435 
rent representation of the solid substance must undergo a modification, 
so that the fundamental objections mentioned here, are obviated. 
How this is possible, we shall consider now. 
In the very first place it should be pointed out that the Rönt- 
genogram gives us only the relative situation of the centres of 
gravity of the atoms, and does not teach us anything about the 
value of the distances between the atoms with respect to the para- 
meter of the lattice. 
About this question, which is of so great importance for us, we 
can get to know something by way of estimate. 
In the first place the representation that LINDEMANN ') formed of 
the atom movement in the solid substance yields a value for the 
distance between the atoms, which is negligible with respect to the 
atom radius; it becomes even so small that the compressibility 
cannot be taken into account without assuming compressibility of 
the atoms. | 
Another indication of the smallness of the distances between the 
atoms resting on a firmer ground, is furnished by what follows. 
From the determinations of the critical data follows that for normal 
substances the critical volume is about 2,4 times the value of the / 
from VAN DER WAALS SR.’s equation of state. 
If 6 is given the value which holds for the rarefied gaseous state, 
Le. four times the volume of the molecules, the real value of the 
volume will certainly be found too small, as the factor 4 decreases 
for smaller volumes. The minimum value v,, for the volume of the 
molecules is, therefore, given by the equation vj, — 9,6 wv, in which 
vj, represents the critical volume. 
For ether the critical density is 0,26 according to Youne, and at 
O° the density of the liquid is 0,72. Hence the following relation 
exists between the volume at O°, v, and the volume of the molecules: 
0,26 cus 
ae SA em 
0572 
It follows from this that in liquid ether at least 2/7 of the volume 
is filled by the molecules. The temperature of 0° C. being about 
0,6 times the critical temperature of ether, the just calculated ratio 
will always exist between the volume of the liquid and the volume 
of the molecules at a reduced temperature of 0,6 according to the 
law of corresponding states. 
If the molecules are now considered to be spheres, which are 
arranged cubically, then the free distance between the spheres in the 
1!) Physik. Zeitschr. 11, 609 (1910). 
28* 
