(799 ) 
Physics. — “On the course of the isobars for binary systems LI.” 
By Prof. Pu. Konystamm. (Communicated by Prof. J. D. van 
DER WAALS). 
(Communicated in the meeting of February 27, 1909). 
8. The point z=w2,, v=0, the signification of which for the 
eee Oe. dp ree ; 
course of the lines En =0 and EEn 0 we set forth in the preceding 
paper (These Proc. 599), is also an exceptional point for the isobars 
themselves. If we approach this point along the line w = x,, coming from 
large volumes, the pressure is first zero, ascends then to a maximum, 
at least for positive a, after which it passes again through zero, and 
continues to descend to — o, as appears easily from the formula 
MRT a ° . 
—-. If, on the other hand, we arrive at the point «= «,, 
Dn 
(2) 
v= 0 along the line v=b, we find for the pressure the value + oo. 
Also all the intermediate isobars pass through this point, as appears 
5 _ db ed eek _ (dv 1 /d'v ; 
when we substitute 6 = a.” + nn and » = (a) + a a a 
in the equation for the isobar, so assuming the point y= 2,, v=0 
ee ek dv db 
as origin of coordinates. If further we put ER we get, 
u Pp ri 
disregarding the higher powers: 
_1| 2MRT a 
aide db (db ? 
dz? dx \de 
and so, however small w be taken, we can find a point for every 
value of p satisfying the equation. When a is positive the condition 
En 
db dv 
for this is that a aye 80 that the isobar touches »=6, and 
wv wv 
2 2 
dv Mins I 
further Pret so the isobar has a smaller radius of curvature than 
Hg 
da?’ 
v =, and so has greater volume with equal z. 
9. What was said in 7 and 5 enables us to indicate the course 
of the isobars in the neighbourhood of «= .«x,, v= 0. Coming from 
d 
the said point and touching there wy =b (and so also ze ='0) an 
v 
isobar for a high negative value of p will soon intersect the line 
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