122 
and “plane of symmetry” are no more sufficient. Besides the position 
of the particles it is necessary to take also into consideration the 
time. For moving point-systems we may then introduce as analogous to 
the screw-axis a time-axis of rotation with n periods, with the meaning 
that the system becomes equal to and similarly placed with itself 
° 
after a momentaneous rotation of in a definite sense round 
n 
that axis, followed by a certain time-interval. It is apparent that 
the above mentioned moving system can have such axes, namely 
° 
ternary ones. According to the sense of rotation of the time 
n 
Alf 2 2 
interval in question is then en period of the electrons. For 
the configuration of the electrons in the binding rings then only the 
following possibility remains: 
1st Looking from a nucleus the sense of circulation in the four 
surrounding rings is the same; 
2nd. Consider a plane through two of the lines connecting one 
nueleus with the four surrounding nuclei. When an electron of the 
ring round one of these lines passes this plane, this is also passed 
by an electron of the ring round the other line and that in the 
opposite direction. In this case the electrons in parallel rings have 
the same phase, in non parallel ones the phases are connected by 
a simple relation. 
Now introducing into the discussion of the time-space-symmetry 
as analogue of a plane- and centre- of symmetry, a reversal-plane 
resp. centre of symmetry viz. a plane (centre), which acts momen- 
taneously as a mirror for the point system, while also at a definite 
moment all velocities are reversed’), the above discussed system 
has also three quaternary reversal mirror-axes of rotation and six 
reversal-planes of symmetry. 
$ 3. Now we can easily prove that the radius of the binding 
rings may be chosen in such a way that the structure-factor for the 
plane (222) will be nearly O at every moment and not a maximum, 
as was obtained by D. and Scu. with their approximation. 
1) This proceeding is analogous to the operation of reflection by a plane or a 
centre, where resp. one or three coordinates change their sign, while the time 
must be kept constant. This is evident when the reversal of all velocities is regarded 
as the “changing of the sign of the time at a certain moment” or as the “reflection 
of the time in a definite moment”. In connection with this is also the assumption 
of a definite sense of rotation for a time-axis of rotation. 
