INTRODUCTION. 17 



ssion introduced in the preceding equation gives 

 I fkdl T C 1 . dt 



-JT + J-T -T. f 



in which / t and 7. are the u-mjKTature by the thermometer of freezing, 

 ami the corresponding absolute timjKraum-. The first part of the 

 above expression for the entropy of the- liquid can be computed readily, 

 and the M-toml part (wlmh is small) can be determined graphically 

 with great i I : 'hod was used for the tables of the 



of saturated steam. 



To obtain the entmp\ of any liquid named on page u, we may 

 ditTerentiatc tin- prnju-r equation to obtain dq and then integrate as 

 .tied by the equation 



-f'f. 



J I 



The values given in Tables IV to 1 <letcrmined in this way, 



and those for the two following tables were computed in the same 

 mannrr. 



Entropy of a Mixture of a Liquid and its Vapor. The increase in 

 entropy due to heating a unit of weight of a liquid from freezing-point 

 to the temperature / ami then vaporizing x portion of ; 



where is the entropy of the liquid, r is the heat of vaporization, and T 

 is the absolute temperature. For steam - maybe taken from the tables; 



for other vapors it must usually be calculated. 



For any other state determined by *, and /, we shall have, for the 

 iru rease of entropy above that of the liquid at freezing-point, 



The change of entropy in passing from one state to anoth 



