HOOOLEERAAR IN DE FACULTEIT DER RECHTSGELEERDHEID
VOLGENS BESLUIT VAN DEN SENAAT DER UNIVERSITEIT TEGEN
DE BEDENKINGEN VAN DE FACULTEIT DER WIS- EN NATUUR-
KUNDE TE VERDEDIGEN OP MAANDAG 6 JULI 1931, DES NA-
MIDDAGS TE 3 UUR

■nbsp;TMr.riS\'I U ai Tt3T!?\'gt;nîYIVt\'i^Jîgt;{iW .HH \'/IAA.
. \'\'•îni-U,lOAM,}K/rD:m Î^AV nAS;}0\'K)

Bij het beëindigen van mijn academische studie breng ik gaarne
mijn oprechten dank aan U, Hoogleeraren in de Faculteit der
Wis- en Natuurkunde, die tot mijn wetenschappelijke vorming
hebben bijgedragen.

In het bijzonder geldt deze dank U, Hooggeleerde Ornstein,
Hooggeachte Promotor, voor den voortdurenden krachtigen
steun en de levendige belangstelling, die ik niet alleen bij mijn
wetenschappelijken arbeid in Uw laboratorium, maar ook in
andere opzichten van U mocht ondervinden. Uw voorbeeld van
energie en volharding heeft een diepen indruk op mij gemaakt
en steeds moge dit voorbeeld mij in mijn verder leven in her-
innering blijven.

Ook betuig ik mijn dank aan allen, die mij op eenigerlei wijze
behulpzaam zijn geweest bij dit onderzoek.
Ten slotte een woord van dank aan Prof. Dr. A. F. Holleman
voor zijn bereidwilligheid om dit proefschrift als artikel te
willen opnemen in de „Archivesquot;.

After investigating the thermodynamic wave theory of light-
scattering for many years Prof. C. V. Raman at Calcutta noticed
for the first time in 1921 a new phenomenon in scattered light. He
found that in the case of a great number of liquids the depolari-
sation increased very strongly when a violet filter was placed in
the path of the incident light. In the summer of 1923 Ramana-
than working on the same subject described this phenomenon as
quot;a trace of fluorescencequot;. He showed, that the measured dcpolari-
sation depended on the prcscncc of a blue filter in the path of the
incident beam of the scattered light, it being smaller in this case.
The possibility of the effect being due to impurities was eliminat-
ed by careful chemical purification. Further investigations on 60
liquids showed the effect to be very general in character.

The well-known test of the complementary filters first applied
by Stokes for detecting fluorescence was used and gave an analo-
gous result as in the case of fluorescence. After preliminary ob-
servations with sunlight an important and decisive step was taken
by using a monochromatic source of light, viz. the very powerful
quartz-mercury-lamp which gives a few sharp bright lines in the
visible region of the spectrum.

The first attempts were made with benzene as a liquid. In the
spectrogram many lines appeared which were not present in the
incident light and some of these lines disappeared when certain
wave lengths of the incident radiation were cut off by suitable
filters. Further researches showed similar modified lines in the
case of many liquids, some of them being accompanied by diffuse

bands or by a continuous spectrum. It was also found that the
new hnes were polarised more strongly than the unmodified
scattered light.

The disco very of the phenomenon was published in the Indian
Journal of Physics, Vol. II, Part III, 31st March 1928.

About the same time Landsberg and Mandelstam (1,2) two
Russian physicists at Moscou found independently of Raman the
same effect in the light scattered on crystalline quartz.

Many ;^iters however have called the new phenomenon the
Ramaneffect . In the following we will do the same.

As a tentative explanation Raman in his first paper on the
subject assumes that of the incident quantum of light {hv) the
part is absorbed by the molecule and that the remaining
part {hv -h ) is scattered. The absorbed energy is used to enable
the molecule to pass from state m into state n, the energies of
which are E„. and E,., so that,nbsp;= hnbsp;^

^ A similar idea was first put forward by Smekal (3) in discussing
incoherent scattering of this kind. This assumption was also used
by Kramers-Heisenberg (4) in deriving a quantum theory of
dispersion and the wave mechanical treatment of light scattering
was based upon the same idea. These theories supported the in-
terpretation given by Raman.

Further observations show however that the original inter-
pretation is not sufficient to account for many consequences of
the experiments. Langer (5) and independently Dieke (6)
pointed out, that the formule which gives the intensity of a
Ramanline does not depend directly on the transition probability

for the two states m and n concerned, but on a sum which can
be written 2 A,„jAj„ extended over «all j states which can combine
with m and As a consequcnce of this the appearcncc of Raman-
Imes IS mmnly governed by the actual existence of those j states.

from the above explanation it will be apparent that there must
be a certain relation between the frequency-shifts of the modified
hnes and the spectrum of the molecule. Raman first and many
others after him showed a connection between these shifts and
intra-red absorption-frequencies of the examined substance. This
may be understood by assuming that the above mentioned transi-
tion occurs between two oscillation- or rotation-levels of the
molecule.

In all cases however a great difference has been observed be-
tween the intensities in the Ramanspectra and those in the infra-
red. In some cases the infra-red absorption is quite absent, be-
cause the molecule is not a polar one, yet many Ramanlines ap-
pear which are independent of this condition.

For illustrating this fact on the basis of the explanation given
by Langer and Dieke we consider the simple case of a rotation
spectrum giving rise to an infra-red absorption. The appearence
of absorption lines is restricted by the selection-principle. Aw =
± i, m being the rotational-quantum-number. In the Raman-
spectrum however the lines with corresponding frequency-shifts
will not appear, because there is no possibility of combining with
a third state. The selection principle .gives here as may be easily
shownquot; Am = o or ±2. On the other hand the corresponding
transitions are forbidden in the rotational spectrum.

A very convincing proof of this explanation are the experiments
on HCl made by Wood (7); the so-called missing line (/2-branch)
was found in the Ramanspectrum, the other lines [P- and Qr
branch) were absent. Also the observations of Mc Lennan and
Mc Leod (8) lead to a similar conclusion in the ease of the rotation
spectrum of hydrogen.

Notwithstanding this incomplete correspondence between
infra-red- and Ramanspectrum the effect is a very powerful
means for studying molecular spcctra, because the main pro-
blems are not the rotation- but the vibration-cnergy-levcls. In
the latter case the questions about sclcction-principles arc more
complicated than in the above mentioned simple example.

Since the first paper of Raman very much attention has been
given by physicists to the problems of modified light-scattering.
In the three years since the discovery of the effect a considerable
number of publications has appeared not only from the school of
Raman in India, but also from other laboratories in all parts of
the world, especially with regard to wave-length measurements
and determination of the shifts v,„„. It is impossible to give even a
short account of the very interesting results within the limits of
this short introduction.

We shall treat in the next chapters intensity problems arising
from the Ramaneffect.

Anti-Stokes Ramanlines. It will be seen that moreover this re-
search gives the possibility of a determination of the fundamental

Further we shall give a complete survey concerning the way the
scattered energy in Ramanspectra depends on frequency These
expenments were suggested by the analogous problems in the
classical scattering and it will be seen, that to a certain degree
similar results may be obtained in the case of modified scattering
Ihe first problem was treated qualitatively by Raman and
Krishnan (9, 10) and by Dadieu and Kohlrausgh (ii) About
the second question Daure (12) gave quantitative results in a
first paper on the subject. In a further publication (13) he called
these results inexact, but did not give the corrected results\' his
conclusion however is that the energy increases as the fourth
power of the exciting frequency.

Landsberg and Mandelstam (14) found with quartz that the
energy increases more rapidly than a fourth power law in the
ultra-violet. They consider however the results not to be so
accurate as to draw certain conclusions about the problem.

From different points of view the measurement of the ratio of
intensities between Stokes and Anti-Stokes lines is of importance

m the quantum theory of hght. We must take advantage of this
possibility because only in a few other cases such a test can be
carried out. We mention in this connection the measurements of
the intensities in the bandspectrum of nitrogen recently made by
Ornstein and v. Wijk (15). They have found a Maxwell-
iioltzmann distribution among the rotation levels of nitrogen

In the second place it will be seen that the investigation of the
above mentioned ratio leads to a new optical determination of
the important constant ^ (h = PLANCK-Constant; k = Boltz-

L. S. Ornstein and J. Rekveld; Phys. Rev., Vol. 34 (1929), 720
L. S. Ornstein andJ. Rekveld; Zs. f. Phys., 68 (1931), 257

mann-constant). The resulting value for this quantity is in a good
agreement with those obtained in various other ways. Although
the measurements which we are going to describe do not permit
of such a high degree of accuracy as already obtained, it will be
shown that the principle of the method may be used for a more
exact determination. This method would be a very simple one for
obtaining the important quantity.

Finally we draw attention to the fact that our experiments in
combination with the theoretical formula seem to indicate an
extension of the well-known summation rule so as to include the
Ramaneffect. This extension points to a very general validity of
the rule which is also indicated by a few other measurements in
bandspectra.

In different ways several writers have already derived a theo-
retical formula for the ratio of intensities between Stokes and
Anti-Stokcs lines.

On assuming, that the probabilities of the two emission pro-
cesses are equal, Raman (i 6) was the first to find for the ratio of

energies the expression: e i^mn transition
frequency). The same result has been obtained by Daure (13).
In the case of crystalline matter Landsberg and Mandelstam ( 17)
gave an interpretation of lightscattcring on the basis of the Born-
theory of crystal-lattice. They arrive at a formula of the type:

The same formula was found by Tamm (18) on applying the
dirac-theory of hght-scattcring. Carelli (19) with the help of
quantum-mechanics obtains the ratio: {NJiN,)^. Placzek (20)
also applied dirac-methods to solve the problem, but in a more
general manner by also taking into account the dispersion of the
matter. His formula therefore contains the absorption-frcquen-
cies v., of the substance considered. In the case of one single ab-
sorption-frequency the expression has the form:

In order to derive an expression for the ratio of intensities in a
very simp e way we will make use of a consideration of thermo-
dynamical eqmhbrium, reasoning on the same lines as Einstein
did when deriving the radiation-law of Planck.

We therefore consider a system of molecules in thermodynami-
cal eqmhbnum with radiation of the absolute temperature T
Among the different states of energy, which are possible for a
molecule, we select the two states indicated by the letters m and
n. Let the energies of these states be E,„ and E

If we assume that the distribution of the quot;energies is according
znbsp;Maxwell-Boltzmann, the numbers of molecules

Now we suppose this system to be immersed in a field of radia-
ùon with a density p (v). The way of excitation of the Ramanlines
IS the following: a quantum of light of frequency v strikes the
molecule and is scattered as a quantum of frequency v - v while
the scattering molecule passes from state m to state n-\'ov the
scattered quantum has a frequency v v„,„ and the molecule
passes from state /z to state m. The lines thus scattered are called
btokes and Anti-Stokes lines, provided that E„ gt; E,„ and the
transition frequency is given bynbsp;= h„,„. We will not

enter into further details about the mechanism of this transition
but only start from the experimentally given fact of the transition\'
We will represent the transition probalities from state m to state
n and inversely by cD,„„ and clgt;„„,. Then the energies of the Raman-
lines of frequencies v- v„,„ and v are given by

h{j-v,„„)p{v) M„. 4gt;„,„(v) dv and h{v v„,„) p(,) jV„nbsp;dv (Ha)

In order to obtain further information about the functions fj)
and 4),„ we assume that the density may be represented by
the law of Wien, consequentlynbsp;^

This assumption is not an essential restriction of the generality.
For under the actual experimental conditions the frequencies con-
sidered are rather high and consequently ~ amounts to about

100. In this case we may take the law of Wien instead of the
general radiation-law of Planck.

As a consequence of the supposed equilibrium between radia-
tion and matter the number of quantums having a frequency v
must be constant. This number however is changed by two
processes:

a.nbsp;the excitation of Stokes and Anti-Stokes Ramanlines with
frequencies v—v„,„ and v

b.nbsp;the excitation of Stokes lines having a frequency v (excited
by a frequency v v,„„) and of Anti-Stokes lines having a fre-
quency V (excited by a frequency v — v,„„).

This loss must be compensated by the process b. The energy
thus obtained is represented by

hv p{v-\\-V,„,,)lt;igt;,„4v V,„„)X,.-\\-p{v — K.»)\'igt;nm{v — V„„)M„ dv (V)
Putting V equal to IV we get with I and III:

{v — g„ (v — v,„„) e ^^ .
This equation must be satisfied for all values of which only
enters into the exponent of the ^-power. Therefore we get the two
equations:

From the first of these equations we can obtain the second one
by substituting v v„„, instead of v. The two functional equations
for the probabilities and lt;t\'„,„ are thus obviously identical.

In order to solve equation VII we use the assumption, suggest-
ed by the idea of a virtual resonator, that the energy of a Stokes
line, excited by different incident frequencies, increases as the
fourth power of the frequency of the modified scattered light.
This energy may therefore be expressed by a formula

if we put the incident energy equal to unity. From this it
results, thatnbsp;has the form C(v —v,««)^, C being a con-

stant as Z), independent of v. If we substitute this in the equa-
tion VII we obtain:

and this equation is satisfied by putting g,^ lt;P„,„ (v—v„,„) = Cv^ or
=nbsp;Putting the expressions for g,„(tgt;,„„ and g„ lt;Igt;„,„

in the formulas II, the formula for the ratio between the
energies of Stokes and Anti-Stokes lines as may be easily seen
takes the form

It must be understood, that this formula has been found on the
assumption, that a fourth power law for the modified scattered
light is valid. As will be shown in the next chapters, however, this
is only the case in regions of the spectrum remote from absorption
frequencies. It is evident that our formula has the same res-
trictions to its validity.

The above expression is the same as that obtained by Lands-
berg, Mandelstam and Tamm and also the formula given by
Placzek is similar, if such conditions prevail that an influence of
absorption may be neglected.

1) This assumption has moreover been verified by the results obtained
in Chapter II and IV.

If we assume the validity of the formula, it is evident, that the
experiments may be used for another purpose, viz. for a new

As all quantities in the right hand member of this equation are
known from the experiments the determination of — is easily

Anticipating on the good agreement between theoretical and
experimental results we shall draw a further consequence of the
theoretical considerations.

We will now replace the radiation emitted by the transition
from state m to state n by the radiation of a virtual oscillator and
similarly for the radiation emitted by the transition n to m. This
means, that in order to describe the intensity of the radiation
which actually takes place we adjoin a complex vector of am-
plitude to each transition process. Suppose, that the oscillator has
an electric moment given by =nbsp;v representing the

emitted frequency. Then as is generally known, the transition-
probability and the amplitude rt are connected in the following
way:

and we can interprété this with the aid of the virtual oscillators by
writing:

Consequently the intensities of the light emitted by the two
transitions are proportional to the statistical weights of the final
states of the molecule after the transition. This result has evi-
dently a great analogy with the summation rule for the case of
atom multiplets. By the above considerations this rule has been
extented to the intensities connected with the radiation in the
Ramaneffect.

Besides there are some other investigations which lead to a
similar extension of the summation rule. Elliott (21) found from
his intensity-measurements in the bandspectrum of 5 0, that the
assumption of the summation rule being valid in the case of band-
spectra as well gives a right interpretation of the results obtained
by the optical determination of the relative abundance ofisotopes.
A similar application of the rule has been justified by the ex-
periments published by Ornstein and Brinkman (22), concern-
ing the determination of temperature from bandspectra oï C JV.

In conclusion we may remark, that by these extensions it is
made highly probable, that the summation rule is of a very
general character and may be applied in various cases.

As intensity-ratios can be determined in the least complicated
manner if the ratios are not too great, we have looked for a sub-
stance suitable for this purpose. It will be very clear that the
intensity of a Stokes Ramanline is mainly governed by the tran-
sition probability from the normal to the excited state, whereas
the value of the frequency-shift v,„„ has no influence on the in-
tensity: a line for which v„,„ is rather large may be much stronger
than a line with a small v,„«.

on the number of molecules already in the excited state and this
number will decrease with increasing v„,„. For this excitation of
molecules is caused by thermal motion and the greater the diffe-
rence of energy between an excited state and the normal one the
smaller the number of molecules in an excited state will be. Now
at room-temperature the mean thermal energy of a molecule is of
an amount of about 32 X loquot;\'^ ergs, which corresponds to a
frequency-shift of 160 cmquot;\' (wave-number). At this temperature
Anti-Stokes lines with a transition frequency near this value will
consequently appear very strongly. But the intensity of Anti-
Stokes lines will fall off very rapidly with increasing value of v„,„.

These considerations lead to the choice of a substance for
which the values of the transition-frequencies are relatively
small, so that the ratios between the intensities of Stokes and
Anti-Stokes lines are alsos mall and thus favourable for the measu-
rements. This is realized by the liquid carbon tetrachloride (CC/4)
the main lines having shifts v,„„ of 215, 312 and 456 cmquot;\' (wave
number); moreover these lines are very strong and may be easily
photographed. Before the experiments the liquid was purified
carefully and distilled into the investigation tube. As a matter of
fact impurities do not affect the results of all our measurements,
provided that they do not give rise to absorption. For we chose
our method as to be always independent of mechanical im-
purities; but with all investigations concerning the Ramaneffect
it is of great practical importance to rcducc the intensity of the
disturbing back-ground obtained on the photographs to a mi-
nimum. For \'this back-ground besides by fluorescent light is
caused mainly by the scattered energy of the continuous spec-
trum given by the exciting light-source and wc must avoid
dust-particles in the liquid, which scatter very strongly this con-
tinuous spectrum.

The tube filled with the liquid was of the type first indicated by
Wood (23). It is a glass tube, having a length of 25 cm and a dia-
meter of 4 cm. This tube is bent at the one end and has a plane
window fused on the other end. The bent part of the tube is
painted black on the outside, and this curvature serves to get rid
of the reflexion from incident light on the back of the tube. In
this way practically a black back-ground was obtained for ob-
servation which is necessary for the measurement of a such faint
spectrum as the Ramanlines offer.

rubber stops and provided with a supply-pipe and an outlet-pipe
for a water-circulation to keep constant the temperature of the
liquid during the exposures. For this purpose a very quick cir-
culation was maintained by means of a centrifugal pump from
a tank filled with water of the desired temperature.

Before beginning an exposure we waited for an equilibrium
state of the temperature. Measurements of the temperature of the
liquid in the tube and of the water in the tank showed, that in all
cases a slight difference in temperature persisted. By means\'of a
thermo-element this difference was observed and a correction for
it applied to the measurements.

The Ramanspectrum was excited as usually by a quartz-
mercury-lamp. This light source is very powerful and has the
advantage of giving a relatively small number of strong lines. A
polished aluminium reflector having an elliptical cross-section
was put over the lamp which was placed in one focus and the
tube in the other one; a reflector of the same material was put
under the inner tube.

This arrangement for exciting Ramanlines can hardly be im-
proved, because a great volume of the liquid placed at a very
short distance from the light-source is exposed to a strong
radiation from all sides.

The light scattered through the plane window was focussed on
the slit of the spectrograph by means of an achromatic lens. This
spectrograph was a Hilgcr-quartz-spcctrograph (type E-^ with a
large dispersion in the visible region of the spectrum. In order to
get sharp images on the plates it proved necessary that the tempe-
rature of Ihc room was kept constant within about one degree;
the small fluctuations in temperature were damped by a heavy
lagging of the spectrograph with cotton-wool. Thanks to these
precautions it was possible to obtain good pictures with an ex-
posure time of five hours.

Ilford Special Rapid plates were used being most sensitive in the
region desired; moreover the grain of these plates is sufficiently
fine to admit of reliable intensity-measurements. The plates were
developed with Rodinal.

The densities thus obtained were measured with a Moll-
selfrecordingmicrophotometer. On each plate a set of calibration-
spectra was photographed, obtained by means of a tungsten-
filament lamp with a known energy-distribution. The different
steps of one series of spectra were got by varying the width of the

slit of the spectrograph. For each wave-length it is thus possible to
draw density-curves; although the distance between the lines
which we have measured is not very large (at most 200 A) it is
not allowed to neglect the variation of the plate sensitivity over
this distance, A correction which can be easily found from the
calibration-curve of the tungsten-lamp was always applied.

The (corrected) temperatures during the exposures were the
following: 274°, 300°, 312°, 323.5° and 339.5° K. Of the incident
light we used for excitation the two wave-lengths 4047 A and
4358 A. In the Ramanspectrum of carbon tetrachloride each of
these lines gives three rather strong lines on both sides of the
unmodified scattered line, corresponding to the frequency-shifts:
215, 312 and 456 cm~quot; (wave-number). These frequency-shifts
point to three absorption-bands in the infra-red spectrum near
46.5,32.1 and 21.9 ju., which however have not yet been measured.

At the above mentioned temperatures the ratio of intensities
between Stokes and Anti-Stokes lines were measured and the
results are put together in the tables I, II and III.

For comparison between the experimental values and those
obtained from the ilieorctical formula we have also given the
theoretical ratios. For the calculations of the just-mentioned

Michel (24) by the measurements of isochromates. He found the
value 0.476 X io~quot; degree-sec. and it seems to be a very accurate
determination of the constant.

It will be evident from the tables, that a very good agreement
exists between theory and experiment.

In order to examine more closely these results we have put for
each frequency-shift:

With the aid of the methods of mean squares we found, that the
value of a is very near zero and that consequently the formula

This result may also be observed from the diagram given m
fig. I, where the In of the intensity-ratio has been plotted against
the inverse of the temperature. The three lines corresponding to
the three frequency-shifts pass through the origin and thus
confirm the assumption oc = o.

It will be seen, that this fact permits us to put together in one
diagram the results obtained for the different frequency-shifts.

with the value of the constant j and consequently a determi-
nation of this fundamental quantity is possible.

We have calculated from the fifteen mean ratios, given in the
tables I, II and III the following value:

a relatively simple and good one. Of course its practability is to a
certain degree independent of our formula; for the only thing of

importance is, that the factor e really enters into the ex-
pression giving the ratio of intensities. The other factor in this
expression may be different from that which we have found by
our theoretical considerations, provided however, that it is in-
dependent of the temperature. In order to obtain a precision
measurement it is obviously necessary to introduce a few im-
provements, especially as regards the method of intensity-
measurements and the constancc of the temperature in the in-
vestigation tube. An exact determination of the shifts v,„„ will also
be wanted, although this determination is made rather difficult by
the great width of Ramanlines, which amounts in certain cases to
about 2A.

A comparison between our results and the formula given by
Placzek shows that within the limits of accuracy obtained by
the measurements the influence of absorption, predicted in this
formula, has not been found. We may first point out, that the
circumstances have not been very favourable in this respect, as
the absorption of carbon tetrachloride starts in the extreme
ultra-violet, the position of the maximum not being measured up
to the present time. This fact in connection with the small values
of the shifts v„,„ makes the factor which expresses this influence,

tant reason. As will be shown in chapter III and IV an influence
of absorption is only observable for that Ramanline, which is in-
ternally connected with the absorption-transition. Now it is quite
improbable, that each of the three lines would correspond to the

same absorption-frequency, provided that really one of the lines
does so. It follows therefore, that it is possible that no influence of
absorption will appear in this case.

Bychoosingasubstancemoresuitablefordetectingthisinfluence,
and taking into account the results obtained in Chapter III,
the formula may be confirmed. Nevertheless, because of the
predominant character of the ^-power a supplementary factor will
in general be hardly perceivable.

Dependence of the scattered energy in Ramanspectra on
frequency in non-absorbing substances.

The problem, which will be investigated in this chapter is the
following: when we examine RamanHnes with a given fre-
quency-shift but excited by incident lines of diflTerent fre-
quency, what is the dependence of the scattered energy of these
lines on frequency. This problem is suggested by and has to solve
the same question as the investigation of the frequency depen-
dence of classical scattering. It is wellknown, that when light of
frequency v strikes a medium, part of the incident energy is
scattered into a given direction and has the same frequency v.
The part of energy thus scattered is proportional to the fourth
power of the incident frequency v. This fact is usually called the
law of Rayleigh and has been stated experimentally and theoreti-
cally by a great many writers and in various ways. The validity
of this rule however must be restricted to regions of frequency in
which the scattering substance does not absorb or which arc not
very near such absorption frequencies. In both cases the fourth
power law does not hold.

It seems to be very interesting to investigate this problem also
for the case of modified scattering. As a consequence of the
remarks just made about the validity of the law of Rayleigh for
the scattered energy in the classical case, it seems necessary to
divide the problem into two:

a. the dependence of the scattered energy in Ramanspectra
excited in regions which are far away from absorption frequencies,
of the substance,

b.nbsp;the same question for Ramanspectra excited in regions
which are at a very short distance from absorption frequencies.

About the question whether in the absorption region itself the
Ramanlines do not exist at all, or whether they are relatively very
strong we cannot give any information. We can expect that cer-
tainly very long exposure times are necessary before the lines can
have through the absorbing matter any effect on the plates. But
we have not investigated this point.

Theoretical predictions about this subject have been made by
Placzek (20). Taking the dispersion of the matter in question
into account he arrives with the aid of quantum-mechanics to
an expression for the frequency-dependence of modified scattering.
The expression he gives can be simplified and written:

(E5 = energy of a Stokes-line, v,„„ = frequency-shift, =
absorption-frequency, Cj„ is a quantity connected with transition
probabilities by the absorption process considered).

fl. v}„ gt; gt; V\'; this means that the exciting frequency lies at a
great distance from the absorption frequency. In this case the
formula states, that in a first approximation the scattered energy
will be proportional to the fourth power of the modified fre-
quency.

h. Vj„ lt; v; this possibility is for instance realised in regions
near infra-red absorptions. The energy would decrease more

c.nbsp;Vj„ gt; v; this occurs near ultra-violet absorption regions.
In this case the energy according to the above formula must
increase more strongly than (v—

a. The first method may be the following: the Raman-
spectrum is photographed together with the scattered exciting
lines. Now in the usual way the ratio of energies of each Raman-
line and of the corresponding scattered unmodified line is made
up. The dependence of the energy in the RamanUnes on fre-

quency is in this way determined in connection with the energy
of the unmodified lines and about this dependence we assume
the Rayleigh fourth power law. From the comparison between
the obtained ratios a conclusion results about the considered
energies and about a possible deviation from the classical law of
scattering.

This way of investigation however has in our opinion various
difficulties. The substance to be considered must be made dust-
free very carefully in order to avoid scattering on dustparticles
which does not follow the fourth power law, as for the Raman-
lines dustparticles have not direct influence. Further one has
to use various screens during the exposure in order to prevent
light reflected either on the walls of the tube containing the
liquid or otherwise to enter into the spectrograph and spoil the
results. These screens however involve an important loss of light
radiated from the tube and therefore very long exposure times
are necessary.

Apart from these practical objections which are at least not of
fundamental importance there is according to our view a
radical error in this method. We have namely assumed the validi-
ty of the fourth power law for the unmodified scattering. Now as
a matter of fact this law has been stated theoretically with some
discrepancies about the influence of the dispersion of the scatter-
ing substance, but strictly speaking has never been checked ex-
perimentally in a more restricted manner. The school of Raman
has measured the scattering of many substances in order to make
this point clear, but these measurements gave always only the
integral effect of a range of wave-lengths not of individual
frequencies. With each given substance we must make out first
whether circumstances are such that an application of the law is
allowed. This makes necessary to determine the energy of un-
modified scattered lines in connection with the energies of inci-
dent lines, at least if we will not carry an uncontrolled assump-
tion into our measurements. These considerations suggest the

b. The Ramanspcctrum is photographed and the energies of
the lines are measured. After that the relative energies of the
exciting lines are determined. The ratios of the energies of Ra-
manlines and of corresponding exciting lines are made up and
from this the dependence on frequency is acquired in a direct
manner.

Because with this substance each exciting line gives rise to three
very strong Stokes lines and to the three corresponding Anti-Stokes
lines, it has the advantage ofoffering six objects for investigation
at once. Therefore we can obtain results of a high accuracy.

The Stokes lines and the Anti-Stokes lines were photographed
with different exposure times necessary to obtain suitable den-
sities. It is evident, that for comparing the variation of energy
of a given Ramanline with frequency, all the lines to be compared
ought to be acquired with the same exposure: as only in that case
these lines are photographed under exactly equal conditions.

The method of exciting the Ramanspectra was the same as
described in Chapter I. This time however it was necessary not
only to keep constant the current and voltage of the mercury
lamp during the exposures but also to use the same current and
voltage during all of them, in order to make sure that each time
the energy of the exciting lines is exactly the same. From some
preliminary researches it appeared, that in order to get the
mercury lamp in a state of equilibrium the lamp had to be set
going one hour or two beforehand. To reproduce equal current
and voltage one must work under exactly the same circum-
stances as regards the mercury lamp, especially as to the placing
of screens around it. The circulation of air in the room in connec-
tion with temperature fluctuations seems to influence the state of
equilibrium. To prevent the continuous background on the plates
from being too strong the temperature of the lamp may not be too
high, which means that the energy put into the lamp may not
be too much increased.

The radiation from the tube through a plane window was
concentrated on the slit of the spectrograph by means of an
achromatic lens. This spectrograph (Fuess) was very powerful
owing to the relatively large aperture of the apparatus. The
photographs were taken on Ilford Panchromatic plates.

The C Cli received in a highly purified state was distilled into
the investigation bulb. Further purification was superfluous for
our experiments; it is sufficient that eventual fluorescing sub-
stances are eliminated as giving a disturbing strong conti-
nuous background. A few particles of dust do not harm for
reasons already mentioned.

With this arrangement it was possible to get good photographs
of Ramanlines excited by the mercury lines from 4047 till
5791 A with an exposure of two hours.

Our method presupposes a knowledge of the relative energies
of mercury-lines. These have been acquired in the following way:

To take a photograph of the lines as they are radiated from
the mercury lamp the tube containing the liquid was replaced
by a reflecting plate. For this plate we have chosen a layer of
gypsum covered with magnesium-oxyde. This is applied on the
gypsum by burning magnesium-ribbon under the plate; to fix it
it was necessary to hold the plate into boiling steam and to
repeat these manipulations several times.

The plate thus acquired will last for a long time and reflects
diffusely the radiation from the lamp in the direction of the slit
of the spectrograph; for this purpose the plate was made slanting
at an angle of 45 degrees. Before comparing the lines thus obtai-
ned with the corresponding Ramanlines the question must be
solved whether the energies thus measured are still in accordance
with those actually active in the tube in exciting the Raman-
lines, these energies only being of interest.

For it might be, that the light from the mercury lamp entering
the tube be affected by reflexion, diffraction and eventual ab-
sorption to an amount which to a certain degree depends on
wave-length. If this amount exceeds the limits of accuracy of the
measurements it would appreciably alter the relative energies of
the mercury lines and lead to wrong results.

For make sure we have compared the lines radiated directly
from the lamp and the lines having passed through the tube.

To be quite certain about this result as regards absorption we
have paid special attention to the possibility of its presence. For
this purpose a tube 8 cm long with plane windows paraflel to
each other at the ends was filled with carbon tetrachloride. The
mercury lamp was placed before a monochromator and in this
way the light of the lines was made to pass successively through
the tube. The energy was measured with the combined thermo-
pile and galvanometer. Within the limits of accuracy (about a
few percents) an absorption effect was not perceivable. Such an
affirmation enables us to use the distribution of energies acquired
from the direct radiation of the lamp, it being the same as the

distribution really active in exciting the Ramanspectrum and
this means an important simplification in the manipulation of the
method.

The time of exposure for the mercury lines is compared with
that for the Ramanspectra very short and it was therefore
necessary to increase this exposure time by means of suitable
screens put in the path of the light from gypsumplate to spectro-
graph. In this way both exposure times were made of the same
order of magnitude.

To determine the energies of the lines from the densities on the
plate, one or two sets of calibration spectra were photographed
on each plate. These spectra were obtained from a tungsten-
filament lamp, the alteration of energy in one set being reahzed
by varying the width of the slit of the spectrograph. It is evident
that as the shift in frequency of the Ramanhnes compared with
the exciting lines is small, the actual problem of intensity-
measurement is not essentially different from homochromatic
photometry. Therefore the exposure times necessary to obtain
Ramanspectrum, mercury-lines and calibration spectra need not
be the same. For it follows from the experiments carried out by
v. d. Held and Baars (25), that a variation of exposure time
only means a parallel shifting of density curves. Although the
amount of this shift may not be the same for all wavelengths (see
e.g. Chapter HI), we can not go wrong by assuming, that the dis-
placement is the same for wavelengths which are very near one
another. Notwithstanding the small difference in wavelength we
have corrected for the slight difference in the plate-sensitivity.
Therefore a calibration of the tungsten-lamp was necessary.

The background appearing on the plates was subtracted from
the energy of Ramanlines after having determined the energy of
this background from the measured density. To obtain exact
results it is of great importance, that the energy respectively
the density of this background is neither too large nor too small-
in the first case the density of the lines differs too little from that
of the ground and in the other case it is impossible to determine
an exact value for the background, because of the general fact
that small densities can not give reUable results in our photo-
metry.

On the plates appeared the Ramanlines excited by the follow-
ing mercury lines: 4047, 4078, 4358, 5461, 5770 and 5791 A.
With each of these lines the following frequency-shifts gave
rise to Ramanlines: 215, 312 and 456 cmquot;\'(wave-numbers),
Stokes lines as well as Anti-Stokes lines, except the mercury-
lines 5770 and 5791 A (yellow lines) where the Anti-Stokes lines
were apparently not strong enough to give noticeable den-
sities during the usual exposure times. Besides some other
lines are too weak for being reliably measured in comparison
with other corrcponding lines on the same plate. Moreover the
plates which we have used show a maximum of sensibility in the
vicinity of the yellow lines, and these lines being very near
together some of their Ramanlines coincide. Both circumstances
gave particular difficulties for photometry, the first since in such
regions the energy is a rapidly varying function of wavelength and
the second because an analysis of the coinciding lines is necessary,
which analysis is a difficult one in the case of Ramanlines of
which the contour is not exactly determined. As a consequence
of these considerations only the Ramanlines excited by the mer-
cury-lines 4047, 4358 and 5461 A are measured. This must not
be thought of as a restriction, since in any case the lines excited
by 4078, 5770 and 5791 A could not give really new information,
because of their close vicinity to the lines measured.

For the Ramanlines just mentioned we have obtained the
energies in the above mentioned manner and each of these
energies has been divided by the energy of the corresponding
exciting line. The ratios thus formed have been normalized in
such a way, that the reduced energy of all the lines excited by
4047 A are put equal to 100. This normalization has only a
practical signification. The numbers acquired for the relative
energies are given in table IV and V. For comparison the relative
values of v^^ and v^ are put into the tables, equally normalized
on 100 for the lines excited by 4047 A. (the frequencies of the
lines are respectively: 24705, 22938, 18308 cmquot;\' (wave-number)).

Each of the results, mentioned in these tables is the mean value
of repeated measurements. A comparison between the ratios
obtained for the same exciting frequency but for different shifts
shows, that there is a relatively small spreading of the values
Ihe evidence of an analogous behaviour of different Ramanlines
authorizes us to make up the mean of the energies from different
lines excited by the same mercury line. We get therefore the
following mean ratios:

which Ig V is the abscissa and Ig E the ordinate. It is evident, that
the slope of the line in this diagram immediately gives the value
of the exponent x. A reproduction of this diagram is given in
Fig. 3 and for comparison the line having a slope corresponding
to a; == 4 is also drawn in the diagram. It is very clear that the
line, drawn through the experimental values is parallel to the line
showing the slope for a; = 4 and from this it follows, that the
energy of Ramanlines increases as the fourth power of the ex-
citing frequency.

This result obtained we can divide each value of the relative
energy by the fourth power of the exciting frequency. Doing so
we get for all lines numbers which are in good agreement with
each other.

On assuming the validity of this fourth power law we have
put into the tables IV and V the relative values of v^g and v^?.
Now we have stated the dependence deduced from our experi-
ments to be a fourth power law of exciting frequencies.

On comparing however the values of the fourth power of the
frequencies of the mercury-lines and those of the Ramanlines
we see at a glance, that there is only a very slight difference
between the relative numbers. As a matter of fact a decision
between the two assumptions is impossible. A dependence cor-
responding to the fourth power of the frequency of Ramanlines
signifies a different behaviour for different frequency-shifts. This
however is not apparent from the tables, no systematic progress
being detectable for different lines. It is very clear that the diffe-
rence just mentioned falls within the limits of error, obtainable by
intensity measurements, because this difference is only of the
order of about 1%. So all things considered we must leave open
the possibility for both assumptions. Measurements with a sub-
stance where the frequency-shifts are much larger could possibly
give a decision. We shall return to the question in the next
chapter.

We choose the substance C Cl^ because no absorption occurs in
the visible or ultra-violet region. In the results no influence of
an absorption can be detected. We are obviously too far away
from the proper frequencies of the substance to perceive this
influence. We will conclude this chapter with the remark that
the results of our experiments confirm the theoretical predictions

In the next chapter we shall try to continue the researches
about this problem especially as regards the influence of absorption
trequencies of the substance.

We have shown in the foregoing chapter that in the case of
tv C/, the scattered energy of a Ramanline increases according
to a fourth power law just as with the classical phenomenon of
unmodified scattered light. As has been shown there, however
the problem is not solved completely with this result.

We have namely pointed out, that the whole of the investi-
gation must be divided into two parts by the occurence of ab-
sorption frequencies.

Now in the case of carbon tetrachloride we have made our
experiments m a region far away from the absorption of this
substance. In the following the second part of the question will
be examined, viz.: the dependence of the scattered energy in
Ramanspectra on frequency in a region which is fairly close to a
proper frequency of the substance. The expectation that in this
case a different law will hold has been suggested by the analogous
case of the unmodified scattering, where in the regions just men-
tioned the fourth power law breaks down.

predicts an influence of absorption. The way the frequencies
enter into this expression may be understood by the following
considerations:

To explain the Ramanlines we assume a quantum of light with
frequency v to strike a medium. Part of the energy falling upon
a molecule of the scattering substance will be absorbed by the
molecule, the remaining energy being scattered as light of a

frequency differing from v. The energy absorbed is used by the
molecule for the transition from state m to state n, the latter state
having the higher energy.

We must now assume as has been stated theoretically and also
has been made clear by the experiments giving a selection prin-
ciple for the Ramanhnes, that this transition between the states
m and n is not a direct one, but is performed via an intermediarv
statej which can combine with both states m and n.

To deduce the formula for the intensity of a Ramanline we
must therefore consider all transitions m to n combined with all
intermediary statesj provided they are not forbidden transitions
In order to arrive at an expression representing this intensity we
can use anyone of the dispersion theories given by Ladenburg
Kramers or Schrodinger which do not differ essentially The
probabilities of all possible transitions will enter in the formula

will occur in the expression for the scattered energy of the Raman
hne and this will take the form as is usual in dispersion-formula
i.e. the well-known resonance-denominators of the type v^. —v^\'
This means, however, that in the vicinity of the absorotion
frequency the energy of the modified scattering will increase more
rapidly than according to a fourth power law.

For the problem under investigation at first sight one might
think that a great many substances be suitable. On second
lieuw \'\'nbsp;^o^ditions arise from experimental point of

In the first place the Ramanspectrum must be fairly strong
but absorption may not be too strong, because in that case the
lines would become too weak in the vicinity of the region of the
absorption.nbsp;°

The absorption line must be narrow, so as to enable us to get
very near the maximum of absorption. It is further desirable that
the absorption hne occurs either in the infra-red or in the remote
ultra-violet parts of the spectrum. Further it is of great imnor
tance that the substance in question is not altered bv ohotor^he
mical reaction particularly when using ultra-violet light For
this reason it was impossible to use the liquid carbon tetr^
chloride for this investigation as was obvious from some Dreli\'
minary experiments.nbsp;pi en-

Most of the conditions mentioned are fulfilled rather\'well with
methyl-alcohol. In his publication about ultra-violet absorptions
Henri (26) gives the position of an absorption maximum of
methyl-alcohol near the wave-length 2200 A, the intensity of
the absorption not being very strong. The Ramanspectrum has
been measured by several scientists and they found that only one
very strong line appears on the photographs. The frequency-shift
of this line amounts to 2832 cmquot;\' (wave number). The line is a
doublet with components of equal intensity, but being a very
narrow one we get only one point for our determination of the
dependence of scattered energy on frequency.

As the mercury-lamp itself gives a great many lines in the
ultra-violet region, the fact that only a few or even only one
Ramanline arise from each exciting line is of great practical
importance.

we had to alter the apparatus and the method described in the
foregoing chapters accordingly.

The tube containing the liquid was of the usual type first in-
dicated by Wood (23) and was made of quartz with a plane
window of quartz fused on at one end. To cool the liquid the
tube was placed in a small receptacle of tin-sheeted iron with in-
and outlet-pipes for watercirculation from the main (see e.g.
Rao (28) and fig. 4).
This receptacle was open at the top and the inside was painted

dull-black to avoid reflexions from the incident light; for this
reflected energy would to an unknown extent form part of the
energy giving rise to the Ramanlines which part can not be
taken mto account in determining the relative energies of the
mercury-lines radiated from the lamp.

In accordance with the size of the mercury-arc we painted a
part of the tube, which has a total length of about 20 cm and a
llghT^^^^ cm, leaving thus only 12\'/. cm open for the incident

We may therefore assume if we wish to take the absorption
corrections into account that pro unit of volume the incident and
therefore also the scattered energy is a constant for a given wave-
length.

The aluminium-reflector placed over the mercury-lamp was
covered with a layer of magncsium-oxyde in order to obtain a
diffuse, non metallic reflexion. The purpose of this will be ex
plained in the following.

The photographs were taken with a Hilger-quartz-spectrograph
(type E,) which is very powerful and gives a good dispersion
in the ultra-violet necessary for avoiding a too strong continuous
background on the plates. This spectrograph was placed directly
in front of the plane window of the investigation-tube, without
lenses. The lenses of the spectrograph being entirely\'filled by
this arrangement we have no loss of intensity in the exposures and
moreover we are able to work without the usual lenses which
are not achromatic for the whole region, as is required for our
measurements.

The exposure time for obtaining suitable densities was about
7 hours. These photographs were taken on Ilford Special Rapid

Determination of the energy of the mercury-lines.
As the principle of the method used in this investigation is
quite the same as that described in Chapter II we must now
determine the relative energies of the mercury-lines. This is done
in the following way:

The tube filled with liquid was replaced by a thin plate of
black-backed amorphous quartz reflecting the light from the
mercury-lamp in the direction of the sHt of the spectrograph
The amount of the reflexion must, of course, be known This can
be easily calculated by means of the formula given by Fresnel

To make sure of the correctness of this assumption we covered
the reflector of the lamp with magnesium-oxyde, then getting
nd ol the metallic polarized reflexion and obtaining a diffuse
unpolarized reflexion of the mercury lines.

To avoid complicated calculations necessary for the evaluation
qulrtznbsp;^ plate of amorphous

The time of exposure, though increased through the use of
reflected mstead of direct light, would of course have been still
exceedmgly small. But as we must take density-marks with the
same time of exposure (see further on) this must at least amount
to a measurable duration. So, to reduce the light to the intensity
required we applied a diaphragm of which the holes were
big enough to avoid diffraction.

Because of the fairly great distance between the exciting line
and the Ramanline with each wave-length, the method of photo-
metry is essentially different from that described in the preced-
ing chapter.

There we could apply the method of homochromatic photo-
metry because the distance of the Ramanlines from the exciting
hnes amounts at the most to about lOO A. Of course a correction
must be applied for the variation of plate sensitivity, even over
this short distance.

In the case however of methyl-alcohol the distance between
Ramanlines and exciting mercury-lines varies from 200 to 300 A.
Taking into account the strongly decreasing sensitivity of the
plate and other properties which are of importance in photometry
e.g. the variation of the Schwarzschild-constant p, it is necessary
to measure the lines separately and to combine the measured in-
tensities. This means however that it is necessary to apply a me-
thod of heterochromatic photometry. We have determined the
relative energies of the mercury lines and also those of the Raman-
lines; the ratios between corresponding energies give values
which represent the energy of a Ramanline in the energy of the
exciting line as a unit.

We will now give a more detailed description of the way
followed in our experiments in order to carry out the hetero-
chromatic photometry in the ultra-violet region of the spectrum.

The problem is as follows: of the photographs of two or more
spectral lines of different wave-lengths the densities, arising in the
same time, on the same plate and using the same apparatus, are
given. Determine the ratio of the energies of these lines.

If the lines do not differ in wave-length it is sufficient to take on
the same plate, with an exposure-time which may vary within
certain limits with regard to that of the lines, a series of density
marks, caused by a light source which gives a continuous spec-
trum when one prefers to graduate the steps with the aid of the
method of slit-widths variation. This light source need not be
constant if only the different steps of one series are taken
simultaneously.

In the problem of heterochromatic photometry, however the
distribution of the energy in the source of light must be known as
we need a definite radiation which we can reproduce at will
knowing its dependence on external conditions. We used for this
purpose a quartz-lamp with tungsten-ribbon in order to have a
source also suitable for the ultra-violet part of the spectrum. For
calibrating this lamp we used the Utrecht-method which gives
the true temperature of the lamp as a function of the current
used. To obtain the various steps of energy required to get a
series of density marks with a fixed temperature of the lamp, we
used the method of slit-widths -variation. We assume that the
energy thus active on the plate is proportional to the width of
the slit, provided the latter is not so narrow that diffraction-
effects occur. As will be explained further on, it is necessary to
use the same time of exposure for the calibration-spectra as for
the spectrum under investigation. Since for our experiments the
exposure time for the Ramanhnes was several hours we have
tried to find out a method for obtaining a set of density marks
in one single exposure. For this purpose we made use of a quot;step-
sHtquot;, first applied by Elliott (21).

This consists of six short slits of different widths which form a
geometric progression. The widths of these steps were determined
by direct measurements with a comparator. This step-slit was
placed immediately in front of the proper slit of the spectrograph,
which was opened as far as possible. This method has the same
advantages as that with the so-called step-reducers but without
the complication of being dependent on wavelength. Of course
care must be taken to prevent the light passing through the

^ep-sht from fillmg he lenses and the prism of the spectrograph
for then the proportion between the energies falling on the plate
would not be the same as that of the slit-widths.nbsp;^

It IS also of fundamental importance to have a homogeneous
distribution of light on the slit of the spectrograph. As L haVe
no used lenses during the exposures, this homogeneity is ei\'W
obtained by putting the tungsten-lamp at a relatively great dis-
tance from the sht of the spectrograph. Moreover, a distribution
at random was made of the widths over the step-slit in order to
detect irregularities of this kind or of those caused by other
circumstances such as sensitivity or treatment of the plate Since
we have investigated a rather large range of wavelengths one
series of cahbration spectra is, for two reasons, not sufficient
iMrst the sensitivity of the plate decreases with shorter wave-
engths, and secondly the energy of the lamp falls off very rapidlv
towards the region of shorter wavelengths. Generally speaking
a given set of density marks can therefore be used for one single

wavelength only, and for the whole range different sets must be
taken on the plate.

a.nbsp;T^ placing of a diaphragm in front of the constant light-
source. This way may be convenient for a narrow range of wave
lengths, but when an alteration is necessary within a wider range
the margin of the variation is not sufficient, especially considering
that when the opening of the diaphragm is too small, diffraction
effects may occur and, because of their dependence on wave-
length, may alter the distribution of energy.

b.nbsp;Variation of the distance between light source and slit of the
spectrograph. This arrangement has also the disadvantage of not
being apphcable over the wider ranges occurring in our experi-
ments. Moreover, the way in which the light fills the speJ^tro-
graph would be different for various distances if the same appa-
ratus is used.nbsp;^^

and marks as in both cases the light must fill the spectrograph in
the same way.nbsp;^

This method would be fundamentally wrong, although it has
often been applied by others. The reason for this may be traced
to a wrong interpretation of the facts published by v. d Held
and Baars (25) about parallelism of density-curves with varia-

don of exposure-time. Their experiments show that if the varia-
tion does not exceed a factor looo, the density-curves are paral-
lel. From this it is obvious that in homochromatic photometry
the exposure time may differ for spectrum and density marks
as this means only an additional factor for the energy in all
the measured lines which is not essential in making up their
ratio. For hetcrochromatic photometry the circumstances are
totally different. In the latter case not only the parallelism is of
great importance but also the question whether for different
wavelengths the curves are shifted to the same amount or not. It
can easily be seen that the shift is not determined by the same
factor for different wavelengths, if we assume, for instance, the
law of schwarzschild to bc valid. According to this law the
density D is given by the equation D = C E t^ ox Ig D = Ig C E
pi gt. The above mentioned facts are easily understood from
this formula: alteration off only enters into an additional term
and means a parallel shift of the curve which gives Z) as a
function of Ig E, the amount of the shift being pig [t^—t^.
The question whether this shift depends on wavelength is now
reduced to the dependence of the exponent p on wavelength.

As may be generally known, however, p varies fairly strongly
with wavelength. In order to illustrate this fact we have deter-
mined for a number of wavelengths the value of/) for a given
plate. These values have been obtained by drawing isochroma-
tcs (density curves for one definite wavelength) with different
cxposuretimcs; the factor of shifting gives at once a determina-
tion of the value of p using the formula of Schwarzschild as
given above. The results are given in the table VI and in figure 5.

These results will probably vary with the treatment of the
plate, certainly they do so when using other plates. It would
therefore be necessary to determine for each plate the values of
p by this method, which would be tedious work and moreover a
source of errors that had better be avoided. From these conside-
rations and experiments it is very clear that to obtain accurate
results the times of exposure for calibration-marks and spectrum

This expression gives the energies, with as a unit, as a
function of the product IT. This function may be drawn once
for all. In the case of a black body and various temperatures the
energy corresponding to a given wavelength is easily found by
multiplying the energy from the diagram by a factor proportional
to TK

Now in our lamps the ideal case of black-body-radiation is not
realized and some corrections must be applied to the energy
thus determined. This is usually done for the visible part of the
spectrum by introducing for each temperature of the lamp a
so-called colour temperature. This colour temperature represents
the true temperature of a black body to which the same distri-
bution of energy would correspond as the lamp actually possesses
at its true temperature. Up to the present time the possibility of
introducing a colour temperature for the ultra-violet has not
been tested experimentally, and anyhow it is certainly impossible
to render the whole range of the spectrum from the utra-violet
to the visible part by assuming a colour temperature.

Therefore we have used the true temperatures of the lamp, but
have also applied corrections for the emission of tungsten. This
emission coefficient e (k, T) is also a function of gt;1 and and its
value as a function of wavelength and temperature have been
measured by many physicists, the results being in good agreement
with each other. By multiplying the energies from the diagram
above mentioned by jsand by e{l,T) the distributions of energy
for all currents of the lamp and all wavelengths are known.
Finally, the usual correction for the varying dispersion of the
spectrograph must be taken into account. If we take this dis-
persion d to be Angstrom per millimeter, it is very clear that
the energies mentioned above must be multiplied by a factor
proportional to this dispersion. Summing up, we have thus for
the relative energy at a given wavelength active on the plate

The densities were measured with the Moll self-registering
microphotometer and so for each wavelength the relation bet-
ween energies and densities is known, and the energies as func-
tion of the wavelength as well. From the densities of the lines
given by these curves the relative energies of the lines were
deduced.

To check the entire method, especially the corrections which
have been applied as described above, we made several tests in
the following way. Isochromates were made, i.e. for two tempe-
ratures of the lamp the density curves are drawn, obtained from
the two corresponding sets of density marks at the same wave-
length. When all corrections have been carried out these two
curves ought to be identical. This check has given satisfactory
results in many cases.

Finally we must draw attention to the fact that it is not
necessary to carry out this work for all wavelengths occurring
in our measurements. It is sufficient to pick out a few wave-
lengths from the range to be examined, being careful as to where
the sensitivity of the photographic plate has an extreme value.
The curves obtained for these few wavelengths enable us to
draw diagrams representing the energy as a function of wave-
length for each density. The density curve for a given wave-
length may be easily found afterwards by interpolation from the
energy-wavelengths diagrams.

We have thus determined the relative energies of both the
mercury-lines and the Ramanlines.

a.nbsp;All mercury-lines have been measured by means of reflexion
on quartz. Therefore it is necessary to calculate the coefficients
of reflexion of amorphous quartz, which is easily done, using the
fresnel-formulce. The measured energies of the lines must be
divided by these coefficients. The values thus corrected represent
the relative energies of the lines as they fall on the investigation-
tube.

b.nbsp;For some of the mercury-lines a small correction must be
applied in order to account for the slight weakening by the
absorption of the light on its path from the wall of the
tube to the axis. As already mentioned, the shape of the
scattering volume of the substance is nearly cylindrical, the
diameter of it being a fraction of that of the tube. So in taking the
absorption-correction just mentioned, we have a sufficient mean
for the whole diameter. This correction amounts to only a few
per cents.

ed for the absorption of the scattered energy of each element of
volume, on its way from this element to the window of the tube.
To obtain these corrections we first remark that by our method
of investigation the whole scattering volume of the tube is ex-
posed to homogeneous radiation. The diffuse reflexion from the
reflector covered with magnesium-oxyde does not depend on
wavelength. And therefore we may assume that the distribution
of energy over the wavelengths is the same for each element of
volume of the tube, which is under irradiation and that for each
wavelength the incident energy is the same for each element of
volume Therefore the energy scattered by each element per unit
of incident energy is independent of the position of the element,
and depends only on the law of scattering, holdmg for the
particular wavelength considered.nbsp;, . ,

If we consider a unit of volume at distance x from the wmdow,
the intensity I of the light passing through the window wiU be
connected with the intensity /„ scattered per unit of volume by
the formula

/ = ƒ(, .10quot; {t — molecular coefficient
of extinction, c = concentration of the substance in mol/liter).
Thus, the relative energy h falling on the slit per unit of area
is given by

Therefore, the total amount of relative energy, scattered by
the whole volume is expressed by integrating the foregoing for-
mula over the axis of this volume. By dividing the energies
obtained for the Ramanlines by the value of this integral, the
influence of the absorption is eliminated. We have calculated the
integrals graphically.

As already mentioned, each of these hnes gave rise to one
strong Ramanline with a frequency-shift = 2832 cmquot;^
(wave-number) corresponding to an infra-red absorption band
near to 3.5 fx. The positions of the Ramanlines which we have
measured are therefore: 2733 A, 2866 A, 3152 A, 3239 A,

The corrected ratios for the energies of Ramanhnes and exciting
hnes are given m Table VII.nbsp;^

in oraer to make clear the meaning of these results we have
drawn the diagram reproduced in fig. 6. where Ig E has been

chosen as ordinate and Ig v^ as abscissa. For comparison a line is
drawn in the figure showing the function E = Cv);. The diagram
shows that for the first two or three lines the fourth power law
holds, but at shorter wavelengths, i.e. with greater frequencies
the ratio increases much more rapidly than according to the

fourth power of the frequency. Although in this case, too, the
values of v\'r and v do not differ very much, the position of the
first points of the diagram are decidedly in favour of the v^f.
We can hardly expect a still more convincing indication, for the
differences between vr and vng will always remain relatively
small.

We may, for this reason draw a conclusion which settles the
question left open in the foregoing chapter and state that:
in regions far from absorption frequencies the energy of a Raman-
line increases as the fourth power of its own frequency.

If we now consider the formula given by Placzek (20) it is
easily seen that qualitatively our results are in agreement with the
theory. To examine this agreement more closely in a quantitative
manner too, we assume that in the vicinity of one absorption-
frequency the above given formula is simplified to:

(va = absorption-frequency and C is a constant). It must be
mentioned however that this simplification involves a sharp
maximum of absorption which does not occur in the case of
methyl-alcohol and also that the other absorptions are remote
from this one.

Moreover, the formula is, properly speaking, deduced for
regions where absorption of the substance is absent.

We may assume for a moment the validity of the above ex-
pression, especially in the vicinity of the absorption-frequency
considered. It must be possible to determine an approximate
value of this absorption-frequency v« by computing the quotient
of two ratios {E) representing the scattered relative energies.

We have carried out this division for the ratios obtained for
the exciting lines 2537 A and 2652 A. We thus get the following
calculations:

Va being the only unknown quantity. We found in this way
v^ = 43.900 cmquot;\' or X« = 2280 A.

This result agrees satisfactorily with the position of an absorp-
tion-maximum of methyl-alcohol indicated by Henri (26) near

the wavelength 2200 Â. As no other absorption-maxima occur
in this region we must identify both frequencies and assume
that the transition giving rise to the Ramanline is connected
with this proper frequency of the substance. Now the absorption-
maximum just mentioned appears in the case of a great many
substances and has been ascribed by Henri to the group C-//which
these substances have in common.

We conclude, therefore, that the Ramanline under consi-
deration is characteristic for the group C-H. This fact has already
been shown in different ways by several writers (see e.g.
Venkateswaran and Karl (27)).

From these experiments an influence of the absorption-
frequencies is made very clearly. We may state that, generally
speaking, on approaching an absorption frequency of the sub-
stance, the scattered energy of a Ramanline, connected with the
same group of the molecule as the absorption process, increases
much more rapildy than according to a fourth power law.

In conclusion we draw attention to the fact that by our method
a decision is possible about the question to which group of a
molecule a Ramanhne must be ascribed when the absorption
spectrum of the substance is known and its frequencies have been
ascribed to certain groups of the molecule,

In the preceding chapters we have given the method and
results of our experiments concerning the dependence of the
scattered energy in Ramanspectra on frequency in two cases:

a.nbsp;working with six Ramanlines of which the frequencies
differ greatly from the absorption-frequency of the substance,

b.nbsp;working with one Ramanline of which the frequency is
close to the absorption-frequency of the substance.

To settle this question definitely we felt the necessity of exam-
ining the second problem once more, and this time with a sub-
stance in which each exciting line gives rise to two rather strong
Ramanlines with each exciting frequency, whereas the lines do
not belong to the same group of the molecule. For it was found

in Chapter III that the Hne influenced by the absorption must be
ascribed to the same group as the absorption process, and we
have to show that other lines, not related with this absorption
process do not undergo such an influence. Moreover a confirma-
tion will be obtained in this way for both cases because in the
investigation which we are now going to describe the two parts
of the problem are, to a certain extent, combined.

The substance used for these experiments was aceton (C H^
COCH) Its absorption has also been measured by Henri who
found a strong absorption in the near ultra-violet with a maxi-
mum near 2700 A. On one hand, therefore, the conditions of
working are more favorable than in the case of methyl-alcohol
because we can carry out the experiments for the greater part in
the visible region of the spectrum and in the near ultra-violet.
But on the other hand only a few exciting lines can be used
because of the relatively strong absorption which prevents going
belowthe wave-length 3650 A. The light of each of the mercury-
lines incident on the substance gives rise to two fairly strong
Ramanlines, the corresponding shifts being 795 and 2925 cm \'

The method followed in this research is exactly the same as
that described in Chapter III, the apparatus, too, being similar
Of course, in order to get an idea of the different behaviours of
the two lines, appearing with each exciting hne, it would be
sufficient to make up their ratio and then to see how it varies
with different frequencies. If the ratio is not constant it means
for our problem, that the influence of absorption differs with
each Ramanline. A more quantitative result however showing
the actual dependence for each line would not be obtainable on

The method ofphotometring the plates and the evaluation of
the densities has been the same as in the case of methyl-alcohol.
Only one detail has been altered. To avoid the tedious calcula-
tions necessary for combining the several sets of density marks
obtained by different currents of the quartz ribbon-lamp, we
have taken one set giving in only a few steps at each wave-
length of the whole range densities fit for use e.g. with longer
wavelengths the narrower steps, with shorter wavelengths the
wider ones must be used. In this way we have a few points at

each wavelength and we can combine these points in the way
described in the preceding chapter. In order to obtain the den-
sity curve passing through these points we have, moreover taken
a few sets of marks giving at each desired wavelength densities
enabling us to draw this curve. And thus the calibration of the
plate is carricd out completely.

Contrary to the case of methyl-alcohol the measurements on
aceton did not require corrections for absorption.

We could measure the Raman-lines excited by the following
mercurylines: group 3650 A (i.e. 3650 A, 3655 A and 3663 A),
4047 A and 4358 A. As the frequency-shifts are 795 cmquot;\' and
2925 cmquot;\' the Ramanlines appeared for the first shift near
3758 A, 3763 A, 3771 A 4180 A and 4514 A and for the second
shift near 4086 A, 4093 A, 4103 A, 4595 A and 4990 A. Making
up the ratio between the energies of a Ramanhne and its exci-
ting mercury-line we get the values given in table VIII and
table IX. For the sake of comparison the relative values of v^k
are added to the tables. It must be remarked that some of the
lines are in a very unfavorable position for the measurements
because of their overlapping with other lines, or because of their
being at a too short distance from mercury-lines. The results for
these lines not being reliable, they have been omitted:

We have given these results in the diagrams reproduced in
fig. 7 and fig. 8, in which the lines corresponding to v^^ have also
been drawn. We can gather from these diagrams that, in the
case of the frequency-shift 795 cmquot;\' the fourth power law holds,
but not with the other frequency-shift. Here with increasing

exciting frequency the energy increases much more rapidly than
according to a fourth power law. The different behaviours of
the two Ramanlines are shown very convincingly in these results.

We might try, as we did in the case of methyl-alcohol, to
determine the maximum of absorption indicated by the strong
increase of the energy. The circumstances are, however, very

unfavorable for this purpose. As already mentioned the ab-
sorption is very strong and prevents us from approaching
nearer than 3650 A. Now the position of the maximum as given
by Henri (26) is 2700 A and in the case of the exciting line
3650 A, too, we, are at a fairly great distance from the maximum,
whereas in the case of methyl-alcohol we could approach the
maximum to within about 350 A.

Yet we made an estimation of the influencing absorption
wavelength by proceeding in the same way as described in
Chapter HI.

From this we get the value v« = 35-500 cm-\' or L = 2820 A
As no other absorption-maximum has been found but the
one indicated by Henri in this region we must identify our

value with that given by him. This absorption has further been
ascribed to the group C-H of the molecule aceton just as the
Ramanline with a frequency-shift 2925 cmquot;\' is characteristic

The experiments just described confirm strongly the results
obtained in Chapters II and III and justify once more the laws
concerning the dependence of the scattered energy in Raman-
spectra on frequency there given.

Starting from the assumption of thermodynamical equilibrium
between radiation and matter a theoretical formula is derived
giving the ratio of intensities for the Stokes and Anti-Stokes
Ramanlines. This formula is:

The experimental determination of these ratios in the Raman-
spectrum of carbon tetrachloride is in good agreement with this
theory.

It is claimed that these measurements afford a new optical
method for the determination of A calculation from the

The dependence of the scattered energy in Ranaanspectra
on frequency is investigated. The experiments made with carbon
tetrachloride, methyl-alcohol and aceton show the existence of
two regularities in this dependence.

a.nbsp;When the exciting line lies in a region of the spectrum
remote from an absorption-frequency of the substance, the scatter-
ed energy of a Ramanline increases as the fourth power of the

b.nbsp;In the region of the spectrum near an absorption-frequency
of the substance the scattered energy of a Ramanline increases
much more rapidly than according to a fourth power of the

absorption-frequency, using a theoretical formula given by
Placzek (20). The value found is in fairly good agreement with
that given by Henri (26) which he obtained from absorption
measurements. Moreover the results confirm the theoretical
assumption, that the energy of a line is only influenced by an
absorption-frequency when connected with the same group of
the molecule as the absorption process itself.

11.nbsp;A. Dadieu and K. W. F. Kohlrausch: Phys. Zeitschr. 12 (1929)» 390-
12!nbsp;P. Daure: Compt. rend., 187 (1928), 826.

24.nbsp;G. Michel: Zs. f. Phys. 9 (1922), 285.
E. F. M. v. d. Held and B. Baars: Zs. f. Phys. 45 (1927). 364-

25-

26.

27.nbsp;.J. . _____________________________________- -

28.nbsp;I. R. Rao: Proc. Amsterdam 33 (1930)» 632 Nr. 6.

T (absolute)	exciting line 4047 A	exciting linc4358A	mean ratio	calcul. ratio
274°	3-1	2.9	3.0	3-1
300°	3.0	2.6	2.8	2.8
312°	2.55	2-5	2-5	2.65
323-5°	2.7	2.5	2.6	2-55
339-5°	2.4	2.6	2.5	2.45

T (absolute)	exciting line 4047 A	exciting line 4358 A	mean ratio	calcul, ratio
274° 300° 312° 323-5° 339-5° Fr	5-4 4-4 4.1 4.4 3-6 TA ■equency-shi	5-5 4.2 4-3 3-9 3-8 BLE III. ft: v,„„ = 4^	5-45 4-3 4.2 4-15 3-7 j6 cmquot;\'	5-1 4-4 4-15 3.95 3-7
T (absolute)	exciting line 4047 A	exciting line 4358 A	mean ratio	calcul, ratio
274° 300° 312° 323-5° 339-5°	11.9 9-0 7-4 7.0	12.0 9.0 8.1 7.0	11-95 9-35 7-75 7-0	10.8 8,8 8.1 7-5 6.8

	exp.		vie
24705 22938 18308 Fre(	100 72 32 ijuency-shift: v«„	100 74-3 30.2 = 312 (Stokes H	100 74.1 29.8 nes)
^Hg	exp.	vW
24705 22938 18308 Free	100 74 30 uency-shift: v,„„	100 74-3 30.2 = 456 (Stokes h	100 74.0 29.6 nes)
V««	exp.
24705 22938 18308 Frequer	100 73 31 TABI icy-shift: = :	100 74-3 30.2 .E V. 215 (Anti-Stokes	100 73-9 29.4 1 Hnes)
^Hg	exp.
24705 22938 Frequer	100 70 icy-shift: =	100 74-3 312 (Anti-Stoke	100 74-5 s lines)
^Hg.	exp.
24705 22938 Frequen	100 74 icy-shift: v«„ =	100 74-3 456 (Anti-Stokei	100 74.6 3 lines)
quot;^Hg	exp.	■^\'hs
24705 22938	100 75	100 74-3	100 74-7

Wavelength	2450 A	2532 A	2667 A	2850 A	3062 A
Value of p	.76	•77	.80	.88	.90

Wavelengtli of i?-line	2733 A	2866 A1 3152 A	3239 A	3305 A	3430 A
ratio (£)	17.0	10.0	3-4	2.6	2.4	2.0

_	_
30.	22.1
28.	21.9
14.	13-9
10.	10.