32 PROCEEDINGS OF THE AMERICAN ACADEMY. 



or RTlu^-^^ U' ^RTln'-^ + U". (48) 



This equation permits the calculation of the solubility of a substance 

 in any solvent if the solubility in any other solvent is known and the heat 

 of solution in each solvent, or the difference between these heats of solu- 

 tion, and if the ratio of the volume corrections for the two solvents is 

 known. 



The heat of solution may be found from the change of solubility with 

 change of temperature by the well known equation 



dJ-l-J^^ .49) 



which may be obtained by direct application of equation (20), since the 

 conditions for which (20) was obtained are all fulfilled in this case, and 

 since the molecular volume, t"o, of the solid may be considered constant. 



K = VqS ; In K = In Vq + In s ; d In K = d\n s. 

 Uniting equations (-18) and (49), 



RT\u'^ + RT^'^ = RT\n'^+ RT^"^-^, 



Ti d I I'n dT 



a In — 

 or 1d?-1 4- 2^^^_ln!i = 0. (50) 



Si d 1 To 



When the values of r are known for the various solvents, if we know the 

 solubility of a substance in two solvents and the temperature coefficient 

 of the solubility in one, we may find the corresponding coefficient in the 

 other solvent. I hope soon to verify these formulas experimentally, and 

 to determine the values of r for some common solvents. It will be inter- 

 esting to see how r compares with the value of v — h found for the 

 solvents by equation (33). 



IV. Polymolecular Systems. 



(^.) Homogeneous Systems. 



In accordance with the considerations advanced on page 27, the general 

 equation of equilibrium (11 a) may be put into the form 



[r (I'l — 6i)]"i ... J To T 



