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 DINSDAG 21 OCTOBER 1930 DES
NAMIDDAGS TE 4 UUR

Het beëindigen van dit proefschrift geeft mij een welkome
gelegenheid mijn hartetijken dank te betuigen aan allen, die
tot mijn wetenschappelijke vorming hebben bijgedragen.
U, Hooggeleerde Heeren, Professoren in de Faculteit der
Wis- en Natuurkunde, dank ik voor het genoten onderwijs.
In het bijzonder echter gaat mijn dank uit naar U, Hoog-
geleerde Ornstein, Hooggeachte promotor, voor Uw immer
opwekkende leiding en steun bij mijn experimenteel werk op
Uw laboratorium.

De Nederlandsche eclips-commissie ben ik dankbaar voor de
gelegenheid die zij mij heeft geboden om aan de expeditie
naar Idi (Sumatra) deel te nemen. In het bijzonder ben ik
haar leden Dr. M. O. f. Minnaert en Dr. J. van der Bilt
erkentelijk voor hetgeen ik op zoó\'n prettige wijze van hen
heb geleerd.

Tenslotte een woord van oprechten dank aan Prof. Dr. A. F.
Holleman, die door toe te staan dat deze dissertatie als artikel
in de „Archives Néerlandaises\'\' werd opgenomen, mij een grooten
dienst heeft bewezen.

.H .K .aCInbsp;iXivviV \\\\\'iN\\Vjiu\\Q fttt\'i

; ■ ....nbsp;♦nbsp;a^^\'jwÀ V^nnùv

In most band spectra the intensities of the band lines regarded
as a function of the line-number suit to a continuous curve

Also, however, in some cases it has been found that every
other line is weaker or even missing.

As this alternation of intensity has only been observed in the
spectra of molecules formed by equal atoms, the explanation has
been sought in the symmetry of the molecule. It remained however
as also for the other resonance phenomena for the new quantum
mechanics to give a satisfactorily explanation of this fact (i)
Moreover as it was ascribed to a resonance in the atomic
nuclei, a new way for mvestigation of the nucleus was opened, (i)
One of the most interesting cases investigated is undoubtly the
alternation of intensities in nitrogen, and in this case the expec-
tation that the study of this phenomenon should lead to most
interesting conclusions on the structure of the atomic nucleus
seems to have been fulfilled.

From the intensity-measurements (2) the electron has been
found to lose its spin (3) in the atomic nucleus whereas from the
Raman effect (4) the non applicability of the principle of Pauli
in its ordinary form has become clear. (5)

With this deep difference between the properties of the electron
out and inside of the atomic nucleus it is doubtfull whether the
electron has to be regarded as a particle in the nucleus. (5)
But for a good understanding it may be desirable to explain

first briefly some properties of diatomic molecular spectrum
structure, as have been revelled during the last years by several
investigators. (6)

There is first the electronic energy due to the movement of
the electrons in the field of force of the nuclei, further there is
the vibrational energy of the nuclear masses and finally the
molecule considered as a top, can have an energy of rotation.

Of course there is no sharp division between these three com-
ponents possible, but if one neglects the mutual interactions, one
can get an approximate idea of the molecular energy-scheme by
superposing successively the energy of a molecule possessing only
one of these three energy-possibilities at a time.

On account of the axial symmetry of thefieldof force in which
the electrons are moving, their azimuth in a plane perpendicular
to the line joining the nuclei (the molecular axis) is a cyclic
variable, wich means that the electronic moment of momentum
A has a constant integral value along the axis.

There is a degeneration of first order in case Agt;o caused
bij the indefiniteness of the sense of rotation, which gives rise to-
the so called A type doubling if that degeneration is removed.

If the resultant spin S of the electrons differs from o, each
term with Agt;0 is split up into a multiplet by the different
possible orientations of the spin, whereas the multiplicity is, just
as in the case of atomic spectra, given by 25 i. These sublevels
are characterized by a number 0 where ÎA-5|lt;Ûlt;|A 5|.

The energy of the vibration of the nuclei is mainly that of the
harmonic oscillator, but it may be mentioned that if a change of
electronic state takes place at the same time as a vibrational
change, the selection principles of the harmonic oscillator do

As the subject of this chapter is not directly connected to the nitrogen
problem, no littérature is given here but the reader is referred to ref. 6. The
notation for the rotationallevels by n is adopted for obtaining the same
notation in both bandspectra. For the negative bandsystem n corresponds
to N in the usual notation (Faraday meeting) and for the positive bands to J.

not even approximately apply. So in the case of nitrogen the
bands corresponding to a o-o vibration transition are strongest.

Then there is the energy of a rotating rigid molecule, which, if
the electronic masses are neglected, becomes the problem of the
rigid rotator.

Also the component of jVin an arbitrary direction is constant
corresponding to a non-appearance of the azimuth 0 of the
rotator in the Schrodinger-equation. So the factor of the charac-
teristic functions, depending on cj) takes the formexp. ±\\im^\\gt;gt;
In the case of equal nuclei it is clear that by interchanging the
nuclei all coordinates are left unchanged except what passes
over into (Igt; ± Thus the characteristic functions are left un-
changed for n even and reversed in sign for odd n values (sym-
metrical or antisymmetrical in the nuclei respectively).
Thus the total energy of the molecule can be written as

The different lines of one band are caused by transitions from
rotational energy states to others, the electronic and vibrational
part for all initial levels being identical; the same is true for
the final levels.

In the case of the third positive nitrogen bands (7) (»ri-an)
electronic transition, (this designation means that A = i in both
initial and final state and the multiplicity is 3) and also in the
negative bands (8)nbsp;A = oin final and initial state,

6 = V2), only the transitions with A n = i i remain strongly pre-
sent, moreover in the positive bands il docs not change and
so the following schemes of the bands arc applicable, the arrows
indicating the strong transitions.

(arrow to the left: line of the R branch A;2=—i)
(arrow to the right: line of the P branch A;? = i)

1) In the ease of the negative bandsystem of nitrogen « = o, i, 2
l-or the third positive group n = 11,11 i, 11-[_ ...........gt; • • • •

Now the structure of the bands from which in fig. 2, at the end
of the article, there are given photometer traces is easily under-
stood.

Every level in the negative bands is degenerated, by the
influence of the electronic spin.

In the positive bands the A doubling causes a doubling of the
lines of the Ilo-lTo series (denoted as c series) and a broadening
of the ITi-lli lines {b series). In the llg-IIg lines (a series) the
effect is undetectable.

In the negative bands for «gt;0 the degeneracy caused by the
two orientations of the electronic spin is removed and so every

For convenience the old notation is beheld. The designation of the
lines is that given by Zeit (ref. 7).

level splits up into two, so that for large quantum numbers the
hnes appear as double. The plate from which the photometer
trace in fig. 2 has been taken was photographed with too low
resolving power to show this doubling.

The characteristic function of the molecule in the limiting
case of neghgeable interaction can be written as a product of
factors, depending on the electronic coordinates referred to the
fixed nuclei (including the electronic spin) and of the coordinates
ot the nuclei due to the vibration and rotation.

The electronic factor is either symmetricai in the nuclei
JN) or antisymmetrical in the nuclei [An N) if A = o but if
A gt; o from the two sublevels one is Sjgt; N, the other An N (q)

The function dealing with the nuclear vibration is always
N, as only the distance of the nuclei comes into it The
symmetry of the rotational part, however, has already been
discussed before, and the subsequent functions corresponding
to n = 0,1,2 etc. arc alternately Sy N and An N. The trans-
lation of the molecule has been ncglected till here. Its charac-
teristic function is always SjN.

The total characteristic function thus is ^ N or N according
to the even or odd number of An N factors figuring in it

If there is a coupling between the different motions in ihc
molecule, the separation of the characteristic functions into
factors IS impossible, but the symmetry properties remain
unaffected. Now the o and x signs in the fig. i can be under-
stood. The X mean Sjgt; N, the o An N terms.

With these considerations on the symmetry properties the
phenomenon of alternating intensities can be understood For
If according to the extended Pauli principle only the functions
which are antisymmetrical in both electrons inclusive nuclear
electrons and protons correspond to actually existing states
in the case of equal nuclei containing an odd number of particles
(electrons -f protons) all Sjgt; N terms do not occur and so the

It is the case if there arc no other coordinates than its space-
coordinates required for defining the nucleus.

Biit if the nucleus possesses a spin, a formerly forbidden state
{^y N) can be transformed in a permitted one by the mutual
orientation of the nuclear spins. Then this state docs appear

Generally speaking with a nuclear spin oim units, the weights
of the different Sy N and An N spin-orientations are in the ratio

orientations of the spins which give resultants of 2W2, 2wz - i, 2m - 2,
.... i, o, units. Of these, the states am-^k [k integral number)
are Sjgt; N, the others An N. Because of the statistical weight of
2 {2m - 2k) I for the spin 2m - 2k, the sum of the weights for
the Sy N states is 2m^ -j- 3m i and that for the An N states

From the Kramers-Heisenberg dispersion formula governing
the intensities in the light scattered by atoms or molecules it
follows that only the frequency-difference of two energy-levels,
which both combine with a third, appear as Raman-frequency.

So in the application to diatomic molecules only the combi-
nation-frequencies with Aw =-- o or i: 2 occur in the Raman-Hght
if the transitions between the rotational-levels are governed
by the combination rule An = ±1.

Actually in the Raman-effect in Nitrogen, the lines resulting
from a 2-0, 3-1, etc. and from a 0-2, 1-3 etc. transition have
been found. The lines corresponding to An = o transitions,
however, have been blurred by the exciting line.

Also in these Raman-lines the alternating intensities have been
found, although no attempt was made for measuring the ratio.

The lines due to a transition between levels of even rotational
number have been found more intense.

This indicates that also without regard to the nuclear spin
the characteristic functions for these states arc antisymmetrical
in all particles.

If one assumes a nucleus as built up from protons and electrons
(i.e. they may form a: particles), then the nitrogen-nucleus with

its atomic weight 14 and atomic number 7 must contain 14
protons and 7 electrons, that is an odd number of particles.

Therefore the states corresponding to N functions N
neglecting the nuclear spin!) should be less frequent.

Moreover if it is possible for a system of electrons and protons
to form a nucleus by an adiabatic transformation, upon which
assumption the foregoing rules of symmetry and antisymmetry
in the particles are based, the total spin of the nucleus should
be formed by addition and subtraction of the individual spins
for the free particles. As the protonic and the electronic spins

integral amount of nuclear spin. But the measurements in the
negative and positive band spectra of nitrogen indicate the
integral value one for the nuclear spin (3). Besides in the Raman-
effect in nitrogen it has been found that the rotational levels in
which n is even arc more frequent.

As there seems to be no doubt that the ground level of jVg is
Sjgt; N, this result is also not in agreement with the simple point
of view which considers the jV nuclcus as formed by an odd
number of particles. (5)

The hypothesis has been made that the electron loses its
spin and its influence on the statistics of the nucleus. In fact this
hypothesis explains both discrepancies in this case.

On the other hand, however, there seems to be an indication
that the «electrons in the nuclei of the atoms of atomic weight
4 / (/ = 1,2....) are grouped in shells containing an even
number of them, which may mean that the Pauli-principle docs
apply and that also the spin remains for the nuclear electrons.(10)
Consequently general conclusions cannot yet be drawn and
further experimental research is wanted. In the following a
critical discussion and extension of the intensity measurements
is given.

of Nitrogen, due. to the Ng molecule and also in the third positive
group, which is emitted by the neutral JV« molcculc.

In the cases where the number of protons is odd, a half-integral nuclear
spin-value has been found.

Of the negative bands the following four have been measured:
3914, 3884, 4278, 4237 A corresponding to vibrational transitions-
o - o, i - i, o - i and i - 2. Of the positive bands: 3371, 3805
and 3755 have been investigated (vibr. trans o - o, o - 1,0-2).
(fig- 2.)

In both cases, the light source was a hollow cathode of sheet
nickel about i cm high, 2 cm deep and 0,1 to 0,3 cm broad; the
dimensions varying from tube to tube. A nickel plate mounted
together with the cathode on a lamp-bridge at a distance of about
0,5 cm, served for anode. This apparatus was sealed into a glass
sphere of 15 cm diameter provided with a tube, 20 cm long,
bearing a (if necessary quartz) window at its end.

When filled with nitrogen at a pressure of about a millimetre
and put on high voltage (500-1000 V), a strong light appears
only in the inner part of the hollow cathode. If the current is
strong (50 to lOomA) the cathode comes to a red or even yellow
heat. The small dimensions of the radiating gas layer and its
enclosure by a metallic box are very favorable for securing a
^constant temperature throughout, which is of importance for
the intensity-distribution in the bands. For as the intensity-
distribution over the lines in a band depends on the relative
concentrations of the upper rotational-levels, (which concen-
trations in turn are determined by the temperature of the gas),
only in the case of a radiating gasmass of uniform temperature,
a simple intensity-distribution in a band can be expected. (11)

The nitrogen used, was produced by heating sodium-azidc in
vacuo. The spectrograph used was the 6 M grating of this institute,
of which a description is given elsewhere. (12) Generally a
slit-width of 0,003 ~ 0,004 cm was used for the bandspcctra-
photographs. Also two plates of band 3914 A have been made
with 0,007 and 0,009 cm sUt-width to see if variation of the slit-
width did alter the results. For the objection could be made to
the way by which the density marks have been taken, that it
gives the density curve for broad lines, as the density marks were
about 0,008 cm broad (see below).

As the results of the bands taken with the wider sliths were in
good agreement with the others, such an effect seems not to
have occurred.

The density marks have been taken in the usual way with an
incandescent lamp burning on constant voltage and a small
prism spectrograph (glass or quartz as was necessary), in which

the slit-width has been varied in several (12 or 10) steps. Before
use this slit has bf^en tested under a measuring microscope. Also as
a check density marks have been put by using a mercury arc on
constant current and placing reducers before the slit of the grat-
ing. As is mostly the case in working with reducers, the points,
giving the density-curve, spread more, due to the inhomogene-
ities in the reducersteps, but systematic effect were not detected.
The difficulties met in finding rehable reducers, especially for
the ultraviolet region were the reason for taking the density
marks by the method of slith-width variation.

The great difficulty in taking density-marks is in most cases
due to the stray fight. By the use of a very short slit of only 0,008
cm height this stray light has been removed to a large extent.
Moreover by a diaphragm behind in the spectrograph the
scattered light from one exposure was kept away from the other
density marks.

In the case of the ultraviolet bands 3805, 3755, 3371, also a
nickeloxide glass has been put before the slit of the spectrograph
to filter out the intense visible spectrum of the quartz band
lamp, what also is a source of stray light.

With these precautions the stray light is rcduccd in any case
too much below i % of the intensity in the spectral region used.

There was generally a difference in time of exposure between
the band spectra and the density marks. In a research on its
influence on the density curve, carricd out in this institute, the
maximum time differences arc determinated for which the
results are not affected. (13) Care has been taken that these limits
were not exceeded. Also for the strong 3914 A band in the first
order an exposure has been made with the same time as used for
the density marks, from which plate quite similar results as
from the others were obtained.

Bands and density marks have been taken on Ilford special
Rapid H and D 400 plates from the same box, as it was impossible •
to put them on the same plate on account of the small dimen-
sions (9-6 cm) of the plates to be used in the prism spectograph.

In the beginning the plates of size 12-9 cm have been cut into
two and on one half the band-exposure, on the other the density-
marks have been taken. Control experiments have shown how-
ever that in our case no greater scattering in the density-intensity
relation appears for plates from the same box than is obtained
from a single plate. Therefore furtheron, for the plates exposed

at the same time only once density-marks have been taken. Also
for p\'.ates from different boxes but treated in the same way, the
density curves were fairly parallel to another.

All plates (band spectra photographs in different orders of the
grating and density marks) have been put together on a glass
strip and fixed on it by rubber bands, so that intense shaking
during the development process (8 min. in 5 % Rodinal at
18° G.) was possible without fear for an overlapping of the plates.
It is essential for avoiding disturbing developments-effects that
the developer should be kept into incessant vehement motion,
and if this is done one can get rid of them to a large extent. Also
several times two plates with density marks were taken and fixed
at different stages on the glass plate. They showed no systematic
difference in their density-curve.

Especially in the case of the positive Batnds these development
effects are very disturbing, for the lines to be compared lie close
to one another (distance about 0,004 cm).

It may be mentioned that the development effect (Eberhard
effect) is probably due to partial fluctuations in the concentration
of the liquid, so that near a strong line the concentration is
lower. This causes a dependance of the density-intensity relation
on the density in the neighbourhood, which especially in the case
of an analysis, where the intensities in regions with a large
density-gradient is sought, gives rise to great errors. In the peak
of a line this gradient equals zero and so one might suppose a
smaller influence of these effects in peak-intensity measurements,
what has been checked experimentally in this institute.

For recognising the presence of such developer effects directly,
the plates of the band 3371 on which the most accurate measure-
ments have been made (it was the only band which could be
taken in the 4th order of our grating), were developped a longer
time, 9 or even 10 min., than the others, till a strong chemical
fog appeared. The Eberhard effect, if there is any, then shows
itself by clearing up of the fog near a strong line. At last plates
could be obtained what showed no trace of such an effect.

After the development the plates were washed for several
minutes and then fixed in a solution of Sodium hyposulfite.

After drying, the plates were photometred with the Moll-
microphotometer of this institute. Whereas an analysis of the
curves was necessary, much care was given to obtain correct
focussing of the instrument. The instrument was used therefore

with a primary sht of 0,025 cm and a sht-width varying from
0,0025 cm to 0,0050 cm on the thermopile. A narrower slit
decreased the measuring accuracy, in causing a too small galva-
nometer deflection, whereas a much wider one (0,008 cm) was
not narrow enough with respect to the linewidth. These values
were found experimentally, as the same line-doublet was taken
several times with different slit-widths.

No longer distance than about 2 cm on the plate was taken in
one run, after which the plate was refocussed.

The overlapping of the different parts taken in several runs
gave a good check on the adjustment of the instrument.

Immediately before and after each run zero-marks were taken
and also an unexposed part of the plate close to the measured
lines, was photometred on the same part of the registration. By
doing thus any inconstancy of the photometer-lamp could be
taken into account and also local fluctuation on the plate could
be detected and if so, corrected for.

Especially in the case of small densities, an exact knowledge
of the galvanometer deflection for the unexposed plate is
neccssary. Different relations between the distances on the plate
and registration on the drum have been used. The registrations
were developped with Hydroquinonc A - B or Metolhydroqui-
none. If an analysis was aimed at, the registration was enlarged
by means of an epidiascope, if not they were measured dircctly
with a glass scale.

Negative Bands. In -1 - bands the lines possess a fine structure
so that for large quantum numbers, they appear as doublets of

nearly equal intense components. Nearer to the origin there are
theoretically three components (except for the first P and R
branch lines which are really double), and also the intensity of
the components should differ greatly; but the fine structure is
so narrow that for lines below n — lo, even in the third order of
our grating no sphtting up could be detected. From the intensity
measurements there are, however, indications that for the lines
near the origin the structure is more complicated (seepage 15).

For the purposes of this research, only the total intensity of
the line, (without regarding its fine structure) was needed, so
that the densities of the plate had only to be reduced to intensities
and the intensity-curve of each fine integrated by means of a
planimeter. Whereas the fine structure pattern becomes wider
with the quantum number, the shape of the line alters and there-
fore it is incorrect to use the density of the peak as a measure for
the total intensity.

But the reduction of a line into intensities means a deter-
mination of the intensity of about fifty points, so that it is a
lasting work to measure one band containing about forty or
even more lines, which could be measured with accuracy.
Therefore a way has been chosen by which it was possible to
use the peakdensities, so that only one reading was necessary
for a knowledge of the intensity of the line.

From some lines of the band, the surface of the intensity curve
and also the topdensity was determined and their ratio taken.

Both values are in a quite arbitrary unit, depending on the
density of the densitymarks and on the position of the planimeter
arm, so that for each plate the ratio should differ. Therefore in
the case of no overlapping of the intensity curves in the top of
the line (wide spaced doublet) this ratio was taken to unity and
the values were reduced in proportion. Thus this value of surface
intensity divided by peak intensity goes towards 0,50 with
narrowing of the fine structure.

Then the values got from the chosen lines were plotted in a
diagram with this ratio on the j-axis while on the x-axis the
number of the bandlines were plotted.

As an example a reproduction of such a diagram is given for
the band 3914 Â taken in the second order. The lines analysed
were in this case the numbers 16, 17, 18, 21, 22 of the R branch.

It can be seen from the figure that for lines of higher quantum
number than 23 no correction in the peak intensity had to be

carried out whereas for all numbers lower than 14 the peak-
intensity had to be multiplied by 0,50. For the lines of the third
order exposures these numbers were 22 and 3 respectively. Now
from the curve drawn through these points the surface intensity
could be found by multiplication of the intensity in the top of
the line by the ratio corresponding to its number.

In this way the analysis of all lines (about forty) was made
superfluous. Moreover the same curve could be used for other

plates taken with the same focussing of the grating, so that no
analysis was necessary at all for later plates.

Of course a check was made. So in one case the 3914 A Band
photographed in the third order, was worked out fully in both
ways by drawing the intensity-curves and planimetring them
and also in the way described before.

If the procedure is correct, the intensities got in these two ways
should have a constant ratio throughout the whole band. (They
do not give the same value because of the arbitrariness in the
value mentioned before). That this was the case can be seen
from fig. 5, wherein the crosses represent the values got from
direct planimetring and the circles those from peakdensities.

The exact parallelism of the two straight lines shows the correct-
ness of the procedure.

In this way for the third and second order a reducing curve
has been drawn, but for the first order the topdensity could be
used without any correction for a sufficiently large number of
lines (about 25 or 30).

carried out. By analysing the intensity-curve for the widely
separated doublets into its components, the curve of a line pos-
sessing no fine-structure was obtained. Then an attempt was
made to account for the experimentally found ratio of surface-
and peakintensity by assuming that the actually line was built
up from two equal intense components, whose distance varied
with their quantum number n.

In this manner the distance of the components could be
measured. For the high numbers n gt; lo this distance was a

s ,L /s ID Llf U 31 J6 VP
Fig. 6. Showing doublet-distance as a function of line number.

linear function of n in concordance with theorie, but for n =
7,6,43, the doublets width seemed to become quite irregular,
what should indicate for an unequal intensity of the components!

In fig. 6 the distance of the doubletcompoenets is plotted on
the axis of T against on the Aquot;-axis, the number of the fine.

In total there have been worked out from band 3914 A
2 third-, 2 second- and 2 firstorder plates; from band 3884 A 2,
from 4278 and 4237 A i plate, all taken in the first order.

The intensity of a spectrumline is proportional to a product
of two factors sc. the radiationchance from the upper to the

lower level (where from boths their statistical weights have to
be taken into account) and the concentration of the upper level.
In this case the former factor is proportional to n for both the
wth P as well as the nth R line, understanding under a line the
total complex of fine structure components.

If one suspects that the latter factor can be described with a
Maxwell-Boltzmann distribution function, the following graphical
representation of the measurements seems to be preferable.

On the axis of T the logarithms of the line intensity divided
by n are plotted against the rotational energy of the upper level.

The nth /2-line corresponds to a transition from the nth rota-
tional energystate to the (n - i)th; the nth P-line to a transition
from the (n-i)th to the nth (see fig. i).

(P-line) one should obtain a straight line if there is a
Maxwellian-distribution among the upper rotational levels i.e.
if the concentration of the nth state is proportional to

the absolute temperature. In fig. 7 results of the four measured
bands are given.The bands4237 and 4278 were takenin one expo-
sure. They show the same slope indicating that the distnbuUon
temperature was the same in both. In the 4278 band, the lines
of lower number were too intense for accurate measurement.
Several further lines have been measured; they fall however out of
the figure to the right side. As the slopes of the lines are equal to

The calculation of the temperature from the slopes of the hnes
using the value 1.34.10-39 for / gave temperatures varying from

1) As professor Ornstein remarked to me, perhaps the inertia moment
of the lower level should be taken, this depending on the rules for excitation
by electron-impact. This should alter the temperature of the distribution
bij about 0,5 % but it does not affect the straightness of the lines at all.

The alternating intensities give rise to two straight lines for
each band whose distance along the T axis give the ratio of the
statistical weights of the consecutive rotational states.

Of these the value of the 3914 Â band is the most accurate,
due to the great number of lines which could be measured in
one band (to 35 or even more) and to the absence of disturbance
of its lines.

Only in the third order for one line a shght correction had to
be carried out for a ghost fallen on it.

The lines of 4278 are also free from overlapping, but the
relatively weak 3884 and 4237 bands are severely disturbed
by the 3914 and 4278 bands, so that only a few lines could be
measured with accuracy.

It is of interest to see whether this value depends on the
excitation conditions or pressure. A research for such an
effect has been carried out for the 3914 A band.

Instead of using a hollow cathode the nitrogen was excited
in an ordinary discharge tube containing a glow-cathode and
anode (distance from another about 0,5 cm). The tube was
connected to a pump-installation, for it was necessary to have
a continuous supply of nitrogen in the case of the two lowest
pressures.

Commercial nitrogen gas was used, supplied by a steel cyliiider
and the gas was passed without extra purifying through a capilla-
ry tube into a space which could be connected to the low vacuum
of the oil pump. This space was joined to the discharge-tube
by another capillary tube.

By varying the pressure at the begin of the cappillary, the
pressure in the discharge-tube could be kept sufficiently constant

1) The real temperature was estimated from the colour of the glowing
cathode. Also the tube has been put in a furnace at 300° C. That raised
the distribution temperature from 650° C. to 1000° C. The uncertainty
in the calculated temperature is of about 30quot;^ or less.

at any value in the region 0,005 to 0,10 mm. The lower pressures
were measured with a kenometre (von Reden), the lowest also
with a Mac-Leod gauge; the two higher pressures were measured
with a manometre.

These instruments were placed as near to the dischargetube
as was possible, whereas a short wide capillary tube (dimensions
2 cm long, 0,5 cm diameter) was sealed between the kenometre
and the pumps. In the exposure at the lowest pressure a liquid
air trap was placed between tube and mercury pump.

in the first order of the grating at pressures of 0,003, 0,05, 18
and 30 mm. The first value is correct at 50 % only, the second
at about 20 %, the other two are more accurate. In the latter
two cases the tube was not connected to the pump-installation.

Thus the pressure has been varied in a ratio i to 10000 whereas
at the same time the discharge-conditions also have been varied.
No alterance of the 2,0 : i value could however be perceived.
The results obtained from the four exposures are at 0,003 mm :
1,9:1, at 0,05 mm : 1,95 : i, at 18 mm : 2,0 : i, at 30 mm : 2,0 : i.
The first ratio is less accurate on account of the weakness

of the photograph so that the densities felt in an unfavourable
part of the density-curve.

In fig. 8 the curves are reproduced. In the curves corresponding
to 18 and 30 mm there are lacking some points; these have been
omitted because they were too strong for accurate measurement
or also in one curve because the plate was stained there.

The temperatures calculated from the slopes of the lines were
380, 680, 870 and 870° abs. respectively. These values give
strong support to the idea, that it is the real gastemperature,
which determines the distribution of the energy among the
rotational-levels.

In case of the lowest pressure the light-phenomenon was
extended over the whole tube, whereas in the other three
exposures it was bounded to a region more or less close to the
electrodes. The temperature of the gas far from the electrodes
being undoubtedly much lower than that of the electrodes them-
selves (glaswall of the tube at 0,003 about 50° C.),a smaller
value of the distribution temperature should be expected in
that case, in accordance with the experiment.

In the third order of our grating the bands 3805 Â, 3755 A,
and 3771 Â have been photographed. They showed the fine
structure of the ITq - Hq branch as described in the first chapter.
A broadening of the lli-lIi lines was visible from the registrations
for the lines of high quantum numbers, whereas the Ha-Ilj lines
appeared quite narrow. The different behaviour of these three
multiplet component bands has been explained by theory.

In particular the relatively wide fine structure of the IIq levels,
which is independent of the rotation has been explained by the
fact that the sublevels pass over into a P^ and P^. level, if the
axiality of the molecular field of force is removed. The great
number of lines occurring in one band and the narrowness of
the fine structure (0,025 quot; 05030 causes great difficulties in
the intensity measurement.

Whereas the top of the weaker components was not undis-
turbed, the intensity-curve of the doublet had to be analysed in
any case. On account of the strong overlapping, the disturbance
by ghosts and other lines and the unequal intensities of the
components, which causes difficulty in finding the true distance

of the doublet-components in the registration, the reached
accuracy was not great. The intensity-ratio of the components
found from planimetring and from the peakintensity of the
analysed components, differed mainly 30 % and in several
cases even 50 % or more.

The intensity- ratio taken from the surface measurements
were systematically higher than those from peakdensities.

At first this errors were ascribed to development effects, but
also when the plate was certainly free from such effects in
showing no clearing of the plate, close to strong lines after a
long development, the same discrepancies occurred and so
these great errors must be e.xplaincd by the supposition of several
small ones due to the causes mentioned above.

If the maximum and therefore also the one side of the weaker
component Were undisturbed by the stronger one, the procedure
of doublet analysis is much more accuratc, for no uncertainty
occurs in finding the distance of the components. Also there are
two undisturbed slopes of the doublet-curvc so that the analysis
can be carried out from two different sides. Therefore it was
recommendablc to go to a higher order.

But only for the band 3371 A a photograph in the fourth order
was possible, the other bands in this order falHng too near to
the grating. In this order, the maximum of the weaker com-
ponent in fact is undisturbed as an analysis of five doublets
showed. In this analysis the lines of the a series served for
determining the shape of a single line.

On the other hand, the ghosts arc more intense and also there
was a strong continuous background throughout the whole
band. In the third order of the positive bands such a background
also occurs but relatively much less intense.

But at this background varies slowly in the band, it (jannot
greatly affect the measurements in one doublet although it
mights cause systematic errors in the determination of the
intensity-ratio of two different doublets.

First it has been shown that this background was due to light
of the same frequency as that of the band, as its structure
already leads one to suspect, for the ground has its maximum near
the head of the band and decreases slowly towards both sides.

By photographing the line 3341 A of the mercury spectrum,
while keeping away the visible light and the resonance line by
a nickel-oxide glass combined with a nitroso-dimethyl-anihne-

gelatine filter, it was shown that its background was really of the
same wavelength as the line.

Beyond a certain distance from the line the ground was found
to decrease almost linearly towards zero.

From this plate also the intensities of the ghost were deter-
mined. In procents of the intensity of the main line the following

values were obtained:
14% for the ist ghost, 5%
for the 2nd, 3% for the
3rd, 8% for the 4th
whereas the following
ghosts were less than 3%.
_ But once stated that

to substract the intensity
of the background from the total intensity of line together with
ground, for obtaining the real intensity of the line.

That correction has been carried out in this way, that the whole
continuous ground between Û25 ^^^d «33 was plotted as a function
of the wave-length and its mean was taken by drawing a straight
line through the points.

Commonly the correction for a ground is made by substraction
its value close to the fines from the total intensity.

For this procedure the assumption has to be made that the
background under the line does not differ appreciably from
that close near.

But this assumption is not correct in our case for there arc
strong variations in the intensity due to the at random-dis-
tribution of the ghosts.

For example it is visible from the fig. 3 that it should be quite
incorrect to subtract the value of the ground at the right side
of the doublet. In any case the mean value over a large extended
part has to be taken. This was done in the described manner.
The straight fine was drawn also with regard to further points
and other plates.

Then by measuring the plate under the comparator and also
from the wavelengths measurements, the lines which had to be
corrected for ghosts were determined.

As the intensity-ratio for mean Hne and ghost has been deter-
mined before, the intensity curve of the line reduced in this
ratio could be substituted on the spot, where the ghost was

2.8

2.7

2.6

2.4

2.3®

2.2

2.0

■-30

quot;31

\'•32

•■33

-34

expected. Then the intensity which feel under the maxima of
the doublet components was corrected.

The latter correction was only a slight one, whereas that
for the continuous background could reach a value up to 40 %
of the weaker component.

From these measurements a mean value of 2,11 for plate i
and of 1,93 for plate 2 for the intensity-ratio of the components
is obtained. These both values allow the value 2,0 found for
the negative bands within the limits of accuracy, but exclude
the values 1,7 and 3,0.

In both band systems the same value of the intensity-ratio
thus has been found, although in the latter case the accuracy
is not so great as in the former.

A research for hyperfinc structure in the atomic spectrum,,
has also been carricd out but, without success. (14) The lines

in the spectrum of jV corresponding to the - (15). They
did not appear in the hollow cathode discharge but were strongly
present in a condensed spark. Unfortunately, in this light source
they appeared broadened. By lowering the pressure to io~\' mm
and varying the discharge conditions (series spark-length, capacity
and self-induction), it was possible to get them much more
narrow, but even in the most favourable conditions used, they
possessed a half-width of 0,03 A in the third order of the grating.
In this order the grating possesses a resolving-power of nearly
240.000, which is not very large for hyperfine structure research.

The intensities of the ghosts were: 14% 5% 3% 8% for the four
first ghosts respectively; the following were less than 3% of the the chief line.

It is worth to notice that, if one omits the two outfalling values of
Cgg in plate i and Cgg in plate 2, one gets 2,05 and 2,02 for the mean value
of the ratio.

but for these unfavourable wave lengths there was no higher
resolving-power available.

On the registration a slight broadening towards the longer
wavelengths was observed in the density-curve. It is, however,
possible that this is an ordinairy spark-broadening.

As the hyperfine structure of these lines, if present, should
be probably due to that of the ^S level, only from the intensities
of the components (and not from their number) the amount
of nuclear spin could have been determined.

Therefore at the same time a research was undertaken to see
wether the intensity-measurements do agree with the other
criteria (Multiplicity and Zeeman effect) for asigning a definite
value to the nuclear spin.

The line choscn for this research was the resonance line of
Thallium at 3776 A emitted by the transitionnbsp;(15).

This line shows a hypcrfme structure of three components
and from this structure, together with the Zeeman effect a
nuclear spin of | has been assigned to the nucleus. (14)

The lightsourcc in this case was a 440 FPfund-arc with coppcr
electrodes, on the cathode of which pieces of Icad-Thallium-
alloy were placed. (16)

In the third order of the grating all three components were
sufficiently resolved. In the first order the line appeared as
a doublet.

The theoretical intensities calculatcd on the basis of a spin i
for the three components are i : 2,0 : i respectively and for
the doublet components in the first order i : 3,0.

The results showed that even in the case of an alloy containing
only io~5part of Thallium^) and an arc-current ofonly 0,5 Amp.
there must have occurred a strong self-absorption. The intensities
found from both, peak and surface measurement, were as

The thallium poorer alloys have been made by diluting an alloy with
its ten or hundredfold weight of spectroscopically thallium free lead. The
new alloy was then assumed to contain a lo-\' or i osmaller concentration
of thallium.

The self-absorption did not manifest itself in the shape of the intensity-
curves, which was the same for all components.

for a third order photograph. The intensity-ratio for the doublet
components in this case was i : 2,80.

It appears thus that the theoretical intensity-ratio is really
reached in the limit for very low concentration.

But the most interesting point of this research is that even in
exceedingly small concentrations there is a strong self-absorption.
Since in many cases the hyperfine structure is caused by the
ground-level (alkalies), great care has to be taken in drawing
conclusions as to the nuclear spin from the intensity-ratio of the
components and repeated measurements with varied concen-
tration or (and) current density seem to be unavoidable.

Intensity-measurements carried out on the green Thallium
line 5350 Â {^S^Ps) confirm the results got from the ultra-
violet Une.

In the second order of our grating the green line shows a
doublet fine structure arising from the splitting of the S level.

Theoretically with a spin | of the Tl. nucleus the intensity
ratio should be 3,0 : i, whereas the value 2,7 has been found
experimentally.

As for this measurement an alloy containing parts of Tl.
has been used, this result indicates also a much less selfab-
sorption for the green line as compared to the ultraviolet line.

This should be expected on account of the fact that the latter
(3775nbsp;the resonance line.

For the photographic intensity measurement of an undis-
turbed narrow line, having a density in a not too unfavourable
range of the density-curve, the mean error is about 8 %. Of
course this value refers only to the kind of plates and develop-
ment-process used in this research.

So for the fines of the band 3914 Â of the negative system the
mean error can be set at this value. This makes a probable
error of 2 % for a band measurement consisting of thirty lines.

Here a table is given for the results from the registrograms of
the band 3914, all containing at least thirty lines so that the
weight for all values is the same.

In total taking the mean for all bands the probable error in
the intensity-ratio comes out to about i %.

Of course there must be assumed that the errors occurring
in the single results are quite unsystematical.

But the excellent concordance of the results taken from first,
second and third-order exposure, which also showed the same
temperature for the rotational levels, gives strong support for
the correctness of that assumption. So in every case from com-
paration of the different values for the single plates, the accuracy
(probable error) of 2 % seems to be reached.

For the other bands the accuracy is less. The band at 4278 A
is also undisturbed but as the plate was over-exposed, only
10 fines were easily measurable.

As the results from it, both, in regard to the distribution tem-
perature and to the ratio of stronger and weaker lines, did
agree with that of the 3914 A, it was thought that no new
exposure was necessary. So the accuracy for that band is 4 %

The bands 3884 and 4237 arc strongly disturbed which rcflccts
itself in the larger spreading of the points.

Also the errors seem to be not quite unsystcmatical 1) for in
both measurements of 3884 the ratio alters rom about 1,8 to
2,0 through the band. It is then difficult to give a taxation of
the mean error, but if one takes the mean of the divergencies
of the points, one finds about 12 % in this case for a single
measurement. With this value the accuracy rcachcd, is cal-
culated to about 7 % for the 3884 band and 12 % for the
4237 band.

1) The overlapping of the strong 3914 or 4278 band is more serious
for the lines of lower quantumnumber.

For the plates taken in the fourth order of the 3371 band the
mean divergence from he mean value is of about 7 0/ for plate
one and 10 % for plate two, which should give an accuracy of
the same order as in the 3914 Â band of about 3 %

But on account of the strong corrections carried out, one can
iccl fear for systematic errors, although there are no indications
tor them m comparing the results of the two plates, whereas
also no systematic discrepancy between surface- and top-
mtensity was observed. On the other hand if the mean of the
continuous ground on the photogram was taken, the ratio for
plate one comes out to 1,94.

Now there is no doubt that this latter method of correction
where the mean value over the density instead of over the
intensity has been taken, is not the right one but this demon-
strates the great systematic influence of the corrections on
the result.

In any case the mean value of the plates never had been
found to excced the range 1,90 - 2,11, so that in each case it
seems highly improbable that the true value should lie out of
this interval.

For the Thallium measurements the mean error is 8 %.
As the theoretical values for the relative intensities of the two

2 : 4; 3 : • • • • there is no doubt that of the theoretical values
only that for a spin f comes into account, although the value
of i : 3,0 was not reached on account of the strong self-absorption

After an introduction the essential features of bandspectrum
structure, including Raman effect, as far as necessary for an
understanding of the following pages are exposed (page
to ). The difliculties in the interpretation of the experimental
data are dealt with (page 006 to 006).

The essential points of the experimental methods are given-
of the discharge tube (p. 008), of the photographic data
(p. 009 to 010), of the photometring of the plates (p. 010). The
reduction of the measurements giving a value 2,0 for the ratio
of alternating intensities of the negative bands 3914 3884
4278 4237 A IS explained (p. 010 to 018). A Maxwell-Boltzmann
distribution among the rotational levels has been found A
description of the arrangement for a research on band 3914

under varying pressure is given where no alterance of the ratio
has been found, (p. oi8 to 020).nbsp;°

In the band 3371 of the third positiv group the same value
was found, (p. 020 to 024).

Measurements caried out on the thalliumline 3776 indicate
a strong self-absorption, but notwithstanding the intensities seem
to confirm the value | for the nuclear spin p 025

The accuracy is discussed in p. 026 to 028. For the valuetaken
trom one plate of band 3914 Ä a probable error of 2 % is found
I he mean ratio taken from six plates is 2,03^. For the other
. negative bands the accuracy is 40/^ to 8%. In the band qq7i
the ratio lies in the range 1,90 to 2,10. The thalHum measure-
ments arc affected with a probable error of 6 %.

2.nbsp;Ornstein u. v. WlJK, Zt. f. Ph. 49, 315, 1028.
v. WlJK, Zt. f. Ph. 59, 313, 1930.

4.nbsp;Rasetti, Proc. Nat. Acad. Sc. 15, 515, 1929
Rasetti, Zt. f. Ph. 61, 598, 1930.

6.nbsp;Several papers on band spectrum structure have appeared A brief
expose containing a littcraturc list is e.g. given by Hund in the Er^eb
nisse d. exacten Naturwissenschaften» band 8. For Raman eSti
diatomic molccules see Manneback, Zt. f. Ph. 62 22^ inon

7.nbsp;Zeit, Zt. f. Wiss. Phot. 21, i, 1921.nbsp;^^
Lindau, Zt. f. Ph. 26, 343, ,924; 30, 187, ,924.
HuLTHEN U. JoHANNSON, Zt. f. Ph. 26, 308, IQ24

9.nbsp;Mulliken in the discussion of the Faraday society, September 1929 gives
a theoretical and experimental survey of the alternating intensity da^
His notation of Sy N and An JV is used herenbsp;\'niensity data.

14.nbsp;For the intensities in hyperfine structure see
Fermi, Zt. f. Ph. 60, 320, 1930

for collection of data and interpretation of Tl. fine structure
16. Vonwiller, Phys. Rev. 35, 802, 1930.

iïn;;ii .uü iil ..nbsp;j. -i •;■•••{lüT.r. ■•.\'ir -fbri»;«i -»vrj/.y/»/!

t .u .j::fU\'lnbsp;«lil \'h\' 7 )•;■](.quot;- \'nbsp;■ ;■ \' \'-\'iK-iï.\':. /;\' \' -

Terecht meent K. T. Compton, dat de ionisatie van het gas
tusschen de electroden van een electrischen lichtboog over-
wegend van thermischen oorsprong is.

De beperking dat ccn volume clement vele moleculen moet
bevatten, zooals in de leerboeken der kinetische gastheorie
wordt vooropgesteld, is in dc meeste gevallen overbodig.

Bovendien geeft de daarop berustende wijze van behandeling
der gaswetten aanleiding tot misverstand.

De bewering van Tamm dat de behandeling volgens het
correspondentie principe van de incohaercnte lichtverstrooiing
niet tot ondubbelzinnige resultaten voert is onjuist.

De waarde die Jenkins cn Harvey voor het kernmoment
van Lithium (3/2) opgeven is vermoedelijk te groot.

De door hen gebruikte methode van intensitcitsmcting is in
het algemeen niet van toepassing op een absorptie spectrum.

Bij voorkeur zou men liypcrfijnstructuur onderzoekingen in
een bandenspectrum moeten verrichten.

Zeer ten nadecle van de practischc bruikbaarheid hebben de
meeste medewerkers aan het ,,Handbuch der Physikquot; en het
„Handbuch der Experimentalphysikquot; het idee „leerboekquot;
vooropgesteld.

Tegen de hypothese van Rosenthal over den oorsprong der
coronalijncn zijn nog andere bezwaren dan dc door hem zelf
genoemde aan te voeren.

Bertrands bezwaar tegen de oorspronkelijke afleiding van
de Maxwellsche wet der snelheidsverdeeling berust op mis-
verstand.

De afwijzende houding, die in de Physica tegen door sommatie
van niet convergente reeksen verkregen resultaten wordt aan-
genomen is niet gerechtvaardigd.

In het lemma I § 619 bladz. 545-546 Goursat III 1923
zouden de woorden „ainsi que sa dérivéequot; beter achterwege
gelaten kunnen worden.

Line	Uncorrected Intensity	Mean of Bcakground	disturbing ghosts	Corrected Intensity	Ratio-
^25	1 41-6 } \\ 24-3 i	6.5	I c\'28 ^quot;28	( 34.6 I ( \'7.8 ^	1-94
^26			strongly disturbed
	i 34-4 ) \\ 18.4 i	6.0	IV c\'29	.( 25.8 ) ( 12.4 i	2.09
	j 33-5 /	5-9	I 27\'\' 27 II 2a\'\'\'\'26	i 2.50 (	2.03
^28	( 18.3 \\	III b,.	1 12.3 i
^20	i 25.5 j i 14-0 (	5-7	IV	\\ \'9-8 I } 7.5 j	2.64
	i 26.5 i	5-4		i 21.I I
	1 16.2 )	III fl33	\'( 10.0 j	2.11
	i 24.0 }	5-2		\\ 18.8 (	\'•95
•lt;^31	\'1 14-8 i		1 9.6 j
	\\ 22.7 1 1 12.0 \\	5.0	IV ^29	! \'5.91 \\ 7-0 )	2.25
^33	i 20.8 ) ) 12.0 j	4-5	I	1 14.3 } \\ 7-5 j	1-94
^34	i 19-3 I i quot;.3 ^	4.0		i gt;5.3 / \\ 7.3 j	2.10

Order of the grating	Ratio
i	2.09
i	1.98
2	2.03
2	1.96
3	2.05
3	2.10

II1............. .....
I I I \'J s	to	IS	h ahanchj
IIIIIM . -
			P B\'H.ylNCH	j9»y a
II111 M 1 1 11 1 1 1 1 1 1
u li jo	J5		P B\'ranch

	ex. t tmcs	-1 1 1 1 \' M 1 1 1	L-P-J-
		1 1 1 1 1 1 1 1 1	1 1 1 1
jjr/ A	i SEKiCS		J5
	C jrSHlBg	-i-LI 1 1 1 1 1 1 ii JO	-MrJ-J-

1	\\	1	I	1	1	1
	£ji	a. 3/	C Jo	tJO	a JO	- ,



. ,■■ -,	f.\' ■







m-:	\'l/r: quot;j