(62 ) 



[We above derived tlie condition ^\/a=zav from the general 



dv dv db 



expression for — - . If we knew^ this condition beforehand, ^- ^ — - 



o,v Ox ax 



would immediately follow from this by differentiation, and then it 



dv 

 would not be necessary to start from the general expression for ^ 



Ox 



b. On p. 651 [equation (5)] of the paper cited the perfectly 

 general expression : 



ö''0_ 2 {av—^[/ay 

 bx^~^ 2ö/„ {v—by 



was derived for r-— , which becomes therefore = 0, when again 



ox 



Jo"© d^v 



pdv — pv=za) — pv. And as r-^ and t— are 

 Ox' o.r" 



both = when av = ^[/a, also r — will be = 0, in other words lo 



ox^ 



is a linear function of x. 



c. The heat of dilutmi. It is given by the formula 



L — — 7'^ — [^h!^ _ ^h^ 

 "" ~ or L ^ T 



This is viz. the so-called differential heat of dilution per Gr. mol. 



/ m \ 



of the solvent when an Gr. mol. solvent ( x = — ■ — I are added to 



\^ m -\- nj 



a solution consisting of m Gr. mol. dissolved substance and n Gr. 



mol. solvent. 



This becomes [see equation (1)] : 



L. = -T 



d ri I / do)\ ( dv\ 



If ::-— = 0, then vi — x c — = <o,; and v — x :— will be = i\, when 

 ox^ Ox a.^■ 



Lf " ' 



t— - z=: 0. But then L^ =0. q. e. d. 



And hence also the total heat of mixing will be = 0, when x Gr. 

 mol. of the 2"^ component are mixed with 1 — x Gr. mol. of the 

 1^^ component. 



d. The peculiarities mentioned in \ 2 under a, h and d, which 



