26 Mr. W. Sutherland on Weak Electrolytes and 



the whole of the water to change into hydrol. Probably 

 the two processes overlap a little. Nevertheless this ex- 

 planation of the facts in Table I. implies that there is no 

 significance in the symmetry pointed out above. From 

 p { = to 0*5 the process is the change of trihydrol into 

 dihydrol, from jt9 1 = 0'5 to 1 it is the independent change 

 of the dihydrol into hydrol. From the table we can now 

 derive the laws of these changes. As Mendeleef froze out 

 a mixture of alcohol and water having the composition 

 C 2 H 5 OH + 3H 2 0, which we shall see would be better written 

 (G\H 5 OH) 2 + 3(H 2 0) 2 , it seems to me more prudent to 

 assume that the potential energy conditions cause the whole 

 of the change of trihydrol into dihydrol to be almost com- 

 plete when a gram molecule of alcohol, that is 46 grams, 

 is mixed with 3 gram molecules of H 2 0, that is 54 grams. 

 Thus we suppose the first process to end when p, = 0'46. 

 The contraction due to the change of trihydrol into dihydrol 

 in 0*54 parts of water is 



0-54 x 0-333(1/0-88 - 1/1-09) = 0-0393, 



the tabulated value for ^ = 0*46 being 0*0408. The agree- 

 ment between these two numbers is close enough to show 

 the strong probability of the explanation now being proposed. 

 It is reasonable to assume that the minimax in (A + £>A 2 /2)/ 

 P1P2P near p 1 = 0*5 is a maximum of the first process, that of 

 converting trihydrol into dihydrol, at jt> 1 = 0'46, merging 

 into the minimum at the commencement of the second 

 process, that of changing the dihydrol into hydrol. 

 These considerations suggest the form 



(A+ P A 2 /2)/p 1 p 2 p=a + bp 1 (p-92-p 1 ) . . (9) 



up to ^ = 0*46, and with p^O'92—p^ as abscissa and the 

 term on the left as ordinate a locus is obtained which is 

 nearly a straight line with a = 0*0655 and fr = 0'5445, though 

 the two halves of the locus have slight opposite curvatures. 

 The maximum error of the contractions A given by (9) is 

 3 per cent. As the maximum contraction is about 4 per 

 cent, of the volume before mixing, it may be said that 

 (9) gives the density of mixtures of alcohol and water up to 

 ^ = 0*46 with a maximum error of the order of 1 part 

 in 1000. We can take account of the curvatures just 

 mentioned by using the more elaborate equations 



from Pl (0' 92-^0 = to 0'104 



(A + P k 2 l2)l PlI ) 2 p = 0-0655 + 0-5445^(0-92 -/>,) - 0-0027 



-f{ / > 1 (0'92- / > J )-0'052} 2 . , (10) 



