726 Isopiestic Temperatures of Saturated Vapours. 



Now in his Treatise on Thermodynamics Bertrand showed 

 that the equation 



P=&(^P^} > or pn= 9 (l- |J 



is a very accurate expression for representing the vapour- 

 pressures of most substances. In the case of water vapour the 

 best values of the constants are 



72 = 42-855 and a = 88'2; 



the error in the temperature corresponding to any given 

 pressure is less than *3° C. for all temperatures between 

 -30° C. and +230° C. A formula with only -5° C. tempe- 

 rature error is obtained by taking n = 50 and a = 78*3, and 

 this value of n gives practically the same accuracy for 

 numerous other substances tested. 



Such a formula is not as accurate as Bankine's complete 

 formula, but it is much more so than the shortened formula 

 as the following table shows. In column 3 are shown values 

 of the pressure of water vapour calculated from the formula 



logioj? = 8-4937o ^ — 



in column 4 the differences from 



Begnault's experimental values; while columns 5 and 6 

 contain similar values for Bertrand's formula (n = 50). 



T. 



P 

 observed. 



Rankine's 



Formula. 



Bertrand. 



P 

 calculated. 



Ae. 



Calculated. 



As. 



273 



4-6 



6-7 



+ 2-1 



4-54 



- -06 



323 



9198 



102-7 



+ 10-7 



93-07 



+1-09 



373 



760 



760 







760 







433 



4651-60 



4556 



-956 



4633-55 



-18 



473 



11689 



11682 



- 7 



11682-84 



- 6 



503 



209264 



21454 



+528 



21036-00 



+ 110 



Now Bertrand's formula carries with it the complete 

 accuracy of Bam say and Young's Law, for it is of the 

 general form mentioned above. Since, moreover, it is far 

 more accurate than Bankine's shortened formula, it follows 

 that the Bamsay and Young law is also in general more 

 accurate than Professor Everett's criticism would seem to 

 imply. 



