( 708 ) 
adjoining Sp (sphere with radius o round 4). We shall call the line 
which connects A with the centre of gravity of w 4 the axis of the 
atom 4. (AZ, ). 
By making use of the quantities which determine the situation of 
the axis, we can express the condition on which two atoms are bound 
somewhat more simply, viz.: Two atoms whose centres are A and 
B, are bound, if B lies in an element dw of the region w 4, the 
axis of B lying inside a cone of the opening 4. The configuration 
of the atom B with respect to the atom A is known if we know 
the element dw where its centre lies and the elementary cone dà, 
which contains the direction of the axis of the atom. The forces are 
always directed along the line connecting the centres; the mutual 
energy of the chemical attraction — 4,, does not depend on the 
angles which determine the direction of the axes. If BZ lies outside 
A.%, = 0. On this supposition the chemical forces have no influence 
on the rotations of the molecules round axes through the centre, 
nor have the forces occurring in a collision (compare the suppositions 
of page 707.') So the kinetic energy of the rotations mentioned is 
invariable, we shall put it zero. 
8. We now consider a canonic ensemble of the modulus @, which is 
built up of systems, in which # atoms of the deseribed kind are 
found in a volume J’. Now we shall inquire into the number of 
the systems in this ensemble, in which », atoms are free, and 2n, 
atoms bound to 7, molecules. We shall, however, apply the simpli- 
fication that the density of the considered system is so small that 
we may ignore the size of the molecules when determining the said 
number. First of all we shall note down the number & of the systems 
in which n, definite atoms are free, and 2n, definite atoms are bound 
to molecules in a definite combination. 
We denote the coordinates of the centres by x, ...2,, the conic 
elements in which their axes lie by dà, ... dà. The potential energy 
depends exclusively on the coordinates w,...<2,, the kinetic energy 
being determined by the corresponding moments. According to GaBBs’s 
… 
definition the number 8’ of the systems, in which the mentioned 
moments have all possible values, but the coordinates lie between 
#, and 2z,-+-dz,;:..z, and z,-+ dz, the interval d2,...d4, bemg 
left for the axes, is given by: 
ssa! — = 
2 5 . 
c’— Ne® (2 Om) ae Ati.» dende od. 
1) If we put that «A lies entirely within SZ, only one atom can be bound 
with A in the sphere «4 by the forces ut the same time. 
