- . ; v:\' -,. ,v v^;^-. \'^f.;• - :. V.\' \'
; ^. ij V- -. i; \'■ \' ■ ■ ■ - •

.... ..... .....- . ■ ..- , .......

■r.k.\'i

■■if.

TER VERKRIJGING VAN DEN GRAAD VAN DOCTOR
IN DE WIS- EN NATUURKUNDE AAN DE RIJKS-
UNIVERSITEIT TE UTRECHT OP GEZAG VAN DEN
RECTOR-MAGNIFICUS
Jhr. Dr. B. C. DE SAVORNIN LOHMAN
HOOGLEERAAR IN DE FACULTEIT DER
RECHTSGELEERDHEID VOLGENS BESLUIT VAN
DEN SENAAT DER UNIVERSITEIT TEGEN DE BE-
DENKINGEN VAN DE FACULTEIT DER WIS- EN
NATUURKUNDE TE VERDEDIGEN OP MAANDAG 17
NOVEMBER 1930 DES NAMIDDAGS TE 4 UUR DOOR,
ARTHUR ELLIOTT
GEBOREN TE CLEADON

BO {/3 syskm, O-^z)

o
ogt;

A.U.

II ii ji

li t! I

P
R

bloU

B,.o

Plate I — Above, 0—2 band of BO in arc.
Below, Photometric Registration of 2—6 band of BO excited by Active Nitrogen.

vi.quot;.-.

The writer has received so much help and kindness during
the course of two years in Utrecht that it would be impossible
to thank everyone separately; there are, however, several to whom
he is especially indebted, and he takes this opportunity of thank-
ing them.

Professor Ornstein, in particular, has been most kind in
giving his valuable assistance at all times, and in placing the
facilities of his laboratory at his disposal. His friendly interest
in matters othet than those directly concerned with scientific
work have been greatly appreciated.

To Dr. Burger, Dr. van Cittert and Dr. Minnaert the writer
wishes to express his thanks for help on problems which arose
at various stages, and to Mr. Willemse he is greatly indebted
for assistance in the solution of technical difficulties experienced
from time to time.

Finally, he wishes to thank the society 5- for the many
enjoyable and instructive outings in which he participated, and
which formed a pleasant feature of the social life of the labo-
ratory.

Chapter II — The Isotope Effect in the Band Spectrum of
Chlorine, and the Determination of the Nuclear Spin of CI

Chapter IV — The Relative Abundance of the Isotopes of
. Boron, as determined by Intensity Measurements.

m\'- \'-.I--

e?/

The possibilty that elements of identical chemical properties
may have different atomic weights was first revealed in the
domain of the radio-active elements. Somewhat later, observat-
ions by Sir J. J. Thomson showed that the positive rays of neon
were not homogeneous, and behaved as if they consisted of a
mixture of particles of masses 20 and 22 times that of the
hydrogen positive ray.

Subsequent researches of Aston with the mass spectrograph
have shown that very many of the elements are not homogeneous,
but consist of two or more constituents of different mass; the
name quot;isotopesquot; has been given to these constituents. All
attempts to separate isotopes chemically have failed; they appear
to have identical chemical properties. Physical methods, such
as diffusion (where the difference in mass gives rise to a
difference in the rate of diffusion) have succeeded in partially
separating isotopes in a very few cases, but the separation
achieved is very small. Isotopes are interpreted as atoms in which
the net nuclear charges (and for neutral atoms, the sum of the
€xtra-nuclear electronic charges) are identical. Since the masses
differ, we must suppose that the nucleus of one isotope contains
more protons than the other, and that the extra protonic charges
are neutralized by the same number of electrons in the nucleus.

Much interest has centred around the spectra of isotopes, and
much work has been done with a view to establishing the
«xistance of an quot;isotope effectquot; in spectra. In what follows, a
brief summary of the results hitherto achieved is given.

Several investigations have been carried out in an endeavour
to quot;find a difference between the atomic spectra of isotopes

(see (1) for referances), but only in the elements lithium, neon,,
lead and thallium has anything been observed which may be
attributed to an isotope effect.

The first to find a definite displacement of a line when diffe-
rent isotopes of the same element were investigated appears to
have been Aronberg, (2) who found that the wavelength of the

The displacement, though small, is however many times that
required by the theory, assuming that the effect may be cal-
culated in the same way as in ionized helium, and has not yet
been accounted for.

The resonance line of lithium ( A = 6708 A.U.) has frequently
been examined for an isotope, and indeed a weak companion has
been found on the long wave-length side by Schüler and
Wurm (3).

This is attributed by them to an isotope effect, and it is
suggested that the observed companion is the weak component
of the Li6 doublet.

In the case of neon, more extensive observations and measure-
ments have been made. All the lines which have an s-term as
the ground term have been found to possess a faint satellite,
and Hansen (4) has pointed out that the separation is not
greatly different from what would Be expected if the satellite
were due to Ne^z.

Further observations have been carried out by Nagaoka and
Mishima (5) and by Thomas and Evans (6).

The former workers showed that every strong line in the
yellow and red portions of the spectrum of a neon tube (cooled
in liquid air to reduce the width of the lines) shows the faint
companion, and further that the separation is nearly constant
for lines of the same series, and a little greater than is required
by Bohr\'s formula (7). They also examined the Zeeman effect
of the lines, and found that the same effect is shown by the
strong lines and satellites. The separations of the satellites
have also been measured by Thomas and Evans, and similar
values arrived at. The expected intensity ratio is-9 : \'1, and

On the whole, the evidence for attributing the satellites to
Ne22 appears to be very satisfactory.

Since isotopes have identical extra-nuclear structure, and
only differ in nuclear mass and perhaps also in nuclear spin,
we should naturally expect to find more evidence of an isotope
effect in those spectra where the properties of the nucleus
play an important rôle in determining the spectral terms and
intensities. Consequently, since in molecular spectra the rota-
tional and vibrational energy of the nuclei determine the fine
structure and spacing of the bands as a whole, respectively,
-comparatively large effects may be looked for. An isotope effect
due to the electronic transition may be expected to be of the
same order of magnitude as in atomic spectra, and can be left
out of consideration.

The theory of the isotope separations in band spectra was
■developed for vibration-rotation bands by Loomis (8) and
Kratzer (9).

MulHken (10) has worked out the theory of isotopic separat-
ions for electronic bands very fully, and most of the later work
has been based on his paper. Further contributions have been
made by Gibson (H), Patkowski and Curtis (12) and Birge (13).

Since we are concerned chiefly with intensities rather than
-energy separations in the isotope effect, only the results of the
theory of isotopic separations will be indicated briefly. If the

which is called the quot;reducedquot; or quot;effective massquot;, enters into
the formulae for rotational and vibrational energy. If now one
of the atoms of the molecule has isotopes, for the molecule
containing the isotope we have a different value of the effective
mass.

We may suppose that the molecule of effective mass /t is the
more abundant; this will be referred to as the quot;,main moleculequot;,
and the other molecule will be called quot;the isotopequot;. The

constants of the latter molecule will be indicated by the super-
script i above the various symbols. If the vibrational energy
levels (expressed in wave-numbers) for the main molecule be
represented by

It may be seen from these equations that the vibrational
isotope effect causes a separation of the band origins of main
molecule and isotope; the separation, at least for low values of
v\' and vquot;, increases with increasing distance from the origin
of the system (i.e. the point at which the change in vibrational
energy is zero). For higher values of v\' and vquot;, this is no longer
true and the individual cases must be worked out.

The rotational effect causes a similar, though generally
smaller separation of the lines, also increasing with increasing
distance from the band origin (i.e. the position where the change
in rotational energy is zero).

When vibration and rotation states change simultaneously,
as is generally the case, the separation for the isotope is of

■course obtained by adding the vibrational to the rotational
.separation. If there are more than two isotopes, then we may
expect as many components of the band lines as there are
isotopes.

The first evidence of the isotope effect was found by Loomis
•lt;8) and by Kratzer (9) in Ime\'s data on the infra-red spectrum
of HCl. Then followed several investigations of Mulliken (33),
(14) amp; (15) in which the effect was found and measured in boron,
copper and silicon in the spectra of BO, CuBr. Cu CI and SiN.

Since the discovery of the effect in these spectra, much work
has been done with a view to extending our knowledge of
isotopy, and important results have been obtained.

Summaries of the results achieved up to the year 1929 are
to be found in refs. (16) amp; (17). Up to that time, only corrobora-
tions of Aston\'s results had been obtained, but still more recent
^ork has resulted in the discovery of four isotopes hitherto
unknown, viz. 0quot;,nbsp;C\'^ and N\'\'^ existing in very small

quantities relatively to the main isotope. (An isotope of chlo-
rine (mass 39) has also been reported (see p.)

Having now briefly considered the isotope effect, we proceed
to a consideration of the relative intensities of the spectral lines
of isotopes.

The intensity of a spectrum line is governed by the number of
emitters in the initial state, and by the probability of transition
between the levels concerned.

Since the energy states of isotopic molecules never differ
very greatly, it is clear that differences in intensities of isotopic
lines will be chiefly due to the relative abundance of their
respective molecules. It is, however, of interest to consider to
what extent the mass may affect the above two factors, apart
from the relative abundance of the isotopes.

tion (under particular conditions), may be expressed as a funct-
ion of the vibrational energy. These various properties will in
general have different values for the same quantum state in
isotopic molecules, and it is required to determine these values
for the isotopes. In order to do this, we make the assumption
that the various properties under consideration are the same
functions of the vibrational energy for the isotopes. This is a
very reasonable assumption, since the potential energy functions
of isotopic molecules are almost certainly identical. The energy
states which are allowed by the quantum conditions are, however,
different for the isotopes, and these must be used in deriving
the values of the required quantities from the relation which
expresses these quantities as a function of the vibrational
energy. In other words, if we plot each of the various quanti-
ties against the vibrational energy for one isotope, then the
values of these quantities for other isotopes are given directly
by inserting the appropriate vibrational energy values in the
graph.

We will first take the case of zero rotation, and consider
vibrational transitions within an electronic band system.

Where temperature equilibrium holds, the numbers of mole-
cules in the different levels are proportional to the Boltzmann
\'Ev

stant and T z= the absolute temperature).
If p be the transition probability, the intensity of a band ¹) is

1nbsp; Strictly speaking, in order to derive the number of emitters from
the number of molecules, the statistical weight of the levels should be
considered; this Is probably constant with respect to the vibrational Quan-
tum number, however, and hence docs not effect our problem.

In bands observed in high temperature sources, (arc bands,
for example) it is unlikely that the exponential factor will
ever differ appreciably from unity. In bands at low tempera-
tures, the factor may have considerable influence on the inten-
sity ratio, however. It does not appear to have been considered
hitherto, but as the results of Chapter II show, it is not so small
as might at first sight be expected.

If thermal equilibrium does not exist, then the distribution
of energy states does not follow the Boltzmann law, but may
be supposed to be a function of the vibrational energy; we
suppose that the same function holds for different isotopes. If
this is so, then

depends upon the form of the function, and on the values of E
and EJ, , Particularly in the case of excitation by active nitro-
gen, it appears that this factor may have a decided influence
on the intensity ratio, and the results on the intensity ratio of
the isotopes in the spectrum of BO, (chap. IV), may be consult-
ed in support of this.

The possibility of p depending on the nuclear mass must
nom be considered. At first sight this does not appear probable,
but it must be remembered that the transition probability is a
function of the energy of the levels involved.

a Vquot; progression (i.e. with v\' constant) are plotted against vquot;
(fig. (6), p. 48.

In general, as predicted by Condon\'s theory (21), we should,
expect two maximum values of the intensity; since all tran-
sitions are from the same level, the ordinates are proportional
to the transition probabilities p. We may again assume that
this curve would be the same for both isotopes if they both had
identical upper levels. The values of p would then be given by
the ordinates at the appropriate values of the vibrational energy,,
as shown by the full and dotted vertical lines, representing,
existing states of the two isotopes. It is evident that at large
values of vquot; and when on a steep part of the curve, the values
of p for the isotopes may differ appreciably. We have, however,,
assumed that the two isotopes have identical upper states, but
these differ also. If we can draw a whole quot;famillyquot; of transition
probability curves, one for each of the various upper states for
one isotope, we can form an idea of how the curve depends on
the vibrational energy in the upper state. Again assuming that
the transition probabilities are the same functions of the twO\'
isotopes (but that the energies of existing states are different)
we can insert the appropriate energy values and so arrive at
the curves giving the transition probabilities from each of the
upper states to the various lower states, for the other isotope.
Inserting in these curves the appropriate energy values, we
obtain the transition probabilities for the isotope. Whether the
values of p differ appreciably for the two isotopes depends on
the energy separation and on the form of the p-E^ curves, and
it is impossible to draw general conclusions. An example is
provided in chap. IV where the case of the BO bands is worked
out. The experimental results, however, do not support the
above theory, as will appear later.

With regard to the distribution of the molecules over different
rotation states, the same considerations apply here as in the
vibrational energy states, and the different energies of two
isotopes will cause a difference in concentration, this being

again given (when temperature equilibrium holds) by the Boltz-
mann factor (see equation (7). Here, however, the energy diffe-
rences are in general smaller than those for vibrational energy,
and the effect is probably always negligible. When temperature
equilibrium does not hold, a small difference may be expected,
but this is not likely to be appreciable. The bands of boron
monoxide, where the energy differences for the two isotopes
are relatively great, should provide a suitable case for revealing
the effect, if it exists, but as will be shown in chap. IV, no such
effect has been found.

The transition probabilities for a particular rotational tran-
sition are proportional to the larger of the two rotation quantum
numbers involved (22), consequently no difference for the two
isotopes is to be expected.

From the foregoing, it will be seen that the measurement of
the intensity ratios of isotopic bands may be expected to give
a reliable and exact value of the relative abundance of isotopes,
when the necessary corrections are applied. It seemed, how-
ever highly desirable to test the method first on elements
where only two isotopes exist in appreciable quantity, so that
a comparison with the isotope ratio calculated from the atomic
weight might be made. Measurements were first made on the
absorption band spectrum of chlorine, but that spectrum is too
complicated to be suited for exact intensity measurements, and
further measurements on the spectrum of boron monoxide were
made. These experiments will now be described.

The isotope effect in the band spectrum of Chlorine, and the
determination of the nuclear spin of C135

Chlorine, like its related elements bromine and iodine, pos-
sesses an absorption spectrum which is characterized by many
thousands of lines grouped into bands, followed on the short
wave-length side by a wide region of continuous absorption.
The vibrational structure has been analysed by Kuhn (23) and
Nakamura (24).

The bands consist of P and R branches, as was shown by the
rotational analysis carried out by the writer (25), and have
generally been attributed to anbsp;transition. Recently, how-

ever, Mulliken (26) has pointed out that the upper state cannot
be and that the transition involved is probably ^IJ\'fr

Since chlorine has isotopes 35 and 37 (1), three molecules
must exist viz. 0135-35^nbsp;andnbsp;In his earlier work

on the chlorine isotopes, Aston (1) found a faint line
in the position corresponding to mass 39. Later investigations
made him consider that this could not be ascribed to
chlorine, and that an isotope Cl^s could not be present in
appreciable quantity. Recently, however, Becker (27) has found
a third component of the band lines of the vibration-rotation
band of HCl, and this is ascribed to an isotope of chlorine, of
mass 39. Should this be correct, the relative abundances given
below may require a small correction; the isotope Cl-^^ can only
be present in very small quantities, however, and can hardly
affect the figures seriously.

Taking the atomic weight of chlorine as 35.457 and the masses
of the chlorine atoms (correcting for O^^ and O^^) as 34.980 and
36.976, the ratio C|35 : Ciquot; is 3.185 : 1. The molecules Cl^^-^s^
(];i35 37^ and Cl^^\'®^ must therefore occur in the proportions
10.144 : 6.370 : 1 respectively. The vibrational isotope effect
in this case will cause a tripling of all the bands in the system,
the separations being given by inserting the appropriate value
of the coefficient ^ in equation (5) p. (12). For the two mole-

The bands due to Cl^s-^s^ which are the strongest, are easily
observed, and have been analysed for the 1-11, 1-12, 1-13, 2-6,
2-7, 2-8 and 2,12 vibrational transitions (25). These bands show
the phenomenon of alternating intensities, as is to be expected
in a molecule with equal nuclei (28) and (29).

In the case of the 1-12, 2-6 and 2-12 bands, the weaker bands
due to the molecule Cl^s^^ have been identified and measured;
here the nuclei are no longer identical, and no alternation in
intensity results, again in accordance with theory. A search
for the bands of Cl^^-^^ (which must be very weak) was made,
but without success. It would be of very great interest to
carry out intensity measurements in these bands, since alter-
nating intensities are again to be expected here. The measure-
ment of the alternating intensity ratio enables the nuclear
spin to be determined, and if it could be carried out for the
two symmetrical chlorine molecules, a comparison of nuclear
spins for the isotopes could be made. The complication of the
spectrum has hitherto prevented this from being done, how-
ever, and the nuclear spin has only been determined for the
more abundant isotope. The determination of this quantity, and
of the intensity ratio of the molecules Cl^s-^s and C135-37 will
now be described.

The chlorine absorption bands were photographed in the
first and second orders of a 6m. grating, with an absorbing
column up to 9m. in length. As a continuous source, the posi-
tive pole of a carbon arc was employed.

In all the intensity measurements, the usual method employed
at Utrecht (30) has been used, and from the photographic
densities (measured from the microphotometer record), the
corresponding intensities were found from a calibration curve.
The latter was obtained from a plate developed simultane-
ously with the chlorine plate, on which spectra of a tungsten
lamp were photographed; the intensity of these spectra was
varied in a known manner by means of \'\'step reducersquot;, and

the densities corresponding to these intensities (at the required
wave-length) were measured. From these, a density-intensity
curve was drawn, one for each band; this was desirable since
the form of the calibration curve alters somewhat with wave-
length, though within one band it was sufficiently constant.
The absorption coefficients for the centres of the lines were
then calculated.

frequency v in the usual absorption formula I = Iq 6 ^
and the determination of the absolute intensities would involve
the integration of ay over the whole breadth of the line, for
every line. Since the determination of the absolute intensities
was not the chief object of this work, the integration has not
been carried out for these lines, and the maximum value of
ay i.e. the coefficient of absorption for the centre of the line,
has been determined.

If all the lines measured were of the same shape, then it is
clear that the ratio of intensities of two lines 1 and 2 would

aimax)! jaimax)» and no error could be introduced by employing
the latter. There is no reason for thinking that the shape of
single band lines will alter, at least within one band, and the
different shapes of the lines which appear on the photometer
curves must be chiefly due to blending with other lines. Now
the integrated absorption coefficient would be at least as
much in error as the central absorption coefficients on this
account, and might conceivably be even more disturbed than
the latter, which has consequently been employed as a measure
of the intensity.

In all absorption measurements, the finite resolution of the
spectrograph and the width of the slit cause the absorption

lines to appear less deep than they are in reality. So far as
relative measurements are concerned, this would not matter
if all the lines were of the same shape, but the lines as actually
observed differ somewhat in this respect.

To determine the correction for each line would have neces-
sitated very great labour, but the influence on the intensity
relations could be investigated as follows. The band 1 —gt; 12
(which on account of its strength could be observed with a
single tube and consequently did not require very long
exposures) was photographed in the first order with the slit
width employed throughout this work (namely 0.02 mm.) and
also with a slit width 0.04 mm., and in the second order with
slits of 0.03 and 0.04 mm. The intensities of seven of the
narrowest lines were then measuered from these four plates.
Although the absolute intensities varied considerably, the
values of the intensity ratio for strong and weak lines only
differed from the mean by -4.5, 0, -2, and 1 % for the slit widths
0.04 mm. (first order), 0.02 mm. (second order), 0.04 mm.
(second order), and 0.03 mm. (second order). These results
indicate that the true ratio may perhaps be somewhat larger
than the measured one, but it is also possible that the differen-
ces are accidental. Since the lines on which these test measure-
ments were made are narrower than most of the lines whose
intensities have been measured, the effect (if real) will in
general be smaller than that above, and has been neglected in
the final result for the intensity ratio.

The differences in the absolute absorption coefficients are
irregular and much greater, being even as large as 100%. This
is not in the direction which would be expected if it were
due to the finite resolution of the spectroscope, and is pro-
bably due to developer effects, which are known to occur when
there is a steep density gradient on a photographic plate, as
in narrow absorption lines.

The average value of the lines in one branch having odd J —
values has been compared with that of the even J lines in the

same branch, for the 1-)-11, 1-gt;12, 1 ^ 13, 2-gt; 7, 2-gt;-8, and 2-)-12
bands. This is equivalent to finding the ratio of intensity of
a strong line to that of the mean of the two adjacent lines;
since the intensity of the chlorine band lines does not vary
quickly with J, this procedure does not introduce any appreci-
able error. The results are given in Table I. The mean of the
ratio for the P and R branches for each band is fairly consist-
ent, A weighted mean value for all the bands has been taken,
in which the value for each band has been weighted according
to its closeness to the mean. This final value for the ratio of
the alternating intensities (1,36 : 1), has been derived from
more than 170 lines, and may therefore be considered fairly
reliable; the mean error calculated from the divergence of the
individual values for each band from the mean is 0,057.

By taking an average over a very large number of lines in
this way, one can to a considerable extent get rid of the errors
due to blending i,e, to the fact that the lines are overlaid by
other lines. But even if a sufficient number of lines has been
taken to ensure that, on the average, the same intensity of
overlying lines has been added to both strong and weak lines,
the measured ratio of these latter will still be in error, and will
be smaller than the true ratio by an unknown amount. Con-
sequently the figure 1,36 must be regarded as a lower limit.
It appears exceedingly probable that the true ratio is not
greatly in excess of this, since even if the average intensity
of the overlying lines amounted to 20% of the intensity of
the weaker lines, the ratio would then only be raised
to 1,45 : 1, and this estimate of the intensity of the
overlying lines is probably too high. In view of these
considerations, it is likely that the true ratio is very
close to 1.4 : 1, which is the theoretical one corresponding to a
nuclear spin of 5/2, and the latter is therefore taken as the
most probable value for this quantity. The fact that an odd
number of units of spin is found is in agreement with the fact
that C135-35 has an odd number of nuclear particles (18 35).

(a) Alternating Intensities (ratio of intensity of strong to
weak lines in Cl^s ^s).

Band

P branch

Mean

1—11
1 — 12
1 — 13
2— 7
2— 8
2—12

1.25
1.40
1.38
1.35
1.40
1.34

1.43
1.49
1.62

Weighted Mean 1.36
(b) Isotopes (ratio of intensity and abundance of CI 36-35 to
CI 35-37 ^.

The intensities of CI 35-35 and CI 35-37 have been compared by
taking the average ratio (over the lines having the same J-
values) for the bands 1—12, 2—6 and 2—12 (see Table I).

In order now to arrive at the real relative abundance of the
two molecules, we must first correct for the effect of the
Boltzmann factor. Inserting the appropriate quantities in equn.
(8) p. ( 5 ) for the initial states of the bands, we find the values
K-E,

order to find the real abundance ratio of the molecules. As
Table I shows, this is an important correction to the ratio,
amounting in the case of the vibration state vquot; = 2 to 9%.

In order to determine the correction due to the difference
in transition probability for the two isotopes, extensive in-
tensity measurements of the bands would be necessary. It can
be said, however, that the correction on this account is likely
to be very small, since the intensity of the bands in a progres-
sion does not vary quickly with vibrational quantum number;
this is revealed by an inspection of the spectrum. We may
therefore take the average abundance ratio for the three bands
viz. 1.46. This is again a lower limit. The same assumption as
to the amount of overlying lines would raise the figure to 1.58.
This is in excellent agreement with the value calculated from
the atomic weight viz. 1.59. The experimental error, as evidenc-
ed by the deviations of the values for the three bands, is how-
ever rather great, and the assumed 20% for the overlying
lines quite arbitrary. It is difficult to assess the magnitude
of the probable error, but it must be certainly less than 20%.

No evidence is found of a disagreement between the abun-
dance ratio of the isotopes determined by band spectrum
measurements and calculated from the atomic weight, provided
that the former is corrected for the effect of the different
energies of the isotopes on the Boltzmann factor. The suggest-
ion, made by the writer in (25) b, that the molecule CI 35-37
had a greater absorption coefficient than CI 35-35 account
of its asymmetry (see (18) c,), is consequently not supported
by the interpretation here given.

Two molecular spectra of boron are known, both of which
are attributed to the oxides. The one consists of diffuse,
headless bands, which even under high dispersion show no
structure; it is emitted by a bunsen flame or a carbon arc
supplied with boric acid, and is usually attributed to the mole-
cule B2O3. The writer has also observed it very strongly
developed in a discharge tube containing boron trichloride
with an excess of oxygen, with an uncondensed discharge.

The other spectrum consists of bands which have the struc-
ture found in diatomic molecules, and was probably first
observed by Ciamiacian in the spark spectrum of boron
fluoride. It also occurs in the arc with boric acid on the poles,
and has been observed by Hagenbach and Konen, and Kuhne
(see references (32)_(35) for literature).

A further source of the bands was discovered in 1913 by
Lord Rayleigh, who observed that a greenish blue colour is
developed when the vapour of boron trichloride is led into
active nitrogen. The spectrum was examined by Jevons (32),
who measured the wave-lengths of the band heads, and showed

6371 Â.U., and from 2141 A.U. to 3496 Â.U., which he design-
ated a and ß respectively. The a system consists of bands
of complicated structure, with double-double heads, though
the structure of the system itself is fairly simple. In the ß
system, the reverse is the case, and the bands are single-headed,
but form a rather complicated system. In addition to the main
bands of this latter system, he found two weaker systems,
which he designated ß^ and ß^ respectively. As he remarks,
these subsidiary systems are not entirely indépendant of the
main ß system, since the heads are single, and the intervals
and second differences are of the same order of magnitude.

m connection with a search for evidence of the isotope
effect m band spectra, and he was able to show that the
subsidiary systems were due to the less abundant isotope of
boron (Bgt;0). The complete systems due to this isotope were
Identified and measured, and it was shown that the magnitude
of the isotopic separation could only be accounted for by
assuming that the emitter of the spectrum was BO and not
BN as Jevons had concluded from chemical evidence In

the system, while the final state is identical with the initial
state of the a bands.

The a bands have been photographed under high dispersion
and analysed by Jenkins (34), using the active nitrogen source
and Mulliken\'s classification of these bands asnbsp;(33)

was confirmed, but the doubling of the level could not be
detected. The existance of a vibrational isotope displacement
for the 0—0 band provided very definite evidence for the
vibrational half-integral quantum numbers required by the
quantum mechanics; this had already been indicated by Mulli-
ken\'s equations for the isotopic displacement. The rotational
isotope effect was examined, and the nuclear separation was
found to be identical for both isotopes.

A number of the bands of the same system developed in the
arc have recently been analysed by Scheib (35), who finds the
same structure as Jenkins, and also failed to find a doubling
of the 22quot; level.

The two methods of excitation give spectra of very different
appearance. In the arc, the rotation structure is greatly develop-
ed, and the band heads difficult to distinquish, whereas in the
active nitrogen source, the heads are very prominent.

In the p system, there appears at first sight to be only one
branch present in most of the bands, as in general only one
series of lines is associated with each head. Mulliken (33) first
interpreted this as a single R branch, and considered that the P
branch was missing. The writer (36) was also of the same

opinion, but understands from Mr. A. Harvey that Prof. Mulli-
ken has come to the conclusion that both P and R branches
are present in the bands excited by active nitrogen and in the
arc. The R branch forms the head, and on account of the low
temperature it fades out soon after having turned back upon
itself at the head. Since the lines in the neighbourhood are
closely spaced and are not resolved with the spectrographs
used, the lines of the R branch are not observed as lines. The
P linesquot;, however, do not form, the head of the band, and not
being crowded together like the R lines, are observed as a
series of lines. The net result is that the bands consist of a
strongly developed head and a single series of lines viz. the
P branch.

This explanation of the apparently missing branch seemed
very probable, and the frequencies of the lines in the 0—2 band
excited by active nitrogen were measured. These, when com-
pared with the lines of the same band in the arc (see Table IV)
show clearly that the lines in the band excited by active
nitrogen form the P branch. It is, therefore, almost certain that
the R branch is contained in the head, and that P and R
branches occur in both sources.

In the a bands, the same structure has been found for arc
and active nitrogen sources (34) and (35), and we may suppose
that the differences in both systems which result from the
two modes of excitation are (at least for a great part) due to
the difference of temperature of the sources. The much higher
temperature of the arc causes the maximum of intensity to
lie at higher rotation levels than in the active nitrogen source,
and gives a much greater developement of the rotation
structure. In the ^ bands in the arc, the R branch is so far
developed that it extends far past the head, and may be observ-
ed as a series of lines lying amongst the P lines.

Boron is a particularly favourable element for the study of
the isotope effect; it is light (atomic weight 10.82), and
consequently the difference in mass of the two isotopes is a
considerable fraction of the mass of either. Further, the
relative abundance is not high; taking the masses of the atoms

as 11.0110 and 10.0135 (37). or, correcting for O^^ and
Cy as 11.0096 and 10.0122, the relative abundance for the
above atomic weight is 4.22 : 1 or 4.26 : 1 respectively

For the boron monoxide molecule, the isotope coefficient
( p i) (see equation (5) p. ( 12) is high viz. 0.0292, and the
isotopxc separation of the band lines is in consequence great
compared with that in most spectra where isotopes are present.
Further the spectrum is not unduly complicated, particularly
xn the ft system excited in active nitrogen, nor is the band
structure too fme for resolution with spectrographs of
moderate dispersion, except quite near the heads.

During the course of the investigation on the intensity
ratios of the isotope bands in boron monoxide, the author
was led to examine the ft bands in the arc. A Hilger El quartz
spectrograph was used to photograph the region 2400-2600-
A.U., where the dispersion is about 3 A.U. per mm.; a repro-
duction of the bands in this region, taken with an exposure of
four minutes, is shown in Plate (I). A narrow slit was used
and since no appreciable temperature shift could occur in the
short exposure time, the maximum resolution was obtained.

The doublets in the bands of BnQ mentioned by Mulliken (33)
were examined, and it was found that at some distance from the
head, each member of a doublet was itself double, the separation
being, however, greater for the series of lines which appears
also in bands excited by active nitrogen. The (fine) doublet
separation increases with distance from the band head, and
resolution begins at about the thirty-sixth and forty-fifth\'lines
from the head in the wider and narrower series of doublets
respectively.nbsp;\'

The frequencies of the lines in the 0—1 and 0—2 bands were
measured, using iron arc lines as standards. In these measure-
ments, the lines from the twentieth to the fiftieth from the
head have been measured, and since the determination of the

fine doublet separation was not the immediate object of the
work, the mean frequency of these doublets has been deter-
mined.

The appearance of the arc /3 bands described above is just
what would be expected for anbsp;transition with all the

branches present. Bands of this type have a P and an R branch,
each of them consisting of doublets whose separation increases
linearly with the rotation quantum number; a consequence of
the connection between these latter is that, when the R
branch forms the head and the doublets become resolved after
this branch has turned at the head, the R lines are resolved
nearer the origin than the P lines. Since the two bands
Tneasured have a common initial level, identical combination
differences of the type R(jn) — P(ni) — A^ F\', where m is
the effective quantum number in the lowest electronic level,
should, be found if the two series of fine doublets are P and
R branches (neglecting the fine doubling).

Two such sets of combination differences have in fact been
found and are given in the second and third columns of
Table II. The agreement is good enough make it exceedingly
probable that they are genuine zlg F\' values. A further test can,
however, be applied, since the a and ^ system have a common
final level, and the zlg Fquot; values must therefore be identical
for bands which have the same vibrational quantum number
in the final state in the two systems. For the (i bands, the
values of A^Fquot; = R(m—1) — P (m 1) can readily be calcul-
ated from the line frequencies after the A.2 F\' s have been
determined. For the a bands, Scheib gives the same combin-
ation differences for the 0—2 and 0—3 bands from his analysis;
in columns (6) and (7) of Table II these differences for the
0—2 band in both systems are reproduced. The agreement is
such that there can be no doubt that the Fquot; s for the p
band are genuine. We may therefore conclude without hesitat-
ion that the two series of fine doublets are P and R branches,
and that the bands have the structure of 22quot;—bands.

where m is the quot;effectivequot; rotation quantum number. The
combination differences for the upper and lower states are
then respectively

The values of m were determined by plotting A2F\' (mean
values of 0—1 and 0—2 bands) against an arbitrary series of
consecutive whole numbers, and extrapolating the curve (which
shows a slight departure from linearity) to A^V = 0. Since
at this point m = — Y^, the absolute values of m may be
determined from the curve (fig. (1)).

It is found that integral values of m are required in equation
(11). After the determination of the m-values for the zl2F\'s
for the upper state, those for the lines can be found at once.

The value of B is in first approximation one-quarter of the
slope of the zJgF-m curve. The values so obtained (for both

upper and lower states) may be substituted in equations (12)
and (13) and the values o£ D determined. This serves to
determine D sufficiently accurately. Then B may be re-calcul-
ated, using equations (12)and(13) with the known value of D.

The Relative Abundance of the Isotopes of Boron, as determined
by Intensity Measurements.

As has been stated in chap. HI. two methods o£ exciting the
spectrum o£ boron monoxide are available viz, the arc with
boric oxide on the poles, and active nitrogen (containing a
race of oxygen) into which the vapour of boron trichloride is
led. The former method involves the use of a much higher
temperature than the latter, and as is to be expected, gives a
greater developement of the rotation structure. In consequence
the spectrum as excited by the latter source is much simpler\'
and the isotopic lines can be more readily distinguished; their
mtensities are also very much less subject to disturbance on
account of superposition of structure lines of other bands.

These considerations led to the choice of the active nitrogen
for exciting the boron monoxide bands for a measurement of
the isotope ratio. The method has been described by Strutt (31)
Jevons (32), Mulliken (14), and Jenkins (38), but for convenience
will be again briefly described.
A pparatus.

The apparatus is shown schematically in fig (2). Commercial
nitrogen from a cylinder (connected with the flasks Fi and F,
which acted as a reservoir and safety device) was passed succes-
sively over two tubes containing moist phosphorous by which
most of the oxygen was removed. The nitrogen was then partly
dried by contact with calcium chloride, passed over sodium
hydroxide to remove any carbon dioxide, and further dried with
phosphorous pentoxide.

The tubes were 1 m. long and 3 cm. in diameter, with the
exception of the Pj O^ tube, which was 60 cm. X 1 cm.

It was found that the nitrogen contained phosphorous vapour,
which attacked the tap-grease of the discharge tube during long
exposures, and a liquid-air trap L^ was inserted between the
last drying-tube and the discharge tube; this device lessened

the difficulty considerably. The nitrogen entered the discharge-
tube A, where a powerful condensed discharge was passed
between two nickel electrodes 10 cm. apart. It was found

necessary to make the tube of hard (suprax) glass, as the heat-
ing was considerable. The diameter of the tube was 1.5 cm.,
a wider tube having proved less succesful. The discharge was
provided by an induction coil, with 6 amp. in the primary, in
which circuit was inserted a mercury break. The terminals of
the secondary were connected to the coatings of two large
Leyden jars (the latter were in parallel) and through a spark-
gap of about 0.5 mm. to the dicharge tube.

With this arrangement, the nitrogen was activated and
passed through a black-painted light-trap T to the after-glow
tube G (of 0.8 cm. diam.) and thence through a second liquid
air trap Lj to the pump.

A fairly high pressure was mainained in the discharge tube-
usually the discharge was of the forked type which occurs at a
pressure of several centimeters.

The boron trichloride (supplied by Kahlbaum and stated to be
prepared from Chilian boron) was contained in the bulb B
connected to the afterglow tube through a capillary K. A by-pass
with a three-way tap Cg was provided for rapid evacuation of
the bulb during the procès of filling with boron trichloride.

When the after-glow tube was filled with active nitrogen,
the vapour of boron trichloride was admitted. As a result of
the chemical reaction which takes place between active nitrogen
(containing the necessary trace of oxygen) and boron trichloride,
excited molecules of boron monoxide are formed, and these
emit the band spectrum of that substance. The after-glow tube
was provided with two quartz windows Qi and Qg, behind the
second of which an antimony mirror M was placed to reflect
as much light as possible in the direction of the spectrograph
(shown by an arrow on fig. (2).) The spectrograph used for the
arc bands (Hilger Ei) was again employed for this work, an
image of the afterglow tube being formed on the slit by a
quartz lens.

With the amount of phosphorous used, it was found that too
much oxygen was removed for maximum brightness of the
bands, and for some of the exposures, a little air was admitted
through the stopcock CgC Mulliken (33) describes a similar
phenomenon. It was found, however, that with the oxygen cont-
ent adjusted for maximum brightness, the beta bands of nitric
oxide were strongly developed. In later work, the tap C5 was
always kept closed, and the gas velocity (on which depends the
amount of oxygen removed) adjusted so that there always
remained a trace of the yellow glow of active nitrogen in the
tube between L and G. Under these conditions, most of the
nitric oxide bands disappeared; the 2—7 band of BO was how-
ever never quite free from a strong neighbouring NO band.

The strong BO bands 2—5 and 2—6 were obtained with
exposures of three hours, but for other bands, exposures up to
twelve hours were necessary. It was, of course, necessary to keep
the temperature constant during the exposures, and the spectro-
graph was heavily lagged. The external temperature was
regulated by a small electric radiator, being kept constant to
within about 0.5° C.

The fluctuations were then damped out by the lagging, and
the internal temperature remained sufficiently constant to give
sharp spectrum lines.

The densities of the lines were measured with a Moll self-
recording microphotometer, and on each plate, calibration
spectra were photographed with the same spectrograph used
for the bands. The purpose of the calibration spectra was to
enable density curves to be drawn, giving the photographic
density as a function of the intensity of the light incident on
the plate; the method employed is described below. The bands
in which the isotope ratio was measured lie in the region

3100—2600 A.U., in which the sensitivity decreases with wave-
length, although it was found that the density curves are nearly
parallel throughout this range. The variation is, however,

gradual, and since the isotope separation is of the order 20 A.U.,
it was possible to read off the intensities of both isotopes from
one density curve, and then apply a correction to the intensity
ratio on account of the change in plate sensitivity. The latter
quantity was determined by using a lamp in which the energy
distribution was known (see below).

In the earlier experiments, Ilford Iso-Zenith plates were used,
but the grain was found to be somewhat coarse. The effect of
this was minimised be photometring each spectrum line three
times (at different heights) and averaging the intensities. The
labour involved was very considerable, however, and experiment
showed that the Special Rapid plates of the same firm were
equally sensitive in the spectral region used, and the grain was

much finer. Still later, the photometer was arranged so that a
spectrum line of about 3 mm. length could be photometred
(previously only about 0.8 mm. was used), and the effect of
the grain was in this way automatically averaged out. The very
satisfactory nature of the registration may be seen from Plate
I, in which very little irregularity due to grain may be seen.

Rodinal was used as developer, and the developement was
carried out until a slight fog appeared on the plate.

Calibration of the plate for determination of the intensity ratio
of the isotopes.

The relation between photographic density and light intensity
was determined from six calibration spectra photographed on
the same plate as the boron monoxide bands, the intensity in
these spectra being varied in known steps.

The calibration spectra were taken with a gas-filled tungsten
band lamp, of quartz, which gave a continuous spectrum strong

enough for the purpose as far as 2400 Ä.U. The intensity was
altered by using different slit-widths on the spectrograph, the
intensity being proportional to the slit-width provided that the
latter is not so fine that diffraction effects are prominent.

Since the exposure for the band lines was some hours it was
desirable that the time of exposure for the calibration spectra
should not be too short, and the lamp current was adjusted to
give a suitable density with an exposure of half-an-hour. Since
it would have required much time to take the necessary sets of
calibration spectra in the usual way, a quot;step-slitquot; was devised.
This consisted of six short slits of different widths, ranging

from 0.07 mm. to 1.9 mm., one above the other, as shown in
fig. (3). It was made by making six fine, horizontal cuts in a
brass plate of 1 mm. thickness with a circular saw. Tinfoil was
then pasted over the cuts, leaving, however, different lengths
uncovered; these formed the slits. The slit of the spectrograph
was opened as wide as possible (shown by the dotted line in
fig. (3), and the step slit mounted immediately in front of, and
as close as possible to the former slit. It was of course necessary
to arrange that the light falling on the prism did not fill it,
otherwise some of the light from the end slits would not have
been transmitted, and the intensities on the plate would not
have been proportional to the slit-widths. This was accomp-
lished by two arrangements.

(a) For the region 2700—3000 Â.U., where the radiation from
the lamp was rather strong, the lamp was placed at a distance
of about 2]/^ metres from the slit in order to illuminate it
uniformally. Then a quartz lens of suitable focal length was
placed immediately in front of the slit, forming an image of
the lamp filament on the prism. By screeening off part of the
filament, the image could be made quite small, so that there
was no possibility of the above effect occuring.

;b) For the region 2700 A.U.—2400 A.U., the radiation of a
tungsten lamp is very feeble, and another arrangement was
adopted. An image of the filament (considerably enlarged) was,
thrown on the slit by means of a quartz lens. This lens was
provided with a suitable diaphragm, and an image of the
diaphragm aperture was formed on the prism by the lens immed-
iately in front of the slit. Uniform illumination of the slit was
secured by the fact that the filament of the lamp was in the
form of a flat ribbon, and that the image of this ribbon was
considerably larger than the slit.

The widths of the steps were determined by direct measure-
ment with a comparator, and the intensity of the light producing
the spectra was directly proportional to the widths so obtained.

An advantage of the method was that, as all six calibration
spectra were taken simultaneously, it was not neccessary to

Since the highest accuracy was not required in the determin-
ation of the intensities of the bands as a whole it was decided
to determine the band head intensities, and to use this as a
measure of the total intensity of each band. The band system
extends over several hundred Angstrom units, and it was
therefore necessary to take the variation in plate sensitivity
into account. For this purpose, density marks were made with
a lamp in which the energy distribution in the spectrum was

known. For the region 2400-3100 Â.U., the quartz band lamp
was used, and the intensity distribution was calculated from the
colour-temperature. For the region below 2400 Â.U., a smaller
quartz spectrograph was used, since the exposures with the
large instrument would have been excessively long. It was not
found practicable to use the quartz band lamp in this region
as the energy radiated is so small relatively to that in the region
of maximum sensitivity of the photographic plate, and much
trouble from stray light was experienced. The positive crater
of a carbon arc, which with its high temperature has a much
more favourable energy distribution, was accordingly used
The researches of Lummer (39) have shown that the temperature
of the brightest spot of the crater is indépendant of current
and arc length, and is determined only by the properties of
the carbons. Consequently, although not an ideal source, it
was possible to take calibration spectra with the arc, using the
slit width variation method.

In order to avoid the rapid decrease in sensitivity which
occurs in the region 2150 Â.U.—2400 A.U., oiled plates were
used. A mineral oil used for machine lubrication was found
suitable, and was applied with the fingers. After some minutes,
the coating became fairly uniform. It was found that the\'
sensitivity was everywhere reduced by the oil, but the reduc-

colour temperature of the type of carbon employed has been
determined in this laboratory, and found to be 4200° K. From
this, the energy distribution according to Planck\'s formula was
calculated, the carbon being assumed to be gray.

Since the band heads may be considered as parts of a contin-
uous spectrum (they consist of many superposed lines of differ-
ent wave-lengths), no correction for dispersion was applied, the
dispersion correction being the same for calibration spectra and
band heads. The intensities were calculated in the usual way
from the calibration curves, with the addition that the variation
in intensity of the standard lamp with wave-length had also to
be taken into account.

In order to connect the two series of band head intensities, the
spectrograph was arranged so that the series overlapped. The
intensities in one series were then reduced by the appropriate
factor to make them comparable with those of the other series.
The reduced results are given in Table V. All the band heads
appearing on the plates with exposures up to four hours have
been measured; Mulliken lists several, however, particularly in
the v\' = 4,5 and 6 progressions, which did not appear on the
writer\'s plates. At the long-wave end it would probably have
been possible to have obtained one or two more members for
some of the progressions by photographing the region above
3100 A.U., but since these bands are not strong, and further
the greater plate sensitivity there makes them appear consider-
ably stronger than they really are, is is considered that the
effect of these bands on the intensity sum (the determination
of which was the object of these measurements) is negligible.

The ideal method of comparing the intensities of the isotopic
bands is to determine the intensity ratio of corresponding lines
in the bands. It has been found possible of do this for several
bands in the BO spectrum, and the results of this method must
be considered to be the most accurate. In some of the weaker
bands, however, this is not possible because the structure is
not sufficiently developed to give the lines which are well

resolved, and only the heads can be seen. These, consisting o£
about 12 lines of the R branch, are much stronger than the
individual lines, as may be seen from the registration (Plate I).
It is not, however, permissible to compare the maximum intens-
ities of the heads, as is done in the case of single lines, because
the heads of the isotopic bands are not of the same shape, due
to the fact that the rotation constants differ.

The only sound way of comparing the intensities of the heads
is to determine the shape of the band heads, integrate the
intensity over the whole head, and then compare integrated
intensities. In order to do this, enlarged drawings of the
registrations of the heads were made with the aid of an
epidiascope. The densities at a sufficient number of points
were then calculated, and the corresponding intensities read
off from the density curve. The heads were now re-drawn, the
ordinates being the intensities so determined, and the areas
under the curves were calculated. The ratio of these areas for
isotopic bands gave a value for the intensity ratio which,
although not so accurate as a line-for-line comparison, was
certainly much more reliable than the ratio of maximum intens-
ities would have been.

The intensity ratio of the isotopic bands of BO has been
determined by a line-for-line comparison for the 1—4, 1—5

2—5,nbsp;2—6 and 3—7 bands, and by comparison of the integrated
intensities of the heads for the 0—3, 1—4, 1—5 and 2—5 bands.
The latter three were intended as a check on the agreement of
the two methods. Some of the bands have been measured on
several plates, and the individual values found are given in the
second horizontal column of Table VI. The fourth horizontal
column of the same table gives the ratios corrected for plate
sensitivity.

3—7nbsp;band, which is considerably higher than any of the others.
No band of BO is known which might be superposed on the
main band and so account for a high intensity ratio; on the
contrary, however, the observed ratio may be slightly too low,
as the 0—5 main band is superposed on the weaker isotope of

ratio must be taken to mean that this also is real, and that
considerable differences in the intensity ratio of the isotopes
exist.

The most promising method of arriving at an explanation of
this fact appears to lie in a determination of the excitation
function /quot;(E^) of the molecule. Mulliken has already pointed
out (33) that the excitation of BO with active nitrogen is non-
thermal, and from eye estimates of the intensities of the bands,
he was able to form some idea of the distribution of the molec-
ules among the different initial vibrational states. It seemed,
however, highly desirable to make measurements of the band
intensities in order to determine the function more accurately,
since eye estimates may be quite misleading when a consider-
able range of wave-lengths is involved, and the measurements of
the band head intensities described above were therefore made.

The sum of all the intensities of the bands in each vquot; progres-
sion (i.e. a progression in which v\' constant) may be represent-
ed by

etc. are the transition probabilities for the various bands
It is required to find the values of ƒ (E^.) for the variousquot;
progressions, the band intensities being known.

In the application of the summation rule in atomic multiplets
the number of emitters (statistical weight) in a given sub-level
in the upper state is obtained by summing up the intensities
of lines due to transitions from that state. Actually, not the
intensities, but the square of the amplitude of the virtual oscil-
lators are summed up, and these are obtained by dividing the
intensity of each line by pi, v being the frequency of the
line in question.

The transition probabilities p are different for the different vquot;
progressions, but we may assume that the sum of all the p —
values will not be very different for the different progressions.
Making this assumption, we obtain the relative values of ƒ (E .)
by summing up l/v* for each progression.nbsp;\'\'

Whether Xjv^ or even simply I is used makes actually very
little difference to the shape of the resulting curve when these
quantities are plotted against E,-. This is because each
progression is displaced with respect to its neighbours by a
frequency interval which is small compared with the band
frequencies.

The sum of the I/v^ values for each vquot; progression is given,
at the foot of the appropriate colums in Table V, and is plotted-
against the vibrational energy in the upper state in fig. (4;.

The remarkable shape of the curve shows that the excitation-
is strongly selective, with a very pronounced maximum between
v\' = 2 and v\' = 3. It is at once apparent that, if the premises
of Chap. I are correct, we may expect that ƒ ( E\'^ ) will differ
very considerably for the two isotopes. The vibrational energy
levels of the isotope B are indicated by the dotted lines ; on
account of the fact that the energy of the lowest level is not
zero but possesses a half quantum of energy an isotopic separa-
tion exists in this level also. The form of the ƒ ( E^- ) curve is
such that it cannot be accurately determined from the few points
available, and in particular the position of the maximum is very
uncertain. Nevertheless, results of considerable value may be
deduced from it.

We assume that the values of ƒ (E^,- ) for B to O are given
by the intersection of the dotted lines with the curve for B^\'O.

It is evident that the number of molecules of Bif\'O which are
brought into the v\' — 3 state is about 17% smaller than the
number of BHQ molecules in the same state (quite apart, of
course, from the real relative abundance of the isotopes),
whereas in the v\' = 2 state, the B i^O. molecules preponderate
by about 4%. In the other vibrational states, the differences
are almost inappreciable. The effect of this, of course, is to
make the ratio of isotone intensities greater for v\' = 3, than
for the other values of v\', just as has been found experiment-
ally, and in this way the variation of intensity ratio of the
isotopes is explained.

of the relative abundance are given. The agreement of these
latter for the different bands measured is very satisfactory.

The possibility of the vibrational transition probabilities p
being appreciably different for the two isotopes must now
be considered. The relative transition probabilities are obtained

by dividing the band intensities by the relative number of
molecules in the initial state (i.e. by the intensity sums in
Table V). These are plotted as a function of E/ in fig (5),.
and as a function of E/ in fig. (6). The full and dotted
vertical lines represent the vibrational energy levels of the
main and isotopic molecules, respectively. Considering first
fig. (5), it may be seen that, for the bands measured, there is-
no appreciable difference in p for the isotopes. Consequently
the transition probabilities are not influenced by the isotopic
separations of the upper level.

Turning now to fig. (6), these curves may be expected to
give directly the values of p for the isotopes. For the 2—5
and 2—6 bands, therefore, we should expect from this curve
that the measured ratio would be approximately 7% lower
and 7% higher, respectively, than the true ratio. Actually,.

however, Table VI shows that these bands give isotopic ratios
differing by only ^ %. The isotope ratios for these bands
(which are strong and capable of accurate measurement) are
considered to be very reliable, and the predicted difference
in intensity ratio must therefore be considered to be in error.
The fact that all the bands measured give ratios which (when
corrected for the differences in the number of molecules of
both isotopes in the excited state) are in excellent agreement,
may perhaps be taken as evidence against the variation of p for
the isotopes. It is not at all certain whether the transition
probability may be represented by a smooth curve drawn
through the points in figs. (5) and (6).

It may be remarked that in fig. (6), three maximum values
of p occur for the states v^\' = 3 and 2 respectively, whereas in
general only two (21) are to be expected. Until more is known
about the transition probability for vibrational transitions, we
may consider that the direct experimental evidence does not
show an appreciable dependance of transition probability on
the nuclear mass. Finally the existance of a rotational effect

Pig (7) _ Line Intensities in 2—6 band of BO
(m in arbitrary units).

similar to the variation of / (E^.) for the isotopes must be
considered. In fig. (7), the intensities of main and isotopic lines
m the 2—6 band are plotted on a logarithmic scale against an
arbitrary series of numbers. (The true values of the rotational
quantum numbers are not known for the bands whose in-
tensities have been measured). The fact that the two curves
are separated by a constant vertical interval shows that the
isotope ratio remains constant, and consequently no dependance
of ratio on rotational state exists.

The masses of the boron atoms have been determined by
Aston (37) with the mass spectrograph, and are given by him to
four places of decimals. The present measurements give the
relative abundance of the isotopes as 3.63 0.02, and the
atomic weight of boron calculated from this (after correcting
for O-i^ and see p. (28)) is 10.794 0.001. The probable
error is calculated from the divergences of the individual
results from the mean, and possible systematic errors are
naturally not taken into account in this way. Aston (40) has
remarked on the accuracy in atomic weight determinations
which it is possible to reach with even rough measurements
of isotope ratios, and this is well shown by the above figures,
where an error of ^ % in the intensity ratio means only an
error of 0.01% in the atomic weight. The atomic weight of
boron has been the subject of several investigations in recent
years, and it is only during the last ten years that anything
like satisfactory accuracy has been attained, boron being
apparently an unfavourable element for accurate atomic weight
determination. The results obtained since 1920 are shown in
the following table.

SAgCl
SAgBr

10.82

3Ag
3Ag

(41) BCI3
BBrg

Baxter and Scott

Birckenbach (42) BCI3 : 3Ag
Stock and Kuss (43) BgHg: 3H2
Briscoe and Robinson (44) BCI3 : 3Ag

10.82
10.806
10.818

10.817

10.818
10.841
10.830
10.847
10.825
10.825
10.823
10.794

3AgCl

1 Asiatic
boron

Californian
boron

1 Tuscan
boron

Elliott

B2O3 (density)
BCI3 : 3Ag
BCI3 (density)
B0O3 (density)
BCI3 : 3Ag
BCI3 (density^
B.2O3 (density)
Relative abundance of
isotopes (Chilian boron)

From the above, it will be seen that there is evidence that
the atomic weight o£ boron varies slightly according to the
origin of the boron. The variation is very small, however, and
it is highly desirable to confirm it by another method. Since
the difference in atomic weight means a comparatively large
difference in isotope ratio (the atomic weights 10.82 and 10.84
give isotope ratios 4.26 : 1 and 4.88 : 1 respectively), the
measurement of the intensity ratio of the isotopic bands, as
described in this thesis, would appear to be the most promising
method of attacking this problem.

(Corrected for initial distribution of molecules over the
different v\' states).

The factors governing the relative intensities of isotopic
bands in molecular spectra are considered, and a theory is
given by means of which they may be calculated. It is shown
that, in general, the intensity ratio of isotopic bands does not
give the abundance ratio of the isotopes directly.

The experimental determination of the intensity ratio of the
isotopes C135-35 : CP^-^t and Bquot;0 : B^OQ is described, and
a simple method of calibrating photographic plates for
intensity measurements is given. The determination of the
absolute intensities of the band heads in the system of BO

For CI2, the experimentally found intensity ratio of the
isotopes agrees better with that calculated from the atomic
weight when the correction predicted by the theory is applied.

For BO, different intensity ratios of the isotopes are found
for different vibrational transitions. When these are corrected
for the influence of the peculiar excitation conditions, they
agree to a high degree of accuracy. It is thus rendered improb-
able that the transition probabilities for two isotopic molecules
are different, as certain considerations would lead one to
suppose. The corrected ratio of intensities of the isotopic bands
in BO (3.63 : 1) is lower than that (4.26 : 1) calculated from
the accepted atomic weight; the variations in the different
determinations of this latter are only slightly smaller than that
requiredquot; to explain this divergence, however.

It is considered that accurate atomic weight determinations
may be made in favourable cases by intensity measurements
in band spectra.

18.nbsp;Qiauque and Johnston, (a) Nature, 123, 318, 1929, (b) Jour Ampr
Chem. Soc., 51, 1436 1929, and (c) Nature, 123, 83 , 1929

19.nbsp;Kmg and Birge, (a) Nature, 124, 182, 1929. (b) Astrophys j\'our,, 72, 19,

39,nbsp;Lummer, Verflüssigung der Kohle und Herstellung der Sonnentem-
pcrätur«

44. Briscoe and Robinson (a) Journ, Chem. Soc,, 127, 696, 1925, (b) Bris-
coe, Robmson, and Stephenson, ibid. 70, 1926,

The granularity of photographic plates plays at least as impor-
tant a part as the sensitivity in putting a limit to the faintness
of spectrum lines measurable by present photometric practice.

Quartz spectrographs for the extreme ultra-violet would be more
useful if constructed to use prisms of 10° refracting angle instead
of the usual 60°.

It is desirable that the quantity of energy 1 erg/sec./cm.^ be
adopted as the unit of radiation, and that a name be given to
this unit.

The outline of a theory of the bright lines in stellar spectra given
by Milne (Handbuch der Astrophysik, Band 111, p. 164-166-170)
does not correspond entirely with modern conceptions of the
radiation process in stellar spectra.

The apparent absence of series in the spectra of some elements
may be due to the variation of intensity ratio of the multiplets.

The conditions governing the formation of metallic deposits in
electrolysis are worthy of closer examination than they have re-
ceived.

The result for the nuclear spin of indium round from hyperfine
structure observations by Jackson (Proc. Roy. Soc., 128, 508, 1930)
is difficult to understand in terms of modern theory.

The attempt of Deubner (Phys. Zeits. 20, 909, 1930) to explain
the alleged increase in Brownian movement of particles when
they are subjected to light (Pospisil, Physikal. Zeits., 31, pp. 65,
78, 447, 1920) cannot be considered successful.

^^.\'îî\'Hhi.i; \'•■} Ju;jfnövo!ri f.rnbsp;ni \'.•r-.r/narii baj\'pU?: v^^}

Ka;

: ua;

.•■v \'\'-vïm^\'	y- T\'yyf^ \'

• , « \' ■ , ••			quot;i: \'-V. »ff
* • • ^	y • . . ■ \' ^ ■	r \' ¹ \' 1	\' * \' \' *
• . • • • . 1 «» V * \'	* » • \' \' ^ a *	h - \' \\ r- y : r.	•* 1
* gt; .			■ . ., \'

Band	Intensity Ratio	Relative Abundance*
1—12	1.35	1.42
2— 6	1.28	1.40
2—12	1.42	1.56

	4F\'	4Fquot;
m	0—1	0—2	Mear	bands	abands*
	\' 0—1	0-2	0 2
		cm.-i
	cm.quot;^	cm,-^	cm.-^	cm.-i	cm.-\'
9	57.7	57.3	57.5
10	63.8	63.3	63.5	73.9	72.8	72.84
11	69.4	69.1	69.2	80.8	80.2	80.00
12	75.5	75.4	75.4	87.7	87.5	86.64
13	81.2	81.6	81.4	95.0	94.0	93.84
14	87.1	87.5	87.3	101.9	101.0	100.62
15	93.2	93.8	93.5	108.6	107.9	107.71
16	99.1	99.5	99.3	115.5	115.2	114.59
17	104.9	105.8	105.4	122.7	122.1	121.43
18	111.3	111.3	111.3	129.5	129.2	128.34
19	117.4	116.9	117.2	136.7	135.4	135.42
20	123.0	122.7	122.9	144.1	142.2	142.00
21	129.1	128.8	128.9	150.8	149.1	149.16
22	134.9	135.0	135.9	157.6	155.7	156.11
23	140.9	140.8	140.0	164.7	163.4	162.95
24	147.1	147.0	147.3	171.7	170.1	169.75
25	152,9	152.5	152.7	178.7	176.8	176.42
26	158.4	158.4	158.4	185,7	183.6	183.38
27	164.4	164.8	164.6	192.2	190.5	190.47
28	170.3	170.7	170.5	199.3	197.4	196.79
29	176.4	176.1	176.3	206.2	204.7	203.89
30	181.9	182.1	182.0	213.0	211.1	210.84
31	187.7	187.9	187.8	219.8	217.7	217.67
32	193.8	193.8	193.8	226.6	224.9	224.34
33	199.3	199.2	199,3	233.9	231.5	231.23
34	205.3	204.9	205.1	241.2	238.0	238.00
35	211.8	211.5	211,7	247.4	244.7	244.86
36	216,6	216.6	216.6	253.9	251.8	251.57
37	222.5	221.9	222.2	260.6	257.9	258.90
38	228.1	227.8	227.9	268.1	265.1	265.67
39	233.9	233.9	233.9	274.3	271.9	272.05
40	239.5	239.3	239.4	281.3	278.2	279.01
41	245.1	245.2	245.2		285.2	285.71
42		250.8		294.4	292.3	292.15
43	256.3	256.7	256.5	301.5	298.5	298.89
44	262.3	262.1	262.2	308.0	305.2	305.13
45	267.6	267.7	267.6	315.2	311.9	312.34
46	273,5	273.3	273.4	321.3	318.8	318.92
47	278.7	279.0	278.9	328.5	325,0	325,24
48	284.8	284.5	284.7	334.6	331.7	331.63
49	289.4	289.7	289,6	341.6	338.6	338.17
50	295.3	295.6	295.5		345.6	345.13
51					351.8	351.23
52					357.5	358.08
53					364.8	364.68

Upper (y =	state : 0)	B cm.\'^	D X 10quot;^ cm.-^	I X lO\'^^gm. cm.quot;	r X10®cm.
1.512	— 1.05	18.26	0.649
Lower	state
V = 1	Iquot;\'	1.761
	W	1.760	— 0.75	15.69	0.6016
V = 2	r*	1.745
		1.745	— 0.8	15.82	0.6041

Active nitrogen source	Arc source
P branch	R branch
39,049.6 cm.\'i	39,048.9 cm.-i	39,044.7 cm.-i
038.1	037.4	033.2
026.0	025.5	020.8
013.8	013.2	007.5
000.4	000.3	38.994.3
38,987.3	38,987.0	981.0
973.2	973.3	966.2
959.2	958.6	951.2

Band	0—3	1—4	1-5	2—5	2—6	3-7
Intensity ratio of isotopic band. a a = from lines b = from heads b	3.56	3.49 3.20	3.41 3.53	3.34 3.22 3.49 3.42	3.50 3.17 3.45 3.49	4.30 4.38 4.05
Average	3.56	3.35	3.47	3.37	3.40 1 4.24
Corrected for plate sensitivity	3.63	3.44	3.56	3.48	3.50	4.37
/ (E/) /(EV).	1	0.985	0.985	0.95	0.95	1.21
Isotope ratio	3.63	3.50	3.61	3.66	3.68	3.61

Band	Int.		IM	Band	Int.
0—0	90	33	2.7	1-0	127	38	3.3
0—1	78	28	2.8	1—1	26	32	0.8
0 2	77	24	3.2	1—2	—	27	—
0—3	28	20	1.4	1—3	59	22	2.7
0—4	14	16	0.9	1—4	50	18	2.8
0—5	—		—	1—5	29	15	1.9
				1—6	14	12	1.2
Sum			11.0				12.7
2-0	400	42	9.5	3-0	125	47	2.7
2—1	—	36	—	3-1	98	40	2.5
2—2	124	31	4.0	3—2	—	34	—
2—3	42	25	1.7	3—3	20	29	0.7
2—4	17	21	0.8	3—4	77	24	3.2
2—5	103	17	6.1	3—5	—	20	—
2—6	92	14	6.6	3—6	16	16	1.0
2—7	32	12	3.2	3—7	41	13	3.2
				3—8	24	11	2.2
			31.2				15.5
4—5	12	23	0.5
4—6	10	19	0.5
4—7	—	16	—
4—8	7	13	0.5	5—7	7	17	0.4
			1.5				0.4

v\'-7 f	1	j j 1 \\ i \\	! i 1
W\'- li E --		1 1 i / 1 / 1	j 1
			i /	j 1 I
		i i i /		j j -1_

\\ Vquot;	0	1	2	3	4	5	6	7	8
0	0.24	0.25	0.29	0.13	0.08
1	0.25	0.06	—	0.21	0.22	0.15	0.11
2	0.30	—	0.13	0.05	0.02	0.19	0.20	0.10
3	0.17	0.16	—	0.04	0.20	—	0.08	0.21	0.14
4						0.33	0.33	—	0.33


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