( 61 ) 



whereas the terms pv are now the same. In tliis case 7^ would have 

 to be <[ 7\, because the temperature exerts an opposite influence 

 on the change of ft from the pressure. 



In consequence of the lei'm RT loij (1 — ai), ftj {x) will be <^ [i^ {o). ^^ 



must therefore be increased. Now— ^ =: v^ , hence positive , whereas 



op 



— - I — I = — (é?i -\- pi\), so negative. So the value of /.tj (.f), which is 



too small in consequence of x, can again be made equal to that 

 of fij (o), either by Increase of pressure ("osmotic" pressure), or hy 

 lowering of the tem'perature ("osmotic" temperature). 



It would, however, be advisable to banish the idea "osmotic 

 pressure" altogethei' from theoretical chemistry, and oidy speak of 

 it, when such dilFerences of pressure arc actually met with in case 

 of semi-permeable walls (cell-walls, and such like). 



6. Appendix. Proof of some properties, mentioned in § 2. 



a. In a previous paper in these Proceedings (April 1905) I 



èv 

 derived for — the perfectly accurate expression [equation (4), p. 651) : 



dh da 



With ^- = /? and — = 2« ya, in which {i = b.^ — l>i and « = \/a.. — i/a, , 

 dx dx 



this becomes : 



2a)/a {v—by 



dv _ ~ RT^ ^"^~ 



RT v' 



, .. . ^^ 



And now we see at once, that this passes mto /? or — , when 



dx 



/? [/a i=z ctv ^ 



a\/a 

 For then in the numerator becomes equal to "/f hi the de- 



dv dh d\' d^'b 



nominator. But when ^— =:-— , then also t — =0, as — ^=0, andv 



Ox dx ox^ dx* 



is a linear function of x. 



