New volumes of the Encyclopædia Britannica > Volume 30, K-MOR

466
MAGNETO-OPTICS
When the magnetic force is at right angles to the direction
of propagation of the light, the line is resolved into a
triplet, of which the middle line occupies the same position
as the undisturbed line; all the constituents of this triplet
are plane-polarized, the plane of polarization of the middle
line being at right angles to the magnetic force, while the
outside lines are polarized on a plane parallel to the lines
of magnetic force. A great deal of light is thrown on this
phenomenon by the following considerations due to H. A.
Lorentz.46
Let us consider an ion attracted to a centre of force by a force
proportional to the distance, and acted on by a magnetic force
parallel to the axis of z : then if to is the mass of the particle and
e its charge, the equations of motion are
cPx
mW + aX =
-He-
\
d2y TT dx
‘mW*+°-y=Kcdti
cPz n
m-^ + az = 0.
The solution of these equations is
a:=A cos {p^ + j8) + B cos (p2t + /3X)
2/ = A sin (pjt + /3) - B sin (pzt -I- /3X)
2=0 cos (pi+ 7)
where a - mp12= - Iiep1
a — mp2 — Hep2
p2=a/m,
. .He .He
or approximately Pi=P + £—, P2=P-i—-
Thus the motion of the ion on the xy plane may be regarded as
made up of two circular motions in opposite directions described
with frequencies p1 and p2 respectively, while the motion along z
has the period p, which is the frequency for all the vibrations
when H = 0. Now suppose that the cadmium line is due to the
motion of such an ion ; then if the magnetic force is along the
direction of propagation, the vibration in this direction has its
period unaltered, but since the direction of vibration is perpendicular
to the wave front, it does not give rise to light. Thus we are left
with the two circular motions in the wave front with frequencies
p1 and p2 giving the circularly-polarized constituents of the
doublet. Now suppose the magnetic force is at right angles to the
direction of propagation of the light; then the vibration parallel
to the magnetic force being in the wave front produces luminous
effects and gives rise to a plane-polarized ray of undisturbed period
(the middle line of the triplet), the plane of polarization being at
right angles to the magnetic force. The components in the wave-
front of the circular orbits at right angles to the magnetic force
will be rectilinear motions of frequency px and p2 at right angles
to the magnetic force—so that they will produce plane-polarized
light, the plane of polarization being parallel to the magnetic
force ; these are the outer lines of the triplet.
If Zeeman’s observations are interpreted from this point
of view, the directions of rotation of the circularly-polarized
light in the doublet observed along the lines of magnetic
force show that the ions which produce the luminous
vibrations are negatively electrified, while the measurement
of the change of frequency due to the magnetic field shows
that e\m is of the order 107. This result is of great interest,
as this is the order of the value of e\m in the negatively
electrified particles which constitute the Cathode Rays (see
Electeicity, Electric Discharge, Ency. Brit. vol. xxviii.).
Thus we infer that the “ cathode particles ” are found in
bodies, even where not subject to the action of intense
electrical fields, and are in fact an ordinary constituent of
the molecule. Similar particles are found near an incan¬
descent wire, and also near a metal plate illuminated by
ultra-violet light.
A more extended study of the behaviour of the spectro¬
scopic lines has afforded examples in which the effects
produced by a magnet are more complicated than those
we have described. Thus Preston47 and Cornu48 have
shown that under the action of a transverse magnetic field
one of the D lines splits up into four, and the other into six
lines; Preston has given many other examples of these
quartets and sextets, and has shown that the change in the
frequency, which, according to the simple theory indicated,
should be the same for all lines, actually varies consider¬
ably from one line to another, many lines showing no
appreciable displacement. The splitting up of a single
line into a quartet or sextet indicates, from the point of
view of the ion theory, that the line must have its origin
in a system consisting of more than one ion. A single
ion having only three degrees of freedom can only have
three periods. When there is no magnetic force acting on
the ion these periods are equal, but though under the
action of a magnetic force they are separated, their number
cannot be increased. When therefore we get four or
more lines, the inference is that the system giving the
lines must have at least four degrees of freedom, and there¬
fore must consist of more than one ion. The theory of a
system of ions mutually influencing each other shows, as
we should expect, that the effects are more complex than
in the case of a single ion, and that the change in the
frequency is not necessarily the same for all systems.
Preston49 has proved that in some cases at any rate the
change in the frequency of the different lines is of such a
character that they can be grouped into series such that
each line in the series has the same change in frequency
for the same magnetic force, and moreover that homologous
lines in the spectra of different metals belonging to the
same group have the same change in frequency. Thus
the behaviour of the spectrum in the magnetic field pro¬
mises to throw great light on the nature of radiation, and
perhaps on the constitution of the elements. The study
of these effects has been greatly facilitated by the inven¬
tion by Michelson 50 of the echelon spectroscope.
There are some interesting phenomena connected with
the Zeeman effect which are more easily observed than the
effect itself. Thus Cotton51 found that if we have two
Bunsen flames A and B coloured by the same salt, the
absorption of the light of one by the other is diminished if
either is placed between the poles of a magnet: this is at
once explained by the Zeeman effect, for the times of
vibration of the molecules of the flame in the magnetic
field are not the same as those of the other flame, and
thus the absorption is diminished. Similar considerations
explain the phenomenon observed by Egoroff and Geor-
giewsky,52 that the light emitted from a flame in a trans¬
verse field is partially polarized in a plane parallel to the
magnetic force; and also Righi’s53 observation that if a
sodium flame is placed in a longitudinal field between two
crossed Nicols, and a ray of white light sent through one
of the Nicols, then through the flame, and then through
the second Nicol, the amount of light passing through the
second Nicol is greater when the field is on than when it
is off. For further information on the Zeeman effect the
reader is referred to a valuable report by Yoight.54
1 Experimental Researches, Series 19. 2 Comptes Rendus, 88, p.
709. 3 Wied. Ann. 6, p. 332; 8, p. 278 ; 10, p. 257. 4 Wisd..
Ann. 23, p. 228 ; 27, p. 191. 5 Wied. Ann. 31, p. 941. 6 Phil
Trans. A. 1885, Ft. 11, p. 343. 7 Wied. Ann. 26, p. 456.
8 Phil. Trans. A. 1895, Ft. 11, p. 621. 9 Wied. Ann. 24, p. 161.
10 Wied. Ann. 31, p. 970. 11 Comptes Rendus, 57, p. 6/0.
12 Comptes Rendus, 43, p. 529 ; 44, p. 1209. 13 Journ. Chem.
Soc. 1884, p. 421 ; 1886, p. 177 ; 1887, pp. 362 and 808 ; 1888,
p. 561 ; 1889, pp. 680 and 750 ; 1891, p. 981 ; 1892, p. 800
1893, pp. 75, 99, and 488. 14 Wied. Ann. 44, p. 377. 18
Ann. 43, p. 280. 16 Zeitschrift f. physikal. Chem. 11, P- 7C,i.
17 Phil. Mag. [5] 3, p. 321. 18 Ann. de Chim. et de Phys. [6}
4, p. 433 ; 9, p. 65 ; 10, p. 200. 19 Wied. Ann. 23, p. 228
27, p. 191. 20 Wied. Ann. 39, p. 25. 21 Wied. Ann. 42, p. H*F
22 Phil. Mag. [5] 12, p. 171. 23 Journ. de Phys. 1884, p. 360.
24 Beibldtter zu Wied. Ann. 1885, p. 275. 25 Messungen uberd.
Kerr'sche Ercheinung. Inaugural Dissert. Leyden, 1893. Phil.
Mag. [5] 5, p. 161. 27 Phil. Mag. [3] 28, p. 469. ^ Die magn.
, Lrehung d. Polarisationsebene desLichtSjYLaWe,!^^. 29 Electricity