towards a Dynamical Theory of Solutions. 55 



The interesting limiting case when p 1 is nearly 1, when 

 water is added to a large excess o£ alcohol, has not, to my 

 knowledge, been studied experimentally. It might show the 

 trihydrol in the film being changed by the alcohol. If (46) 

 is carried to the limit p ] = l it makes p ]5 /p 1 = 0*y6, which is 

 near enough to 1 to show that probably (46) holds nearly up 

 to pi = l. At the other limit when ^is less than O'l equation 

 (46) begins to fail. Down to Traube's lowest p u namely 

 O00288, the following equation holds from p A = 0*068 : 



pJ Pls =Q-88p L + 0-235 + 0'061og 10 p l (47) 



For acetic acid and water the equations corresponding with 

 (46) and (47) are with a maximum error of 4 per cent. : 



Pl /p is =: 0-195 + 0*93 p, when p x > 035 . (48) 



=0'93p 1 + 0'220 + 0'0551og 10 ^ 1 when^<0-35 . (49) 



These equations may be written 



Pilpis=a + bp 1 when p l > <j . . (50) 



= bp 1 + c+flog 10 p 1 whenp l <g, . . (51) 



values of a, b, c, /, and g being gathered in the next table. 



Alcohol : a b c f g 



Methyl 0-334 077 0390 0"08 02 



Etbyl 0-165 088 0235 006 007 



Propyl 004 097 



Isobutyi 0-019 087 



Isoamjl 0'007 0"90 



Acid : 



Formic 0'322 0"S6 0417 014 021 



Acetic 0-195 093 0220 0*055 0*35 



Propionic 0071 T03 0084 00167 017 



Butyric 0009 103 0-0217 0-0066 001 



Isobutyric 0012 1-00 00217 0-0066 003 



Isovaleric 0-0123 0'81 0-0206 O'OOoO 0"02 



The values of b all lie between 0'77 and 1*03. Alcohol 

 and acid containing the same number of carbon atoms in the 

 molecule have nearly equal values of a and also of c, these 

 diminishing rapidly with increasing number of carbon atoms 

 in the molecule. Here we have evidence of an interesting 

 relation between molecular structure and the relations of 

 these alcohols and acids to trihydrol under surface tension. 



If we take b to be 1 and a to be negligible, then (50) 

 makes p u = 1, the limiting case for the higher alcohols and 



