40 On some Thermodynamical Relations. 



must be employed, where */ and t x are the absolute tempera- 

 tures of the ether, and T' and T those of water at any two 

 pressures. If the left side of this equation be multiplied by 



t ' t t ' t 



-— and the right by A -^ being equal to A the equation 

 h h *\ h 



becomes t ' t ( t, 1 



| = |{|4«(T'-T)| 



= |+<.??(T'-T). 



That is to say, if the members of this series of ethers be com- 

 pared with water, both the ratios at any given pressure, 

 corresponding to t 1} t 2 , &c. and the constant c vary directly 

 as the boiling-points (absolute) of the ethers at that pressure. 

 Taking the boiling-point of ethyl acetate at the normal 

 pressure to be correct, and the ratio of the absolute tempera- 

 ture of ethyl acetate to that of water at that pressure therefore 



350*1 

 to be 3^- = 0-9386, and the value of c to be 0-000387, the 



ratio of the absolute temperature of ethyl acetate to that of 

 water at any other pressure is given by the equation 



^ =0-9386 + 0-000387 (T'-373) ? 



where t' is the absolute temperature of ethyl acetate, and T' 

 that of water. 



The calculated and observed temperatures are : — 



Temperature. 



, A 



Pressure. Observed. Calculated. 



1300 , 367-3 367-2 



200 314-4 314-4 



For any other ether in the series the equation is 



¥ = 3^1 {0-9386 + 0-000387 (T'-373)}, 



where t is the boiling-point of the ether at constant pressure. 



For pressures of 1300 and 200 millim. respectively the 

 equation becomes simply 



£'=1-0488* 

 and £'=0-89795*. 



It appears therefore that by determining simply the boiling- 

 point of an ether belonging to this type, and knowing the 

 vapour-pressures of water (.or of one of the other ethers), it is 

 possible to calculate the temperatures corresponding to any 

 other pressure, at any rate between the limits of 200 and 

 1300 millim. 



