The Figure
(a) shows the classical electronic orbits of an electron bound to an
unmovable mass center by an isotropic elastic force in the presence of
a magnetic field, H. The orbits have been slightly displaced for reasons
of presentation. The normal vibrations are labeled s,
s’,
p,
where
s
stands for "senkrecht" = perpedicular and p
for parallel. The oscillator p
is not affected by the magnetic field; the oscillators s,
s’
have frequencies that lie symmetrically below and above the unperturbed
frequency of the
p
oscillator, Figure (c, f). This effect was observed
by Zeeman in measurements of the emission spectra of sodium (the D_{1}
and D_{2} bands) contained in a flame. The splitting amounts twice
the Larmor angular frequency, which is linear in the field and proportional
to the ratio of the charge and the mass of the electron:

(1)

The electron is in accelerated motion and therefore,
radiates permanently at the expense of the amplitude of the oscillations
(of course, this comment applies to the The magnetic
spectra observed by Zeeman revealed an intensity difference in the emission
of polarized light. Thus, the emitted light exhibits an effect called *magnetic
dichroism*. Moreover, the dichroism was found to depend on the frequency
of the light, a phenomenon called *dispersion*. Early in the 19^{th}
century it had been shown by Fraunhofer that absorption and emission phenomena
observed for the same material give rise to spectra with identical line
positions. Thus, the magnetic dichroism described above must also be observable
in absorption spectra, and actually is. Figure (d)
indicates that *Magnetic Circular Dichroism* (defined as the difference
in absorption of *Left* and *Right* circularly polarized light)
is observed in parallel observation. Figure (g)
indicates that *Magnetic Linear Dichroism* (defined as the difference
in the absorption of *Parallel* and *Perpendicular* linearly
polarized light) is observed in perpendicular observation. The differential
spectra are obtained from the Zeeman spectra by flipping the sign of one
of the stick components (Figure (d, g)). Taking
into account the bandwidth of the electronic transition (which, in the
case of molecular systems is considerably larger than magnetic splitting
due to coupling to nuclear vibrations), one obtains the 1^{st}
and 2^{nd} derivative contours for MCD and MLD, respectively, shown
in Figure (d, g). In the current literature, these
spectra are designated A_{1} (MCD) and A_{2} (MLD). The
A_{1} MCD spectrum is proportional to *minus* the derivative
of the absorption band, the sign being for an elastically bound particle
with a *negative* charge. In other words, the differential absorption
spectrum, as deduced from the Zeeman spectrum, provides the sign of the
electronic charge, a matter that remained unsettled till Zeeman’s work
and Thompson’s discovery of the free electron in the same year.

Noting that

(2a)

and
(2b)

(where f is the band shape function) it follows that
the amplitude of MCD is proportional to H and MLD to H