308 
phosphorus (P,) -— probably considerably higher than P, (ScHenn). 
In Il] we saw that the ratio (v,—%,):¥v,, is only dependent on 
the product fu. But — we observed it already above — in this 
it was supposed that the molecular state at 7 and 7, is the same. 
If this is no longer the case, the relation derived there, is slightly 
modified. If the quantities «, 4, and v refer to atom quantities, then 
at the triple point the relation 
a, E 1 Ty 
Sa ne b,)=— RT, 
Vv, ny 
holds ‘y» being neglected), when n, represents the number of atoms 
in the molecule. But for 7% the relation : 
2 az 
Aln EL 
i by 
holds with great approximation (a; and 4; refer again to 1 atom, 
the factor °/, holds for comparatively high critical temperatures), 
because then again the molecular attraction = 7,7 X aj, and the 
molecular volume =n  6;. Hence 
a, 1 RT: br v,--8, RT, 
— x 5 Eene SER 
Aye a NJ. Br Ni 
or 
1 
v, —b Zann v, T. 
aol Pn Dee 
Bride c 
Now 7%: 7,=u,  br:v, =f,, hence we get: 
v, —b, ao 2 arnz 1 De 2 ae i 
v, 7 a, ON rage Pp 
so that now not fu,, but 
a,n, 
Ten TR rl EEE ed ae (1) 
AlN]: 
becomes a measure for the ratio w‚—b,):v, at the triple point. 
As for the two phosphorus modifications the atomic attractions 
, and a’, will be the same at the triple point, the values of fu, Xn, 
will here be decisive for the value of the ratio (v,—6,):v, in the 
two cases. 
Now it is remarkable that 1,31 is about '/, of 5,52 (iu our above 
calculation the values of y are put equal for the two modifications, 
which is certainly not quite true, so‘ that the first value of fu, will 
only be accurate by approximation). If therefore we assume the 
formula’ P, for the yellow phosphorus at the melting-point, then 
the formula Z,, wonid hold for the red phosphorus at the melting point 
of this modification. 
a 
1 
