towards a -Dynamical llieory of Solutions. 33 



Table III. {continued). 



100?! 60 70 80 90 91 92 93 



10 4 p 11425 11656 11861 12045 12060 12079 12100 



10 4 A 167 158 123 69 61 55 52 



10*(A+pA2/2)/p,p 2 p 616 649 653 636 620 620 660 



100^ 94 95 96 97 98 99 



10V> 12118 12141 12159 12171 12184 12203 



10 4 A 46 43 37 27 18 11 



10\A+pA 2 /2)fap 2 p 670 740 790 760 750 910 



Here we see that as with alcohol the contraction is a 

 maximum near p 1 = 0'5, though it is less than half the 

 maximum contraction with alcohol. The most noteworthy 

 fact is that 10\A + pA 2 l'2)/ji 1 p 2 p between p x = 0*3 and 0*91 

 varies in an irregular manner between 700 and 600, so that 

 we may write 



(A 4- p A 2 /2)/yj 1 p 2 p = 0'0642 from ^ = 0'3 to 093. . (25) 



As pi diminishes from 0'3 to 0*01 the value of (A + pA 2 /2)j 

 pip. 2 p rises. Some densities given by Traube (Ann. der 

 Cliem. cclxv. 1891) for dilute formic acid solutions at 15° 0. 

 show a similar rise, but less, as shown in the following 

 supplement to Table III. 



\0Op 1 0-574 1-148 2288 4547 



l'0 5 p 100086 100237 100545 101174 



10*a 67 111 204 401 



lO^A+pA^/piJV ... 117 98 91 92 



This increase of (A + pA 2 /2)lp]p 2 p with diminishing small 

 values of p x did not appear with the other fatty acids or with 

 alcohol. It cannot be ascribed to ionization, because, when 

 p l = 0'l, only 1 per cent, of the formic acid is ionized, while 

 (A + ,c>A 2 /2)/ W ? 2/ o has gone up to 0'081 from O0642. With 

 formic acid some special action takes place when /) 1 <0'3, 

 perhaps the reduction of some higher polymer of HCOOH 

 to (HCOOH) 2 . This requires special investigation. At 

 the other limit when jO!>0*93 the ratio (&+p& 2 /2)p l p 2 p 

 rises, but its values are hardly consistent enough to let us 

 estimate a limit for comparison with the limits for the other 

 fatty acids and alcohol. If a little water in excess of formic 

 acid is being changed partly into hydrol, the amount of 

 change for a 1 per cent, solution of water in formic acid 

 is only half of that for the other acids. A special experi- 

 mental inquiry would be necessary to ascertain whether at 



Phil. Mag. S. 6. Vol. 22, No, 127, July 1911. I) 



