( 524 ) 



Bui if, before drawing conclusions concerning the properties of the 

 components of binary mixtures which admit of no intersection of 



= and - = 0, we consider tlie meaning of the condition 

 dx* dv' 



"\- >' <C ''\"-i more closely, it appears that the above remarks should 



be greatly restricted. Up to now we have been able to draw the 



conclusion that a la a = a x a, leads to a relation between f a and f 3 



which is graphically represented by what we have called the second 



parabola, and we have further observed thai the condition a ls <[fli#j 



leads to values of f- { and *•„ belonging to points lying within that 



parabola. According to this view, however, also points lying at 



infinite distance on or in the neighbourhood of the axis of the second 



parabola, would furnish sets of values for f, and e, which might 



be considered to properly satisfy the condition <^1- For these 



a x a, 



points a„' is indeed <</,'/, , lml ;ls XV(1 " "i as a i am ' a u W0U W 



"is' 



he infinitely large for these points, and the ratio of * for these 



ti a 



1 2 



points is equal to 1. We gel a more accurate limitation of possible 

 values of f x and f s by putting a ls * = /*",", with the condition 

 /- < 1. So let us put : 



4/--VU +M(1 +e,) = (2#i + *, -fn 2 *?,) 2 . . . . (<0 

 or 



Si * _ 2w s 8 1 E,(2Z a — 1) + «V = *" fc (?» — 1) - «Mn — Z) — "(I—/ 2 )! 

 This equation represents an ellipse for ?' <[ 1 ; for /* = 1 a parabola 

 and for l' >> 1 a hyperbola. From the form d" we see thai this 

 locus touches the lines *,=--! and e, == - 1 in the points in 

 which these lines are intersected by the same line P' Q' , which has 

 been mentioned above in the description of the second parabola. If 

 we now again ask if sets of values of s 1 and e 3 are possible belonging 

 to components the binary mixture of which does not admit of inter- 

 section of ' = and - = 0, we notice in the tirst place that 



da;' 'I'-' 1 



then the ellipse (<f) must intersect the tirst parabola and the line PQ. 



Now. dependent on the value of I* in connection with the value 

 of n it is possible that the ellipse remains entirely restricted to 

 negative values of p 2 , in which case intersection with the first para- 

 bola is out of the question. 



This takes place when the relation between / 2 and n is such that 

 the equation: 4/ 2 rc s (1 + e,) = (2n -f eJ 9 yields equal or imaginary 

 values for e lt and so when : 



