320 
(2) as representing (to a certain degree of approximation) the law 
of electric vibration in a molecule. The difficulty of explaining in¬ 
trinsic frictional forces acting on a vibrating electron has been 
pointed out by various writers. H. A. Lorentz however has shown 
in two important memoirs *) that something akin to damping may 
result from molecular impacts disturbing the regular succession of 
(really) undamped vibrations. This theory will be further considered 
in § 10. and it will be seen that (as shown by Lorentz) the general 
form of the equation of motion can on this view be maintained, 
although the constants k and even n 0 will have to be differently 
interpreted. 
There is another damping action on the electron which may be 
expected to take place, namely that arising from the loss of energy 
due to radiation. This view of the subject has been carefully inves¬ 
tigated by M. Planck 2 ). For our present purpose it will be suffi¬ 
cient to note that owing to radiation a term of the^form 
( 4 ) 
will appear in the equation of motion; and since by assumption the 
effect of radiation is small we shall on this view be justified in 
considering equation (2) as still valid if only we take 
( 5 ) 
e 2 n 0 2 
3mc z ’ 
§ 5. Another obvious criticism of the equation of motion of the 
accepted type is that mutual interaction between electrons belonging 
to one molecule is ignored. Generally speaking, a material molecule 
(even in the simplest cases) must probably be regarded as a con¬ 
nected electrical system of high degree of complexity; as yet, how¬ 
ever, we are practically ignorant of the exact nature of the laws 
governing the structure of such systems. 
Leaving aside this, probably the chief outstanding difficulty of 
*) Kon. Akademie v. Wet. te Amsterdam, Verslagen d. W. e. Nat. 
A fd., Deel VI, Amsterdam 1898, pag. 506 en 555. — Kon. Akademie te Am¬ 
sterdam, Proceedings, Meeting of Dec. 30, 1905, p. 591. 
2 ) Sitzungsberichte d. Kgl. Pr. Akademie d. Wiss. zu Berlin; 
J. 1902, p. 470 (1 Mai 1902); J. 1903, p. 480 (30 April 1903); J. 1904, p. 740 
(21 April 1904) ; J. 1905, p. 382 (6 April 1905). 
