( 887 ) 
dv ; 
first approximation, proportional to ae this accounts for the inertia, 
dt 
: ; ao... 
But the force also contains a term, proportional to a? Vig ) 
u 
2 e dv 
AE 
ade tae 
If now the motion is periodical: v = 6 cos yt, we shall have 
dv 
— = — plv, so that we may put 
2 ve? dr 
EO, 
where # means the elongation at the time ¢. 
This term of the force may therefore be considered to express a 
‘resistance’, being proportional to the velocity and having the 
opposite direction. The numerical value of. the coefficient is small; 
and that the resulting attenuation of the vibrations really is insigni- 
ficant, appears from the known phenomena of interference with 
great differences of path, which show that after some 100000 vibra- 
tions the amplitude of an electron has scarcely diminished. On the 
basis of this cause of damping we are not able to account for the 
absorption of the incident light, i.e. for a transformation of the 
radiant energy into heat or other forms of energy. The scattered 
light remains radiant energy of the vibration periods occurring in 
the original beam of light. 
In order to explain absorption, LoRrENTz assumes, that the vibrations 
of an electron excited by incident waves of light, go on undisturbed 
only during a certain interval of time rt, and that then, for instance 
in consequence of the collisions of the molecules, their energy is 
transformed and distributed among other systems. *) This idea may 
be expressed mathematically by giving the damping parameter / the 
9) 
am 
value -—. It is not necessary, however, to identify + with the mean 
Ls 
length of time elapsing between two successive collisions of a mole- 
cule; indeed, after a much shorter interval + the amplitude of a 
resonant (or almost resonant) electron might already have increased 
to such a value, that also the other components of the molecule to 
which it belongs have been thoroughly shaken, and have assumed 
1) Lorentz, The theory of electrons, p. 49; Eucyklopädie der math. Wiss. V. 2, 
188; ABRAHAM, Theorie der Electrizität Il, S. 72, 123. In the above formula e 
is expressed in the C. G. S. unit reposing on CouLoms’s law. 
*) Lorentz, The theory of electrons, p. 141. 
58 
Proceedings Royal Acad. Amsterdam. Vol. XIII. 
