being the electric force. By both signs I shall now denote, not the whole vector, but the part that is due to the vibrations.
The equations may again be written in a form in which the velocity of translation does not explicitly appear. For this purpose, it is necessary to replace the variables x', y', z', t',
and
by new ones, differing from the original quantities by certain constant factors.
For the sake of uniformity of notation all these new variables will be distinguished by double accents. Let
be an indeterminate coefficient, differing from unity by a quantity of the order
and let us put
,
|
(6)
|
,
|
(7)
|
,
|
(8)
|
|
|
,
|
(9)
|
so that t" is a modified local time; then we find
,
|
(Ie)
|
,
|
(IIe)
|
, etc.
|
(IIIe)
|
, etc.
|
(IVe)
|
.
|
(Ve)
|