48 Mr. W. Sutherland on Weak Electrolytes and 



maximum of density, and propionic and butyric acids show 

 a decided maximum of viscosity at a value of p 1 different 

 from that of maximum density. The viscosity of mixtures 

 of water and formic acid is nearly given by the simple 

 mixture formula, and the fluidity also, so I/V—P1/V1—P2/V2 

 is small and negative and of the same order of magnitude as 

 (j>i/Vi+P2/V2)p&> so that ss-lIpz + x^Pi, which stands for 



{1/V—Pl/Vl—P*/V.2 — (P1/Vl +P2/V2)p&}/piP2P 



has small values for formic acid compared with those for the 

 other acids. For acetic acid and water the tabulated results 

 can be expressed by 



Wv-pi/yi-P2/y2—(pi/yi + P2/y2)p&}/piP2P=—l6$ ) 



from pi = to 0*5 I xg-\ 



= - 169 -.11 50(0-25 -P1P2) 



from ^ = 0*5 to 1 J 



Retaini g the same forms, we can write for formic acid \ 



= —13 from pi = to 0*5 I /og\ 



= -13 + 50(0-25 - W2 ) 



from ^ = 0*5 to 1 ; 



for propionic acid = —209 from pi = to 0*5 ^ 



= -209 -2040(0-25 -/>,#,) \ (37) 



from ^! = 0'5 to 1 ) 



and for butyric acid = — 210 from ^ = to 0*5 "\ 



= -210-900(0-25-^) \ (38) 



from ^ = 0-5 to 1 ) 



These equations show a certain similarity of form to those 

 for (A- i r pA 2 /2)/p 1 v 2 p for the fatty acids. The maximum 

 contraction with formic acid is only about half the maximum 

 with acetic acid. Yet with half the contraction there is 

 hardly any departure from the simple mixture rule for 

 viscosity or fluidity in formic acid and water. This fact 

 suggests that there are two opposite tendencies as regards 

 the connexion between contraction and change of fluidity, 

 the one increasing fluidity beyond that given by the simple 

 mixture rule, the other decreasing it. In formic acid the 

 contraction goes so far that these two tendencies almost 

 neutralize one another, so that in spite of the contraction on 

 mixing formic acid and water, the resulting fluidity is the 

 same as if the liquids mingled like a pair of ordinary non- 

 associating liquids. This fact confirms the suggestion 



