( 39 ) 
the so much larger complex molecules so that the ratio between the 
diameter of a complex molecule and the linear dimension of the 
surrounding space is many times smaller than the same ratio for the 
simple molecules. A single glance at the adjoined schematical repre¬ 
o 
O 
o 
o' 
O 
0 
o 
o 
o 
o 
o 
Q 
o 
o 
o 
simple molecules quadruple molecules 
sentation makes this at once clear. In the lefthand figure the relative 
linear extent of the interval is relatively large with respect to the 
diameter of the molecules; in the righthand figure it is comparatively 
small on the other hand. In other words: the complex molecules of 
the righthand figure can no longer move past each other: the molecule 
is too large to do so compared with the intervals; it will now be 
confined to a fixed centre of equilibrium, round which it can only 
move in closed paths; whereas in the lefthand figure the mobility 
is perfectly secured 1 ). 
The transition of the liquid to the solid state is, accordingly, 
brought about in consequence of this, that the solid state is characterized 
by extensive formation of complexes of the molecules; not only two 
simple molecules join to .one double molecule, but possibly ten or a 
hundred to one multiple molecule, quite in accordance with the 
assumption of complex “crystal molecules”. 
q As for liquids and solid bodies under ordinary pressures p may be neglected 
by the side of «/„*; the expression «-b = li±f— follows f or , romthe 
/V* 
equation of state, hence the expression ^ X (1 +13) t; for <9 =Now in 
most cases ^ (liquid) will differ but little from ^ (solid), so the rafio 8 will be 
about proportional to 1 + <3; for multiple molecules with 1 +(«_!) a. S o if in 
the liquid state ft = t, in the solid state ft = 0, we shall have: 
( 9 , : 8 2 = 1 : n, 
so that in the “solid” state the ratio of the intra-molecular intervals to the whole 
vo ume, which ratio may to a certain extent be taken as a measure for the mobility, 
will be about w-times smaller than the corresponding ratio in the liquid state. 
That viscosity strongly increases with association 
►ingham, Viskositat und Fluiditat, Z. f. ph. Gh. 66, p. 245. 
1-known fact. See e g. 
