represent experiments on water vapor with 

 sufficient accuracy for practical requirements, nevertheless a somewhat 

 simple elaboration of its single constant suffices to remove this limitation 

 in a very satisfactory manner. 



The resulting equation is: 



log e = log ir - [A - bX + ?nX 2 -?iX 3 + sX 4 ] ^^, where X = T ~ 453 - (1) 



The quantity within the square brackets in this equation replaces a single 

 term of the Van der Waals equation which was regarded by him as a con- 

 stant. 



In Van der Waals's original equation x and 6 are respectively the 

 critical pressure and temperature (absolute). In the present state of phy- 

 sical science, and from the very nature of the data, these quantities cannot 

 be evaluated exactly. Moreover it is unnecessary to do so for the mere pur- 

 pose of accurately fitting a mathematical curve to the observational data, 



1 Annalen der Physik, 1907, 22: 609-630. 



2 Cederberg, Ivar VV. Uber eine exakte Dampfdruckberechnungsmethode. Physik. 

 Zeitschr. xv : 697, 1914; Uber die Temperaturabhangigkeit einiger physikalischen Eigen- 

 schaften des Wassers in seinen vershiedenen Aggregarzustanden. Physik. Zeitschr. xv: 

 824, 1914. 



