■SBnn

THE INTENSITIES OF THE COMPONENTS
OF MULTIPLE SPECTRAL LINES

H. B. DORQELO

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THE INTENSITIES OF THE COMPONENTS
OF MULTIPLE SPECTRAL LINES

THE INTENSITIES OF THE COMPONENTS
OF MULTIPLE SPECTRAL LINES

ACADEMISCH PROEFSCHRIFT TER VER-
KRIJGING VAN DEN GRAAD VAN DOCTOR
IN DE WIS- EN NATUURKUNDE AAN DE
RIJKS-UNIVERSITEIT TE UTRECHT. OP
GEZAG VAN DEN RECTOR-MAGNIFICUS
Dr. A. J. P. VAN DEN BROEK. HOOG-
LEERAAR IN DE FACULTEIT DER GENEES-
KUNDE. VOLGENS BESLUIT VAN DEN
SENAAT DER UNIVERSITEIT. TEGEN DE
BEDENKINGEN VAN DE FACULTEIT DER
WIS- EN NATUURKUNDETE VERDEDIGEN.
OP MAANDAG 19 MEI 1924. DES NAM.
TEN 4 URE DOOR

HENDRIK BEREND DORGELO
GEBOREN TE AVEREEST (O.)

EUECTHISCHL- DHUKKEHIJ ..DE INDUSTRIE " l VAN DHUTEN - UTRECHT

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AAN MIJNE OUDERS

liet is mij een voorreclil ü, Hoogleeraren van do
Faculleif der Wis- en Natmirknnde, mijn oprochten dank
le kunnen brengen voor het onderwijs, dat ik van U heb
mogen ontvangen en voor de welwillendheid, waarmede
gij mij zoo vaak zijl tegemoet gekomen.

Allermeest geldt mijn dank U, Hooggeleerde Ornstein,
Hooggeachte Promotor. Met hartgrondige dankbaarheid
denk ik terug aan alles wat gij voor mij hebt willen zijn
gedurende den tijd, dat ik uw assistent was en aan de
voortdurende steun en bezieling bij de bewerking vnn
dll proefschrift ondervonden. Gij bezit hel geheim, om
U heen le scheppen een sfeer van vriendschap, waarin
gewerkt wordt uil liefde voor de arbeid en voor de
wetenschap. Ik acht mij gelukkig deel uil le maken
van den kring Uwer leerlingen.

Hooggeleerde Julius, door mij indertijd tot Uw as.\'sislpnl
aan to stellen, hebt gij mij zeer aan U verplicht. Ik dank
U voor de welwillendheid mij toon cn later betoond.

II, Hooggeleerde Heeren Dk Viues, Niji.and, Dknjov,
Van EvEiU)ixfikn, breng ik dank voor hol onderwijs van
U genoten. Dat ik gedurende «Ie mohilisatiejaren Uwo
(\'olloges niol ton volle heb kunnen volgen, heb ik sleods
betreurd.

Zeergeleerde Hurcif.», sleods hebt gij onverflauwdo be-
langstelling gotooud voor don gang en de resultaten van
mijn onderzoek. Uw sleun, vooral bij do bewerking van

liet laatste hoofdstuk van mijn proefschrift, waardeer ik
in hooge mate.

U, Zeergeleerde Heeren Moll, Van Gittert en Minneart
dank ik voor de bereidwillige hulp, welke ik van U nooit
vergeefs heb gevraagd.

Niet minder stel ik op prijs de vriendelijke steun en
raad, waarde Van Duck, welke gij mij steeds geboden hebt.

Van den oprechten en aangenamen vriendschappelijken
omgang met U, vrienden, assistenten en personeel van
het Phj\'sisch Laboratorium zal ik steeds zeer prettige
herinneringen bewaren.

CONTENTS.

îninoductory .....

CHAPTER I.

Description of the method
a.

For groups of lines of which the componenls
have small differences in wave-lenglh . . .
For groups of lines, the componenls of which
have great dinerences in wave-lenglh . . .

The slandardized lamp.........

(I. The slanclardizing of Ihe lighl-reducers . . .
r. The photographic plate and the developer . .
/". Discussion of the errors influencing Ihe results.

CHAPTER 11.

CllAPTEU 111.

SlIMMAHV OK tiik hesul.ts

.....

vKî"\'\'

ifai

-m™«

INTRODUCTORY.

By means of the work of many investigaloi-s in the
field of spectroscopy an interesting regularity has been
discovered in Ihe spectra of many elements. This regu-
larity regards the appearance of spedral lines in series and
llie occurrence of characterislic magnetic separations.
These phenomena have been connccted wilh the structure
of the atoms by Bonn, Sommerfei.d, Landf^ n. o.

The investigation of the intensity-ratios of the com-
ponenls in "multiple" spectral lines, which will be dis-
cusse«! In this dissertation, brings out a new regularity
which must be made to fit in the framework of the
theory of the spectral lines.

The intensity of the spectral lines gels a fundamenlal
significance in addition to its wave-length.

Our experiments were restricted to the visible part
of the spectrum.

We began by examining the groups of spectral lines
occurring in the sharp series which according to Honn\'s
tlioory are causetl by the "outer" electron falling from
one initial energy-level to two or more final levels, a
transition from the single «-level In the double and triple
/»-level corresponding to doublets and triplets respectively.
For in the first place the mtios between the intensities
of the components that then appear at once indicate
the ratios of the probabilities of transition, and in the
second place the phenomenon in this case is indépendant
of the excitation-conditions of the atom. The ratios
of the intensities of the various components of the groups
of the sharp series will therefore inunediately be pro-

portional to the ratios of the transition-probabilities of
the electron from the single s-level to the various
;j-levels.

With the aid of the methods to be described in the
first chapter we therefore first measured the ratios of
the intensities of lines of

I. Doublets of the sharp series of the alkalis Na, K,
Bb and Cs.

II. Triplets of the sharp series of the earth-alkalis iV//,
Ca, Zn and Cd.

We found with the triplets such a regularity in the
numbers which indicated the ratios of the intensities of
the three components of the earth-alkalis, that it induced
us to a further examination of triplet-, quartet-, quintet-,
sextet-, septet- and octetsystems. We were able to do
this for:

III. a triplet of the sharp series of a sextetsystem of Mu

IV. a triplet of the sharp series of an octetsystem of .1/«.
The groups of lines of the difTuse series {pd series)

with the alkalis consist of doublets if the S-levels are
not separated or only so little thai this does not cause
a perceptible separation of the spectral lines.

These doublets are caused by the transition of the
"outer" electron of a still unseparated ^-energy-level to
the two -1- and s-a-energy-levels. \')

The ratio of the intensities of the two componenls will
therefore here represent the ratio of the probabilities of
transition of the electron from the ^-level to the two
;7-levels.

In consequence of the ^-levels being more separated
with the heavier metal the so called "complex"-
doublets *) appear consisting of three componenls.

\') Ah regurdH the symbols of tho H|>cctrnl linm wo «dopt iho
notulioii of A. Fo\\vi,i:ii. (IUi)ort dii Hcuw in Lin« »<i>orlra ML»-»).

*} The«c grou|w of linw aro rall(>,l by I.anpk "VoIUliindigo
Dublelle". A. La.sdk Z. f. I\'hyrt. V, 232, lit»!.

Willi the /)f/-groups of the earth-alkalis, where the/)-
as well as the rf-levels are threefold, \'\'coinpIex"-triplets
appear with sufficient separation of the f/-levels, which
triplets consist of a group of six lines.

Of the groups of lines of the diffuse series we measured:

V. single doublets of lYn, K, Bb.

VI. the \'\'complex"-triplet I t — 5 a of Cs.

VII. the \'\'complex"-triplel — of Ca.

The ratios of the intensities of the components of Ihe
groups of lines of the bencmann-series <J)-series) of the
alkalis could not be examined by our method, partly
because of their too weak intensity partly because of
their lying in the infra-red.

Of Ihe bergmann-series of the earth-alkalis the triplet
1 _ 3 of Ca lent itself first of all to closer examination.
As this triplet appears, its ^-levels being not yet sulfi-
ciently separated to give the "complex"-triplol, wo have
to deal with transitions of the „outer" electron from one
Wevel to the three (/-levels.

In the same way as the ratios of the intensities of the
components of a triplet of the shar)) series will give us
the ratios of the probabilities of Irausition of the "outer"
electron from the single s-level to the three />-levels, the
ratios of the intensities of the components of the.se single
triplets will give us the ratios of tho probabilities of tran-
sition from the single Wevel to the three (Mevels.

In this way we measured:

VIII. The triplet \\ d — \'3 b of Ca.

As in tho numerical values which we obtained for Ihe
ratios of the intensities of the components of this triplet
an interesting regularity was noticed, we have also extended
our investigation to a "complex"-triplot of the <l b-
series. The "complex"-triplet 1 </- 3of .S> could be
separated in the third order spectrum by our spectrograph,
so that we were able to investigate this triplet of the

Bkhomann series.

Therefore was also measured:

IX. The "complex^-triplet 1 r/ - 3 A of Sr.

It appeared that the resulling ratios of the intensities
of the componenls of the "complex\'\'-doublets and triplets
were characterised by the inlernalquanfum-numbers of
the initial and final slates of the atom. This suggested
the question how the components of doublets and triplets
of the principal series would behave in this respect.

With these doublets and triplets the initial levels are
separated but the final level is single.

In consequence for the results for the "complex"-doublels
and triplets, it might be expected that here the ratios
of the intensities ot the components would be characterised
by the internal quantum-numbers of the initial stales
(see on this subject chapter 111).

According to this point of view the ratios of the inten-
sities of the componenls of doublets and triplets of the
principal series must show the same values as these of
analogous groups of lines of the sharp series.

On investigating the groups of lines of the principal
series of the alkalis the dilficully of selfrevor.sion makes
itself felt to a high degree. By diminishing the concen-
tration of the salt in the arc I succeeded in obtaining the
doublet 1 ct-St (A4.555,20, mS.Ki) of C.t practically
free from selfreversion.

It was further possible to investigate the triplet of
the principal series 1 .■<» — (52()S,/|2; nSOCJ.Of) and
5204,51) of the quintet-system of Cr.

Of the various groups of the principal series we nieasnrod:

X. the doublet I <r — 2 r of Ca and

the triplet 1 .s" — 2 of the quintet-system of Cr.

With a view to the rules obtained for the ratios of
the intensities of the componenls of multiple spectral
lines it seems to me to be ol great importance lo investi-
gate quantitatively the ratios of the intensities of the
components with the anomalous ZEEMAN-separalions as
well.

This investigation has already been started.

The "method A" we are going to describe lends itself
innnediately lo Ibis purpose.

It is also interesting to investigate, whether the ratios
of the intensities of multiple spectral lines is dependent
on the conditions of excitation. We have investigated
this for some doublets and triplets of the sharp series,
but the result was in the negative (see page 32 and 3i.)

Finally I wish lo point out, that "method B" (chapter 1 h)
also makes it possible to investigate how under definite
conditions for excitation the intensities of the lines of
the successive numbers of a series decreases.

CHAPTER I.

Description of tlie Metliod.

Method A.

a. For f/roups of Unea of which fhe components have
small differences in wave-lemjih.

If two intensities of light of the same (or almost tlie
same) wave-length are equal, they cause in Ihe same
time the same densily on diflerent places of the same
photographic plate.

We can avail ourselves of this fact to measure intensities
wilh the aid of the photographic plate. The method
most commonly used to compare the intensity of two
close-lying spectral lines consists in photographing the lines
with a properly chosen time of e.xposure and of making
some more exposures on the same plate after reducing
the light in definite degrees.

From the photographs obtained in this way tho curve
of densities is constructed (comp. p. 15).

This method has not only the drawback that it takes
much time but still more that it rctpiires a constant
source of light, which condition is hut poorly fulfilled
with most sources of light which emit line-spectra.
Especially for groups of weak lines which require a long
exposure this method takes very much time. The pho-
tograph must be taken with five intensities at the veiy
least, so that, if each exposuie requires already a con-
siderable lime, the method referred to will take a live
times longer time.

Instead of taking the spectrum a few times, weakened

to certain kwown degrees, markes of intensity are often
applied, by exposing tiie same plate during the same
time "of the original exposure lo light of the same wave-
length arid kwown ratio of intensity.

The marks of intensity provide us with the functional
relation between density and intensity, that holds good
for the plate in question, i. e. the curve of densities.

This method takes a good deal of time as well and
moreover it has the drawback that it is impracticable
with intermittent sources of light in consequence of the
intermittence-effect.

These drawbacks do not occur with the method which
will be described below.

A source of light Li (see lig. 1) illuminates uniformly
a lens Lei, which forms an image of the source of light
Li on a second lens Lc-i.

I 0

i

FJ(5. 1.

This lens Lr-i gives a well-denncd inuige of a series
of snmke->;lass-i»lalos (Hauchglas) V which weaken to a
known degree the light that has passed through Ln on
the .slit Sp of the spectrograph. The used smoke-gliiss-
plutes were supplied by Zeiss. By moans of Canndabalsem
they were stuck on a plan-parallel glass-plate so that a
scale was formed, the dilTerent parts of which transmitted
± 70, ± 55, ± 35 and ± "/n respectively of the

incident light.

The curves of llg. page 28 represent the power of
transmitlance of the reducers for dilTcrent wave-lengths.
From these curves it is evident that these reducers show

little selective absorption.

In this way the slit of the spectrograph is as it were

divided into parts, on which light falls of various degrees
of intensity^).

Care has been taken that a maximum amount of
light falls on the grating of the spectrograph and in such
a way that all tiie light that falls on the slit is used.

The spectra of the source of light weakened to different
degrees are therefore formed simultaneously on the plate
(see plate I).

If the ratio of the intensities, which one wishes to
measure, does not depend on the total intensity of the
source of light 2), the drawback with earlier methods
caused by the instability of the source of light is remo-
ved by our method.

Now one must take into account the fact that the
densily caused by the same quantities of energy is de-
pendent on the wave-length.

The method, which we have described, is therefore
restricted to a comparatively small difference in wave-
length.

Let us remark for the present that by means of a method
to be described in chapter I b an extension of my method
can easily be obtained for the investigation of spectral
lines, which are lying so far apart tliat the supposition
in question does not hold good any longer.

The spectrograph wilh which the photographs were
made is the graling-speclrograph ol the Physical Labora-
tory at Utrecht =\').

Its arrangement gives i)erfeclly stigmatic images, which
is of course necessary for our method, because from
every point of the slit a sharp image must be formed
on the plate.

It i« nlHO poiwiblo to lako uniformly blackcnwl photographic
plate» inHtead of tho «mokc-gInKH-j)latcH. Thwo cauho however
scattering of iho light, that full» on them. Soo dlMscrtnlion
Utrecht l\'J23, R. Riwmn, pag. 17.
*) Which is confirniwl by tho renull«.

») P. H. van ClTrKlir. Z.b. für InHtr.k. 41, 110-118, MtM.

The speclrograph is mounted on two columns of
masonry: a rectangular one A (see fig. 2) and one in
the siiape of the quadrant of a circle wilh a radius
of 2 iM.

Fiu. 2.

In the centre (r of this quadrant a bronze vertical
axis J is placed, on which rests a double T shaped
heavy iron l)eam EF about 2 M. long.

At the other end this beam is supported by a small
bron/.e carriage ir, which can move over Ihe cohnnn/i/>.

This little carriage has Ihe shape of the segment of a
circle of a radius of 2 M. and rests on wheels, the
axes of which are directed towards tho centre (/, so thai,
even when it moves freely the carriage describes a circle

of a radius of 2 M.

In G the concave grating is mounted in such a way
that its normal is parallel to the beam K F.

The grating is an original Rowlandgrating of the size
of 2 X 5 c.iM^ and contains 508 lines lo the ni.M.
The radius of curvature amounts to 2 M. The whole
apparatus is placed in a room apart from the optical

cellar of the Institute. --

The light, after passing the lens Le, (fig. 1) and the
reducers falls on the lens Le, and then through an
opening R (fig- 2) in the wall on Ihe slit « and is refiected
by a total reflecting prism P, which is placcd immediately
behind the slit, to a concave mirror //, the focus of

which coincides with the slit.

In this way the grating receives parallel light from

the slit. J , II

The place, where the spectrum is produced meets the

200

line E F at a distance r =• y q.—\'1 cos":t "

from the grating; li represents the radius of the concave
grating and ^^ the angle HGF. On moving the beam
the visible pari of the spectrum therefore moves over
a parabola NO iV. Accordingly we would have to change
the position of our camera each lime to another part of
the beam (in the case represented in the diagram e. g. at ()).

To avoid Ihis difiicully the light diffracted in Ihe di-
rection I\'JF is made to pass through a concave lens
(/•=70,5 c.M.) so Ihat an image is not formed in 0 but
an enlarged and wel-defined one in C. The dispersion
amounts lo about 5 A per tn.M. for a wavc-lenglh of
5100 A in the first order, 3 per m.M. in the second
and 1,8 A per m.M. in the third order.

The source of light which was used was an electric
arc, the carbons of which arc cored and packed respecti-
vely with suitable salts of those melals of which the
spectra would be examined (concerning Ihis see the state-
ment of the results for doublets and triplets of the va-
rious metals).

\') Fabuy ct Buisson Jourii. tie Pbyn. 40 ts. U, jmg. 933,1910.

The electric arc was with the necessary resistance
connected with the current 220 Volt of the town\'s
powerstation. The lens Lci had a tocal-lenglh of 60 c.M.
and Lc2 of 80 c.M.

In front of the lens Let was a diaphragm which screened
off the continuous light of the carbon rods.

A few of the photographs obtained with the arrange-
menl described are reproduced on plate I.

On this plate we see nine photographs ol the triplet
Ip—is (A 5183, 5172, 51G7) of Mg.

The photographs 3 and i (see plate 1) which are barely
visible on the reproduction were of course to weak to
bo measured. The rest of the photographs on the plate
lent themselves very well to be measured.

Table I gives further parliculurs concerning the photo-
graphs which have been reproduced on plate 1, with
respect to the intensity of the current in the arc and
the time of exposure.

The photographs 1, 5, (>, 7, 8 have been taken with
the same intensity of the current of the arc but with
dilTerent lengths of the arc.

The length of the arc with photograph 1 was about
live limes, with iiholograpli 0 en 7 about threo times
and with photograph 8 about eight limes longer than
with pholograph 5.

TMWA\'l I (IMalo I Mg.)

Part a (see plate I) of the spectral line is unweakened
being caused by the liglit of the arc, which has not
passed through a reducer. This intensity we call 100 "/o.
The densities of the parts 6, c, d, e and f have been
caused bij relative intensities of 69 (6), 5G °/o (c), 35 "/o [d)
and 26 \'/o (e), corresponding with the power of transparency
of the reducers, for light of a wave-length of b\\8

The density of part a as well as that of part f
of the line has been caused by the intensity of the
unweakened light. We always investigated whether the
density of part a was equal to that of part which
was a test whether all reducers V (see fig. 1) were
uniformly illuminated by the source of light. When
the densities of the parts a and f are not equal this
can also be caused by lack of uniformity in the sensiti-
veness of the photographic plate over the surface. All
plates, on which the density of the parts a and f
differed considerably have been rejected.

Every spectral line is therefore produced on the plate
in different degrees of density (according to the number
of reducers), caused by intensities of which the ratio\'s
are known, so that for every spectral line the curve of
densities can be conslructed.

The densities were measured wilh the niicro-photomelcr
of Moll. \')

A more detailed description of this instrument, which
is particularly well adapted to measure quickly and
accurately the density of narrow spectral regions, may
be omitted here.

By density of a homogeneously affected part of the
photographic plate is usually meant Biuau\'s logarithm of

in which i and /\'o represent the intensity of the

radiation, which has passed Ihrongh the exposed and
"ihe unexposed part of the plate respectively. The ratio
between these intensities is found by measuring the

~Y KonrAk. V, Wet. 27, 506, 1910.

ratio between the corresponding deviations u and i/o of
the mirror of the galvanometpr of the microphotometer.

For the deviation of the mirror is proportional lo the
thermo-current in the galvanometer and this current is pro-
portional to the energy, which falls on the places of
contact of the thermopile.

So we can write for the density Z

„ , \'0 , «0
/== logy = log--

The way in which the ratio between the intensities of
the lines of a group was determined from the obtained
densilies will be described by taking as an example
the investigated triplet 1 /) — I « of Mg (X5I83, 5172,
51G7) of plate 03\'.

For the different parts a, b, c, f/, e and f (see plate 1)
of the spectral linos A 5183, 5172, 5107 the deviations »
were measured with the aiil of the microphotometer.

These deviations m and the deviation i/o for part (rof
the plate not alTected by light are given in table 2.

TABLE 2.

Plate 03\'.

From the obtained vnhies t/o, «i, «2, and j/b the
value 2 = log - for each pari l>, c, r/, and f of

a line can be comput.ed. When the density Z of these
different parts of the spectral line is plotted against the
intensy I of the light that has fallen on the plate (the
abscissa being taken proportional not to the intensity
itself, but to log I as is usually done) we get the curve
of densities. We did not however plot as ordinate the

value log — but the value —. In the case that all devi-

® U «0

ations wo are equal for all unaffected parts near the
investigated line, we can readily plot as ordinales the
values M obtained with the photometer for the different
densities on the plate.

This way of doing has in the first place the advantage
of requiring less computing (for we plot at once the
values n given by the photometer, which are read off
visually) and in the second place the inclination of the
curve of densities obtained in this way gives us an
indication, whether the plate has been well developed.

The more sleep the inclination of the obtained curves
the stronger the contrasts between the densities caused
by different intensities.

In this way the line A.\')183 gave the curve A B of
fig. 3, in which the intensity of the investigated line of
the nnweakenod spectrum a^ has been arbitrarily su|)posed
to be equal to 100, so that the intensilies of the other
four parts h, c, d and e have the values, given by the
power of transmit tance of the used reducers expressed
in table 2.

Now, if for the second (weaker) line A 5172 of the
triplet we suppose again that the intensity of the unwoa-
kcnod line is 100, we obtain the curve 6\'for this line.
The intensity of the unweakened line is however not 100
but less and the diminished intensities of this line are less
in the same ratio. Accordingly cach of the points of
C I) must be displaced to points, where the intensity is
smaller in a definite ratio, the value u being retained.

As the abscissa represents log /, this means a shifting

Fio. 3.

of the points of C D over equal distances towards the left.
The amount of this shifting, is not known a priori, but
must be chosen so that alter the displacement to C D\'
the points of 0 I) lie as well as possible between those
of A B. This process may be repeated once more for
the still weaker line A 5167. In the curves of densities
the crosses indicate the observed and the circles the
.shifted points.

In this way we obtain a curve A B, which has been
fixed by many points*).

Now, the average amount of the shifting determines
also at once the ratio of the intensities of the weaker
lines with respect to the stronger, while the spreading
which is contained in the amount of the shifting for the
points of a curve at once gives us an idea of the magni-
tude of the errors, which this melhod may still give.

Hence we can read inmiediately from the curves of
fig. 3 that the ratio of the intensities of the lines
A5183, 5172, 5167 of Ihe triplet 1 - I of Mg is
given by:

/5188 :/6172 : /fiifiT = 100:63:23.

The method, which we have described hero, we shall
further refer to as "method A".

Method B.

b. For (jroups of Ihiefi, the components of which hare
(jreat differences in ware-length.

A nece.ssary condition for the use of method A for
measuring the ratio between the intensities of spectral
lines is that their wave-lengths do not difTer .so much,
that (!qual energies of these «lilTerent wave-lengths cause
a measurable difference in the densities.

\') This melhod of "the Hhifling «f tho curve« of deiiHllim."
waH descrilxxi by H. C. Muikikk and 1\'. II. va.v Cittkut, k\'on.
Ak. van Wet., AniHlcrdam XX11 N-, 5, lO.U

With the doublets ot Nn and Ka this condition is
practically satisfied, and the same is true for the triplet
1 p — 1 s of Mg.

For the doublets of Rubidium and Caesium e. g. the
sensitiveness of the plate however is not the same for
the different components.

The same holds good for the triplet 1 — 1 .s of Zn
and C<i and for many other groups of lines. The sketched
"method A\' cannot therefore be used unaltered in such
cases.

It was of great importance for my further investigation
that a method had been worked out\') at Utrecht in the
Physical Laboratory (with the aid of an energetically
standardized lamp) which made it possible to investigate
as well those groups of lines, the components of which
have a great difference in wave-length.

The method is based on the use of an energetically
standardized lamp, which serves to fix the relation be-
tween energy, wave-length and density.
. This method will further bo called "Method H".

This "Method H" is closely connected with the "Method

A", which has already been described.

The groups of lines, which we want to investigate
are photographed in the same way as with "Method A".
We can of course measure the densities of the photo-
graphs obtained in this way, which are caused on a
photographic plate hy the three lines and plot Ihe curves
of densilies for the different lines, but the ratio between
the intensities wo cannot infer at once from those curves
of densilies, for the density does not only depend
on the intensity but also on the wave-length of the
incident light.

\') P. nooRNKNliAt. Phy-^icR 3.187.1023. In principle the Mand-
ardizing of ihi« lamp Hm already boon do.cribo<l in -Scripta Un ver-
Mlali, nlquo IJibliolheoao Hicrosolymilarum" L. S. Oknhtkin 1023
VIII

In chapu>r-lc wo «ball give a nhort account of this Hlandanliring.

To find the true ratio between the intensities it is
necessary first to measure the functional relation between
the sensitiveness of the used plate and the wave-length.

This was obtained by using a lamp energetically stan-
dardized by Mrs v. d. Bosch and Doornenbal.

On the same plate on which the group of lines, to be
investigated were photographed a photograph was taken
for that same region of wave-lenglh using the said lamp
as source of light. Plate II gives a reproduction of a
plate, on which the triplet 1 /) — 1 s (A 5085, 4799, 4678)
of Cd has been photographed.

The spectrum of the standardized lamp is photographed
entirely after the method A so that the continuous spectrum

«a.
N

S
1

§
1

wav£ IIH6TH

Met tS» M«o

FlO. 4.

is also photographed with difTerent intensities in one
photograph.

In order to make better understood the necessity of
using the standardized lamp, we have plotted in fig. 4
for the region of wave-length 4700 A to ± 5100 A

as ordinates the relative energies causing the same
densiy Z on the same plate (in this case ^ = ± 0,5).

It appears from the curve given, that about twice
as much energy of light of the wave-length 5100 A
is required as of light of the wave-length 4800 A to
give about the same density.

It appears further from the curve in fig. 4- that e. g.
for the wave-length 4910 A and 4900 A the ratio be-
tween the energies, which cause the same density is
18,8 : 18,2 = 100 : 97. Hence it is obvious, that for groups
of lines lying in this range of wave-Ieiigth, having a
difference in wave-length greater than 10 A "method A"
cannot directly be applied.

The way of computing the ratio between the inten-
sities of the lines, will be explained in more details with

the aid of an example.

For this purpose we take the measurements of the
ratio between the intensities of the components of the
triplet \\p- \\ s {X 5085, 4799 and 4()78) of Cd on one
of our photographs (N®. 93). The triplet in question was
photographed on a panchromatic Wratten-Wainwright
plate.

Tho intensity of tho current in the arc was ± C.
Ampère.

In tig. 5 the curves of densities obtained by means
of plato N°. 93 are given.

\') Tho bonrin« of oar molho<l B will bcvumo pnrticuUrly clcnr
from what follow«. O" one of o«r ,.Uto« lino -I 170» ofOlcn.mcl
n grcAter density then tho lino -I r.oa-i where«« "f\'«\'\'"\';«?
tho rnlio of ,ho.cnHiUvcncHHoflhorlnlofor.howRVC.lenRlb«-im5A
and ^^79!) A the energy of lino 4790 A nppcAf«! to bo ±00 /.

of ihnt of lino .m\'iA. .

Aeeordingly .he inten-ilic« given o. g. \'"^^\'\'Vl.wïich

(A. Fow,.kh Won on Sorio« in LinoSi»eclrn 19 2 page 43). wh eh
for tho groator part havo been viM.ally clia.at«! according to tho
density of the photographic plalc, aro not correct.

Fio. 5.

Curve I is the curve of densities of line 5085 Â,
curve II of line 4799 and curve 111 of line 4678.

These curves can be shifted fairly well.Curve V
is the curve obtained from the photograph of the stand-
ardized lamp for A 4678, Curve IV for A 4799 and A 5085
(the curves for these two wave-length coincided).

It appears from these curves of densities, that 90"/o—
91 °/o of the energy of line A 5085 A causes the same
density as 100 °/o of line A 4799 A. 43 °/o of the energy
of line A 5085 A causes the same density as 100 °/o of
line A 4678 A.

If therefore the plate had been equally sensitive to the
light of these three wave-lengths the ratio between the
intensities of the lines would have been:

100 : 91:43. (a)

The spectrum of the standardized lamp photographed
on the same plate for the range of wave-length in question
gives according to curves IV on V that IOO"/o light of
A 5085 of the standardized lamp caused an equal density
as mVo light of A 4799 and that

92 °/o light of A 5085 of the standardized lamp caused
an equal density as 100% light of A 4678.

From the energy-curve of the used lamp it appeared
Ihat the energies Ni of the wave-length in question have
the following ratio\'s to each other

Emi.: Aum : A\'««T8 = 7.1 : 4,57 :3,75 (6)

The ratio between the sensitivennss Gi of the plate for
the three wave-lengths considered is therefore:

In order to obtain the correct ratio\'s between the
intensities of the lines, wo must still divide the values

\') Arconling to Fahrv cl Buihhon, Rcviic d\'opliquo N*. I p«goiJ«

UVJ4, thiK will not bo the ciwo any longer for two curvw of «ionMhe-,

one of which corrciiiwnd« to visible light, tho other to «Urn-
violet light.

obtained under («) respectively by the numbers mentioned
under (c). This gives for the correct result:

/5085 : /4799 : he7s = 100 : 90 a 91 X : 43 X
75085 : /4799 : /4678 = 100 : 58 a 59 : 24 a 25.

c. The standardized lamp.

For standardized lamps, we used Philips Arga-lamps
investigated by Mrs. v, d. Bosch and Doohnenral. \')

The lamp was investigated, the voltage being 5 Volts.

Because of the great importance of this lamp for our
investigation we shall give a short account of the arran-
gement for the energetically standardizing of this lamp.

Tlie incandescent lamp A burns at a constant voltage
and whith the aid of the monochromator M *), when
used with its central slit gives an almost monochromatic
image of the slit in I\\

This image was used as a source of light for comparison.
The energy /v\'; (U was measured wilh a thermopile T

P. DOORNKNIIAL Phynica 3. 1923.

P. H. VAN Cittkrt. PhyHica 3. 182. 1923.

» llcviic d\'opliquo 2 57.00. 1923.

connected with a galvanometer of Moll. The deviations
were registered.

It is evident that in this way only ratio\'s of energy
are determined. The dx was kwown because once for
all the range of wave length, coming out of the slit at
a fixed position of the central slit of the monochromator,
had been measured.

The following consideration gave the solution of the
problem.

The ratio of the energy </: 6 of the lamp A of e. g.
a yellow and a blue range of wave-length is kwowri.
Required is 7\': b* for the same ranges of wave-length
of the ligth-source (the lamp L) which is to be stan-
dardized, the distribution of intensity being, unknown.

If we can measure g: 6\' and 6 : b\' then g\': b\' is kwown
from this.

The measuring ot g: g\' and h : 6\', that is the measuring
of the ratio\'s between the intensities with the same wave-
length, was done by photography. If we remove tho
central slit of the monochromator we get a white imago
of the slit.

Of this light-source thus formed in P an image was
formed on a photographic plate with tho aid of a lens
Li and the spectrograph Sp.

The density which was caused was measured. Light
of different wave-length on its way from P to the photo-
graphic plate is absorbed, refracted etc. to a dilTercnt
amount.

Now this was completely eliminated, for a certain
mtio between the intensities of light of dilTcrent colours
that reached the photographic plato corresponds to a
certoin ratio between tho energies in P measured with
tho thermopile. And so tho whole optical instrument,
consisting of tho lens Lr,, spectrograph Sp and photographic
plato was standardized.

If now, on tho same plato the spectrum of the lamp,
wiiich was to bo standardized and which was also placed

in F (this is essential for the method) was photographed
with the same standardized instrument, with the same

mu UNOTH

Fkj. 7.

of exposure and if we measure the density it
l)0ssil)le directly to determine from this Ihe ratio

between ihe energies of the same r/A-ranges, of which
the energies in P were measured with the tiiermopile.

Division by rf A gave for the lamp to be standardized
the functional relation between the wave-length and the
evergy E-,. The curve which represents this functional
relation for one of the two used standardized lamps is
given in fig. 7.

d. The standardizing of the light-reducers.

We used for reducers a series of Zeiss\' smoke-glass-
plates. These reducers of smoke-glass are to be preferred
to the photographic reducers, if the power of transmit-
tance of the reducers cannot be measured in the apparatus
itself, in which they are used, as the latter give rise to
scattering

As these reducers of smoke-glass might show selective
absorption Ihe degree of weakening had to be measured
for each dilTerent colour.

The percentage of the incident light transmitted by the
reducers was measured in two ways. Tho first method
which we shall call "method a" was worked out for
the measuring of absorptions by Mrs L. S. Ohnstein and
II. G. Burger«).

It starts from tho point, that light, passing through a
monochromator and concentrated by a condensor on a
thermopile, which is connected with a galvanometer,
causes deviations of its mirror which can bo registered.

This remarkably quick method gives very reliable
data for tho power of transmitlance of tho reducers
especially in tho red up to tho blue part of tho spectrum.

\') Rasha Riwmn DiwprUlion Utrccht 1»\'23.
\') L. S. Oiushtki.s nnd H. C. HuiUiKK, Kon. Akml. vnn Wet.
XXIX, 1020.

SceaUo M. A. C. Dknikr van ni:u Oos Arrhive« Ncorlftnd*i«oi«,
M5rio III A, tome VII, p. NO, (1023).

On account of the intensity of the nitralamp being
too slight for the ultra-violet and violet part of the
spectrum this method cannot be used satisfactorily for
these parts.

For the rest the same difficulties arose with our
measurements as are mentioned in the communication of
Mrs L. S. Ornstein and H. C. Burger, viz. the drawbacks
caused by the light scattered in the monochromator.

The second method used and which we shall call
"Method /3", made it possible to measure the power of
Iransmittance of the reducers in the apparatus with which
our measurements of the intensity had been made, so
that the optical conditions were exactly llie same during
the standardizing of the reducers as during the measure-
ments of the ratio\'s between the intensities.

This was not the case with the "Methode" oc.

"Method /3" starts from the fact, that the intensity of
the light of a small range of wave-length of a continuous
spectrum which falls on the photographic plate, may be
supposed to be proportional to the width of the slit of the
spectrograph. In this case the slit may not bo too narrow
as by the diffraction then arising a part of the light that
has passed through the slit does not reach the grating.

In the place of the light-source Li (see fig. 1 page?)
was put a little nitra-lamp, burning at a constant voltage.

Photographs were then taken of tho continuous spec-
trum of this lamp, the successive widths of the slit
corresponding to 100, 60 and 111 divisions\') of the screw
of the micrometer.

On plate III such a photograph is reproduced. Wo
know therefore that the intensities, which are caused
by the spectra «i, r/a and <it (see plate 111), are to each
other as 100:60:31, likewise those offc, and 63.

With the aid of the "shifting method" of the densily-

>) Each of tho divisions corrcuponde«! to a width of tho Mil of
«peed of tho »crow of the micromelcr.

curves described in chapter 1» we were able to measure
in a simple way the power of transmittance for the
various reducers.

Statidardizing of the reducers (A = 5844).

spectra a, b, c, d and e are equal to 100: G9 : 55 : 33 : 25.

Here again we have plotted the deviations u of the
galvanometer of the niicrophotometer against the inten-

Poxcer of transmittance of the reducers.

POWtfl OF TKANSHITTANU OF THE. RtDUCtHS

Fin. 0.

sitics of the light that has fallen on tho plate (for the
latter the logarithmical scale is used).

The values obtained in this way for the power of
transmittance of the reducers deviated 3 ®/o at tho very

highest relatively to the unweakened light from those
which were measured according to "Method a."

In fig. 9 giving the curves for the power of transmit-
lance of the reducers and where the wave-length has
been plotted against the percentage ot the transmitted
light, the circles indicate the values obtained with Ihe
method x, the crosses the values obtained with the
method /3.

For the region 500 — G25 (i (j. we have drawn the
curves through the circles because a higher weight could
be attached to these values then to those, obtained by
"Method /3."

e. The photographic plate and the deceloper.

For the red and yellow part of Ihe spectrum we used
chiefly Panchromatic Wratlen and Wainwright plates.
A few photographs were also taken with panchromatic
Paget and Ilford plates. For groups of lines in tho
green up lo the violet part of the spectrum orthochro-
matic Paget plates were first used. It appeared however
that in this part the panchromatic Wratlen and Wainwright
and also tho Ilford and Paget plates caused stronger
contrasts in the density lor difTerent intensities than the

orthochromatic ones.

This is the reason why we almost exclusively used
Wratlen and Wainwright plates for later measurements
as long as our supply hold out.

For developer wo haven chosen glycine \') in a dilulion
of I :2\'/i nl a lemporaluur of ± 15® centigrade.

The lime for dovelopmonl is about G minnles.

\'J l>oil<xl (llnlillcd wAtpr 600 gr.

Hiil|ih!to of Mxlium 150 gr. ,

glycin« 30 gr. I of wnlor.

oirboniitcof {wliuwiuiu 150 gr. !

f. Discussion of the errors influencing the results.

It appears from the above how inportant a part the
photographic plate played in all our measurements.
Janssen has rightly called the photographic plate "la
véritable rétine du savant". Owing to the plate a more
close investigation of many natural phenomena has been
made possible. But after having stated the possibilities
which the photographic plate offers for scientific inves-
tigation we must now also point out its imperfections
and these imperfections form the principal source of
errors in our method.

The errors of the photographic plate may Ije divided
(as has been traced at length by Miss Riwlin \') into
errors caused hy the glass-plate, by the layer of gelatine
and by the silver of the plate.

A second circumstance which influences the exactness
of our results, is the accuracy with which the power of
transmittance of the reducers was determined. The error
caused by this however is not great. As has already
been remarked on page IG our \'shifting method" of the
density-curves gives us an indication of the magnitude
of the above-mentioned errors by tho spreading which
appears in the amount of the shifting.

The amount of this spreading always increased in
the same degree as the groups of lines showed a greater
dilTerence in wave-length.

As far as "method A" was used, the largest error for
lines which are not too weak can therefore be estimated
at 1 to 2 °/o of the intensity of the strongest line.

In "Method B", whore the standardized lamp was used,
the errors of the standardizing make themselves felt also.

Therefore it is a matter of course that the accuracy
of the final result is less wilh "Method B"\'then with
"Method A".

») Ra88A Riwlin. DisBcrUlion, Ulrccht, pag. 25, 1923.

Yet the largest error Ihen obtained in the resulting values
for the ratio\'s of the intensities may be considered to
be about 5 ®/o of the intensity of the strongest line of
a group.

To avoid the errors, occurring in the proximity of
the edges of the plate, the groups of lines and the con-
tinuous spectra were as much as possible and moreover
repeatedly photographed in the central part of the plate.

If the intensities of the groups of lines, to be inves-
tigated are weak, so that they require a long time ot
exposure the photograph shows a continuous background
caused by the continuous light of the glowing particles
of the carbons in the arc.

The density on the place of the spectral line is
therefore caused by the sum of intensities, of the line
itself and the continuous light for tho wave-length of
the spectral line in question.

From tho average of tho densities to tho loft and
to the right of the spectral lino in question tho relative
intensity can then be determined with the aid of the
continuous background relatively to the total intensity
which caused the density on tho place of tho line.
The corrections to bo applied in this way did not as a
rule amount to more than ± 2 to 5 °/o of tho total
intensity. In a few cases however (seo results for Cs
page 34), it amounted to ± 25 °/o.

CFIAPTER II.

Kesnlts.

a. Sharp Series of the alkalis (Table III).

For the case of all investigated alkalis their chlorides
were brought into the arc.

Of the sharp series of Na the doublets 1 rr-Sr (A 6160-G154)
and lr-4<j- (A 5153-5149) were investigated. The intensity
of the current of the arc was varied to make out whether
the transition-probabilities of the electron were influenced
by the conditions of excitation. It appeared however
that no measurable influence existed.

Of the sharp series of Ka were investigated Ihe doublets
lff-4(r (A 5802-5782) and lz-5(r (A 5339-5323).

The intensity of the current of the arc was not varied
while taking these photographs.

For the AV as well as for the Aa-doublets "Melhod A"
was followed.

With lib and Ch the components of the doublels are
already at a greater distance from each olher so thai
for the investigation of the doublets of these metals
"Melhod B" was used.

Of Jib the doublet l?r-4a-(A G1G0-G071) was investigated,
of Cs the doublet Ir-5a- (AG034 and 5839).

In the following table the strongest line is always
arbitrarily supposed to be 100, the amounts to which Ihe
measured intensilies must be corrected on account of
the continuous background of the lines are given for Na.

For the olher lines these amounts have not been given
but the given ratio\'s between the intensities represent
the corrected values unless the contrary is expressly stated.

TABLE 3.
Sharp Series.

viiit

The intensity of the continuous background, given in
table 3, with the iVa-doublets is expressed in per cents
of tiie intensity of the strongest line.

The lines, of the photographed Cs-doublet were very
weak. The intensity of the continuous background in
the neighbourhood of the lineG034 was about 20 "/o, that of
line 5839 was ± 25 % of the intensity of the strongest
line. So if we correct for this intensity of the background
the ratio between the intensities of the components of
this doublet becomes also ± 100:50.

Hence it appears, ihat the. ratio\'s brtween ihe intensiiies
of thi\' donhlets of ihe nil,-alia is equal to 2:1 and independent
of the nature of the metal and ihe ordinal number of the
doublet in ihe sfries.^)

b. Sharp Series of ihe JCarth-alkalis.

Of the earth-alkalis we first invesligated the triplet
l/>-l.s (a 5183, 5172, 5107) of magnesium. The cored
carbons were packed wilh magnesium-powder.

As appears from Table 1 page 11 with magnesiun» the
intensity of the current was varied, but here as in the case of
Na page 32 no influence on the ratio between the inlen-
sities of the components of the lines was measurable.

The continuous background appearing wilh this triplet
was very slight and could be neglecte«! entirely. As was
already staled at length in Chapter I "Melhod A" was
followed for this triplet.

üfCfMhe triplet Ip-ls (AO 102,0122,0102) was investigated.
The first measurements of this triplet were made wilh
the aiil of "Method A". Tho photographs showed a rather
strong continuous background. The results obtained
by the first measurements gave as ralio between the
intensities of the three components 1(X):80:\'40.

•) Thi« rmilt in annlogoiiH U) iho rule of I»r<-Ht(.n for ihi-mnpnclic
neparMliaiii« of tho t<|KH:trul iincx.

These resiills showed a deviation from the regularity
which could be observed in the results obtained for
Mg, Cd and Zn (see table 4).

Presuming that the selfrevei-sion of the lines, which
will of course be greatest with the strongest line, was
the cause of this deviation, a few more photographs were
taken, the concentration of the vapour of the metal in
the arc being much smaller.

This was done by mixing with carbon the salt, that
was put into tho cored carbons. .Moreover "Method B"
was used in these investigations. Corrections were made
for the light of the continuous background, which was
rather strong. For salt in the arc we used Ckt /«Yj, as
with this salt tho arc could be kept much steadier than
with CitCh.

Tho results obtained are given in table 4 and agree
with those obtained with Mg. The accuracy in the case
of this triplet is loss than in the case of Mg, owing to
the unfavourable circumstances, mentioned.

Of Zu and Cd tho triplets Ip — U wore investigaloil.
Hero too the conrontration of tho vapotn- of tho metal in
the arc was kept as low as possible in order to limit
the possibility of solfrovorsion.

For both motals the chlorides wore used to 1111 the
carbons.

Tho accuracy attained is higher for Zn than for
Cd, because with Cd tho three components aro further
apart than with Zir, antl therefore the unequal sonsi-
tivonoss of the plate over its surface makes itself more
felt.

From tho above it is obvious ttiat the ratio hot ween
the intonsilios of tho components of the triplets of tho
second series of tho (>arth-alkalis is approximately equal
to 100:00:20 or 5:3: 1, and independent of the nature
of the metal.

Wo have not yet investigated whether the ratio be-
tween the iutonsities of the compononts of a triplet aro

inilcpendenl of tho ordinal number in Ihe series. This
may be done for the triplels of Mg, as soon ns our
methods will have been properly worked out for the
ultraviolet pari of tho spectrum as well.\') .

\') The melh<xlM worktHl out in the Phynicftl I.«lH)rntnry nmk.\'
a Btamlanliziiig of the rc<luc«TH f.)r thi-i HiHttlrnl-rcgion iOri»ible.

c. Sharp Series of MuUiplet systems.

As a consequence of invesligalions made by Catalan \')
and Miss Gieseler mulliplet systems of spectral lines
have been discovered in the spectra of Mn and Or.
Since then more multiplets have been described in rapid
succession viz. by Catalan for Cr, Mo, Sc; by Pascuex
for C and 0 by C. C. and H. I{. Kiess for Mo and
Fe, by Walters") for Fe, by Laporte and by Meggers
for V.

From these investigations could be concluded that with
all these multiplet systems the «-term is single and the
^)-term threefold.

According as the permanent maximal number of these
terms is three-, four-, five, sixfold etc. we speak of
of triplet", quartet-, quintet-, sextetsystems etc.

Hence the />-term in all these systems being always
threefold we can distinguish triplets from triplet-, quartet-,
quintet-, sextetsystems etc. Now it was important to
investigate what were the ratio\'s between the intensities
of the components of these triplets.

Professor Sommehfkld suggested that as the intensities of
the components of a triplet of a triplet-system are lo

r \'1 J

each other as , presumebly tho ratio\'s would bo

() 4- iJ

for a quartel-.syslen) : ir \' T

\') M. A. Oatai.AN. Trnn... Soc. 223 S. 127, III22.
\') n. {1UWKI.ku. Ann. d. Phyn. (i» S. H7.

.M. A. Catalan. Ann. Soc. Ti«. y Quim LM. S84 nnd
213, I«23; 20 H. WW, I»22.
M F. I\'awhkn. Ann. d. rhyn. 71. i?. 537, 11123.
\') C. C. and 11. K. K\'iksh. inionc« WJ. S. iKilC 11)22;

•toiirn. Wnnh. Ac««l. of St-icnrc 13. 6. 270, 11)23.
*) F. M. Waltkiw. ill. 13. 8. 213. 1»23.

O. Lai\'oktk. Nauirwiw. II. S. 771), ll»23; I\'hy«. ZoilHchr.
24, 11)23.

") W. F. .\\IwiUKUS Journ. \\V»Au Acad, of tkieiiro 13. S. 317.1023.

i.l
2 \' 2

i. A
2 ■ 2

... 975
for a septet-system

. . . 10 8 G
for a octet-system — : — :

lie was so kind as to mention in a letter to us
triplets, suitable for an experimental investigation.

Of these triplets 1 investigated the triplet A 0021,0016,
0013 of Mn (sextet-system) and the triplet 4-823, 4783,
4754 of Jfn (octet-system). With the other groups of
lines which were mentioned, dilliculties arose wilh our
method of investigation, partly because of their being
too faint, partly because they were for our melhod too
far in the red part of the spectrum.

The results concerning the Mn triplets are given in
in table 5. The agreement between the measured and
the expocted ratio\'s is indeed very striking.

TAHLK 5.

d. Diffuse Series of the alkalis.

Of the diffuse series of Na we invesligated the doublets
1 r-3 3 (A5G8S-5082) and 1 IS (X 4982—Î-978).

The hivestigated doublets of tho first diffuse series of
Kn are 1 t—(A 5832-5812) and 1 s—5 S (A 5359—
5343), of lib 1 --4 5 U G298-G20G), 1 --5 3 (A5724-
5G48) and 1 --G 5 (A 5432—53G3).

As salt in the arc we used chlorides of the above
mentioned metals.

The doublets of the metals Aa and A\'^r were investigated
with the aid of "method A", for the doublets of lib
"method H" was used.

As the ^-levels are practically not separated wilh these
doublets, single doublets are caused by Ihe transition
from Ihe h level to tho t energy-levels.

Wilh the melal Cs the doublet 1 t—5d is a complex
doublet consisting of the lines A G127, G213 and GO 10.

For the investigation of this group we used "method H".

Table fi gives Iho results.

We may mention here that the doublet I t — 3 o of
A\'rt was photographed with different intensities / of tho
current in the arc. For photograph G4« (see table G)
/ =£ V An)pèr<!, for photograph GG\' i was G,4 Ampère
and for tUi"^ i was 2,5 Amp. An influence on the ratio\'s
between intensities of the components of this doublet was
however not observe<l.

On considering tho results concerning Ihe diffuse series
of Ihe alkalis, it appears that the ratio\'s between Iho
intensities of the components of single doublets of this
series are equal to 100:50 or 2 : I, exactly as wilh

those of tho sharp series.

It is remarkable that with the complex doublet of
Cs the ratio between the sum of Ihe inlensities of the
lines G2I2 and G217 ami the intensity of line GO 10 is
also ap|)roximalely ecjual to 2:1 (this is more closely
discussed in chapter 111).

e. Diffuse Serii\'s of the earth-alkalis.

Of this series the complex triplet of Cf/(1 p — was
investigated. For this purpose the carbons of the arc
were packed with a mixure of fluoride of Calcium and
carbon.

This complex triplet consists, as is well known, of
six lines which are represented in iig. 10 in the way
introduced by Sommerfeld.

cC,

/ /s ^00

Fki. 10.

The occuring lines are A44r)(),Gl (1 />i — 2 r/s)

A 4455,88 (i - 2 ih)
A 4454,77 (1 -2(/,)
A 4435,07 (1 — 2 r/s)
A 4434,95 i\\ Pi- 2 r/s)
A4425,43 (I />» —2^/3).
Tho observed intensities L\'x|)resscd in the intensity of
the line A 4454,77, this latter being arbitrarily put equal
to 100, are given in table 7.

The mean values of the relative intensities given there
have been printed in the vertical arrows in fig. 10, which
represent the occurring spectral lines.

TABLE 7.

If we call the. sum of the relative intensities of those
lines for which the />i-level is final Ihe sinn of the
relative intensities of those lines for which the /)2-level
is final Sj,^ and S^^ the relative intensity of the line for
which the /)3-level is final, it appears from the relative
intensities represented in fig. 10 that

= 119:73:25

or appro.ximately

= 5:3:1.

The.se are the same ratio\'s a.s between the intensities
of tho components of the triplets of the sharp series.

f. Ikrgmann-serien of the earth-ulhdh.

As we have already seen in the introduction the group.s
of lines of this series are observed as single triplets as
long as the 6-Ievels of this series are not yet wide
enough apart to obtain a perceptible separation in the
spectrograph. These three observed components correspond
to the transition of the electron from a single />-enorgy-lovel
to the three levels d-i and f/3. This case occurs
with the triplet of Ca 1 — 3(A 4585, 4581 ami 4578).
The results of the measurements are given in table 8.

Tlie ratio\'s between the intensities of tiiese components
are tlierefore approximately given by

7:5:3.

The group {d — \'ib of St\' was taken in the lirst
as well as in the third order spectrum.

Wilh those taken in the first order Ihe slit of the
spectrograph was taken so wide, that Ihe componenls
A 4803,12, 4892,69 and 4892,03 overlapped, likewise
the componenls A 4809,19 and 4868,74. In this way
the sum Sj^ of the intensities of the lines A 4893,12,
4892,69 and 4892,03 for which tho (/,-level is final
are compared wilh tho sum of the intensities of the
lines A 4869,19 and 4869,74 for which the f/a level is
final and with the intensity .S,/^ of the line A 4855,08 for
which (/a is final.

The result of the measuring was:

Photograph 117*: : : = 100 : 70 : 41.

Hence tho ratio\'s obtained hero arc the same as for
the components of the single triplet I f/ - 3 /> of Cn.

In the third order this group I d — 3 b of Sr was
sulliciently separated to measure the ratio\'s between tho
inlensilies of the six lines of the complex triplet 1 r/ — 3 b.

The result is given in table 9, the intensity of the
strongest line being again supposed to be equal to 100.

While photograph 132 was being taken the arc con-
tained comparatively nmch salt while for photograph
134 it contained little.

g. Principal Series.

Finally we shall mention a few measurements concerning
some groups of lines of the principal series. As has
already been indicated on page 4 and as will appear
more clearly in Chapter 111 page 49 it proved to be
advisable to investigate some groups of the principal
series too.

The doublet 1 a- — 2 s- of (7« (A 4555,20 and 4593,1 (>)
was investigated. By making the concentration of the salt
in the arc very slight, selfreversion was avoided as much
as possible.

The result of the measurements is given in table 10.

TABLE 10.

Further the triplet U" — 2 //\' of the principal.series of
6V (a 5288,42, 5200,05 and 5204,51) was investigated.
The result of the nieasurement with "Method A" was:
hiw Jmi: hiOi = 100: 72 : 45.

CHAPTER III.

Summary of the results.\')

On surveying the results, mentioned in the preceding
chapter, it appears:

1°. that the ratio between the intensities of the com-
ponents of the doublets of the sharp series of the
alkalis is equal lo 2:1 and independent of llie
nature of the metal and of the ordinal number of
the doublet in the series (see table 3).
2". that the ratio between the intensities of the triplet-
components of the sharp series of Ihe earth-alkalis

jg I. i . independent of the nature of the metal»)
(see table 4).

3°. that tho ratio between tho intensitios of the lri|)let-
compononts of the shari) series of a sextet-system
is 4:3:2, and of a triplet of an octet-system 5:4:3
(see table 5).

In all Ihe cases mentioned under 1°, 2» and 3" we
have lo deal with linos which arise through Iransition of
the outer electron from one initial level to a complex final
level. Wo will now consider the following fable for tho
^-values which have been intr()duco<l by A. Land^*) for
the characlerizlng of the spectral terms mid with the

>) Thi« chnplcr givcH the contents of ti paper of H. C. lUmdKU
nnd tho author. Zciloohrift fiir Phyn. 11)24.

\') The indp|>entlenco of tho ordinal nnmbor hnx not yot conMidcrwl
here. Thin will bo iwr-sible, when tho nicnM>n<nientj< c. g. for tho
Mg. triplet« CJin Imi ,.,n>tinuc<l inU) Iho uUraviolol. part of tho Bpeotrum.

A. La.s-dk. Z f. I\'hy«. IB. 181». n»2:{.

4G

TABLE of the J-values of the inulliplet-terins.

aid of wliicli he is able lo describe the anomalous.Zeeman-
separations. The J-values have been borrowed from a
table, which Prof. Lande \') has been so kind as to send me.

If we compare the observed ratio\'s between the
intensities wilh Ihese J-values of the final-levels, the
results sub 1", and 3° can be summarized in the follo-
wing rule:

The ratios between the intensities of the doublet- and
triplet-components of the sharp series are equal to the
ratio\'s between the internal quantum numbers J") of the
final levels. (Rule I.)

Now it is very remarkable that Rule 1 also holds good
for the cases in which the inilial levels are multi|)le, but
so close together, that the spectrograph cannot resolve
the multiplicity in question.

For it appears from table G, that the ralio between
the intensities of the components of the doublets of the
dilTuse series of the alkalis is also 2: 1, when the sepa-
ration of the ^/-levels is loo small lo be resolved.

If we consider the f/-level to be single the duplicity
of the ;>-levels gives Iwo components, the intensities of
which, in accordance with Rule I are to each other as
2:1. that is lo say llie same ralio as between the inter-
nal (piantum numbers of Ihe Iwo final levels.

For the group of lines 1(/—3/> of the BEiuiMANN-series
of Calcium this Rule I holds good too. (See for this
page 43 Chapter II).

As the /;.|evol is not separated this group consists of
three components tho ratio\'s between the intensities of
which are the same as between Ihe internal (|uanlum
numbers of the final levels (/, that is lo say, the inlen.silies
of the components are lo each othei as 7:5: 3.

In these cases some of tho componenls are comple.x,

\') Compare «1.0 Z. f. Phyn. 15. 8. IS»-\'. 1923.

») Wo adopt Landk\'h <inantum iininherH. \'Ihf riilioV iMUween
the IntenKilioH cam bIho I)o de^c rilxNl l)y meaiin of ihn iiitoriml qnuii-
tum number» of SoMMKiu-Ki.i).

though not resolved. Hence their intensities are equal
to the sum of the intensities of the components of their
common final level. The accordance just mentioned
with the Rule I in the case of the unseparated initial
levels led us to expect that with separated levels a cor-
responding regularity would exist.

The smn of the intensities of the components of a com-
plex line, which corresponds to transitions of the electron
to the same final level are to each other as the internal
quantum numbers J of these final levels. (Rule II.)

This Rule 11 which is a extension of Rule 1 is con-
firmed by the observation of tho complex doublet
Ir — 5 3 of Cs (see chapter 11 page 39), as well as by
that of the complex triplet 1 p — 2 rf of Ca (see chapter
If e page 42).

Now it is important to realize that a ratio can be
indicated between the intensitios of tho components of
a complex doublet and triplet, for this means that,
when Ihe initial levels of the components to be compared
are different, this ratio is likewise a number characteristic
for the components concerned. Rule II points already
to the same fact namely, that the ratio between tho
concentrations of the initial levels of the components
is a number characteristic for those components, which
depends not at all or only slightly on Ihe circumstances
under which the omission lakes place. Though actually
our rule is an approximation holding good only as long
as the (lifTorence in energy between the levels in question
is sufficiently slight, wo shall consider it in what follows
to he rigorously true and trace to what conclusion this
will lead.

Hence it appears to bo of some purpose to investigate
the intensities of Ihe components of a complex line of
the principal series. These components namely have
difTeront initial levels but a connnon final level.

As a first example we ujontion the doublets of the
principal series of the alkalis. For the ratio between

the intensities of the D-Vines of Na, various investigators \')
have found the value 2:1, the line Dz for which the
internal quantum number of the initial level is 2 being
the strongest.

This ratio 2: 1 which has also approximately been
found by us for the group 1 a-— 2 r of the principal
series of Cs (a 4555,20 -4593,10) (see Chapter 11\' page 44),
is lowered considerably by self-reversion, for the concen-
tration of the absorbing atoms is very great. The more
however the density of the emitting gas is reduced, the
more the ratio between the intensities of the components
approaches to 2:1.\'\')

Here the internal quantum numbers of the initial r levels
are 2 and 1 and so it would seem that in the principal
series the internal quantum numbers of the initial levels
determine the intensities of the components.

This supposition was confirmed by the intensilies of
the triplet 1 - of llg.

For these three components F. Pascuen gives the

ratio

100:00:20 = 5:3: 1,
which numbers are to each olher as tho internal
quantum numbers ./ of the initial levels pi, }h and
As this group [ s — is situated in the infra-red and
the distance between the components is small, tho
invostigalion gives us at once tho ratio between thb
intensities. Our measurements of tho intensities of
tho threo componenls of Iho group A 5208,42; 5200,15;
5204,51 of Cr show lhal the ratio between Iheuj is as
100:72:45 (sec chapter 11« page 44), Tho group in
question belongs to tho quintet-system and has for symbol
1 s" — 2 />".

\') M. Gouv. Ann. «1 chem. et do I\'hy«. f) (18) 70. 18751.
«) In tho CMC of Iho I) linon of Na thin w.w aHcortainod onco

inoro by uh.
») F. Papciikn. Ann. d. Thys. 27, 558, 1008.

7 5 3

The J-values of the initial levels are j. Hence

with these lines of the principal series the intensities
of the three components are also proportional to the
internal quantum numbers J of the initial levels.
We have therefore as counterpart of Rule I:

The ratio between the intensities of multiple spectral lines

of the principal series is equal to the ratio between the

internal quantum numbers J of the initial states of the
atom {Rule III).

As now the initial levels play the same part as the
final levels with the sharp series, we tried to generalize
Rule III and to test the following rule for the intensities
of multiple spectral lines.

The sums of the intensities of components of a complex
spectral line which corresponds to the transition of the elec-
tron from the same initial level are to each other as the
internal quantum numbers J of these initial levels {IMe IV.)

This rule is the counterpart of Rule II and we main-
tain that the intensities of the components of every com-
plex line must satisfy botli rules. As a test we shall
apply both rules to the values, given on page 41 for
the relative intensities of group 1 — 2 rf of Ca. Of these
numbers we give a survey in the following table 11.

The J-values are printed by the side of the symbols
for the levels. Rule II says that the sums of the rows

5 3 1

are proportional to the J-values ^ : ^ : g ^^ p-levels,

whereas according to Rule IV tho ratio\'s between the
sums of the columns must bo equal to the J-values
3 5 7

- : - : - of the initial rf-levels.
2 2 2

We have already tested "the first assertion on page 42,
the second part of the rule requires that the ratio

(1 19-1- 25) : (18 -t- 54)

2 do

holds good. It is true that the stronger lines ares lightly
too faint, but taking into account the selfreversion which
certainly can not be neglected, the agreement may be
considered satisfactory.

Rules II and IV together with the ,selection principle"
which excludes certain transitions are not sufficient for
an unambiguous determination of the intensities of the
investigated lines.

In the last mentioned example of the complex triplet
the ratio\'s between the intensities ot the six components
must be determined, that is to say, the number of the
unknows is five. Rule II and IV give each a ratio for the
three sums in question and together they give four equations.
Hence it follows that one more equation is required to
solve the problem. In order to find this equation we
will first confine ourselves to the simple case of a com-
plex doublet.

Rules II and IV give each an equation and these two
equations are sufficient lo determine tho ratios of tho inten-
sities of the three components of the complex doublet.

We write the result of the simple calculation at once
for an arbitrary azimuthal quantum number fc of tho final
state, the azimuthal quantum number of tho initial state
being equal to A; 1. If we put = 1, 2, 3 .... we

obtain successively the intensities for the series sp, pd,

db---- In the following table the sum of the three

intensities has been put equal to 1.

TABLE 12.

The J-values of the two initial levels are and A;1
these of the final levels k — 1 and k. It is convenient
to introduce instead of the internal quantum numbers J
fractions which have J for numerator and of which the
denominator is the sum of the J-values of all initial-and
final-levels respectively. These fractions are given in the
table and will henceforth be referred to as "relative"
qiiantum numbers. In a table like the one above, the
sum of the inlensities in every row or column respectively
must be equeal to the relative quantum number concerned,
printed by the side of them. We shall now apply
table 12 to the case of the diffuse series series) of
the alkalis. The computed ralio between the intensities
of the components is given by table 13.

TABLE 13.

Pi

P^ IT

- \'f

Only Uie numerator of the fractions for the intensilies
has been given, the common denominator (2 A- — 1)
(2 /c 1) = 3 X 5 = 15 has been omitted. Applying
Rule II and IV the ratio\'s between the intensities ought to be

9 : 5 : 1 = 100 : ± 55 : ± 11.

The observation of the complex doublet In- — 5 ^ of

has given the result (comp. chapter It*\' page 40),
100:55:13

As we see, the agreement is sufTicient to confirm our
rules II and IV.

In order lo determine completely the ratio\'s between
the intensities for the complex triplet and also for more
complicated cases, we generalize table 12. For this we
observe that there is a component the numerator for
which is 1. (lable 12) independent of the azimuthal
quantum number. 11 is that very component, which
according to Sommerfeld\'s intensity-rule \') must have the
smallest intensity, as the change of the internal quantum
immber differs most from the change of the azinnitlial
quantum number.

Generalizing we therefore assume Ihe validity of the
following rule:

The intemitif of a component of a complex line expresxrU
in the sum of all components as a unit is a rational frac-
tion, the denominator of which is the product of the sum
of the internal (piantum numbers J ") of the initial and
final levels respectively. The numerator is 1 for that component
with which the changes of the internal quantum numbers
differs most from the changes of the azimuthal quantum

numbers. (Rule V).

In all cases the rules II, IV and V are sufllcient to

calculate, without further assumption, the ratio between
the intensities of all the components of a complex line.

By the principle of selection exactly so many lines
have been excluded as to make these three rules yield
a sufficient number of equations.

In table 14 the intensities in this way computed for
arbitrary k are given for a complex triplet.

TABLE 14.

(G/,_3) (Gfc 3)
11

(0 ~k - 3) (6 k 3)

12 A:-\')
"(O A:- 3) (O A: 3)

1

Ok 3

__11

14

((; k - 3) (O"/: 4-3)
0

OA; 3

12 A: — 9
(O A"- 3) (G k 3)

0
0

2 A- 3

The intensity-fractions can easily bo deduced by
means of rules II, IV and V from the relative quan-
tum numbers added in tho table; so e.g. the intonsily-
12A:^—12A:-9 ^^^ ^^^^^^^

(d k - 3) (0 k -f- 3)

, 2A- —3
relalivo quantum number

3\'

fraction no other numbers occur. Wo lest table 14 llrst
by means of the pd group of Clalcium, the ratio between
the intensilies of which is" given on page 42. Tho inlen-
silies for k == 2 computed by means of tho above table,
we alter to the elTecl, thai Iho intensity of the s\'lrongesl
line is equal to 100, and in this way wo get:

The results of our measurements have been added in
brackets to the values computed according lo the rules
11, IV, V.

The group of lines 1 r/ — 3 b of Sv is also interestmg.
As wo have seen in chapter 11 it was just possible with
our arrangement to resolve the six components of this
group in the third order of the spectrograph and lo measure
the ratio between their intensities.

In table 10 are given the computed and the observed
intensities (the latter in brackets).

TABLE 10.

bt

For the two complex lines (l/)-2f/) of Ca and
(1 __ 3 h) of Sr the agreement between Ihe results,
ohiained with rules 11. IV and V and the observed values
is striking.

Wo have not yet measured intensities of Ihe components
of complex groupes of lines of quartet- and quintetsystems.

It is possible however to predict in the mamior indicated
above the ratio between tho intensities in these cases.

5G

Finally we may observe the following:

1°. Our measurements hitherto only referred to lines
the components of which differ comparatively little in
wave-length. In this case the ratio between the inten-
sities of the components is approximately equal to the
ratio of the number of transitions of the electron producing
the lines, as the energy-quantum hy which is emitted
at every transition is practically the same for those
components.

In principle it makes an important difference whether
our rules are meant for the intensities or for the number
of transitions.

This can only be determined by measuring the intensities
of components the //y of which differ greatly.

2°. It is important to notice that the intensities
according to the rules given, with increasing values of
the azimuthal quantum-numbers k, all converge towards
zero, except the Sommerfeld\'s "strong" transitions, with
which the changes of J and k are equal.

The components which correspond to these "strong"
transitions all converge with increassing k towards the
same limiting value.

Suffice it to mention this extrapolation which is of
great importance for the correspondence-principle.

3". For a further theoretical discussion of our intensity-
rules we may refer to a publication by Mrs L. S, Ornstein
and II. G. Burger which will shortly appear in the
"Zeitschrift für Physik".

Plate I.

/

c
<f

a.

II

II

<P:: :

STELLINGEN.

y3

Stellingen.

L

Inlensileitsmelingen van spectraal lijnen kunnen dienen
ter J)evestiging en opsporing van spectraal serien.

II.

De resultaten der absorptiemetingen in enge spectraal
gebieden, in het bijzonder die van absorptie lijnen, hebben
zeer geringe waarde.

III.

De voorstelling, welke E. Run» geeft von de lichtemissie
der Nevenserien, is onvolledig.

K. UuiM\'. Ann. der Phyn. 73 8. 10, 1024.

IV.

De quantitatievo verklaring, die G. G. Ahhot en zijno
medewerkers geven van do verandering der energiever-
deeling in het zonnespectrum bij variatie van do zonno-
constantc, is niet houdbaar.

Ann. Smithh. [n«t. IV, blu. 200.

V.

Do wijze, waarop Michki.son en Pf:ase bij hunne methode
tol bepaling van do middellijn van sterren rekening houden
mot do lichlverdceling over het sterrooppervlak, is onbe-
vredigend.

ANlrophyuicAl Journal vol. LUI, pag. 254, 1021.

VI.

Het convergentiebewijs van E. Gzuber voor de integraal
ÜM dx is onjuist.

O ^

E. CzUBER. Vorlesungen über Differential- und Integral-
rechnung, II, III® Auflage, S. 164.

VII.

De integraal j i® voor elke reêele

waarde van n gelijk aan ^ en kan opgevat worden als

bijzonder geval van meer algemeene integralen, welke
een bepaalde waarde hebben, onafhankelijk van den
parameter n.

(Prysvraag 3. Wiak. Genootschap. Amst. 1924),

VIII.

De verklaring van het ontstaan der magnetische stormen
door Cn. Noudmann gegeven, is onjuist.

Annalen dc TobMcrvatoire de Nicc. Tómo IX, HK)5.
Zie ook U Iloyaume de« deux. Cii. Nokdmann, 1923,
bladz. 109.

IX.

De behandeling der lenzenforniule X ^c« = X
by hel gymnasiaal en middelbaar onderwijs is te ver-
kiezen boven die van de in do meeste leerboeken voor-
komende formule 7- - = V

h V . f

t

■-■•.\'Vu

, \' • . ■ -1^..- -, f: . -. ■ .r

■

■ V

■V\'