( 415 ) 
the ion, are entirely destroyed by the remaining part of the mole- 
cule. From these assumptions we find for the equation of motion 
of an ion!): 
dez 
n= — Fen) dats ae ae fe wees 
C 
V dt 
BOM = M) 
(a dt di Fe 
Here m represents the mass of the ion, f a constant factor, « the 
coordinate of the ion, 2, that of the position of equilibrium of the 
ion, e the electric charge. 
The term — f(& —e;) is due to the fact that an ion has a po- 
sition of equilibrium, towards which it is driven back. The second 
and third term of the right hand side indicate the influence of the 
electric forces exercised by the molecule itself. The second term may 
be transferred with the negative sign to the left hand side; it is 
evident that it gives then an apparent change of the mass of the 
ion. If we represent by m the mass of the ion, modified in such a 
way, we may leave this term further out of account. The third term 
has always the sign opposite to that of the velocity and explains the 
damping, which a vibrating particle experiences in consequence of 
the fact that part of the energy is radiated into space. The three 
last terms express the forces exercised by the surrounding molecules 
on the ion. Prof. Lorentz has pointed out that the fourth term is 
great compared to the fifth and sixth. For f we shall take the 
electric force, as it is in the position of equilibrium of the ion. 
The force 4 V?ef, which we take then into consideration, acts on 
the ion and on the rest of the molecule with the same amount but 
in an opposite direction, and has therefore only influence on the 
vibration of the molecule. On the other hand, the forces which 
we neglect: 
dit vee Sem) He Ne x) 
would also give a progessive motion to the centre of gravity of the 
molecule. Afterwards I hope to discuss the influence of these forces. 
For the external force f we shall write: 
1) Lorentz, loc. cit. equation T § 90 in connection with equations 111 and 112. 
