THE
PHYSICAL SOCIETY OF LONDON,
REPORT
ON
-SERIES IN LINE SPECTRA.
BY
A. FOWLER, A.R.C.S., F.INST.P., F.R.S.,
Professor of Astrophysics, Imperial College of Science and Technology
South Kensington, London.
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1922.
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PREFACE
ALTHOUGH the spectra of elements and compounds were studied in the first
instance chiefly as providing a powerful means of chemical analysis, it has
long been recognised that a spectrum must contain an important clue to
the structure and modes of vibration of the atoms or molecules which produce
it. Spectra, however, are most frequently very complex, and there could be but
little hope of progress in the direction indicated if it were not possible to discover
laws governing the distribution of the lines or bands of which they are composed.
The search for such laws has attracted many workers, and organised systems of
lines which can be approximately represented by simple formulae have been identified
in the spectra of many elements and compounds. The recognition of these regulari-
ties has naturally played a fundamental part in the development of theories of the
origin of spectra and of the constitution of atoms and molecules. The analysis of
spectra has thus become one of the main objects of modern spectroscopy, stimulating
the experimentalist to the extension of existing data, and providing material in a
form suitable for the theoretical investigator.
My purpose in the present report has been to give a comprehensive account
of the development and present state of our knowledge of the regularities in spectra,
as deduced from the spectra themselves, with but little regard to theories of their
origin. The report is in two parts, the first of which gives a general account of
spectral series, excluding those which occur in band spectra, while the second is
intended to include the most authentic experimental data available in April, 1921.
It is hoped that the tables of series lines, together with the references to lines which
have not yet been classified, will suggest and facilitate further investigations. The
system of numeration of the series lines which has been adopted is that of Rydberg and
Hicks, but if it should be found convenient to modify this numeration on theoretical
grounds there should be no difficulty in making the desired alterations.
The spectra dealt with are those obtained by optical methods, extending from the
infra-red to the extreme ultra-violet. The emissions of higher frequencies which
have been revealed in the study of X-ray spectra do not form extended series of the
kind met with in optical spectra, and have accordingly not been considered.
I am indebted to Professor F. A. Saunders, of Harvard University, for much
useful help during the preparation of the report, and especially for his kindness in
supplying important observational material in advance of publication. My thanks
are also due to Col. E. H. Grove-Hills, F.R.S., for the photograph reproduced in
Fig. 6 ; to Dr. A. S. King, of the Mount Wilson Observatory, for Plate III. b ; and
to Mr. N. R. Fowler for the negatives from which Plate IV. was prepared. I also
have pleasure in acknowledging the valuable assistance which has been rendered
by Dr. D. Owen, Secretary of the Physical Society, and Mr. H. Dingle, B.Sc., D.I.C.,
in reading the proof sheets.
A. FOWLER.
IMPERIAL COLLEGE,
SOUTH KENSINGTON, LONDON.
February, 1922.
^8! 1.1)5
CONTENTS.
PART I. GENERAL ACCOUNT OF SERIES.
CHAPTER PAGE
I. OBSERVATIONAL DATA 1
Wave-lengths and wave-ii umbers. Correction to Vacuum. Arc and Spark
Spectra : Enhanced lines. Intensities and Characters of Lines. The Schumann
and Infra-red regions. Sources of data.
II. HISTORICAL NOTE 7
1869-1879. The spectrum of hydrogen. Schuster's conclusions. I/aw of constant
separations. B aimer's law for hydrogen. First results of Kayser and Runge. The
work of Rydberg. Kayser and Runge's formula.
III. CHARACTERISTICS OF SERIES 13
General formula for hydrogen. The four chief series of other elements. Relations
between the chief series. The Rydberg-Schuster law. Runge's law. Abbreviated
notation. Doublet systems. Triplet systems. Satellites. Negative wave-numbers.
The combination principle. Enhanced line series. Identification of series. Spectra
with constant differences.
IV. RYDBERG'S FORMULA 27
The Rydberg constant. The constants jz and A . Rydberg's interpolation table.
The order-numbers of the lines. Enhanced line series. Rydberg's special formula.
V. OTHER SERIES FORMULA 31
Runimel. Ritz. Lohuizen. Mogendorff -Hicks. Paulson. Johanson. Ishiwara.
VI. "ABNORMAL" SERIES 39
Intensities. Satellites. Spacing of lines.
VII. SPECTRA AND ATOMIC CONSTANTS 43
General relationships. Limits and atomic weights. Limits and atomic volumes.
Doublet and triplet separations. Homologous lines and atomic weights. Separa-
tions and atomic numbers. Conclusions.
VIII. THE WORK OF HICKS 51
Atomic volumes. Atomic weight term. The " oun." "Collaterals." Constitu-
tion of diffuse series. Links. Summation series. Independent determination of
atomic weights.
IX. APPLICATIONS OF BOHR'S THEORY 59
The spectrum of hydrogen. Ionised helium. Arc spectra. Spark spectra.
Graphical representation of- series systems. lonisation potentials in relation to
series. Spectra and the periodic table of the elements.
APPENDIX I 76
Calculation of formula constants. Successive approximation. Hicks's method.
The differential method. Determination of limits in special cases.
APPENDIX II. 80
TABLES FOR COMPUTATIONS.
I. Corrections to reduce wave-lengths on Rowland's scale to the international scale.
'II. Correction to vacuum of wave-lengths in air at loC. and 760 mm.
I!A. Correction to vacuum of wave-lengths in infra-red.
III. Rydberg's interpolation table (revised) .
PART II. TABLES OF SERIES LINES.
CHAPTER PAGE
X. EXPLANATION OF TABLES 87
XI. HYDROGEN AND HELIUM 89
XII. GROUP I A., THE ALKALI METALS 96
XIII. GROUP IB., COPPER, SILVER AND GOLD 109
XIV. GROUP HA., THE ALKALINE EARTH METALS 115
XV. GROUP HB., ZINC, CADMIUM AND MERCURY 139
XVI. GROUP IIlA., SCANDIUM, YTTRIUM AND THE RARE EARTHS 152
XVII. GROUP Ills., THE ALUMINIUM SUB-GROUP ... 155
XVIII. ELEMENTS OF GROUPS IV. AND V. 163
XIX. GROUP VI., OXYGEN, SULPHUR AND SELENIUM 166
XX. ELEMENTS OF GROUPS VII. AND VIII 173
XXI. THE INERT GASES 174
INDEX OF AUTHORS 181
LIST OF PLATES.
PLATE
I. ARC SPECTRA OF SODIUM AND LITHIUM.
II. ARC SPECTRA OF CADMIUM, ZINC AND MAGNESIUM.
III. (a) TRIPLETS OF ZINC, CADMIUM AND MERCURY.
(b) SATELLITES IN FUNDAMENTAL TRIPLET OF BARIUM.
(c) SHARP, DIFFUSE, AND FUNDAMENTAL TRIPLETS OF CALCIUM.
IV. ARC AND SPARK SPECTRA OF MAGNESIUM, CALCIUM, STRONTIUM
AND BARIUM.
V. SPECTRA OF HELIUM AND IONISED HELIUM.
FIGURES IN TEXT.
FIG. PAGE
1. THE SPECTRUM OF HYDROGEN 8
2. THE THREE SERIES OF HYDROGEN 14
3. THE FOUR CHIEF SERIES OF LITHIUM 17
4. DIAGRAM ILLUSTRATING ARRANGEMENT OF SATELLITES 20
5. (a) SERIES IN WHICH P(l) is POSITIVE ; (b) SERIES IN WHICH P(l) is
NEGATIVE 22
6. PHOTOGRAPH SHOWING AN INVERTED DIFFUSE DOUBLET OF IONISED
CALCIUM 22
7. CURVE OF /* +f(m) FOR THE PRINCIPAL SINGLET SERIES OF CALCIUM. . , . . '. 42
8. THE SHARP SERIES OF Mg, Ca, Sr, Ba, SHOWING INFLUENCE OF ATOMIC
WEIGHT 44
9. THE BOHR ORBITS FOR HYDROGEN 61
10. COMPARISON OF EXTENDED PICKERING SERIES WITH THE BALMER SERIES
OF HYDROGEN ' , ... 63
11. TERMS OF THE HYDROGEN SPECTRUM 66
12. TERMS OF THE SPECTRA OF Na, Mg, Mg + , Sr, Sr + 6T
PART I.
GENERAL ACCOUNT OF SERIES.
CHAPTER I.
OBSERVATIONAL DATA.
WAVE-LENGTHS AND WAVE-NUMBERS.
The study of spectral series calls for a precise acquaintance with the nature of
the available data, both as to the positions and characters of the lines involved.
The position of a line in the spectrum is most generally indicated by the wave-
length (A) of the vibrations which produce it. The unit of wave-length is the
Angstrom Unit, or " angstrom," as it is now beginning to be called. It was intended
to equal 10* 10 metre, and is accordingly often called the "-tenth-metre." It is also
equivalent to 10" 8 cm., or 0'0001/j, where ,a is the micron, or thousandth of a milli-
metre. Wave-lengths in the visible spectrum range from about 3,900A to 7,600A
(A being the modern abbreviation for the angstrom). For the long waves in the
infra-red, however, /i is often taken as the unit, so that Al 2,500 A, for example,
would be indicated by 1'25/j.
The wave-length scale was introduced by Angstrom in 1869, and until about the
year 19QO, wa\e-lengths were referred to his determinations as standards ; they were
meant to represent the wave-lengths in air at 16C. and 760mm. pressure. Later
work, however, proved that Angstrom's values were about 1A too low, and, about
1896, the scale was superseded by that of Rowland, which referred to wave-lengths
in air at 20C. and 760mm. Still more recently it has been found that Rowland's
scale was based upon erroneous values for the D lines of sodium, besides being affected
by other small errors, and Rowland's scale is now being gradually replaced by the
" International " scale. The latter is founded upon interferometer determinations
of the wave-length of the red line of cadmium, which is much superior to the sodium
lines in point of sharpness. The wave-length adopted for this line by the Inter-
national Solar Union* is 6438 '4696, being the value determined by Benoit, Fabry,
and Perot, and in close accordance with a previous measurement by Michelson.
The precision of this value for the standard line is such that the unit of wave-length
which it defines can differ but little from 10~ 10 m., but to avoid all misunderstanding the
unit of wave-length defined by the cadmium line has been called the International
Angstrom ; and is indicated in tables by the letters " LA." ; we thus have
_Wave-length of red Cd line in dry air at 15C., 760 mm., with g=980'67
6438-4696
The majority of published wave-lengths, however, have been expressed on
Rowland's scale, and if new determinations have not become available, it is necessary
to reduce the Rowland values to the international scale in any precise work on series.
From a comparison of the two scales, Kayserf has derived the corrections which are
shown in Table I. These corrections include the small differences depending upon
the differences in the standard temperatures of the two scales (20C. for Rowland, and
15C. for the international scale).
In connection with spectral series it becomes important to specify the positions
* Trans. Int. Sol. Union, 2, 20, 28 (1907). (The Solar Union is now absorbed into the Inter-
national Astronomical Union.)
fHandbuch der Spectroscopie, 6, 891 (1912).
2 Series in Line Spectra. CHAP. i.
of lines either in " oscillation-frequencies," or by " wave-numbers." The most
fundamental figures are the oscillation-frequencies, since these are not changed when
the medium is changed. But the determination of frequency requires an exact
knowledge of the velocity of light, and it is more convenient to use the wave-number,
or number of waves per centimetre ; thus
10 8
Wave-number = v = -
/ in Angstroms
CORRECTION TO VACUUM.
Wave-numbers as well as wave-lengths vary with the medium in which the
vibrations are propagated, and it is therefore necessary to reduce them to standard
conditions. They are accordingly reduced to their values in vacuo, and when thus
corrected the wave-numbers are strictly proportional to the oscillation-frequencies.
This correction can be made when the refraction and dispersion of air have been
determined with sufficient accuracy. Thus
bac. = /* ^air > or A A = A vac . A a/ > = A a; > (^ 1 )
where /^=the refractive index of, air.
The refractive index, of course, varies with the density, and therefore with the
temperature and pressure, of the air. Kayser and Runge have given a formula
indicating the value of p for air at 760mm. pressure, and temperature 0C., and have
derived a table of corrections to vacuum applicable to wave-lengths determined in
air at 20C. and 760mm. pressure.* The most recent observations have been made
at the Washington Bureau of Standards by Meggers and Peters.f who give the
following formulae for the refractive indices of dry air at 760mm. pressure, and tem-
peratures 0C., 15C. and 30C., \ being expressed in angstroms :
0C.: u - 1
30'C.: ( ,
These observations have been utilised in the construction of a table showing
the corrections which must be applied to wave-lengths and wave-numbers measured in
air to convert them to their values in vacuum. An extract from the Washington
tables is given in Table II., indicating the amounts to be added to wave-lengths in
dry air at 15C. and 760mm., and therefore directly applicable to wave-lengths on
the international sca]e.J The conversion to wave-numbers can readily be effected
by the use of a table of reciprocals with seven-place arguments.
When the wave lengths are expressed on Rowland's scale, which refers to 20C.,
the simplest procedure is to reduce them to the international system by means of
* Handbuch, 2, 614.
t Scientific Papers of the Bureau of Standards, Washington, No. 327 (1918).
% Some of the figures have been slightly amended in Astrophys. Jour., 50, 56 (1919).
Observational Data. 3
Table I., and then to correct them to vacuum bv adding the corrections given in
Table II.
The corrections of infra-red wave-lengths to the international system and
to vacuum are subject to some uncertainty. For wave-lengths greater than
10,OOOA, however, the correction to the international scale has but little in-
fluence on the wave-numbers. Thus, at A10,000 the correction increases the wave-
number by 0-4, at A20,000 by 0'2, and at A40,000 by 01. Corrections to vacuum
may be determined approximately by extrapolation of the Washington formula
for the refractive index of air. (See Table Ha.)
ARC AND SPARK SPECTRA : ENHANCED LINES.
The investigation of spectral series often requires a knowledge of the behaviour
of the lines when produced under different conditions of excitation. The
spectra of metallic elements are most frequently obtained by the use of the electric
arc or by the condensed discharge from an induction coil, and the spectrum is usually
different in the two cases. (See Plate IV.) On passing from the arc to the spark
it often happens that some of the lines are diminished in relative intensity, while
others become brighter, and new lines frequently -make their appearance in the
spark. Lines which are relatively enhanced in brightness on passing from the
arc to the spark, or which only occur in the spark spectrum, were called Enhanced
Lines by Lockyer, and this name has been generally adopted. Lines which appear
in the arc and tend to diminish in intensity in the spark are then distinguished as
Arc Lines. The term " arc lines," it will be seen, does not necessarily include all
the lines which appear in the arc spectrum ; and, similarly, the spark spectrum
most frequently includes some surviving arc lines as well as enhanced lines.
It is convenient to distinguish at least three classes of enhanced lines : (I.) En-
hanced lines like the H and K lines of calcium, which are quite strong in the arc
(and appear with greater intensity in the spark) ; (II.) Lines which only appear
with feeble or moderate intensity in the ordinary arc, such as the enhanced lines oi
iron and titanium ; (III.) Lines which do not appear in the ordinary arc, but are
strongly developed under spark conditions, as in the case of the well-known mag-
nesium line A4:,481. It would thus seem that while the energy of the arc is in some
cases sufficient to develop the enhanced lines, the greater energy of the disruptive
spark is required to give rise to them in the case of some of the elements. In other
words, different elements respond differently to a given stimulus.
It should be mentioned that enhanced lines are also often found to appear in a
region close to the poles of a metallic arc, and when the arc is passed in an atmosphere
of hydrogen, or in a vacuum,* they frequently become very pronounced.
Similar variations of the line spectrum are also observed in the case of many
gases, including helium, oxygen, and nitrogen, when the electric discharges which
excite them are varied in intensity. From analogy with metallic spectra,
certain lines which thus appear in the spectra of gases under the action of powerful
discharges may quite properly be classed as enhanced lines. In some cases, a
succession of spectra appear as the intensity of the discharge is gradually increased.
Oxygen, for example, gives a spectrum corresponding to the arc spectrum when the
discharge is feeble, new lines appear with a moderate increase in the intensity, and
still others when the strongest discharges are passed through the gas ; the three
* Fowler and Payn, Proc. Roy. Soc., 72, 258 (1903).
B 2
4 Series in Line Spectra. CHAP. r.
different classes of lines are then conveniently distinguished as arc, spark and '' super-
spark," or as 0i., On., and 0m.* Silicon shows four such stages.
As might be expected, arc lines and enhanced lines have not been found to be
associated in the same family of series.
INTENSITIES AND CHARACTERS OF LINES.
In the investigation of series spectra, it is important also to take into account
the intensities and physical characteristics of the lines involved. A convenient
standard scale of intensities has not yet been introduced into spectroscopic tables,
and tabulated intensities are, for the most part, merely rough estimates on an arbi-
trary scale, in which 10 represents the strongest and 1 the weakest lines. This
range, however, is often too restricted, and in some tables, notably those of Exner
and Haschek, the very strongest lines are represented by the higher numbers 15,
20, 30, 50, 100, 200, 500 and 1,000. In order to extend the scale in the opposite
direction, some observers also follow Rowland's convenient plan of indicating very
faint lines by 0, 00, 000, and 0000, the latter being at the limit of visibility. A
method of estimating intensities on an absolute scale has been devised by Nicholson
and Merton.f but its use has so far been restricted to the spectrum of helium.
While some lines are sharp and well-defined, others may be shaded on one or
both edges, and others again, especially in arc spectra, may be reversed. These
different appearances are usually indicated in spectroscopic tables by the addition
of letters to the numbers showing the intensities. There is, unfortunately, a con-
siderable diversity in the notations adopted by different observers, and it is usually
necessary to rely upon an author to describe the symbols employed in any particular
case. Some of the principal systems which have been adopted are as follows :
Exner and This
Character. Watts. Kayser. Haschek. Report.
Sharp s ... s* ... ... s
Nebulous or diffuse n . .'. j ... + ... n
Broad b ... wf ... br% ... b
f Broad, but sharp on red edge ... b r ... ... ...
\ Diffuse towards violet ... ... ... v, or uv . . . v ... v
/Broad, but sharp on violet edge ... b v ... ... ...
\ Diffuse towards red ... ... ... ... r, or ur . . . r ... r
Reversed r ... R ... ... R
Double ... d ... d ... d
* Scharf. f Unscharf. { Breit. Umgekehrt.
The symbols in the last column will be adopted in this report, and it is to be
understood that the absence of any symbol indicates that the line is of ordinary
sharpness, but not specially sharp.
In a reversed line there is a broad bright line, diffuse at the edges, which is
produced by the denser vapour at the core of the arc or spark used as the source of
light, and a narrow absorption line superposed upon this which originates in the
cooler and less dense vapour in the outer envelope. The reversal is sometimes
unsymmetrical.
* Fowler and Brooksbank, Monthly Notices, R.A.S., 77, 511 (1917).
t Phil. Trans., A, 217, 242.
Observational Data. 5
It should be noted that lines which are ordinarily diffuse in an arc spectrum
can usually be obtained as sharp lines by passing the arc in a vacuum. There are,
in fact, examples of series which might never have been recognised as such if reliance
had been placed upon observations of the arc or spark in air, as the more refrangible
members are sometimes diffused to the degree of invisibility.
Lines which belong to the same series are usually similar in character, but an
apparent exception has been noted by Royds in barium ;* in this case the lines of a
triplet in the yellow appear to be widened unsymmetrically towards the red, while the
more refrangible triplets are shaded towards the violet. The corresponding triplets
of calcium present a le:s extreme exception, the blue triplet being sharply denned,
while succeed.ng members are diffuse towards the violet ; the associated infra-red
triplet may possibly be shaded towards the red.
THE SCHUMANN AND INFRA-RED REGIONS.
The ordinary instruments which are employed in spectroscopicwork do not permit
the investigation of the whole range of the spectrum. Spectroscopes with prisms
and lenses of glass only serve for a small part of the ultra-violet, and a small part of
the infra-red, in addition to the visible spectrum. When quartz is substituted for
glass the range may be extended to about A 1,850 in the ultra-violet, but for shorter
wave-lengths special arrangements become necessary. This part of the spectrum
was first investigated by Schumann, and is commonly called the Schumann region.
In the first instance, fluorite was substituted for quartz, and on account of the opacity
of air for the short waves the whole apparatus, including the photographic plate,
was placed in an exhausted air-tight case. The ordinary gelatine plates being strongly
absorbent for short waves, special " Schumann plates " with a very thin coating of
gelatine are also necessary. Concave gratings have been successfully employed by
Lyman and others, and have permitted observations beyond the region for which
fluorite is transparent. Details of the instruments and methods of work have been
given by Lyman in his book on " The Spectroscopy of the Extreme Ultra- Violet. "t
Observations have now been extended as far as A 584A by McLennanJ and to
22oA by Millikan. Wave-lengths in this region are usually tabulated as observed,
and no correction to vacuum is required in the calculation of wave-numbers. It
should be noted that since dv= - 10 8 /A 2 .^A, errors in the wave-length are greatly
multiplied in the conversion to wave-numbers in this region as compared with
the less refrangible parts of the spectrum.
At the red end of the spectrum, direct photographs ori plates stained with
dicyanin have been obtained by Meggers as far as HO,OOOA.|| The further infra-
red is investigated by thermo-electric methods, emplojnng spectroscopes having
optical parts of rock-salt or making use of gratings. Extensive work with special
reference to series lines has been carried on in this region by Paschen^I and by Randall.**
The extension of observations into the extreme ultra-violet and infra-red has
been of great value in the elucidation of the structure of spectral series, as will
appear in due course.
* Astrophys. Jour., 41, 154 (1914).
t Longmans (1914).
: McLennan, Proc. Roy. Soc., A., 95, 238 (1919).
Astrophys. Jour., .52, 47 (1920).
|| Scientific Papers of the Bureau of Standards, Washington. Numbers 312, 324, 345, &c.
^ Ann. d. Phys., (4) 27, 29, 33 (1908-10), and other Papers.
Astrophys. Jour., 34, 1 (1911) ; 42, 195 (1915) ; 49, 42, 54 (1919).
**
6 Series in Line Spectra. CHAP. i.
SOURCES OF DATA.
The following references to the principal collected tables of wave-lengths and
photographs of spectra may be usefully appended to this chapter.
(1) W. MARSHALL WATTS : " Index of Spectra," with numerous appendices.
(Heywood, Manchester.)
(2) F. EXNER and E. HASCHEK : " Wellenlangen Tabellen fur Spectralana-
lytische Untersuchungen auf Grund der Ultra- Viol etten Funkenspektren
der Elemente." (Leipzig and Wien, 1902.)
(3) F. EXNER and E. HASCHEK : " Wellenlangen Tabellen . . . Bogen-
spektren." (1904.)
(4) F. EXNER and E. HASCHEK : " Die Spektren der Elemente bei Normalen
Druck." I., Hauptlinien der Elemente und Codex der Starken Linien
im Bogen und Funken. II., Die Bogenspektren. (Leipzig and Wien,
1911.)
(5) A.HAGENBACH and H. KONEN : ."Atlas der Emission Spectra." (Jena,
1905.) English edition by A. S. King. (W. Wesley & Son, London.)
(6) J. M. EDER and E. VALENTA : " Atlas Typischer Spektren." (Wien,
1911.) |
(7) H. KAYSER : " Handbuch der Spectroscopie," Vols. V. and VI. (Leipzig,
1910, 1912.) (These include practically all the measures to the dates of
publication.)
Many valuable series of measures have since been published in the " Astrophysical
Journal " and in the " Zeitschrift fur Wissenschaftliche Photographic." The
" International Tables of Constants " also include collections of spectroscopic measure-
ments. Collections of tables for the Schumann region are given in Lyman's book.
CHAPTER II.
HISTORICAL NOTE.
18691879.
The earlier attempts to discover laws governing the distribution of lines in spectra
were controlled mainly by the supposition that the vibrations which give rise to the
lines might be similar to those which occur in the phenomena of sound, and might
correspond with harmonical overtones of a single fundamental vibration. In that
case the ratios of the wave-lengths of different lines would be expected to be repre-
sented by comparatively small integral numbers. Lecoq de Boisbaudran* believed
that he had discovered such relations among the bands of nitrogen, but more exact
measurements which were made later failed to verify his conclusions. In 1871,
however, it was pointed out by Dr. Johnstone Stoneyf that the wave-lengths of the
first, second, and fourth lines of hydrogen were in the inverse ratio of the numbers
20, 27, and 32, and the accuracy of these ratios strongly suggested the existence of
genuine harmonical relations.
The admirable experimental work of Liveing and Dewar,J which extended well
into the ultra-violet part of the spectrum, provided valuable data for further in-
vestigations, and several important features of associated lines were revealed by these
observations. In the spectrum of sodium it was observed that successive pairs of
lines were alternately sharp and diffuse, and that the pairs generally became fainter
and more diffuse as they were more refrangible ; at the same time the distance
between successive pairs was diminished. (Compare Plate I.) It was remarked
that the whole series, excluding the " D " pair, looked very like repetitions of the
same set of vibrations in a harmonic progression, and it seemed that harmonic
relations could be found to subsist between some of the groups. The whole series,
however, could not be represented as simple harmonics of one set of six vibrations
with any degree of probability. Somewhat similar results were also obtained for
potassium, and, later, for the triplets of magnesium. ||
THE SPECTRUM OF HYDROGEN.
The discovery by Huggins^f of a number of prominent lines in the ultra-violet
spectra of Sirius and other white stars (Fig. 1), which seemed to be a con-
tinuation of the regular series of hydrogen lines in the visible spectrum, led
to further search for harmonic ratios in this spectrum on the part of Dr. Johnstone
Stoney.** Evidence that the lines in question were all members of the same physical
system was found in the fact that when their positions were plotted as abscissae
against ordinates which increased uniformly, they fell upon, or very near, a definite
* Comptes Rendus, 69, 694 (1809).
tPhil. Mag., 41, 291 (1871).
J Proc. Roy. Soc., 29, 398 (1879) ; Collected Papers on Spectroscopy, p. 66.
lyiveing and Dewar were careful to explain that their reference to harmonic series of lines
did not imply that the lines were thought to follow the arithmetical law of an ordinary harmonic
progression, but to be comparable with the overtones of a bar or bell.
|| Proc. Roy. Soc., 32, 189 (1881).
jfPhfl. Trans., 171, Pt. II., 669 (1880).
** Quoted by Huggins.
8 Series in Line Spectra. CHAP. n.
curve. A new departure in the investigation was the substitution of the scale of
" wave-frequencies " (the reciprocals of the wave-lengths) for that of wave-lengths.
On forming the first and second differences of these wave-numbers, Dr. Stoney
concluded (erroneously) that the irregularities in the second differences were too great
FIG. 1. THE SPECTRUM OF HYDROGEN : (a) IN SIRIUS, (b) IN VACUUM TUBE.
to be attributed to errors of measurement, and that the lines did not fall exactly on a
smooth curve. Hence it was thought that the lines were not consecutive members
of a single series, but members of two or more series, and attention was drawn to
several apparently harmonic relations between selected groups of lines.
SCHUSTER'S CONCLUSIONS.
A discussion of the evidence for the existence of harmonic ratios in spectra was
given by Schuster in 1881,* and although it was concluded that the number of such-
ratios was not greater than might be attributed to chance, Schuster clearly recognised
that there might be some undiscovered law, which, in special cases, resolved itself
into the law of harmonic ratios. In the light of our present knowledge this is evidently
the case for the ratios of the hydrogen lines discovered by Stoney, which follow
naturally from the simple law which connects all the lines of the series in question ;
the ratios thus have no special significance, but it is interesting to note that they
contain the germ of the true law, and might well have led to its discoveryv
That some law existed was sufficiently evident from the distribution of the lines
in the hydrogen spectrum, and from the maps of the spectra of sodium and potassium
which had been given by Liveing and Dewar, but progress was greatly retarded by
the lack of sufficiently exact measurements of the wave-lengths of the lines. Schuster
found, for instance, that although all the lines of sodium appeared to be double, and
many of those of magnesium triple (compare Plate. II.), the measurements then avail-
able showed no regularity in the distances separating the components: Nevertheless,
ths fact that the hydrogen lines approach each other rapidly as they pass towards
the ultra-violet, and that characteristic groups which are repeated several times in
other spectra also come nearer and nearer together in the more refrangible parts of the
spectrum, was considered by Schuster to furnish a safer basis for further research
than the hypothesis of harmonic ratios. It was, in fact, in this direction that
subsequent advances were made.
* Proc. Roy. Soc., 31, 337 (1881) ; Brit. Assoc. Report (1882), p. 120.
Historical Note. 9
LAW OF CONSTANT SEPARATIONS.
A fact of great importance was established by Hartley in 1883,* namely, that
the components of doublets or triplets occurring in the same spectrum are of identical
separation provided that the positions of the lines are expressed on the scale of
oscillation frequencies (or of reciprocal wave-lengths, which are proportional to the
frequencies) . By the discovery of this law of constant separations, pairs or triplets
occurring in different parts of the same spectrum could be associated with certainty.
A further valuable contribution on the experimental side was made by Liveing
and Dewar in 1883,t when they gave an account of their work on the ultra-violet
spectra of the alkali and alkaline earth metals, and of zinc, thallium, and
aluminium, in each of which there are well-marked series. The characteristics
which they had previously noted in the case of sodium and magnesium were then
found to be equally pronounced in other spectra, and several new series were re-
corded, including what are now called the principal series of lithium, sodium, and
potassium. These observers, however, did not investigate the laws of the series
which they described with such completeness and accuracy.
BALMER'S LAW FOR HYDROGEN.
A new era commenced in 1885, when the law of the hydrogen series was dis-
covered by Balmer.J The number of lines then known to belong to this series, as
produced in the laboratory, had been increased to nine by W. H. Vogel,'and five
more had been recorded by Huggins in the spectra of the white stars. Balmer found
that the series could be represented, probably within the limits of error of the obser-
vations, by a formula of the type
where h is a constant for the series, and mandn are whole numbers. For the actual
lines, using Angstrom's measures of the first four lines, he gave the formula
m z 4
where m takes the values, 3, 4, 5, ....
Thus
Calcd. A Obsd. A 0-C
H a = ?&=6562-08 6562-10 +0-02
5
H 3 = 4 &=4860-80 4860-74 -0-06
a 3
H y = h =4340-00 4340-10 +0-10
ZJL
H & = ?&=4101-30 4101-20 -0-10
8
* Jour. Chem. Soc., 43, 390 (1883).
t iPhil. Trans., 174, 187 (1883) ; Collected Papers, p. 193.
j Wied. Ann., 25, 80 (1885).
Monatsb. Konigl. Acad., Berlin, July 10 (1879).
io Series in Line Spectra. CHAP. n.
The extrapolation to the ultra-violet lines gave values roughly corresponding
to the measured wave-lengths, but it remained rather doubtful whether the law was
exact or only an approximation to the true formula for the entire series. Subse-
quent investigations, however, have shown that the law, with a slightly amended
constant, represents the whole series with extraordinary accuracy.
Although the hydrogen spectrum is in a sense typical of all series, the simple
Balmer formula with modified values of h is not applicable to series in general.
Nearly all attempts to represent series of lines by formulae, however, have been based
upon the Balmer law, with the introduction of one or more correcting terms.
Balmer's discovery of the law of the hydrogen series, together with Hartley's
law of constant separations and Liveing and Dewar's experimental data, provided
a sound basis for further research.
FIRST RESULTS OF KAYSER AND RUNGE.
Shortly after the discovery of Balmer's law, the investigation of series spectra
was taken up by Kayser and Runge, and by Rydberg. The first results of the
former were published in 1888 by Runge,* who announced that formulae had been
found for series of lines of elements other than hydrogen. Their equations were of
the form
, 1 1
/= ; or /=-
where a, b, c are constants special to each series, and m assumes consecutive values
of the series of whole numbers, beginning with 3. The following formula was given
for the principal series of lithium, m being 3 for the line A3232 :
i
A (inmm.) =
T 1 11635r*
It will be observed that the formula is a more general form of that given by
Balmer for hydrogen, which may be written
Kayser and Runge were quick to recognise the need for a more accurate know-
ledge of wave-lengths in such inquiries, and courageously embarked on a new series
of determinations with the aid of a large concave grating, beginning with the spectrum
of iron as a convenient standard of comparison for purposes of interpolation. f
THE WORK OF RYDBERG.
Rydberg made use of data already to hand, and his investigations are of the
utmost importance as having laid the foundation for all subsequent attempts to show
the connection between different series occurring in the same spectrum. His first
* Brit. Assoc. Report (1888), p. 576.
f Abhandl. der Berlin Akad. (1890).
Historical Note. n
memoir was presented to the Swedish Academy of Sciences towards the end of 1889*
and gives a comprehensive account of the results at which he had then arrived. As
in the case of Kayser and Runge, the ultimate purpose of his inquiries .was to
gain a more intimate knowledge of the structure of atoms and molecules, and not-
withstanding the imperfect data then at his disposal, he discovered most of the
important properties of series, and foreshadowed discoveries which were made later,
when experimental work provided the necessary data.
Rydberg commenced his work by sorting out doublets and triplets, largely from
the tables given by Liveing and Dewar and by Hartley, and in this way ascertained
the lines which might properly be associated in the same set of formulae. Although
the terms " doublet " and " triplet " had in general been understood to signify
groups of lines not very far apart, Rydberg showed that there were true doublets
and triplets in which the components were remote from each other, so that while
one component might be in the visible spectrum, another might even be situated
in the ultra-violet, other lines occupying the intermediate spaces. Hartley's law
of constant separations was thus confirmed and extended, with the proviso that the
law was applicable only to members of series of the same species.
Like Johnstone Stoney and Hartley, Rydberg employed the reciprocals of the
wave-lengths in place of the oscillation frequencies themselves, but gave them a
more definite meaning by defining the " wave-number " as the number of wave-
lengths per centimetre ; that is, 10 8 /A in Angstrom Units. He pointed out that the
use of wave-numbers not only saves a great deal of calculation, but is important in
theoretical considerations.
The observation by Liveing and Dewar that pairs or triplets are alternately
sharp and diffuse enabled Rydberg to distinguish two species of series, in addition
to a third species comprising the ultra-violet lines which the same observers had
photographed in the spectra of Li, Na, and K. The first terms of the latter species,
which are the most intense in the spectra, are situated in the visible spectrum and
had not previously been associated with the ultra-violet series. Three chief species
of series were thus recognised as being superposed in the same spectrum, namely :
Principal, including the strongest lines.
Diffuse, of intermediate intensity.
Sharp, including the weakest lines,
and the members of each series might be single, double, or triple.
In each series the distance from line to line diminishes rapidly on passing to
the more refrangible parts of the spectrum, the lines thus converging towards a
definite limit, and in a normal series, intensities also diminish in regular order. In
a graphical representation with the observed wave-lengths (A) or wave-numbers (v)f
of a series as abscissae, and consecutive whole numbers (m) as ordinates, Rydberg
found that each series was represented by a regular curve, which appeared to be
similar in shape for all series, and to approximate to a rectangular hyperbola (see
* Kongl. Svenska Vet.-Akad. Handlingar, Bandet 23, No. 11 (1890) [in French]. Ab-
stracts were given in Comptes Rendus, Feb." (1890); Zeitschr. Phys. Chem., February (1890),
and Phil. Mag., April (1890).
f Rydberg represented wave-number by n, but analogy with the X always employed for
wave-length suggests that v, as used by Ritz, is more appropriate.
12 Series in Line Spectra. CHAP. n.
Figs. 2 and 3, pp. 14 and 17). A rough representation of several series was in
fact obtained by the use of the hyperbolic formula :
C
v=v
where v is the wave-number of a line, m its order number, and v^ , C, and /JL are
constants special to each series ; v x is the limit of the series, being the value of v
when m is infinite.
Further investigation, however, led to the conclusion that the wave-number
should be represented by the equation
v=v w -f(m+jn)
where the form of the function, and any additional constants, would be the same
for all series. The simple hyperbolic formula did not fulfil this imposed condition,
as the value of C was found to vary very considerably from one series to another.
Rydberg then proceeded to investigate the next simplest form of the function, and
adopted it in his subsequent work, namely,
where 2V is constant for all series.
When fj. is zero this formula becomes identical with that of Balmer for hydrogen,
which in terms of wave-numbers, may be written
m 2 4 4v 00 N
~ v m z " v m* ' " Vco ~~ m z
The constant N could thus be calculated from the hydrogen lines, which gave the
value 109,721-6. This, however, was deduced from wave-lengths in air, expressed
on the scale of Angstrom, and was recalculated later as 109,675-00 from wave-
lengths on Rowland's scale, corrected to vacuum.* This number appears in the
formulas for other series, and is generally designated the " Rydberg Constant." Its
value on the international scale has recently been given by W. E. Curtis as
109,678-3.
Rydberg fully recognised that the formula which he employed was only an
approximation to the true function of m or of (m-\-/u,), but by its aid he was able to
trace a large number of series in the spectra of different elements, and to deduce
most of the important properties of series in general.
KAYSER AND RUNGE'S FORMULA.
Almost immediately after the announcement of Rydberg's results, Kayser
and Runge published an account of their investigations of the spectra of the alkali
metals.f These observers also adopted the scale of wave-numbers per centimetre,
and employed the formula
v =A- 2 --
m i m*
where v is the wave-number, m the order number of a line, and A, B, C three
* Congres Internal, de Physique, Paris (1900), p. 211.
f Abhandl. der Berlin Akad. (June 5, 1890).
Historical Note. 13
constants special to each series ; A is evidently the limit of the series ; B is of the
same order of magnitude as Rydberg's constant N, but C varies widely from one
series to another. The formula was by no means capable of giving an accurate
representation of all the lines of a series, and is inferior to that of Rydberg inasmuch
as it fails to show the important connection between the Principal and Sharp series.
A large number of series and many of the properties of series already described by
Rydberg, however, were independently discovered by its use.
Kayser and Runge's formula has passed its period of usefulness, and practically
all the newer formulae represent attempts to improve the original equation of Rydberg.
Kayser and Runge, however, made important contributions to the subject by their
improved tables of the spectra of many elements,* and by their determinations
of the refractive indices of airf which permitted the correction of the wave-numbers
to vacuum.
* Abhandl. der Berlin Akad. (1891, 1892, 1893).
t Abhandl. der Berlin Akad. (1893).
CHAPTER III.
CHARACTERISTICS OF SERIES.
GENERAL FORMULA FOR HYDROGEN.
It should be clearly understood that the series spectrum of hydrogen is of
exceptional simplicity. The Balmer series, however, does not constitute the whole
of the hydrogen spectrum. Another series in the infra-red was predicted by Ritz,
and two members at A18,751 and A12,817-6 have been observed by Paschen. There
is also a series in the Schumann region, of which three members have been
photographed by Lyman. All the series are included in the general formula
v=N ( A m^m
\m^ m i J
where m l =l for Lyman's series, =2 for the Balmer series, and =3 for the Ritz~
Paschen series. For wave-numbers on the international scale, corrected to vacuum,
N=109,678-3 (Curtis).
A graphical representation of these series is given in Fig. 2.
V J10 1OO 9O
70 60
50
44 3O
20
to
a
b
c
TTV
r1
2
8
4-
5
6
7
8
9
m,
1
8
9-\
10
FIG. 2. THE THREE SERIES OF HYDROGEN.
(a) =Lyman series ; (b) =B aimer series ; (c) =Ritz-Paschen series.
THE FOUR CHIEF SERIES OF OTHER ELEMENTS.
The work of Rydberg, and that of Kayser and Runge, revealed the existence
of a large number of series, each of which is generally similar to the Balmer series
of hydrogen. In each series the lines become closer, with diminishing intensities,
in passing from the red towards the violet end of the spectrum, and converge to a
Characteristics of Series. 15
definite limit (Fig. 3, p. 17). Theoretically, the number of lines in a series is infinite,
but no series have actually been traced to their limits. There are no known series in
which the lines converge towards the less-refrangible part of the spectrum.
In the general case there are several series superposed in the same spectrum.
Several such series are intimately related to each other and may be conveniently
regarded as forming a " system " of series. Four of the related series have a certain
amount of independence and may be considered to be the chief series of a system.
The remainder may be looked upon as derived series.
Three of the chief series were recognised by Rydberg and by Kayser and Runge,
namely, in order of intensity :
Principal, Diffuse, Sharp (Rydberg).
Principal, first Subordinate, second Subordinate (Kayser and Runge).
Rydberg's names are most commonly used and are conveniently abbreviated to
P, D, S, while the respective limits may be represented by Poo , Z)oo , Soo .
The fourth chief series long escaped detection because many of them occur in
the infra-red, in which region they were first observed by Bergmann.* They are
called " Bergmann series " by some writers, but as they do not all occur in the
infra-red, and were not all discovered by Bergmann, the name is not specially
appropriate. From theoretical considerations Hicks has named them the
" Fundamental " or " F " series, and though they are probably not more funda-
mental than the other chief series, the name has been so much employed that it will
be convenient to retain it for the purposes of the present report.
Although less exact than some of the amended forms which have since been
proposed, Rydberg's formula is usually a sufficient approximation to bring out the
main characteristics of a system of series, and its simplicity is a great advantage in
approaching the subject. This formula will accordingly be adopted for descriptive
purposes, namely :
N
where A is the limit of the series, N the Rydberg constant for hydrogen, and the
wave-numbers v m are; obtained by assigning successive integral values to m ; p may
be regarded as a decimal part to m, though it is sometimes greater than unity.
Each series is thus represented by a limit, and a series of " variable parts " or
" terms " forming a " sequence."
The four chief series may be represented by the Rydberg formulae :
Principal ......... P(w)=Poo N/(m+P) 2 m=l, 2, 3 . . .
Sharp ......... S (w)=Soo -iV/(w+S) 2 m=2, 3, 4 . . .
Diffuse ......... D(m)=Doo -N'/(m+D) z w=2, 3, 4 . . .
Fundamental ...... F(m)=Foo NI(m+F) z m=3, 4, 5 . . .
where P(m), for example, means the w-th line of the P series, and P, S, D, F
indicate the values of p in the respective series.
These formulae represent the four chief series of a " singlet " system, but in
many systems each member of a series is a doublet or a triplet.
* Dissertation, Jena (1907); Zeit. Wiss. Phot., 6, 113, 145 (1908).
16 Series in Line Spectra. CHAP. HI.
RELATIONS BETWEEN THE CHIEF SERIES.
The relations between the P, S, and D series were most completely traced by
Rydberg. His method may be usefully illustrated by reference to the spectrum
of lithium, which consists of doublets close enough to be regarded as single lines.
Rydberg's original formulae, which are sufficiently accurate for our purpose, were
as follows :
x 109,721-6
w+0-5951) 2
109,721-6
5(w) =28,601-1 -
Dim) =28,598-5--
(w+0-9974) 2
These formulae, and similar ones calculated for series of other elements, showed,
in the first place, that the limits of the 5 and D series were probably identical, i.e.,
Sao =Dco .
Next, it was found that m=l in the variable part of the formula for S(m) gave
approximately the limit of the P series ; thus
W/(l-5951) 2 =43,123-7
And, similarly, ml in the formula for P(m] gave approximately the limit of
the S series ; thus
N/(l-9596) 2 =28,573-l
From such considerations Rydberg concluded that Poo =JV/(1+S) 2 and
Soo =Doo =N/(l-\-P) z , so that the three series could be represented by
N N
N N
(m+D) z
THE RYDBERG-SCHUSTER LAW.
The first line of the P series (given by m=l) is thus identical with that given
by m = l in the S formula, but with opposite sign: i.e., S{1) = P(l). It follows
that the difference between the limit of the P series and the^ common limit of the D and
S series is equal to the wave-number of the first line of the P series. This important
rule was clearly included in the formulae given above, but Rydberg did not express it
in these terms until 1896,* in which year Schusterf also independently announced
its discovery, apparently by reference to the limits of the numerous series which
had been calculated by Kayser and Runge. The law of limits is thus generally
known as the Rydberg-Schuster law, and is expressed symbolically by
^oo -$ - P (1)
* Astrophys. Jour., 4, 91 (August, 1896).
f Nature, 55, 196, 200, 223 (1896).
Characteristics of Series.
RUNGE'S LAW.
Runge* was the first to point out that the difference between the limits of the
D and F series is equal to the wave-number of the first D line (mostly given by
m=2 in Rydberg's formulae). This relation is often referred to as Runge's law,
and is expressed symbolically by
#00 -Foe * D (2)
Thus, in Rydberg's form,
In all series of this type the value of F approximates to unity,
ABBREVIATED NOTATION.
A convenient and now indispensable abbreviated notation for series was suggested
by Ritz in connection with the more complex formula which he employed. It is,
however, of general application, and merely provides that a term NI(m-\-/j,) z or its
V45
30
25
20
o
s
D
F
Tit
1
2
-S
4-
6
6
7
8
9
10
1 -
2
3
4>-
5-
6-
7-
8-
9-
10-
Foo
FIG. 3. THE FOUR CHIEF SERIES OP LITHIUM.
equivalent should be represented by nifi, or by mP, mS, mD, mF in relation to
individual series. Thus the four chief series are written
P(m) = ISmP
S(m) = IPmS
D(m) = IPmD
F(m) = 2DmF
It is to be understood that while .0(3), for example, indicates the line in the D serie.8
for which m=3, 3D is equivalent to the term N/ (3 +Z)) 2 'and represents the interval
from the line D(3) to D x .
* Phys. Zeit-. 9, 1 (1908).
i8 Series in Line Spectra. CHAP. m.
The foregoing relations, in the case of lithium, are represented graphically
in Fig. 3, p. 17.
In order to distinguish series of different kinds, Paschen designated singlet
systems by the use of capital letters, and doublets and triplets by small letters.
Following a suggestion made by Prof. Saunders, however, it will be convenient to
adopt Greek letters for doublets, and small letters for triplets. Thus
P, S, D, F = Singlet systems.
it, CT, d, 9 = Doublet ,,
p, s, d, f = Triplet
For general descriptive purposes, however, we shall occasionally use P, S, D, F
for any class of series.
DOUBLET SYSTEMS.
The special characteristics of a doublet system, such as that of sodium (see
Plate I.), assuming that there are no complications due to satellites, may be
briefly stated as follows :
(1) In the d and cr series, the less refrangible components of the pairs are the
stronger, and the separations of the components, when expressed in
wave-numbers, are constant throughout.
(2) In the n series, the more refrangible components of the pairs are the
stronger, and the first pair has the same separation as d and er. The
components approach each other as the order number increases, and the
two series have the same limit.
(3) The 9 series consists of single lines.
These characteristics are embodied in the following formulae, where the brighter
components are indicated by n v a v d v and the fainter by n 2 , a z , 6 2 :
Rydberg formulae. Abbreviations.
(jii(m)=NI(l+a) z Nl(m+nf = ICT mn^ Shorter A
\7r 2 (w)=Ar/(l+ar) 2 JV/(w+;r 2 ) 2 = l<r W7i 2 Longer 1
(a l (m)=NI(l+n 1 ) z -NI(m+<j)* = In^ma Longer A
\<j 2 (m)=N/(l+n 2 ) 2 Njim+a) 2 = ln z ma Shorter I
(d 1 ( m )=N/(l-\-n l } 2 N/(m-\-d) z = In 1 md Longer A
\<5 2 (w)=]V/(l+7r 2 ) 2 -Ar/(w+<5) 2 = In 2 -m6 Shorter A
9(w)=AT/(2+<5) 2 -N/(w+9) 2 = 2<5 w?
There is sufficient reason to believe that the relations implied by these formulae
are'exact, notwithstanding that the lines composing a series are only imperfectly
represented by the simple Rydberg formula. The doublet separation is evidently
given by \7t 2 \n v
Ritz suggested that the variable part of the formula for the fundamental series
might be represented by mkn, where A:7r=7t 2 7r x ; or, more fully,
The relation, however, is not exact and the fundamental series is now regarded
as one of the four chief series of a system, having a certain degree of independence.
Ritz's form is approximately correct because n 2 n is mostly small, so that
m-\-(ji 2 n^ is nearly an integer.
Characteristics of Series. 10
TRIPLET SYSTEMS.
The characteristics of a triplet system, such as that of magnesium, in which there
are no satellites, may be summarised as follows :
(1) In the d and s series the least refrangible component is ordinarily the strongest
line and the most refrangible the weakest. The wave-number separa-
tions are constant for all members of the d and s series, and the wider
separation is that of the two less refrangible members. The wider
separation is usually rather more than double the narrower.
(2) In the p series, the order of intensities is inverted and the wider separation
is on the more refrangible side (usually excepting the first triplet). The
series formed of corresponding lines converge to the same limit.
(3) The / series consists of single lines.
Thus, in the abbreviated notation, the four chief series in a system. of triplets
without satellites are written in the form
p 1 (m)=1s mp l Shorter A
p 2 (m)=\s mp 2
p 3 (m)=ls mpj Longer
s l (m)=lp 1 ms Longer
s a (w)=l/> 2 ms
s 3 (m)=l/> 3 ms Shorter
di(m)=\p^mi Longer
d 2 (m)lp 2 md
di(m)=\p s mi Shorter
f(m)=2d mf
A triplet system, as will appear from the tables, is nearly always accompanied
by a system of singlets. Combination lines arising from the two systems are found,
.and it is possible that the singlets form an essential feature of a fully observed
triplet system.
SATELLITES.
In many spectra the series are rendered more complicated by the presence of
satellites which accompany some of the chief lines. Evidence of the existence of
satellites was found by Rydberg, who regarded them as secondary diffuse series, but
their true nature was not revealed until Kayser and Runge made their more exact
observations of spectra.
These satellites are found in connection with doublets and triplets of the diffuse
series. In doublet series, it is the less refrangible line of each diffuse pair which has a
fainter companion or satellite, and the satellite is ordinarily on the side towards the
red. The brighter component, <5 1; -is then displaced from its normal position, and it
is the satellite which follows the law of constant separation. The chief line approaches
the sateUite as the order number increases, and the common limit is identical with
that of the normal members of the o^ series.
In a doublet system which includes satellites, the formulae for the principal and
sharp series are unmodified, but the d formulas become
(5 1 '(m)=LT 1 md' (satellite).
d l (m)=ln l mfi (first chief line, longer }).
(5 2 (m}==\x 2 md' (second chief line, shorter A).
c 2
20
Series in Line Spectra.
CHAP. III.
It will be observed that there will now be two limits for the fundamental series,
given by 2<5 and 2<5', and consequently the members of this series will be doublets,
with a constant separation equal to the separation of the satellite and chief line in the
first <5 pair (usually given, it must be remembered, by m=2) . That is
( <p 1 (w)=2<5 my Brighter, less refrangible component.
I cp 2 (w)=2(5' my Fainter, more refrangible component.
These relations are shown diagrammatically in Fig. 4a. An example of a 6 pair
with satellite appears in the spark spectrum of barium, Plate IV.
In a triplet system, the least refrangible components of the diffuse triplets have
two satellites, the middle lines one, and the most refrangible components no satellite
at all. The outer satellite to the first line is the faintest of the group (Fig. 46). It
is the satellite to the middle line, and the outer satellite of the least refrangible com-
ponent which usually show the normal triplet separation given by the sharp series,
and the separation of the satellite from the middle line is identical with that of the two
satellites to the first chief line. (See also PL IIIc.)
(T
d
f
FIG. 4. DIAGRAM ILLUSTRATING ARRANGEMENT OF SATELLITES (a) IN DOUBLET SERIES ;
(b) IN TRIPLET SERIES.
With increase of order number the displacements of the chief lines diminish,
and ultimately vanish. There are thus six series in the d group when satellites are
present, but there are only three limits, which are identical with the three limits
of the s series.
The formulae for the diffuse series of triplets thus require the following extensions^: .
Index numbers.
13
d z "(m) =\p 2 md"
d 2 (m) =lp. 2 md'
d 3 (m) Ip^md*
Satellites
First chief line, longer A
Satellite
Second chief line
Third chief line, shorter
12
11
23
22
33
Characteristics of Series. 21
The index numbers suggested by Rydberg, and still sometimes used, are shown
on the right. d(4) 13 , for example, would indicate the outer satellite of the first
component of the triplet for which w=4 in the formula representing the series.
There are now three values of the term 2d, and therefore three limits for the
fundamental series. The fundamental series accordingly consists of narrower
triplets in which the separations of the components are constant and equal to those
of the first chief line and its two satellites in the first member of the d series. Symbo-
lically we have
f 1 (m)=2d mf Brightest, least refrangible, component.
ft(m)=2d'-mf
f s (m)=2d"mf Faintest, most refrangible, component.
As shown in Fig. 46, the brightest component and the wider separation are
towards the red, as in the s and d triplets.
It is quite possible that satellites are a normal feature of the diffuse series of
doublets and triplets, and that their apparent absence in some cases may be due to
their small separations from the chief lines.
The probable existence of satellites in some of the fundamental series was first
suggested by Hicks. In the case of the triplets of strontium and barium they have
since been fully established by Saunders from photographs of the arc in vacuo (see
tables for these elements). The structure of a fundamental triplet having satellites
appears to be identical with that of a diffuse triplet, the first line having two satellites
and the second line one. Additional terms mf and mf thus make their appearance,
and the triplet is represe: ted symbolically in the following way:
i2dmf" ,,_ ,
fl(m) = \2d-mf /W-W-3' f s (m)=2d"-mf
\2d-mf
The photograph reproduced in Plate III. (6) shows the details of a fundamental
triplet of barium. It is from a negative by A. S. King,* the source of light being an
electric furnace containing barium vapour at a low pressure.
NEGATIVE WAVE-NUMBERS.
It has already been explained that the first member of the S series is identical
with the first of P, but is of opposite sign in the respective formulae. In the doublets
of the alkali metals, the pair which is common to the two series appears with positive
sign in P and with negative sign in S. In the doublets of some elements, however,
as in aluminium, the first pair has a positive sign in 5, and a negative sign
in P. The first P pair then appears to be out of step with the other P lines, and the
stronger component is on the less refrangible side ; also the limit of the P series is
on the red side of the common limit of D and S, whereas in the alkali doublets it is
on the violet side.
It tends to clearness of thought in all such considerations to construct diagrams,
as in Fig. 5, showing the negative as well as the positive scale of wave-numbers, and,
when the series have been plotted, to imagine the negative members to be folded back
into the positive part of the spectrum. This will ensure a proper conception of the
appearance which any negative group will present in the actual spectrum.
* Astrophys. Jour., 48, Plate III (1918).
22
Series in Line Spectra.
CHAP. III.
a,
*
<*,
Q
u^
'> ^"^
_C
P-i <i>
CL,
Characteristics of Series. 23
Doublet series with positive and negative P(l) are thus illustrated in Fig. 5.
When P(l) occurs with negative sign in a triplet series, as is usually the case, the
first triplet is inverted, the brightest component and the wider separation being then
on the less refrangible side, as in the triplets of the sharp and diffuse series. In the
remaining triplets, however, the stronger component and wider separation are on the
more refrangible side.
The first member of the diffuse series also sometimes appears with negative sign,
and the corresponding doublet or triplet is then reversed right and left in the actual
spectrum. An interesting example appears in Fig. 6, where the lines 8662, 8542,
8498 of ionised calcium (see p. 25) form an inverted diffuse doublet with satellite.
In the tables which accompany this report negative members are
indicated by the usual minus sign. The occurrence of these negative signs is probably
of no great theoretical importance, because the " terms " from which the lines are
derived by taking differences are always positive.
THE COMBINATION PRINCIPLE.
The possible existence of other series which would be related to the chief series
already considered was first suggested by Rydberg,* who pointed out that in his
general formula
L 1
where m was usually =1, it might be supposed very probable that wtjas well
would be variable. Such variation oi m 1 would evidently give rise to other series
running parallel to the first. Rydberg was unable to establish any such series, but
the idea was developed later by Ritz.f
The lines of a series always appear as the difference of two terms, one of which
is the limit of the series, and the other a " variable part " or " term " of a sequence
given by successive integral values of m ; the limit itself in the case of the chief series
is the first term of the sequence of one of the other series. Ritz discovered that lines
which were computed by taking differences of other terms of the four cliief sequences
were often found in the actual spectra, and he called them " combination lines," or
" combination series " when more than one line was derived from the same sequence.
Thus, there might be series 2 5 mP, 3 S mP, as well as the chief series, 1 SmP ;
or 1 SmD, 1 PmP, and so on. The fundamental, or " Bergmann," series was at
first regarded by Ritz as the combination series, 2D wAP, as already explained on
p. 18, but is now to be considered as one of the chief series.
The extensive investigations of infra-red spectra subsequently made by Paschen
and his pupils have revealed a very large number of combination lines, and have
shown that the combination principle is probably exact. The application of this
principle has shown that many lines which previously appeared to be unattached
really form part of regular systems, of which the principal, sharp, diffuse and funda-
mental series are the chief members, and it seems possible that in spectra in which
series have not yet been identified the complexity may be due to the existence of a
great number of combinations.
' It is interesting to observe that the proof of the combination principle is indepen-
dent of a knowledge of the true series formula, or even of the exact limits of the various
t
Loc. cit., p. 73.
Phys. Zeit., 9, 521 (1908) ; Astrophys. Jour., 28, 237 (1908).
24 Series in Line Spectra. CHAP. in.
series. The limits can, in fact, be determined with considerable accuracy in most
cases ; but by assuming the Rydberg and Runge laws to be exact, and adopting a
limit for one of the series, all the limits will be equally in error. Then, if the variable
terms mp, ms, &c., be derived by subtracting the observed wave-numbers of the lines
from the adopted limits of their respective series, these terms will be equally affected
by any error in the limit first adopted. Hence, the errors will cancel each other in
taking differences to form the various combinations. An example may be taken from
lithium (see table for this element) by way of illustration. The limit calculated for
the principal series is 43,486-3, and n (!) is 14,903-8 ; thus
n^ .=43,486-3=1 <r (calculated from actual lines)
7t(l) =14,903-8 (observed first principal line)
.-. <r w =d M =28,582-5=1 n (Rydberg- Schuster law)
<5(2) =16,379-4 (observed first diffuse line)
9^ =12,203-1 =2 <5 (Runge's law)
Thus, starting with n^ , the limits of the other chief series are obtained without
independent calculation from the lines themselves. The " terms " mn, ma, md,
my may then be calculated by subtracting the observed wave-numbers from the 1 "
limits of the respective series, and such a combination as 2<r 2n may then be formed
as follows :
o- w =28,582-5 n^ =43,486-3
<r(2) =12,302-0 jr(2) =30,925-9
2o-=16,280-5 2n =12,560-4
2cr 271=3,720-1 calculated
3,719-9 observed
If the calculation be repeated with any other value of TT^ , the final result for
the combination will be unchanged. This not only verifies the general validity of the
combination principle, but also indicates the truth of the Rydberg-Schuster and
Runge laws, since such calculations are based on the assumption that these laws are
true. An exact series formula would doubtless conform with all these relations,
but the above procedure renders the calculated combinations independent of a
knowledge of the true series formula. Including the satellite terms, the possible
combinations are very numerous, as will appear from many of the tables for individual
elements.
ENHANCED LINE SERIES.
It has been shown by Fowler* that the enhanced lines of helium, magnesium,
calcium and strontium form families of series identical in their mutual relationships
with those formed by arc lines. The enhanced series, however, differ from the
ordinary series in the important particular that the series constant takes four times
its normal value, so that the approximate formula for such a series would be
Hicks has since identified the corresponding series in barium, and other unpublished
examples have been found by the author.
* Phil. Trans., A, 214, 225 (1914).
Characteristics of Series. 25
This feature is obviously of importance in connection with theories of spectra.
On Bohr's theory, while the ordinary series lines are emitted during the re-formation
of atoms from which one electron has been displaced, the enhanced lines are generated
when one electron returns to ari atom from which two electrons have been detached.
The multiple 4 thus appears as the square of 2 in the theoretical formula for enhanced
series.
Adopting this interpretation, it has been proposed by Saunders and others that
series of enhanced lines should be referred to as series belonging to ionised elements
e.g., ionised helium, &c. The adopted symbol for an ionised element is He + , Ca + , &c.
IDENTIFICATION OF SERIES.
In seeking to arrange lines in series, it is necessary to bear in mind at the outset
that lines belonging to the same series have usually the same physical characteristics,
and diminish regularly in intensity in passing to the shorter wave-lengths. Thus, it
frequently happens that lines which form a series can be picked out by inspection of
photographs of the spectra, or of maps constructed from tables in such a way as to
show the relative intensities of the lines. General confirmation may usually be found
by drawing a graph with the lines themselves as abscissae, and successive integers as
ordinates, when regularity of the curve would be a strong indication that the lines had
been properly allocated. A further test might then be made by the calculation of a
formula, or by reference to Rydberg's table (Chapter IV.).
In the case of doublets and triplets, one would naturally first sort out pairs or
triplets of constant wave-number separation, and then try to arrange them in a series
system.
One of the most valuable tests of the proper allocation of lines in doubtful cases,
and especially when only a few lines have been observed, is provided by the behaviour
of the lines in a magnetic field ; that is, by " Zeeman effects." Preston* was the first
to observe that all lines belonging to the same series showed identical magnetic
resolutions, not only in type of resolution, but also in wave-number separation of the
components. Corresponding series in the spectra of several groups of elements were
also found to behave in the same way.
When the source is viewed at right angles to the direction of the magnetic field,
the helium lines all show the " normal triplet " appearance. In the case of the
sodium lines, D t exhibits four components and D 2 six, and exactly similar resolutions
are shown by corresponding pairs of the other elements which appear in the same
group of the periodic table namely, K, Rb, Cs, Cu, Ag and Au. Further, the same
types of resolutions were found by Runge and Paschen for certain pairs in Mg, Ca,
Sr, Br and Ra,f and the inference that these belonged to principal series has since
been fully confirmed by the observation of other members of the series in the region
of short wave-lengths and their connection in series of enhanced lines. Pairs of the
sharp series show similar resolutions, but in inverse order, in accordance with the
Rydberg relationship of the sharp and principal series.
Characteristic resolutions have also been observed in the principal and sharp
triplet series. For the diffuse triplets the resolutions are less simply related, being
the same for lines of the same series, but varying in corresponding series of different
elements.
* Trans. Roy. Soc. Dublin (2), 7, 7 (1899).
f Astrophys. Jour., 16, 123 (1902); 17, 232 (1903).
26 Series in Line Spectra. CHAP, in-
A valuable summary of such observations has been given by Zeeman in his book,
on " Magneto-Optics."*
SPECTRA WITH CONSTANT DIFFERENCES.
In the spectra of many elements in which series of the regular types have not been,
identified, there are pairs or groups of lines with constant wave-number separations
which occur several times. This type of regularity was first noted by Kayserf in.
the spectra of tin, lead, arsenic, antimony, bismuth, palladium, platinum and ruthe-
nium. Other examples were found by RydbergJ in the red spectrum of argon and' in.
the spectrum of copper. The spectra of about 40 elements have since been investi-
gated from this point of view by Emil Paulson. Examples of such constant difference
are given in the general tables.
The question naturally arises as to whether this kind of spectrum structure
represents a second type of regularity, as originally suggested by Kayser, or has its-
origin in a multitude of combination terms. The recent remarkable work of Meissner
and Paschen on the spectrum of Neon (see Neon) is highly suggestive in this connection^
In this spectrum a large number of constant difference groups had been identified,
but it has now been found that the lines may be arranged in about 132 series, which,
are closely inter-related. Several of the series run parallel to each other, and thus
give rise to pairs or groups with constant differences. The individual series are mostly
quite normal, but the spectrum differs from those previously described in having;
several series of each type. It would seem possible that other constant-difference
spectra may be built up in a similar manner.
It is of importance to note that there are spectra which are intermediate betweeai
the constant-difference spectra and those which show series of the more usual types.
Thus, in calcium and strontium (see tables) there are constant-difference triplets-
which have the same separations as those falling in the regular series, and pairs having,
separations equal to one or other of the triplet intervals. In copper, on the other
hand, the constant-difference pairs and triplets found by Rydberg have no obvious*
relation to the separations of the pairs which constitute the regular series.
Macrnillan & Co., Ltd. (1913), pp. 65 and 162.
Handbuch, 2, 573 ; Abh., Berlin Akad. (1893, 1897).
t. Astrophys. Jour., 6, 239, 338 (1897).
Beitrage zur Kenntnis der Linienspektren. Dissn. Lund (1914). Astrophys. Jour.,
40,298 (1914); 41, 72 (1915), Y, A. Phil. Mag., 29, 154 (1915), Pd. Ann. d. Phys., 45,
1203 (1914), La ; 46,698(1915), Pt. Phys. Zeit., 15, 892 (1914), Sc. ; 16, 7 (1915), Gd ; 16,
81, Ru; 16, 352, Ru, Nb, Tm ; 19, 13 (1918), Ni. Zeit. Wiss. Phot., 18, 202 (1919), Pd, Y.
CHAP1ER IV.
RYDBERG'S FORMULA.
THE RYDBERG CONSTANT.
As already pointed out, the Rydberg series constant is derived from the lines of
hydrogen, for which the Balmer formula gives
2 t'
m* 4
The wave-lengths of the first six lines as determined on the international scale
by W. E. Curtis * are probably the most accurate at present available for the calcu-
lation of N. The details are as follows :
Line.
m.
XI. A.
Prob. error.
X Vac.
-y> Vac.
N.
a
3
6562-793
0-0017
6564-6022
15233-216
109679-155
ft
4
4861-326
0-0010
4862-6797
20564-793
8-896
7
5
4340-467
0-0006
4341-6830
23032-543
8-776
8
6
4101-738
0-0013
4102-8915
24373-055
8-748
s
7
3970-075
0-0016
3971-1940
25181-343
8-738
t
8
3889-051
-; 0-00 11
3890-1489
25705-957
8-750
It will be observed that there is a small systematic variation in the values of
N yielded by successive lines, the value diminishing as the order number increases,
indicating a slight departure from Balmer's law. The question is complicated,
however, by the fact that the lines are very close doublets (AA in H a =0'145 ^l,and
in #0 = 0-093yl)f, in which the less refrangible components are the stronger. Curtis's
measures refer to the " optical centres of gravity " of these pairs, and it is clear that the
simple Balmer formula does not strictly hold for these points. It is further probable
that neither of the components is exactly represented by the Balmer formula.
From an application of the general Rydberg formula, Curtis concludes that the
most probable value of N, as determined from the hydrogen lines, is 109,678-3, for
wave-numbers on the international scale, corrected to vacuum.
Determinations of the value of N from any other series are at present of little
weight, as the true form of the series equation remains unknown. As an indication
of the approximate constancy of N for most series, however, the following values
calculated by PaulsonJ by the use of the Ritz formula, to be mentioned later, may be
quoted :
Lithium . AT=109347-5
Sodium N=109358-5
Potassium N =110404-5
Rubidium N=110087-0
Helium ]V=109657-2
These values are clearly not inconsistent with a constant N, since the formulae
employed were only approximate.
* Proc. Roy. Soc., A, 90, 605 (1914) ; A, 96, 147 (1919).
t Merton, Proc. Roy. Soc., A, 97, 307 (1920).
t Kongl. Fysiog. Sallskapets Handl., N.F. Bd. 25, No. 12, p. 12.
28 Series in Line Spectra. CHAP. iv.
It should be noted, however, that Bohr's theory of spectra demands a small
variation of N depending upon the atomic weight of the element. (See Chapter IX.)
THE CONSTANTS p AND A.
Rydberg pointed out that the most natural method of calculating the constants
in his formulas would be to apply the method of least squares, but he did not consider
the data then available to be sufficiently accurate to justify the labour involved.
The equation being of the third degree, the. least square method is not directly
applicable, and it would be necessary first to find approximate values which could be
corrected by the more exact method. In fact, it is necessary, or at least useful, to
find a set of preliminary values of the constants of the Rydberg formula whatever
series equation be adopted.
If two consecutive terms of a series be denoted by v m and
AT
aud N N
(m+ft)? (
The value of (m-\-/u,), and thence of A, can thus be determined by successive
approximations, N being taken as 109678-3.
Rydberg's Interpolation Table. It is more convenient, however, to determine
the approximate values of the constants JJL and A with the aid of an interpolation
table such as was constructed by Rydberg, and then to correct them. This table
gives values of the function Nj(m +/J,) 2 or of (A v), corresponding to values of
(m-\-fjL), ranging from 1-00 to 10-00, together with the differences between con-
secutive values of the function aswis varied. Rydberg's table was computed with
2V=109721-6, and is still useful, but for the present report new computations to
the nearest unit in wave-numbers have been made with Curtis's value of N- namely,
109678-3. The revised functions are given in Table III.
The table will at once give a useful indication as to whether lines suspected
of forming a series really do so. Thus, if the interval between two successive lines
is 9,057, the table shows that the next line in a normal series would follow after an
interval of about 3,676, and the following one after another interval of about 1,846.
These would be the intervals if Rydberg's formula were exact, and in practice are
only to be taken as indicating the order of magnitude of successive steps from line
to line.
But although Rydberg's formula is not exact, the table is almost indispensable
in the preliminary calculation of constants when other more accurate formula? are
used. As an example of its use, let two consecutive lines of a series be v!6,226 and
v!9,398. The interval between the lines is 3,172, and from the table we find
Rydberg's Formula.
Interpolation readily gives
Then
A =16,226+8,255=24,481
or, A =19,398+5,083=24,481
The approximate equation for the series, therefore, is
N
!
J
v=24,481-
(m+0-645) 2
Succeeding members of the series would then be obtained by putting w=5, 6
&c., the second terms again being obtained from the table.
As the Rydberg formula does not usually represent a series with an accuracy
equal to that of the observations, different pairs of lines may lead to slightly different
values of p and A. In order to distribute the errors, and so get a mere even repre-
sentation of the whole series, Rydberg's procedure was to weight the lines in proportion
to the squares of the wave-lengths. It is no longer necessary to do this, as when more
than two members of a series are available a more exact formula may be used, such
as that of Ritz or Hicks.
THE ORDER NUMBERS OF THE LINES.
The numeration of the lines when Rydberg's formula is used is by no means a
matter of indifference. The numbers actually found by the formula, or from the
table, are values of (W+/A), so that m and jj. are not separately determined. To
obtain definitive values of m in a system of series Rydberg made use of the relations
which he had discovered between the P and 5 series. Thus the yellow lines of sodium >
having the same separation as the pairs of the D and 5 series, must be P(l), and the
order numbers in the P series must be assigned accordingly. The numeration of the
lines in 5 must also be such that w=l in its formula gives a result corresponding
approximately with P(l). The latter criterion is also applicable to singlet series
when the first P line occurs in the region covered by the observations. Thus, in the
P series of Na, K, Cs, Rb, if m=l is to give the first member, fj. must be >1 ; and in
the associated S series m=l will then give P(l) with negative sign, with ju<l; in
such systems P^ is > S w . In many cases, however, as in the triplet series of Mg,
Ca, Sr, and in the doublets of Al, P^ < S& (i.e., the P series lies on the less refran-
gible side of D and S) , and /u. must then be > 1 in the formulae for 5 in order that
m=\ may give the first P ; 5(1) then appears with positive sign, and P(l) has a
negative sign as given by m=l in the formula for the P series.
The assignment of the order numbers in the D series remains somewhat arbitrary.
Since D and 5 converge to the same limit, the members of the two series come closer
together as the limit is approached, and it would seem most natural to give neigh-
bouring lines the same number in the two series, especially in such cases as potas-
sium, where D and 5 pairs are nearly coincident in position. In most series the
first observed D is given by w=2 when this procedure is adopted, and //, is < 1. In
other series, as in the D triplets of Ca, Sr and Ba, the lines corresponding to m\
also occur in the spectra. When satellites are present, an important indication as to the
real first member of the D series is given by the equality of the separation of th&
satellites and those of the components of the F series.
30 Series in Line Spectra. CHAP. iv.
It should be observed that p is sometimes rather vaguely regarded as the " phase"
of a series, and its values in the series of different elements may be of importance for
purposes of comparison in relation to other physical properties of the elements. The
correct numeration of the lines determines whether /u is to be taken as greater or less
than unity.
ENHANCED LINE SERIES.
The Rydberg interpolation table may also be used for the preliminary calculation
of formulae for enhanced lines, in which the series constant takes the value 4JV. The
intervals between the successive wave-numbers are then to be divided by 4 before
taking out the values of /u ; and in forming the limits of the series the corresponding
adjacent terms have first to be multiplied by 4. The following example from a series
of enhanced lines of Mg will sufficiently illustrate the procedure :
v Av Av/4 (W+/A) /(w+/x) X4 Limit
12,661 Oloq 2527 3\ 6,976 27,904 40,565
22,770 10 ' K 2 ' 52 4/ ^4,449 17,796 40,566
The approximate formula would thus be
v=40,565 4Af/(w+0-965) 2
RYDBERG'S SPECIAL FORMULA.
A series of single lines which was identified by Rydberg in the spectrum of
magnesium (D in the series tables of Mg) was so imperfectly represented by the
ordinary formula that a four-constant formula was adopted namely,
B C
v=A~
where B and C were calculated independently.* Other members of the series have
since been recorded, however, and it has been found that the series may be at least
equally well represented by the formulae of Ritz and Hicks, involving only three
independent constants, and retaining the hydrogen constant N.
It may be noted that the magnesium series in question has not yet been satis-
factorily represented by any three-constant formula, and the departure from the
formulae becomes more pronounced in the corresponding singlet series of Ca, Sr and
Ba, which belong to the same chemical group.
* Ofversigt af Kongl. Vet.-Akad. Forhandl., Stockholm (1903).
CHAPTER V.
OTHER SERIES FORMULA.
RUMMEL.
One of the earliest attempts to improve on the Rydberg formula was that made
Rummel,* who employed a formula which may be written
C
/ A
m
where Aoo, C, JJL and w are constants special to each series.
The same formula, transposed to wave-numbers, was afterwards independently
investigated by Fowler and Shawf in the form
: _. __ C_
(m+p} z m Q
and, later, by Halm} in the form
This formula has been shown to represent many individual series with con-
siderable accuracy, but while giving a more convincing proof of the exactness of the
laws of limits, it has the disadvantage of not retaining the Rydberg constant, and the
calculated term S(l) usually differs widely from P(l). The formula has, therefore,
not much to recommend it, beyond the fact that it admits of an easy direct solution
for (m +/*), and thence for the other constants namely, that in the second of the
above forms
a 3
(~
where a=]
(1/4 V 3 )(v 2 vj
and v x , t/ 2 , i> 3 , v 4 refer to four consecutive lines. The formula may, therefore, be of
occasional use in the determination of limits.
Halm has attached some importance to the fact that this formula may be trans-
posed into one which is adapted to the series of lines composing band spectra. Thus,
if (m-\-fjC) be put =0 in Fowler and Shaw's form of the equation, there results
V Voo-j
m
and, eliminating v 03> it is easily shown that
1 _ 1 e m 2 m a
vv Q C
or, in terms of wave-lengths
* Proc. Roy. Soc., Victoria, 10, 75 (1897) ; 12, 15 (1899).
t Astrophys. Jour., 18, 21 (1903).
t Trans. Roy. Soc., Edm., 41, pt. 3, 551 (1905) .
32 Series in Line Spectra. CHAP.V.
The formula represents band series rather better than most of the forms which
have been employed, as shown by Halm, and by Fowler in the case of the bands of
magnesium hydride.* It is difficult to see, however, what meaning can be attached
to such a transposition of the formula.
RITZ.
An important modification of Rydberg's formula was made by W. Ritz in 1903.f
Ritz's formula was to some extent based upon theoretical considerations and took
the general form
where N is the Rydberg constant, and p, q are the roots of certain transcendental
equations which are expressible in the form of the semi-convergent series,
In the first approximation p=m-{:a, and q=n-\-a', and the formula becomes
identical with that of Rydberg. In a second approximation, for a single series, N
being constant,
/
("++&)
or, in other forms
N
=A-- - i ....... (2)
N
The numeration of the lines adopted by Ritz was not the same as that of
Rydberg. In the P series the first line is given by m=2, in D by m=3, and in S
by w=2-5.
Ritz applied the formulae (1) and (3) to numerous spectra and showed that they
represented the series with much greater accuracy than the three-constant formula
of Kayser and Runge. The formulae also have the advantage of retaining the
Rydberg constant for all series, and of satisfying the Rydberg relations between
the different series with greater accuracy.
The formula (3) was considered by Ritz to be the most exact, partly on the
ground that extrapolation to w=l-5 in the S formula appeared to give a closer
approximation to the first P line than the formula (1). It is doubtful, however,
whether the superiority over (1) in this respect is general, and the formula is less
convenient in practice.
The Ritz formula in the forms (1) and (3) has been largely employed by Paschen
* Phil. Trans., A, 209, 460 (1909).
t Ann. der Physik., 12, 264 (1903). Phys. Zeitschr., 4, 406 (1903). Gesammelte Werke
Walther Ritz ; CEuvres publiees par la Societe Suisse de Physique, Paris (1911).
Other Series Formula.
33
in his admirable and extensive work on series, and the difference in the numeration
of the lines as compared with Rydberg should be carefully noted. Thus,
Series. Rydberg. Ritz.
P 1, 2, 3 ... 2, 3, 4. ...
S 2, 3, 4 ... 2-5, 3-5 ...
D 2, 3, 4 ... 3, 4, 5 ...
A consequence of the Ritz numeration is that a is negative, except for series
in which the Rydberg figures would give /i >1 in the P and D series, or ^> 0-5 in the
case of the S series.
The Ritz formula in form (1) has been further tested on some of the series of
the alkali metals and of helium by R. T. Birge,* who found that while the Kayser
and Runge formula, even with four undetermined constants, was inadequate, the
Ritz formula, with three undetermined constants and a universal constant, was-
quite satisfactory for substances of low atomic weight. The agreement with ob-
servation, however, became less accurate with the increase of atomic weight, and
left much to be desired in the case of caesium.
The Ritz formula, as pointed out by Birge, has theoretically the form of an
infinite series, and the number of terms actually needed to represent a series depends
directly upon the magnitudes of the coefficients of the several terms. The coefficients
are found to increase with increasing atomic weight, and higher terms of the theore-
tical series become less negligible in the case of the heavier elements. The following
Table given by Birge in this connection for the P series of the elements named is
instructive :
Substance.
Atomic
weight.
a
ft
A
H
1
27419-7
He
4
0-0111
-0-0047
32033-2
U
7
0-047
0-026
43482-1
Na
23
0-144
0-113
41450-1
K
39
0-287
0-221
35006-5
Rb
85
0-345
0-266
33689-1
Cs
133
0-412
0-333
31394-2
In the case of Na, the Ritz formula was found to represent the P series with
special accuracy, and to show that for this element the Rydberg-Schuster law was
accurately true. It should be added, however, that atomic weight is not the only
factor which influences the accuracy with which a series may be represented by the
Ritz formula, or by formulas of similar type (see Chapter VI.).
In a theoretical discussion, Sommerfeldt has arrived at the following generalised
form of the Ritz formula :
v A (m, a]
k 2 N
where (m, a} A v= ^
[(w-fa)+a(w, a) -Hz (m, a) 2 + . . . .J 2
For arc spectra, k=l, and for enhanced lines k=2. This formula has been
applied to several series by E. Fues,$ who also explains a method of determining
the constants. For the sharp series of singlets of cadmium (=2P mS in the Ritz-
* Astrophys. Jour., 32, 112 (1910).
f " Atombau und Spectrallinien," 2nd Edition, p. 510.
$ Ann. d. Phys., 63, 21 (1920).
34 Series in Line Spectra. CHAP. v.
Paschen system), the constants are A =28843-71; a= -0-077419; a= 1-41695 X 10' 6 ;
a'= 1-70734 xlO' 11 ; iV=109732-7. The lines of the series, with wave-lengths
on Rowland's scale, and the differences C, are as follows :
m 1-5 2-5 3-5 4-5 5-5 6-5 7-5
I 2288-10 10395-17 5154-85 4306-98 3981-92 3819 3723
mS 72534-9 19226-4 9449-8 5632'! 3737'3 2666-4 1990'8
A/I Paschen 523 0-8 0-36 +0-4 0-4
AAFues 00 +0-02 -0-3 +0-4 -0-3
It will be seen that the additional term gives a marked improvement in the
representation of the series. About the same accuracy is given by Johanson's formula,
to be mentioned later.
NICHOLSON'S EXTENSION OF RITZ FORMULA.
The higher terms of the second form of the Ritz formula have been taken into
account by Nicholson* in a critical comparison of different formulae for the lines of
helium. In this Paper, Nicholson has developed a method of accurately determining
the limit of a series having many lines, and has thereby shown that the Rydberg-
Schuster law is exact for helium, besides deducing that N has the same value for
helium as for hydrogen. f Nicholson also concluded that the most accurate form
of the series equation is an extension of that of Rydberg, dependent on (m-\-/Lt) and
jiot upon m, namely,
N
LOHUIZEN.
An extensive study of spectral series has been made by Lohuizen,J using the
formula
N
It was apparently not recognised that this is equivalent to the Ritz formula no. 3.
MOGENDORFF-HlCKS.
An extensive and critical study of spectral series has been made by Prof. W.
M. Hicks in a series of papers communicated chiefly to the Royal Society. The
formula which he adopted, while yet unacquainted with the work of Ritz, was
or v=A
4- A
w/ \ ' ' ' m m 2 /
* Proc. Roy. Soc., A, 91, 255 (1915).
t It is possible that the observations were not of sufficient accuracy to justify this con-
clusion completely.
J Bidrage tot de Kennis van L/ij nenspectra, Diss. Amsterdam (1912); also Kon. Akad. van
Wetenschappen te Amsterdam, June and Sept. (1912) (in English).
Phil. Trans., A, 210, 57 (1910) ; 212, 33 (1912) ; 213, 323 (1914) ; 217, 361 (1918) ;
220, 335 (1920).
Other Series Formula. 35
This formula was found to give even more accurate results than that of Ritz,
and it was rarely necessary to go beyond the a/m term. If both a and ft are
included, /? is only a small fraction of a. With a alone the agreement with obser-
vation was better than with /? alone.
The first formula had in fact previously been employed by Mogendorff,* who
had applied it successfully to numerous series.
As regards the numeration of the lines, Hicks considers it possible, in the case
of a well-observed series, to find the correct order numbers by ascertaining the
values which represent the series most perfectly when the above formula is used.
Thus, in the P series of the alkalies the denominator (/ denoting a fraction) is
[m-{-(l-f-/) a/w] 2 , and not (m+f a/w) 2 , for the latter will not reproduce the series
within the limits of observational error, and consequently ft^> 1 ; in the S series
H< 1. This unique determination of fj, is regarded as a matter of the first importance
for comparative study, and according to Hicks only fails when the lines are so few,
or the measurements so bad, that either a/m or a/w+1 will reproduce them within
the observational limits. It would seem, however, that this criterion is of somewhat
restricted applicability.
In the case of the S series, it was further found by Hicks that the use of (w+0-5)
in his formula, in place of m, made it more difficult to fulfill the Rydberg relations
between the P and S series, and he consequently adopted integral values throughout.
Thus in general, the Hicks' numeration is identical with that of Rydberg. A special
feature of the work of Hicks is the determination of the possible variations in the
formulse constants depending upon the estimated limits of error in the recorded
positions of the lines involved.
The Hicks formula seems to have been proved by general experience to be even
more accurate than that of Ritz, and it is probably the most generally useful formula
which has yet been proposed. The three-constant form is extremely convenient
in practice, and well serves the requirements of most series investigations ; that is,
it serves sufficiently for the identification of lines belonging to a series, and tends
to demonstrate the truth of the Rydberg relations. It is not to be expected that it
will represent series perfectly. There is usually an outstanding error when it is
attempted to include the first line of a series, or in extrapolation to negative terms.
PAULSON.
Two formulae have been tested on certain series by Paulson, f namely
N A
W
N -
vA - e m * (&}
~ A (m+a}*- e
the first having three, and the second two, adjustable constants.
Thus, for the D series of lithium, Paulson gives the equations
0-0006631
0-003487
109675 . e~ ?
< B > '=28593.13- (m _ .00 3 497)
* Dissertation, Amsterdam (1906).
f Kongl. Fysiog. Sallsk. Handlingar N.F., Bd. 25, No. 12 (1914) (in German).
D 2
Series in Line Spectra.
CHAP. v.
In (A), m has the values 1, 2, 3, . . . . ; and in (B) 3, 4, 5, .... The order of
accuracy resulting from the formulae may be gathered from the appended table,
in which the residuals are compared with those given by Lohuizen (Ritz formula),
by Kayser and Runge, and by Mogendorff :
m
XObs.
b.A
AB
AL
&KR
AM
1
6103-77
(0)
(0)
(0)
(0)
(0)
2
4602-37
(0
(0)
(0)
(0)
(0)
3
4132-44
0-02
+0-31
(0)
(0)
0-11
4
3915-2
0-18
+0-28
0-25
0-20
(0)
6
3794-9
0-29
+0-24
0-40
0-35
+0-09
6
3718-9
2-16
1-61
230
2-25
1-94
7
3670-6
1-30
0-72
1-45
1-41
1-06
It does not seem that Paulson's formulae have any special advantage over
the Ritz' or Hicks' formulae, and the relation S(l) = P(l), which is so important
in the Rydberg system, has not been taken into consideration.
JOHANSON.
A study of numerous series has been made by Dr. A. M. Johanson,* using a
formula which may be written as follows in the notation adopted in the present
report :
N
It will be seen that if a =6=0, and ft is an integer, the formula reduces to that
of Balmer for hydrogen ; while if fj, be a fraction it becomes identical with that of
Rydberg. When a =b, the formula becomes identical with that of Rummel, in
the form given by Fowler and Shaw, except that the Rydberg constant N is generally
retained. Johanson's formula may thus be regarded as a more general form of the-
Rummel formula. For some series the constants a and b have imaginary values.
By development in series, Johanson has also shown that the formula includes
the formulae of Kayser and Runge, and Rydberg's more general formula as special
cases, and the relation to the formulae of Ritz and Hicks is also indicated. The
numeration of the lines in a series begins with zero for the first member.
In nearly all cases Johanson has adopted the hydrogen constant for N, and
has usually assumed the truth of the Rydberg laws in deducing the limits of series
belonging to the same system. But in the case of the D series of aluminium, which
has always been difficult to represent by formulae adapted to other series, the value
of N has been independently calculated, giving the following constants for the less
refrangible components :
AT=80858
^=0-538853
A =48071-89
a=17-269197
6=_0-173823
It is concluded that in this series N cannot have the same value as the Rydberg
constant calculated from hydrogen. It should be noted, however, that even the
five-constant formula does not represent the nine lines of the series with an accuracy
equal to that of the observations, the error reaching 0-41 A in the case of one of
* Arkiv. for Mat., Ast. och Fysik., Band 12, No. 6 (1917) (in German).
Other Series Formula.
37
the lines, so that the series can scarcely be used to justify the assumption of a real
change in N.
In the majority of cases the Johanson formula, with four adjustable constants,
appears to be very successful. A notable improvement appears in the representation
ol the diffuse singlet series of magnesium. This series was considerably extended by
fowler and Reynolds,* who deduced the following formula from wave-lengths on the
Rowland scale :
v=26618-20-
109675
(W+0-314582+0-899929/W 0-269730/w 2 ) 2
Johanson's constants are
,4=26621-00
a=4-638975
^=1-283559
5=0-281555
The respective results from the two formulae are shown in the following table :
Order number
in/.
Authority.
Limit of
Error.
X (Rowland
scale) .
V
X Obs. X calc.
F. & R.
/.
Paschen
Hermann
Rowland
F. &*R.
1-00
0-02
0-02
0-02
0-03
0-05
0-05
0-10
17108-1
8806-96
5528-641
4703-177
4352-083
4167-55
4057-78
3986-94
3938-58
3904-17
3878-73
3859-39
5843-61
11351-59
18082-68
21256-37
22971-14
23988-25
24637-17
25074-91
25382-79
25606-50
25774-45
25903-60
24903
+ 142-5
ot
ot
Of
0-1
0-3
0-4
0-4
0-3
0-1
Of
0-00*
0-00*
0-48*
+0-55*
0-11
0-36
0-50
0-54
0-50
0-27
0-08
+0-11
1
2
3
4
5
/
<j
8
Q
10
11
The lines marked * and f were respectively used in the calculation of constants.
It will be seen that Johanson has been able to include the first two lines of the
series, and to extrapolate to the 12th member without introducing large errors.
Paschen, however, does not now consider the first line to belong to the series. It
is clear, nevertheless, that this series cannot be correctly represented by either
of the formulae. It may well be included with the D series of aluminium as among
the best examples with whcih to test any proposed new formula.
Johanson considers that his formula not only gives a good agreement between the
calculated and observed wave-numbers for series which have been found to be well
represented by other formulae, but also gives good agreement in other cases, and has
the special advantage that lines with the smallest order-numbers may be used in the
calculation of limits. Also, the change from real to imaginary values of the wave-
number given by the formula when m takes the values 1,0, 1, provides a means of
determining the true first line (" grundlinie ") of the series, and thence also the true
order-numbers.
The method of calculating the constants is indicated in the Paper, but cannot
usefully be abstracted. The process is less tedious than might be supposed.
* Proc. Roy. Soc.. A., 89, 142 (1913).
38 Series in Line Spectra. CHAP. v.
ISHIWARA.
In an extension of Bohr's theory of spectra, J. Ishiwara* has deduced a general
series formula which, for arc spectra, may be written
N Na
N is the Rydberg constant, adapted for the element as in Bohr's theory (chap. IX.),
and a is a constant representing 3^ 2 e*/4c 2 A 2 , where e is the unit electric charge, h is
Planck's constant, and c is the velocity of light. The last term is a relativity correc-
tion. For enhanced spectra, N and <r are to be multiplied by 4.
The formula was applied by Ishiwara to the various enhanced series of magnesium
and showed a close agreement with the observations. These series are also closely
represented by the formulae of Ritz or Hicks, but in the case of the A4481 series (with
/?=0) there appears to be a definite improvement. The formula does not yet appear
to have been tested on series of other elements.
* Math, and Thys. Soc., Tokyo, Series 2, 9, 20 (1910).
CHAPTER VI.
" ABNORMAL " SERIES.
INTENSITIES.
For the sake of simplicity the foregoing description of the properties of series
lines has been restricted chiefly to the most generally occurring cases. Some of the
rules which have been stated, however, are not of universal application.
In general, the intensities show a gradual decrease in passing to the higher
members of a series, but there are a few cases in which the sequence of intensities is
irregular. A well-known example is the very feeble appearance of the second
member of the diffuse series of potassium (A6966), although succeeding pairs decline
in regular order. The second member of the P singlet series of calcium, A2721, is
also unduly faint as compared with the preceding very intense line at 4227, and the
following line at 2398. Other examples are found in the diffuse series of calcium
triplets.
SATELLITES.
The laws which have been stated with regard to the arrangement of satellites
are also sometimes departed from. The diffuse series of aluminium provides an
example in the case of a doublet series. Good measurements of these lines in I. A.
have been made by Grunter,* from which the following may be derived for the
wave-numbers of the chief line and satellite, (5 n and (5 12 , and the second line <5 2 :
<5i2 <5 n <5 12 (5 U <5 2 (5 12 <5 2
32323-36 1>34 32324-70 112 ' 04 32435-40
38817-13 4 ' 49 38821-62 112 - 5 38929-18
42121-47 4 ' 05 42125-52 112 ' 03 42233-50
44054-51 2 " 31 44056-82 112 - 9 44166-60
The separation of the satellite and chief line does not regularly diminish as in
the normal cases, and the constancy of the distance from the satellite to the second
chief line shows that it is the first chief line which is irregular, and not the satellite.
The <p series lies in the infra-red, and the separation of the two components is not
known.
The recent very complete investigations of the spectra of Ca, Sr and Ba which
have been made by Saunders have also shown marked irregularities in the arrange-
ment of the satellites in the diffuse series of these elements (see tables).
SPACING OF LINES.
Another kind of abnormality takes the form of an unusual spacing of the lines
of a series, so that the ordinary series formulae will not represent them with any reason-
able approach to the accuracy of the observations. The singlet series of magnesium
to which reference has already been made (p. 37) is one of the best known examples,
but more extreme cases have been found by Saunders in the corresponding singlet
series of Ca, Sr and Ba. The d series of aluminium doublets and the a series of
thallium are also well-known examples.
* Zeit. Wiss. Phot, 13, 1 (1914).
Series in Line Spectra.
CHAF. VI.
Rydberg's simple formula utterly fails to represent such series, and though a
great improvement results in some cases from the introduction of another constant,
as in the formula? of Ritz or Hicks, it is evident that some more drastic change in the
formula is necessary. The study of these extreme cases is clearly of great importance,
since very few series can be considered to be perfectly represented by the ordinary
formulae, and if a general formula be possible the abnormal series would seem to
provide the most suitable data for its investigation.
The nature of the abnormality will be partially gathered from a comparison
with a more normal series, say the P singlet series of Ca with the P series of He.
The wave-numbers of the first nine lines of each of these series are given below,
together with the values of ju taken from Rydberg's table :
Ca (singlet P).
He (doublet P).
m
V
A,
I*
V
&K
V-
1
23,652
9,231
13,080
1-12
16,477
0-939
2
36,732
25,708
. 4,947
. 1-09
5,652
0-934
3
41,679
31,360
2,254
1-14
2,584
0-933
4
43,933
33,944
1,492
0-81
1,392 0-932
5
45,425
35,336
1,055
0-45
834
0-932
6
46,480
36,170
705
0-30
540
0-930
7
47,185
36,710
476
0-25
368
0-93
8
47,661
37,078
338
0-18
264 0-93
9
47,999
37,342
It will be seen that in the He series the successive values- of fj, change very slowly
and regularly, whilst in the Ca series they change so rapidly that Rydberg's table
would not serve to indicate the positions of succeeding lines with any certainty.
The imperfect representation of this series by formulae will be gathered from
the observed minus computed wave-numbers given in the accompanying table,
the formulae employed being as follows :
I. v:=49,148-]V/[w+0-870-{-0-204/w] 2 .
II. v=49,216-Ar/[w+0-345+l-750/w-l-024/w 2 ] 2 .
III. v=49,305 164,970/[w+l-708666 0-172761/w] 2 .
IV. v=49,305-AT/[m+l-528649+2-774349/w-l-190193e] 2 .
V. v=49,305 Ar/[w+0-126879+6-620605/w 2 5-679767/w 4 ] 2 .
VI. v=49,305-AT/[w-l-092198+17-291194/w 2 -50-606112/w 4 ] 2 .
VII. v=49,305
VIII. v=49,376
The limit given by Saunders (49,305) has been adopted in all but the first two
and the last formulae, and in all cases the lines used in the calculation of constants
' ' A bnormal ' ' Series .
are marked by an *. In III., N has been independently calculated. In VI., the
lines have been numbered 2, 3, 4 ... in place of 1, 2, 3 . . . Formula IV. 'was
suggested by the forms first used by Paschen for certain series in the spectrum of
neon, none of which, however, appear to be adapted to the Ca series under discussion.
Paschen afterwards found that such formulae were not required for the neon series.
The last two formulae are in Johanson's form, one with the limit assumed, and the
other with the limit calculated.
Calcium, Singlet P Series.
m
X
v.
I.
II.
III.
IV.
V.
Vl.f
VII.
vin. 5
1
, 4226-73
23652
+2*
+ 8*
0*
0*
*
0*
0*
0*
2
2721-65
36732
+ 1*
0*
0*
0*
3234
1892
1642
1735
3
2398-58
41679
397
0*
0*
0*
*
+ 6*
0*
0*
4
2275-49
43933
686
357
232
394
*
0*
0*
0*
5
2200-76
45425
584
361
176
303
92
44
+ 6
8
6
2150-78
46480
367
223
28
244
67
6
+71
+42
7
2118-68
47185
205
119
+ 68
197
39
+ 16
+ 98
+59
8
2097-49
47661
101
54
+ 114
135
24
+ 22
+99
+51
9
2082-73
47999
28
8
+ 138
92
12
+ 26
+93
+ 40
10
2073-04
48223
0*
0*
+ 125
85
25
+5
+ 62
+5*
11
2064-77
48416
+44
+30
+ 135
56
12
+ 13
+63
2
Numeration begins with m = 2.
Numeration begins with m=0-; and for the first line the
brackets has to be taken.
difference of the two terms inside the
The results of the calculations do not clearly suggest that the necessary modifica-
tion of the ordinary formulae is to be found in a change of the value of the
series constant. As already remarked, however, in the case of the d series of
aluminium, Johanson found it impossible to represent the lines by his formula without
making such a change ; he deduced a value of about 80,000 for this series in place
of the usual 109,678, and found a fair representation of the lines. The constant a
in the formula then had the very large value 17-3, as compared with values which
rarely exceed 2 for most series, while b was small. Ca P has the same features in
greater, degree.
A part of the difficulty of representing an abnormal series such as that of the
Ca P singlets appears to arise from a difference in the rates of convergence of the
earlier and later lines. Lorenser* and Saunders have illustrated this as in Fig. 7.
If the series equation be of the form
N
v=A
we have
If N be assumed, and a value of A be assigned from a consideration of the
later lines of the series, /(w) will represent what Saunders has called " the residual,"
and the curve is drawn by plotting the residual, or p+f(m) against m. It will
be seen that the curve has a point of inflexion in the part corresponding to the earlier
members, so that the residual cannot be a very simple function of m.
* Beitriige zurKenntnis den Bogenspektren der Erdalkalien- Dissertation, Tiibingen (1913).
p. 41.
Series in Line Spectra.
CHAP. VI.
The curve represents the Ca singlet P series, A having been taken as 49,305
the values of ft +f(m) for the eleven lines are
(1) 1-0677
(2) 0-9535
(3) 0-7924
(4) 0-5185
(5) 0-3167
(6) 0-2309
(7) 0-1927
(8) 0-1679
(9) 0-1641
(10) 0-0681
(11) 0-1073
Similar results are shown also by the corresponding singlet series of strontium and
barium, and also for the d series of calcium triplets and the / series of barium,
particulars of which will be found in the general tables.
It will be evident that the representation of series by formulae is a subject
which is far from having been exhausted, and that the " abnormal " series to which
12 345 678 9 10 11m,.
FIG. 7. CURVE OF jx+/(m) FOR THE Ca SINGI.ET PRINCIPAL SERIES.
attention has been directed furnish valuable material for further investigations. The
simpler formulae which represent many of the series very closely are evidently only
approximate, and cease to be of use in extreme cases. They would seem to be
merely first approximations to a more general formula which may be applicable to
all series. Until some such formula has been found, it would seem that some
interesting questions, such as that of the approximate constancy of N for different
elements, cannot be completely investigated.
Meanwhile, in investigations connected with combination series, as already
explained, the use of a formula can be dispensed with. The limit of one of the
main series having been calculated, the other limits are derived by the Rydberg-
Schuster and Runge laws, and " terms " are formed for the lines by subtracting
the wave-numbers from the limits of the series to which they belong. The
combinations of the terms may then be compared with the wave-numbers of other
observed lines.
CHAPTER VII.
SPECTRA AND ATOMIC CONSTANTS.
GENERAL RELATIONSHIPS.
Following the classification of spectral lines in series, it was natural to seek for
relations between the series spectra of different elements. Hartley* and others had,
in fact, previously noted similarities in the spectra of related elements, such that one
spectrum might to some extent be considered to be produced by displacing another
bodily through a certain distance. It is interesting to note that in this connection
Hartley found " a considerable body of evidence in support of the view that elements
whose atomic weights differ by a constant quantity, and whose chemical character
is similar, are truly homologous ; or, in other words, are the same kind of matter in
different states of condensation."
The early work of Rydberg, and that of Kayser and Runge, indicated two definite
influences of atomic weight upon the respective series spectra :
(1) In elements of the same chemical group, the limits of corresponding series
advance towards the red with increasing atomic weight.
(2) In elements of the same group, the wave-number separations of doublets or
triplets in corresponding series are roughly proportional to the squares of the atomic
weights.
These results are illustrated diagrammatically for the sharp triplet series of Mg,
Ca, Sr and Ba in Fig. 8.
Rydberg also drew attention to the approximate constancy of the sums of the
constants /* in his formulae for the sharp and diffuse series in the spectra of elements
of the same group and of their differences in corresponding elements of Groups II. and
III. These relations, however, are very rough, and a similar examination of the
constants of the Hicks formulae has not led to any significant results.
LIMITS AND ATOMIC WEIGHTS.
The' general relation between the limits of corresponding series in elements of
the same group is illustrated in the following table :
Doublets
^00
<*100
Doublets
^00
100
Triplets.
PoQ S 100
Li
Na
43,486
41 449
28,582
24 476
O
s
33,043
31,148
21,207
20,085
Mg
Ca
20,474 39,760
17,765 33,989
j
35 006
21 963
Se
30,699
19,268
Sr
16,898 .31,038
Rb
Cs
33,689
31,405
20,873
19,672
Ba
15,869 28,515
In the case of the alkali metals, if the limits of the subordinate series and the
atomic weights be taken as co-ordinates, the points lie on a fairly regular curve,
except as regards K ; or, if the logarithms of the two sets of figures be plotted, the
points will lie nearly on a straight line, with K again out of order. The Ca group
shows similar results, with Ca discordant.
The limits of the principal series, however, are less regularly connected with the
atomic weights than those of the subordinate series.
* Jour. Chem. Soc., 43, 390.
-
44
Series in Line Spectra.
CHAP. VII.
LIMITS AND ATOMIC VOLUMES.
A possible relation between the limits of the subordinate series and. the atomic
volumes of the elements appears to have been first suggested by Reinganum.* If
the atomic volumes of the elements of Group II. were divided by 4, and those of
Group III. by 6, while those of Group I. retained their ordinary values, Reinganum
found that when the logs, of the modified atomic volumes were plotted against the logs,
of the limits of corresponding series, the points for all the elements considered fell
approximately on a straight line. The relation, however, is by no means precise.
From the consideration that the wave-frequencies of the transverse vibrations
of an elastic body are inversely proportional to the linear dimensions (or to the cube
roots of the volumes) , and that some similar relationship might be found for vibrating
atoms, Halmf also suggested a possible relation between the limits of series and the
'40.000
30
ooo
1
2O,QOO
70,000
I.
Mg
|
\
Ca
i
Sr
i
i
i
Be
Fie. 8. THE SHARP SERIES OF Mg, Ca, Sr, Ba, SHOWING INFI,T. T EXCE F ATOMIC WEIGHT.
atomic volumes of the elements. For elements of the same group, Halm found that
the limits of the subordinate series were approximately represented by an equation
of the form
where v is the atomic value and a and b are constants. Thus, the alkali group was
represented with a=9,934, 6=42,300; Zn, Cd, Hg with a=24,228, 6=38,960;
and so on. The approximate relation, however, was not fulfilled for the group Al,
In, Tl. As in the case of the atomic weights, the limits of the principal series of the
alkalies failed to show the same simplicity as those of the subordinate series ; a fair
agreement, however, was obtained by making a =34,610 and &=2 X 10 4 for Li and Na,
and a=12,758, 6=8x10* for K, Rb, Cs.
The possible atomic volume relationship has also been considered by Birge.J
who found that the constants of the Ritz formulae for the principal series of the
alkali metals were roughly proportional to the atomic volumes, as shown in the
following table :
Element.
a
b
b/a
At. vol.
a/at. vol.
fc/at. vol.
Na
0-14433
0-11302
0-784
23'606
613X 10~ 5
480 XlO' 5
K
0-28692
0-22083
0-770
44-617
642X 10' 5
495X 10~ 5
Rb
0-34559
0-26577
0-768
56-05
627X 10~ 5
473X 10*5
Cs
0-41196
0-33269
0-807
70-584
585 X 10~ 5
472X 10'5
* Phys. Zeit, 5, 302 (1904).
t Trans. Roy. Soc., Edin., 41, 593 (1905).
J Astrophys. Jour. ; 32, 123 (1910).
Spectra and Atomic Constants.
45
It is doubtful if anything more significant is to be gained from comparisons
of the formulas constants than from direct discussions of the limits of the subordinate
series, since the latter are determined by the constants of the principal series.
In the case of the alkali metals, there is certainly a great improvement in the
representation of potassium when atomic volumes are substituted for atomic weights
in the construction of a curve showing the relation with the limits of the subordinate
series. In the alkaline-earth group, however, strontium is notably discordant, as may
be observed by plotting the following figures :
Element.
Sioo
At. vol.
Mg...
39 752
14-0
Ca
33 983
25-5
Sr
31 026
34-5
Ba
28 575
36-63
Further data for the consideration of these questions may be derived from the
general tables of spectra which form part of this Report.
DOUBLET AND TRIPLET SEPARATIONS.
The following extract from a table given by Rydberg* will illustrate the approxi-
mate relation between the separations of doublets and triplets and the squares of
atomic weights in elements of the same group. f
At. wt.
Av or A
Lit
7-03
_
Na
23-06
17-19
K
39-14
57-85
Rb
85-44
235-98
Cs
132-88
553-87
Zn
Cd
Hg
65-38
112-08
200-36
388-97
1170-76
4631-17
32-3
37-8
32-3
31-6
91-0
93-2
115-4
Cu
Ag
Au
Al
Ga
In
Tl
At. wt.
63-44
107-94
197-25
27-08
69-9
113-4
204-15
248-54
920-48
3815-40
112-02
823-6
2212-54
7792-63
61-8
79-0
98-1
152-8
168-6
172-1
187-0
It will be seen that the proportionality between AK and W 2 in the same group is
only very roughly given by the equation
v=y, or =cv
A closer agreement was found by Runge and Precht by using the equation
or log W=log C-\-n log (Av)
Thus, it was found that by taking logs, of the atomic weights and logs, of the
separations as co-ordinates, the points representing elements of the same group lie
nearly on a straight line. In an attempt to determine the atomic weight of radium
from the spectroscopic data, Runge and Precht discussed the enhanced doublets of
the calcium group, for which the equation becomes
log JF=0-2005+O5997 log Av
* Rapp. au Congres Int. de Phys., Paris (1900). *
t NOTE. Rydberg and some other writers have represented separations by v, but, as this is-
more appropriate to wave-numbers, A^ is here adopted for the separations of doublets and triplets..
+ The separation 0-34 given by Kent is out of step with Av for the other alkali metals.
Phys. Zeit, 4, 285 (1903) ; Phil. Mag., 5, 476 (1903).
Series in Line Spectra.
CHAP. VII.
The results are shown in the following table :
Mg
Ca
Sr
Ba
Ra
91-7
223-0
801-0
1691-0
4858-5
W
24-36
40-1
87-6
137-4
225-0
W calc.
23-84
40-6
87-5
136-9
258-0
C
+0-52
0-5
+0-1
+0-5
33-0
The result for Ra is much too high, and it is evident that the formula is not
sufficiently exact for the long extrapolation required. A variation in procedure was
adopted by Rudorf,* who plotted curves for the different groups with 100Av/W a
and W as co-ordinates. The curves were rather complex, but appeared to pass in
all cases through the zero point. No calculations were given, and the method does
not appear to lend itself to such an extrapolation as that required for radium.
Using Runge and Precht's data, Dr. Marshall Wattsf derived an interpolation
formula for the enhanced doublets of the calcium group, namely,
where
log W =4-886242 +0-6231790 0-080391a 3 0-03741750 4
a=log Av-2-813121
The calculated atomic weights were Mg 24-32, Ca 40-08, Sr 87-62, Ba 137-41,
Ra 226-56, in close agreement with the true values. It will be observed, however,
that the formula involves as many constants as there are elements in the group.
A further attempt to determine the atomic weight of radium was made by the
Misses Anslow and Howell,J using the separations of the extreme members of triplets
which they believed they had identified in radium, and comparing them with corre-
sponding terms for other elements of the group. The logs, of the separations and
logs, of the atomic weights gave points which lay very nearly on a straight line,
and indicated 231-7 for the atomic weight of radium.
The separations of doublets and triplets were discussed by Ritz in a different
way. Thus, the main separation in a doublet system in our notation is given by
<7 2 oo GI<X> , and from the relation between the a and n series we have
Av=cjoo -(joo ^
where n z and n may include extra terms introduced for the better representation
of the series. In the Ritz formulae, the denominator terms are indicated by
(m -\-pi~\-n' I m 2 ) and (m-\-p z -}-7i"/m z ), and Ritz found that the quantities (Pi~P^
gave a much smaller range of values in relation to the squares of the atomic weights
than did the separations themselves when different groups of elements were included
in the comparison. His results are shown in the following table :
Na
K
Rb
Cs
Cu
Ag
Mg
Ca
Sr
Zn
Cd
Hg
Al
In
Tl
He
A^.IO'/W"
32-3
37-8
32-2
31-6
61-8
79-0
68-8
66-1
51-5
91-0
93-2
115-4
152-8
172-1
187-0
63-8
in 7
14-2
18-9
18-0
18-6
18-6
24-2
14-6
17-7
15-7
17-2
18-6
22-3
24-8
29-2
32-7
20-4
* Zeit. Phys. Chem., 50, 100 (1904).
t Phil. Mag., 18, 411 (1909).
t. Proc. Nat. Acad. Sci., Wash., 3, 409 (1917).
Astrophys. Jour., 28, 241 (1908) ; 29, 243 (1909).
Spectra and Atomic Constants. 47
The essential difference of procedure as compared with the use of direct values of
Av is that in the form (pj_p 2 ) the doublet or triplet separations are associated with
the limits of the subordinate series. Ritz regarded these results as merely preliminary,
but does not appear to have carried the matter further. A more exhaustive study,
however, has been made by Hicks (see Chapter VIII.).
The results obtained by substituting atomic volumes for atomic weights in
relation to the doublet and triplet separations in the foregoing comparisons do not
appear to be any more definite than those already quoted. Thus, in the elements
of the alkali group, potassium still deviates from the curve which connects atomic
volumes with the separations, or from the straight line when the logarithms are
plotted.
HOMOLOGOUS LINES AND ATOMIC WEIGHTS.
In an attempt to discover the relations, between the spectra and other physical
properties of the elements, Ramage* compared graphically the corresponding or
" homologous " lines in the different elements of the various groups. The character-
istic flame lines Mg 2852, Ca 4227, Sr 4607, Ba 5535, are examples of such lines ;
and, in general, lines of corresponding series which have the same value of m would
be regarded as homologous. Such lines, like the limits of the series to which they
belong, usually advance towards the red with increase of atomic weight. The curves
connecting their wave-numbers with the atomic weights, or with the squares of the
atomic weights, however, were found by Ramage not to be continuous throughout
the whole of a group of elements. In the alkalies, for instance, there was a break
between Na and K. It does not seem probable that the discussion of individual
lines will lead to more definite relations than those of the limits of the series.
Ramage also derived empirical formulae for the series of K, Rb and Cs, in which
the atomic weight was the only variable, apart from the parameter m. Thus, he
found that the second components of the principal series were given by
v=35,349-0-2233J7 2 -iV/[w+M9126+0-00103JF
+(0-04377 +13W* x 10- 7 ) (1 -S 1 '" 1 )] 2 .
The possibility of obtaining such a formula strongly suggested to Ramage that
the diff ere ices between the series of the three elements in question depended solely
upon differences of atomic weights. The number of constants involved, however,
is too large to give confidence in such a conclusion, especially as the formula fails
to include lithium and sodium.
Other relationships between homologous lines and atomic weights were afterwards
suggested by Marshall Watts.f Thus, in each of the two groups K, Rb, Cs, and Ca,
Sr, Ba, the differences of wave numbers between corresponding lines in their spectra
were found to be nearly proportional to the differences between the squares of the
atomic weights. In the first group the lines having the following wave-numbers
were assumed to be homologous :
Cs Rb K
(a) 12,469 (6) ... 13,742 (4) ... 14,465 (7)
(b) 21,764 (6) ... 23,714 (6) ... 24,700 (6)
(c) 21,945 (8) ... 23,791 (8) ... - 24,719 (8)
&c. &c. &c.
* Proc. Roy. Soc., 70, 1 and 303 (1901-02).
t Phil. Mag., (6) 5, 203 (1902).
48 Series in Line Spectra. CHAP. vn.
Adopting atomic weights 132-7 for Cs and 39-9 for K, the rule gives with lines (a)
86-87, with lines (b) 83-24, and with lines (c) 83-11 for the atomic weight of Rb (85-2).
The limits of the principal series, treated in the same manner, give 86-0. Reference to
the general tables will show that the lines (a) are not homologous, and if the correct line
of Cs(13,138) be introduced the deduced atomic weight for Rb becomes 102. The
suggested relation also excludes lithium and sodium and would therefore seem to
have no great significance.
In another class of elements, represented by Zn, Cd, Hg and Ga, In, Watts found
that the differences between the wave-numbers of certain lines of one element
were to the differences between the corresponding lines of the other elements as the
squares of their atomic weights. Among the pairs of assumed corresponding lines
of Cd and Zn given by Watts are the following :
Cd Zn
(a) 30654-4 (10) ..." ............... 32500-0 (8)
(b) 30734-9 (8) .................. 32540-1 (10)
(c) 31905-5 (8) .... .............. 32928-7 (10)
(d) 32446-8 (6) .................. 33118-6 (8)
&c. &c.
The assumption of 111-83 for the atomic weight of Cd then gives 65-44 from (a)
and (c), 65-69 from (a) and (d), and so on, for that of Zn (64'9). Since lines (b), (c) and (d)
belong to corresponding triplets, and lines (a] are not placed in series, it will be seen
that in place of taking the triplet separations themselves to be proportional to the
squares of the atomic weights, Watts has added wave-numbers to the separations
equal to the intervals between the lines (a) and (b) of the two elements. That is,
since (c) (b)=&v lt and (d) (c)=Av 2 , if (b) (a) be called x for Cd and y for Zn.
Watts makes
x (Cd)
For (a) and (c)
jy+Av/ (Zn)
and for (a) and (d)
(Zn) 2
The difference between the two results from members of undoubtedly corre-
sponding triplets, measured with sufficient accuracy in each case, sufficiently indi-
cates that this mode of correcting the triplet separations in forming the ratio of
squares of atomic weights cannot be valid. In fact, the two expressions on the left
could only be equal if Av 2 /Av a * were also equal (Cd) 2 /(Zn) 2 , and this is only approxi-
mately true for these two elements, and very far from true when mercury is taken
as one of the elements. Some of the other lines taken to be homologous by Watts
are certainly not corresponding lines, and it is difficult to understand on what prin-
ciple they were selected. The deduced values for Zn range from 64-77 to 67-08.
SEPARATIONS AND ATOMIC NUMBERS.
Since atomic numbers probably determine the places of the elements in the
periodic table more correctly than the atomic weights, several attempts have been
made to correlate these numbers with the series spectra.
In a graphical repetition of Runge and Precht's work on the doublet separations
Spectra and Atomic Constants. 49
in the calcium group Ives and Stuhlmann* found that the results were somewhat
more consistent than for the atomic weights, but the atomic number derived for
radium was 96, in place of the true value 88. Using the wave-number differences
between extreme members of the triplets occurring in elements of the same group,
it was found also by Anslow and Howell| that when the logarithms of these differences
were plotted against the logarithms of the atomic numbers, the points fell more
accurately on a straight line than with atomic weights, and an atomic number of
87 was deduced for radium.
Separations in relation to atomic numbers have also been discussed by tL
Bell, | who employed two formulae, namely :
(1) A /A7=m(N-.V ) ; (2) log Av=/> log N+q
where AV is the separation, N the atomic number, and the other terms are constants
to be calculated for each group of elements. The figures for the alkali group will
serve for illustration :
At. No. Aj/ obs. Ay calc. (1). Ai/ calc. (2).
L,i 3 ... 0-34, ... 0-25 .:. 1-03
Na 11 ... 17-21 ... 16-48 ... 17-21
K 19 ... 57-90 ... 58-0 ... 56-17
Rb 37 ... 237-71 ... 244-0 ... 237-7
Cs 55 ... 564-10 ... 558-3 ... 560-8
m =0-4447; ^0 = 1-875 ; = 2-1645 ; ? = 1-01832.
A somewhat similar formula was tested by Paulson, || namely
log &=A log (N+n)+B
where N is the atomic number, Av the separation, A and B constants, and n a
positive or negative integer. For each group of elements the value of n was first
determined graphically, and the constants A and B were then calculated ty the
method of least squares. The atomic numbers used were those of Rydberg's system ,^|
which are two units higher than those of Moseley. The nature of Paulson's results
may be gathered from the following data for the triplets of the calcium group :
log Av 1 =2-163129 log N -0-871542
log Av 2 =l-748748 log (N -4) -0-459734
Mg
Ca
Sr
Ba
Ra
The extrapolation to radium does not agree at all closely with the separations
2016-64 and 1036-15 afterwards suggested by Anslow and Howell. It will be observed
* Phys. Rev., 5, 368 (1915).
"i* T oc cit
i Phil. Mag., (6) 36, 337 (1918).
J; Not used in calculation of constants.
ij Astrophys. Jour., 49, 276 (1919).
If Jour. Ch Phys.. 12, No. 5 (1914).
N.
(Rydberg.)
A V1 .
Ai/ 2 .
Ai/! calc.
C.
Ai/2 calc.
C.
14
40-92
19-89
40-52
+0-40
19-45
-j-0-44
22
105-99
52-11
107-72
1-73
54-38
-2-27
40
394-44
187-05
392-57
+ 1-87
182-74
-14-31
58
878-4
370-3
876-96
+ 1-44
371-35
1-05
90
(2268)
(838)
5 C Series in Line Spectra. CHAP. vn.
that no simple connection between the atomic numbers and the doublet or triplet
separations has yet been discovered.
There does not appear to be any published record of investigations of the limits
of series in relation to atomic numbers, but a few trials will show that the results
are generally similar, and not more exact, than for the atomic weights. Thus, in
the alkali group, potassium remains decidedly discordant, and in the calcium group,
calcium again shows considerable departure from the approximate regularity shown
by the other four elements. When the limits of the principal series are plotted against
atomic numbers the points show the same absence of simple regularity which was
found with the atomic weights.
CONCLUSIONS.
These results are in a sense disappointing. It would seem that the spectra
'must for the present be regarded as constants of the elements which show no simpler
relation to other constants than is shown by some of the constants among them-
selves. Thus, in the alkali group, the curve connecting atomic weights with melting
points, or that connecting atomic weights and atomic volumes, is closely similar to that
relating the limits of the subordinate series to atomic weights, and a similar discrep-
ancy is shown by potassium in each case. Again, there is no simple relation between
the atomic weights and densities in this group of elements, just as there is no simple
law connecting the limits of the principal series. It can only be concluded that
although the spectra change progressively with atomic weights, atomic volumes or
atomic numbers, the laws governing the changes are not clearly indicated by any
of the foregoing invest : gations.
CHAPTER VIII.
THE WORK OF HICKS.
The discussion of spectral series which has been made by Prof. W. M. Hicks* is
of so special a character that it is most conveniently treated separately. The
investigation covers a great deal of ground, and it will only be possible to attempt to
give a general idea of some of the methods employed. In the earlier papers Hicks
proves the value of the series formula
N
= A-
/ . . _\
V m)
and makes a special feature of calculating the influence of possible errors of observa-
tion on the values of the constants for the different series. Having determined the
constants for many of the known series, he proceeds to discuss them in relation to the
atomic volumes and atomic weights of the respective elements. The adopted wave-
lengths are on Rowland's scale, and as the conclusions would not be modified by the
substitution of wave-lengths on the international scale, it has not been thought
necessary to recompute the formula constants and the quantities which depend upon
them.
It should be remarked that in some of his papers Hicks departs from the more
usual practice, and writes, for example, p(l), instead of 1 p, for the variable part
or " term " of the first principal line.
ATOMIC VOLUMES.
Among the more striking results obtained by Hicks in his first paper is the follow-
ing comparison of the constants for the stronger components of the principal series
of the alkali metals with the atomic volumes. The limits of the series are also entered
for completeness :
<"
(X,
** 1
H 1+a
At. vol.
Ivimit.
u ...
0-951609
+0-007365
1X11-81
43,486
Na...
1-148678
0-031776
2X0-074339
2X0-058451
2X11-80
41,449
K ...
1-296480
0-062511
4X0-074120
4X0-058492
4X11-15
35,006
Rb. M
1-366399
0-074554
5X0-073280
5X0-058369
5X11-21
33,689
Cs ...
1-450967
0-090077
6X0-075161
6X0-060148
6X11-76
31,405
The constants (jn 1) and (ft 1+a) are thus approximately integral multiples
of constant numbers, and the atomic volumes the same multiples of another number.
Lithium is excluded in this mode of treating the formula constants, and Hicks has
suggested that what is usually regarded as the principal series of lithium may really
be a combination Ismd or Ismf; the easy reversal of the lines, and the similarity
to the principal series of the other alkali elements, however, is directly opposed to
this supposition. Assuming the above relation to be sufficiently general, and
observing that a/( / a 1) is nearly constant, Hicks endeavoured to bring the figures
into closer agreement by the introduction of an atomic weight term as a correction to
* I.. Phil. Trans., A. 210, 57-111 (1910); II., 212, 33-73 (1912) ; III.. 213, 323-420 (1914) ;
IV., 217. 361-410 (1917) ; V.,220, 335-468 (1919). Corresponding numbers are used for references
to these papers in the text.
E 2
Series in Line Spectra.
CHAP. VIII.
ATOMIC WEIGHT TERM.
The atomic weight term, as defined by Hicks, depends jointly upon the separa-
tions of doublets or triplets, and the limits of the subordinate series. Thus, if D
represents denominator, the formulae for the two members of a sharp series of doublets
may be written :
A is then the atomic weight term as represented in the later papers of Hicks, and is
equivalent to the 2W of the first paper. In triplet series the two separations give
A! and A 2 , of which the former is the greater.
Hicks was led to conclude that there is a universal constant, approximately
0-21520, so that the denominator of the principal sequences of the alkalies, or of the
sharp sequences in the elements of the second and third groups might be represented by
m/
m
where a and k are constants for all elements, not very different from 0-002740/(1 k)
and 0-21520 respectively, v is the atomic volume, and s is an integer special to each
element as follows :
Na 2
K 2
Mg 8
Ca 7
Zn 9
Cd 8
Al 8
Ga 8
Rb 2
Cs 2
Sr 6
Hg 6
In 6
Tl 5
If k be taken =0-21520, a =0-003490. W is to be taken as A/2 for doublets, and
as A 2 for triplets.
In order to indicate the degree of approximation given by the general formula,
the following comparison may be made with the values of the denominators calculated
from the regular series formulae :
Element.
Series.
At. vol.
s
A/2
A.
True
denominator.
From general
formula.
K ...
KI
44-60
2
0-001466
(1) 2-233969
2-244315
(2) 3-265225
3-277078
Ca ...
s i
25-5
7
0-001368
(1) 2-484198
2-488903
(2) 3-522799
3-555250
Zn ...
Sl
9-33
9
0-003475
(1) 2-227899
2-229991
(2) 3-257479
3-259785
It will be seen that the correspondence is far from perfect, and after the exhaustive
investigation made by Hicks it may be doubted whether it is really possible to deduce
such a formula which shall be applicable to all elements. The atomic volume,
given by atomic weight divided by density, as Hicks remarks, varies with temperature
and cannot be directly involved in the spectral relations ; it would seem, however,,
that it may be closely related to an atomic property analogous to volume, or sphere
of action, on which the structure of the spectrum in part depends.
It should be particularly noted that the atomic volume term, according to Hicks,
does not appear in connection with the diffuse and fundamental series ; in the
alkalies it is associated with the principal sequence, and in other groups of elements,
with the sharp sequence.
The Work of Hicks.
53
THE OUN.
Reference has already been made (p. 46) to the discussion by Ritz of the
terms {p 1 p 2 )/W 2 , from which it appeared that the range of values was much less
for all elements than in the case of &v/W 2 . Hicks (III.) has made a somewhat similar
investigation, but has taken the whole denominator terms into account in forming
the ratios. Taking W as the atomic weight of an element, wW/100, A the
denominator difference which gives rise to the doublet separations, A x and A 2 the
corresponding numbers for triplets, Hicks concludes that A is in all cases a multiple
of qw 2 , where q has the same value for all elements (=about 90-5, when A is multiplied
by 10 6 ). The quantity qw 2 is that which Hicks has named the oun (cov), each element
thus having an oun peculiar to itself and dependent upon the atomic weight. The
oun is designated d v but the multiple 4<5j occurs most frequently and is indicated
by <5. We thus have :
6 1 =qw 2 =l oun for element of atomic weight 100o>
<5=4g7> 2 =4 ouns
10 6 A=W(3 1 or md, where m is an integer special to each element.
The derivation of the calcium oun may be taken for illustration. The triplet
separations are 105-89 and 52-09. The limits of the sharp series are 33983-45,
34089-34, and 34141-43, and when these are put in the form N/D 2 , the denominators
(D) are 1-796470, 1-793679, 1-792310. The denominator differences are therefore
A 1 =0-002791, A 2 =0-001369, which are multiplied by 10 6 and tabulated as 2,791
and 1,369. The atomic weight is taken to be 40-124, so that 10 6 A 1 /o> 2 =17336-l=48
X 361-169, where the last factor is the number nearest to 4<7 which makes the multi-
plier an integer. The value of 6 for calcium is thus 361-169 x(0-40124) 2 =58-14 ;
or <3=10 6 A 1 /48=58-14.
This process has been applied by Hicks to a large number of series, and some of
the results are given in the following table :
(jjoo
W=100w
AV
(Sepn.)
10 6 A
10 6 A/ze>*
mq
or m.&q
8=4?zw s
= 4 ouns
361-8
Na
K
Rb
Cs
24475-40
21964-44
20871-29
19673-00
22-998
39-097
85-448
132-823
17-175
57-87
237-54
553-80
743
2,939
12,935
32,551
14027-96
19224-86
17715-86
18449-48
155X 90-50
53X 362-72
49X361-40
51X361-74
19-17
55-45
263-77
638-22
0-2, 0-14
0-92, 3-22
0-40, 0-56
0-06, 0-33
The last column gives the difference between 361-8 and the number under 4?,
except that when it is not the 4 x 90-5 term it is brought up to it by multiplying by 4.
The second set of figures in this column shows the limits of permissible variation of
the deduced 4^, due to uncertainties in the measures of the lines. In nearly all cases
the differences from 361-8 are within the possible errors depending upon imperfect data.
In this way, Hicks found from 17 elements, weighted according to the possible
errors
1 oun=<9 1 =(90-47250-013)w 2
4 ouns=<5 =361 -89w 2
The oun, according to Hicks, appears in connection with series in several other
ways. The satellite separations, for example, are dependent upon multiples of the
oun, and in the case of triplets A x 2A 2 is also an oun multiple.
54
Series in Line Spectra.
CHAP. VIII.
It should be observed that formulae for series do not enter into this discussion,
except as regards the adopted value of N and the determination of limits. Except
when the oun is very small, Hicks believes that with the accuracy now attainable in
spectroscopic observations, it should be possible to obtain far more reliable values
of the ouns of the various elements, and thence of the atomic weights, than by pro-
cesses depending upon weighing. There is, however, usually no apparent regularity
in the multiplying integers which determine the doublet or triplet separations, even
among elements of the same group, so that the simplest application of the spectro-
scopic method is to assume an approximate atomic weight in order to evaluate the
multiple, and then to use this to correct the atomic weight.
By this method Hicks has since made determinations of the atomic weights
of copper and gold, taking silver as standard with atomic weight 107-88.* The
results may be summarised as follows :
Doublet
separation
(A,)
Sioo
10 6 A
S
Multiple
of 8
W = 100 ^8/4?
Cu
248-44
31523-48
7307-087
146-1419
50
63-5569 -006
AK .
920-438
30644-60
27786-57
421-047
66
107-88(assumed)
Au
3815-56
29469-85
113951-00
1406-802
81
197-193-003
The value of the constant 4? deduced from Ag is 361 -7837 -0038, and this
was used in calculating the atomic weights of Cu and Au from the d terms. Brauner's
values are 63-56^-01, 197-20-07 respectively for these elements. It should be
observed that the separations of the pairs of lines involved in these determinations
can be measured with great accuracy, but that the exact determination of the limits
of the series is less certain.
In some cases the spectroscopic determination may be made independently
of any previous knowledge of the atomic weight, by utilising the various different
ways in which the oun is considered to play a part in building up the spectrum,
and finding the smallest common factor. An illustration is given later (p. 58).
COLLATERALS.
Further evidence of the oun as a controlling influence on the spectrum is adduced
by Hicks from the supposed existence of what he has called " collaterals." In the
case of doublets and triplets, the second, or second and third components may be
considered as having received a sort of lateral displacement by the atomic weight
term A, or Aj and A 2 , and may thus be regarded as collaterals of the first. Hicks
believes that this kind of displacement is not restricted to doublets and triplets,
or their satellites, but is of very common occurrence. Thus, if the wave-number
of a series line be N/D-fN/D^, lateral displacements may be produced by the
addition or subtraction of multiples of d or A, say xd or #A, to D or D m . When
added to D 1 the operation is indicated by writing xd to the left of the symbol of the
original line, and when added to D m to the right. As an illustration, Hicks
takes the Ca line at 1 6439-36. This may be represented by (2A 1 +10A 2 )
Ca s 1 (2)( + A 2 ), meaning that whereas
Wave No. of Cas,(2) = -
1V ' (1-796470) 2 (2-484994) 2
* Phil. Mag., 38, 6 & 301 ; 39, 457.
Wave No. of Ca 6439-36=
The Work of Hicks. 55
N N
;i-79647U+2A 1 +10A 2 ) 2 (2484994 + A 2 ) 2
N N
(1-815732) 2 (2-4S6362) 2
2791 ; (10 6 )A 2 =1369.
In this way Hicks accounts for irregularities in the satellite separations which
sometimes occur, and for discrepancies between the observed positions of certain
lines and the positions calculated from formulae. In some cases he considers that
the whole set of lines for a given order number m may be replaced by another
strong set displaced by several multiples of A, or by a congeries of fainter lines
displaced by various oun multiples.
The whole procedure, however, seems to be somewhat arbitrary, and it remains
to be seen how it will bear the test when observations of sufficient accuracy for such a
purpose become available. Some of the examples first mentioned by Hicks are
certainly no longer admissible; Mgdj(4), for instance (III., 356), has since been
shown to be perfectly normal by the resolution of the line into two components.*
CONSTITUTION OF DIFFUSE SERIES.
Hicks has further concluded that the diffuse and fundamental series cannot be
represented by a continuous mathematical expression, though they may approximate
to values so represented. He considers it more probable that they depend on
discrete changes which are connected with the oun, or atomic weight term, in a
way which has yet to be discovered. Thus, successive denominators (D) of a diffuse
sequence are thought to differ by integral multiples of the oun. When there are no
satellites, the denominators change by multiples of A in the case of doublets, and of
A 2 in the case of triplets, except that in the oxygen group the multiples are of
Aj. . When satellites are present, the multiples are of 6 or d v In addition, the
decimal part, or mantissa, of the denominator of the normal first line of the diffuse
series is itself a multiple of A, the outer satellite being taken as the normal line.
The general character of this part of the investigation will be sufficiently indicated
by the first chief line and satellite of the diffuse series of caesium :
Cs (10 6 )A=32551, (10 6 )<5 =638-22, Doo =19673-0.
Chief line. Satellite.
2-554329(228) -76|-43 46^ 2-546989(226) -97
30(5
3-535183(200) -2011+40 54^ 3-526567(200) +9
10^
4-533588(160) 424|+1 146 4-524635-161
3<5j
5-533110(400) -768^+22 14<5 5-524175-26
&c.
546989=857(638-2600-233 0-08871) =857<5
In this table the denominator terms have been adjusted within permissible
limits indicated by the possible errors of observation. The number in brackets
following the denominator term is the estimated limit of error in the last three
digits, | is the error of the limit, and the last number represents the difference
* Fowler & Reynolds, Proc. Roy. Soc., A. 89. 139 (1913).
56 Series in Line Spectra. CHAP. vm.
between the observed value of the denominator and the " selected " value entered
in the table. The multiples of 6 or 6 1 in the middle of the table are the satellite
separations, expressed in terms of denominator differences.
It is extremely difficult to form a just estimate of the confidence which may be
placed in these results, on account of uncertainties in many of the observational
data, and the occasional exceptions to the more general rules above stated. Thus
Cs is exceptional inasmuch as the first mantissa is a multiple of 6 and not of A ;
and Cd is irregular because it is the mantissa of the chief line, and not that of the
outer satellite, which is a multiple of A. Very few spectra have been measured
with the accuracy and completeness which would seem to be necessary to justify
the deductions fully, and the adjustment of data within estimated permissible ranges
is not an entirely satisfactory substitute. The apparent absence of any general
law governing the sequence of multiplying integers in the successive denominator
terms is somewhat disappointing, for it is clear that the oun theory does not yet
provide a guide to the identification of series lines such as is provided even by an
approximate formula.
LINKS.
In his fourth paper, Hicks has extended the idea of collateral displacements
with a view to associating the lines which do not fall into the ordinary series with
those which belong to the regular series systems. Each line of a series is regarded
as being connected with other lines in the same spectrum through several constant
differences of wave-number, or links, which may be added or subtracted to an in-
definite extent, and apparently in any order. The various links which occur in
a doublet system are distinguished by letters which have the following meanings,
as given by Hicks, and as written in the more extended notation of this report :
>!- A)
e=p(-3 A) -p(&) =NI(l +#!-3 A) 2 -AT/(1 +^+ A) 2
w=s-s(A)
As before, A is the denominator difference corresponding with the normal
doublet separation. The link b is the normal doublet separation, and link e=
a+b+c+d.
These methods were first applied to the spark spectra of silver and gold, con-
taining 600 and 741 lines respectively in the region covered by the investigation.
It will suffice to take silver as an illustration :
Ag. Links. Corrections to links.
^>=<7 l0 o =3064,4-60 a=880-77 a' a = 0-61*
=A/7(1-891807) 2 6=920-44 &'&= 0-61*
S=JTOO =61116-33 c=962-54 c'-c = -0-66#
=N/(1-339600) 2 ^ = 1007-26 d'd=Q-7lx
Av(sepn.) = 920-435 0=3771-00 e'e=-2-59x
10 6 A =27786-57 **=2458-64 '= 2-25*
<5=10 6 A/66 = 421-0087 u=2616-61 t/-v=-2-47*
The links are, of course, in ordinary wave-number units.
It is further suggested that the links may be varied by making them depend on
The Work of Hicks. 57
displacement operations on values of p and s which have already been displaced by
small multiples (x) of 6 or 6 X ; thus, a'=p(xd} p(xd-\-&) ; b'=p(xd A) p(xd),
and so on. The calculated changes of the links are then as shown under a' a, &c.
It will be seen that in a complex spectrum, with seven links and these permissible
variations in each of them, there is room for many accidental coincidences, but the
discussion of probabilities has convinced Hicks that the existence of the links, in
the main, cannot be due to chance.
The following (IV., 366) are among the numerous suggested links occurring in
silver, the differences in wave-numbers of the lines being enclosed in brackets, and
decimal parts of the wave-numbers of the lines being omitted :
(1) 30514 (2460-39) 32974 (2460-84) 35435 (2461-00) 37896 (2457-26) 40353
(2) 17814 (3777-32) 21591 (3779-86) 25371 (3778-01) 29149 (3778-56) 32928
<3) 30959 (3776-44) 34735 (3777-47) 38513 (3773-79) 42286 (2618-00) 44904
Hicks attaches great importance to these long series of the same links, as proving
the reality of variations in the links. Thus, the differences in the second row are
regarded as representing a modified link of about 3778-44 as compared with the
calculated g=3771-00. The normal e link is thus changed to e( 3d) ; that is,
[3771-00+ (3x2-59)] with an outstanding error of 0-33. The link to another line,
P x (l) at 30471 is 2456-59, which is equivalent to w(<5)+0-20.
Proceeding in this way, Hicks has drawn up extensive tables and maps which
are intended to show that a great number of lines may be connected with ordinary
series lines by links and chains, but most of them are too complex for reproduction.
As giving some indication of the nature of the results, however, the short linkage
starting from Ag <r 1 (4), (/3981-87 ; v=25106-89) may be mentioned. The following
are the observed wave-numbers and intervals between the successive lines :
v Av
ffi(4) 25106
918-71
ff,(4) 26025
3777-54
29803
919-58
30722
-2619-34
28103
It may be deduced from Hicks's table (IV., 394) that these intervals are identified
with links and modified links, such that
28103 :=25106-89+6+g(-2(5) +6(2(5) -y(-(5)
=25106-89+920-44 + (3771-00+5-18) +(920-44-1-22)
(2616-61+2-47)
=28103-65
The observed v is 28103-33 so that a correction of only 0-32, or of AA =+-025-
is required to make the sum of the links exact. a 2 (4) is not a good observation and
'the assumption of the normal separation from a 1 (4) is therefore permissible.
Some of the linkage systems which have been traced out in this manner are of
great complexity; that starting from Ag 7r 2 (l), for example, involves more than
580 lines.
To what extent such results represent reality is not as yet very clear. Since
58 Series in Line Spectra. CHAP. vm.
the numerical values of the various links have been determined from series of arc
lines, it would scarcely be expected that they would be applicable also to spark lines,
which, in all known spectra of this class, form independent series if series are re-
cognisable at all.
SUMMATION SERIES.
An entirely novel idea has been introduced by Hicks in the suggestion that
summation as well as difference series may occur in spectra. (V. 343.) That is,
if there be an ordinary series A y(m), there may also be a series A + cp(w). In such
cases the mean of two corresponding wave-numbers would obviously give the limit
of the series very exactly.
Series believed to be of this type were first noted by Hicks in association with,
supposed fundamental series of the rare gases, and others were afterwards suggested
in connection with series of other types.* In general, the limits of the P, S, and Z>
series are far larger than Foo , so that associated summation series would most fre-
quently lie beyond the range of observation. Hicks considers that the existence of
summation series is fully established by his investigations, but the evidence so far
put forward is far from convincing. It is frequently necessary to introduce hypo-
thetical displacements of unobserved lines which are out of range, and there is no
apparent regularity in the intensities of. the lines in the same set. It would, therefore,
not be possible to recognise any of the suggested summation series as such by ordinary
inspection of photographs, or by any independent procedure. Moreover, it is
remarkable that none of the well-established series having limits less than, say
wave-number 26,000 are repeated in inverse order in the ordinary range of observa-
tions in the ultra-violet.
INDEPENDENT DETERMINATION OF ATOMIC WEIGHT.
As a further example of the possible use of the oun, the determination of the
atomic weight of an element, without assuming any knowledge from chemical,
operations, may be mentioned. The procedure may be illustrated by the spectrum
of zinc.t for which (10 6 ) A x =7204, and (10 6 ) A 2 =3486.
We have A x 2A 2 =232, which may be a small multiple of <5 1} especially as A j
and A 2 are nearly exact multiples of 232.
The satellites to D (2) give denominator differences of 581 and 348; the difference
is again nearly 232, but this cannot be the oun because 581 and 348 are not multiples
of 232. The satellites to D(3) give denominator differences of 504 and 388, which
differ by 116, or half of 232. But 116 cannot be the oun because, although it divides
581 and 348, it does not divide 504 and 388. The half of 116 fails to satisfy the
imposed conditions, but one-third of 116, or 38-7, divides all the numbers given above.
No smaller number than this is required in any connection, and 38-7 is therefore the
small oun of zinc, d^.
A X should be an exact multiple of d lf in this case 186 <5 1( and so a more correct
value of di is given by 7204/186=38-731, or 6=154-92.
The atomic weight is then V (154-92 x 100 2 ) -^361-89=65-43.
The example is merely by way of illustration, since the " adjusted " figures
given by Hicks (III, 346) have been used. As already lemarked, it would be
simpler to assume the chemical determination of the atomic weight, and to use
the spectroscopic data merely as a means of correcting the assumed value.
* Phil. Mag., 38, 6, and 301 (1919) ; 39, 457 (1920).
t The author is indebted to Prof. Hicks for this example.
CHAPTER IX.
APPLICATIONS OF BOHR'S THEORY.
It is not the purpose of the present Report to present an account of theories
of the origin of spectra, but Bohr's theory* calls for some mention, because of the
simplified view which it gives of the structure of the spectra themselves.
Our first idea as to the origin of spectral lines might very well have been that
a line is produced by the revolution of an electron about a centre, and that the
frequency of the line would correspond with the frequency of revolution in the
orbit. The analysis of spectra, however, has shown that the frequency of a line
always appears as the difference of two "terms," neither of which represents a
spectral line, though one may represent the limit of a series. Hence, a complete
theory must in the first place give a physical meaning to these terms, and in the
second place explain how an emitted frequency comes to be the difference of two
of them.
Bohr adopts the " nucleus atom " theory of Rutherford, which supposes an atom
to consist of a positively charged nucleus and a system of external electrons such
that in the neutral atom the total negative charge of the electrons is equal to the
positive charge of the nucleus.| On this basis, with the aid of the quantum theory
of radiation, Bohr has developed a theory of spectra which leads to formulae for
the spectra of hydrogen and ionised helium, and represents these spectra
quantitatively. The theory also gives a general indication of the structure of other
spectra, but the difficulties involved in their calculation have not yet been
overcome.
A summary of the theory has already been given by Jeans in his report on
" Radiation and the Quantum Theory, "{ and later developments have been
reviewed by Silberstein in a report on " The Quantum Theory of Spectra. "
Important extensions of the theory to the explanation of the " fine structure " of
the lines of hydrogen and ionised helium have been made by Sommerfeld.||
THE SPECTRUM OF HYDROGEN.
In the case of hydrogen, the atom consists of a nucleus having unit + charge,
and a single electron in orbital motion around it. The circumstances of this motion
may be calculated from the ordinary laws of mechanics, but the electron is supposed
only to be free to traverse certain specified orbits, which are determined in the
case of circular orbits by the condition that the angular momentum is an integral
multiple of hj^n, where h is Planck's constant of action. When the electron moves
in one of these " stationary " orbits there is no radiation, and emission occurs only
when the electron passes from one stationary orbit to another. Without attempting
to indicate the mechanism of the passage from orbit to orbit, Bohr supposes that the
transition is followed by the emission of a homogeneous radiation, the -frequency of
* Phil. Mag., 26, 1,476 (1913). Dan. Acad. Sc., IV., 1, Parts I. & H., pp. 1-100 (1918).
t The nucleus itself is probably of complex structure, including hydrogen nuclei and
electrons, and its effective charge is the " residual " charge, corresponding to the atomic number
of the element. Rutherford, Proc. Roy. Soc., A. 97, 374 (1920).
J Phys. Soc. (1914).
London: Adam Hilger (1920).
|| Atombau und Spektrallinien, 2nd edition, p. 306 (Braunschweig, 1921).
60 Series in Line Spectra. CHAP. ix.
which can be determined from the quantum theory. The energy radiated is equal
to the difference of the energies of the electron in the two orbits concerned, and is
assumed to be one quantum of magnitude s=hn, where n is the frequency. At
any instant, a single atom contributes to only one line of the spectrum, and it is the
summation of the radiations from a large number of atoms that accounts for the
whole series of lines.
Taking E and M as the charge and mass of the nucleus, e and m as the charge
and mass of the electron, the theoretical formula for the hydrogen spectrum, in a
first approximation, is
where r and r 2 are integers, c is the velocity of light, and v(=w/c) gives the wave-
numbers of the lines.
When the mass of the electron is not considered negligible in comparison with
that of the nucleus, and since E=e in the case of hydrogen, the formula becomes
Mm i 1 !
ch s
The formula is thus of precisely the same form as that which has been found
to represent the spectrum of hydrogen (p. 14), the expression outside the bracket
representing the Rydberg constant. The correspondence is not merely qualitative,
as would be expected from the assumptions which have been made, but the theoretical
agrees with the observed value within the limits of experimental errors.*
When T 1 ;=2 and r 2 =3, 4, 5 ... the formula represents the Balmer series ;
if T!=I, T 2 =2, 3 ... we get the far ultra-violet series observed byLyman, and if
f 1 =3 we get the infra-red series partially observed by Paschen.
The radii of the stationary orbits vary as the squares of the integers T, the
theoretical values being given by
T 2 /? 2
The successive orbits may thus be represented as in Fig. 9 by drawing circles
with radii I 2 , 2 2 , 3 2 . . . In the normal state of the atom, the electron revolves
in the innermost orbit. When the atom is disturbed, as by the electric discharge
in a vacuum tube, so that the electron is removed to a great distance from the
nucleus, the electron will generally occupy successively different orbits on its return.
The first line of Lyman's ultra-violet series corresponds to the fall of the electron
from orbit 2 to orbit 1, the second line to the fall from orbit 3 to orbit 1, and so
on. Similarly, the lines of the Balmer series are produced by falls from orbits 3, 4,
5 ... to orbit 2 ; and the lines of the infra-red series by falls from orbits 4, 5 ...
to orbit 3.
* Using Millikan's data (" The Electron," p. 210), e = 4-774X 10' 10 , A = 6-545X 10' 27 , e/m =
1-767X 10 7 , the theoretical value of N, in terms of oscillation frequency, is 3-294X 10", as
compared with the spectroscopic value 3-290 X 10 15 . The substitution is conveniently made
in the equation
Ts~r
h 3 e/m
Applications of Bohr's Theory.
61
On this view, the line spectrum of hydrogen should include no lines other than
those represented by the general formula
There is no place for any of the lines observed in stars by Pickering, or calculated by
Rydberg, which were formerly attributed to hydrogen. This conclusion, it may be
stated at once, is in complete accordance with our present experimental evidence.
The series of lines discovered by Pickering in the star ( Puppis appeared to
converge to the same limit as the Balmer series of hydrogen, and to be closely
represented by substituting (r 2 +0-5) for T 2 in the Balmer formula. This relation
would be appropriate to the diffuse and sharp series of the same element, and thus
FIG. 9. THE BOHR ORBITS FOR HYDROGEN.
suggested that the Pickering lines were due to a form of hydrogen which could not
be produced in the laboratory, but might be supposed to exist in stars at very high
temperatures. Adopting this view, Rydberg calculated the lines of the associated
principal series, in accordance with the relations found for other elements, from
the formula
= \l&~- ta
The first " principal " line, given by r z =2, would thus be at A4,688, the second at
A2.734, and so on. All but the first lie beyond the region of atmospheric trans-
parency, but the actual occurrence of a prominent line near 4,688 in Puppis, as
well as in many Wolf-Rayet stars and gaseous nebulas, seemed to give strong support
to Rydberg's theory, and the existence of a modified form of hydrogen was widely
accepted. Lockyer designated it " proto-hydrogen," in the belief that it represented
one of the final stages of simplification of matter by the action of high temperatures ;
it was also sometimes called " cosmic hydrogen."
Lines corresponding closely with this hypothetical spectrum were eventually
obtained by Fowler* in experiments on helium in which hydrogen was present as.
* Monthly Notices R.A.S., 73, 02 (1912). Pbil. Trails., A. 214, 254 (1914).
62 Series in Line Spectra. CHAP. ix.
an impurity. The wave-length of the supposed first principal line as determined in
the laboratory was slightly lower than that calculated by Rydberg, viz., 4,685-98
on Rowland's scale, but was at first supposed to be in sufficient agreement. In
addition to the lines 4,688, 2,734, &c., predicted by Rydberg, however, an inter-
mediate series was found, with lines at ^3,203, &c., which was provisionally regarded
as a second principal series, since its limit was identical with that of the " 4,686 "
series. Three of the Pickering lines were also produced, their wave-lengths being
approximately 5,411, 4,541, 4,200. In accordance with Rydberg's theory, these
also were at first attributed to hydrogen, for they seemed to have a close numerical
connection with the Balmer series, and no relation whatever to the known lines
of helium.
The view that the lines in question were due to hydrogen, however, was not
entirely satisfactory, partly because they could not be produced from hydrogen
alone, and partly because the occurrence of lines not predicted by Rydberg broke
the analogy with the series of other elements. Fowler sought to estimate the value
of the numerical evidence on which the identification with hydrogen mainly depended
by a search for other examples of series of the " second principal " type, but the whole
question was satisfactorily settled by Bohr in the extension of his theory to ionised
helium.
IONISED HELIUM (He+).
There is good reason to believe that the helium atom consists of a doubly-
charged nucleus of four times the mass of the hydrogen nucleus, with two electrons
revolving round it. When the gas is subjected to discharges of moderate intensity,
one of the electrons may be supposed to be displaced, and the ordinary spectrum of
helium to be emitted when this moves to different orbits on its return ; the theory of
this spectrum, however, is not yet complete. Under the action of sufficiently strong
excitation, both electrons are supposed to be removed from the normal orbit, and
a second totally different spectrum to be emitted when only one of them returns.
The formula for the series of lines developed will be identical in a first approximation
with that for hydrogen, except that E is now to be replaced by 2e ; thus
8n 2 e*m ( \ 1 \ /I 1
V= Tg- L 2 2 ) =^N ( 2
When the mass of the electron is taken into account
M'm / 1
c/r 1 ' M'+m V Tj 2 i
where M'=4M, and N' differs slightly from N.
When T I is put =3 in the approximate formula, the substitution of 4, 6, 8 ...
for T 2 will obviously give lines identical in position with those calculated for the
supposed principal series of hydrogen by Rydberg, while T 2 =5, 7, 9, will give lines
nearly coincident with the "second principal" series of hydrogen observed by
Fowler. Bohr's theory, however, unites both in a single series of a new type, and
assigns them to ionised helium. The small deviations of the observed lines from
Rydberg's calculated values are accurately accounted for by the difference between
N and N', depending upon the difference of atomic weights.
As to the Pickering lines, Bohr's theory indicated that associated with these in
a single series there ought to be lines nearly coincident with the Balmer series of
Applications of Bohr's Theory. 63
hydrogen, the Pickering lines being given by Tl =4, T 2 =7, 9, 11..., and the additional
.lines by T 2 =6, 8, 10 ... The observation of some of the additional lines by
Evans* and subsequently by Paschen.f together with the observations of the lines
in the absence of all traces of hydrogen, gave additional support to the theory which
-attributes them to ionised helium.
The Pickering series, as thus extended, is compared with the Balmer series in
Fig. 10. The difference in position of the lines at H a is 2-64, diminishing to 1-64
.at H . Expressed numerically, the formulae for H and He + are respectively
=109678-3 -
\ r i *2
v=(4x 109723-22) (- .A
V *i 2 *2 2 J
The ratio ^ e as thus determined from Fowler's observations is 4-001638.
The theoretical ratio is , H * , g , .', and taking MiT/w=1845 in accordance
M H (M He +m)
-with Millikan's experimental result, the numerical value is 4-001626, in close accor-
dance with the observed ratio.
Conversely, the observed ratio may be utilised to derive the mass of the electron
in terms of that of the hydrogen nucleus, giving M H /w = 1831. %
Paschen has made a further investigation of the spectral constants, with rela-
tivity corrections and other refinements, and has obtained M ff /m=1843-7.
There is now ample evidence both theoretical and experimental, that Rydberg's
X 40 50 60
Fie. 10. COMPARISON OP EXTENDED PICKERING SERIES WITH BAI.MER SERIES OF HYDROGEN.
hypothetical lines of hydrogen have no existence, and that the lines observed in
stars and in the laboratory near their positions are really the enhanced lines due to
ionised helium. Further support for this conclusion is afforded by Fowler's demon-
stration that enhanced lines of other elements also have 4.ZV for the series constant.
It will be observed that on Bohr's theory the Balmer and associated series repre-
sent the final simplification of the hydrogen spectrum, and that the " 4686 " and
associated series similarly represent the simplest possible spectrum of helium. In
other elements, however, it is conceivable that further simplifications may occur,
corresponding to the loss of two or more electrons and giving rise to series having
9Af, or still higher multiples, for the series constant. The existence of such series
*Phil. Mag., 29, 284 (1915).
fAnn. d. Phys., 50, 901 (1916).
JFowler's original value, when the measures were expressed oa Rowland's scale, was
183612.-
Loc. cit.
64 Series in Line Spectra. CHAP. ix.
has not yet been completely demonstrated. On account of the high value of the
series constant, the strongest lines of this class will probably lie in the extreme ultra-
violet.
ARC SPECTRA.
The theory has not yet been developed so as to give a complete representation
of the spectra of elements other than hydrogen and ionised helium. In neutral
helium, which is the next in order of simplicity of atomic structure, the ordinary spec-
trum arises from the interaction of a displaced electron with a system consisting of
the nucleus and the other electron. The residual charge of the central system is
thus one unit, as in hydrogen, and the force on the electron, when at a great distance
from the nucleus, will be nearly the same as in the hydrogen atom. The series con-
stant for the spectrum of the neutral atoms will therefore be nearly the same
as that for hydrogen. The detailed discussion of the possible stationary orbits
indicated by the actual spectrum, however, is very complicated.
A similar consideration of the spectra of elements in which the atoms include
a larger number of electrons suggests an explanation of the appearance of the Rydberg
constant in the formulae for series of other elements.
The series constant may be expected to show a small variation with the atomic
weight of the element, as already indicated in the case of helium. Thus, if M be
the mass of the atomic nucleus, and m that of the electron, the Rydberg constant
for hydrogen is of the form
Mm
H ~ k W+m
For any other element of atomic weight A in terms of hydrogen,
AMm
/V A /v , ,-_. ;
AM+m
and we have the ratio
N A A(M-\-m) M/m+l
N H AM+m M/m+l/A
Taking Millikan's value for hydrogen M/m 1845, we get
N A 1846
With Curtis's value 109678-3 for N H , we thus find N fle =109722-9, N K =
109729-25, and 2V 00 =109737-7.*
It is only in connection with hydrogen and ionised helium, however, that the
precise value of N is at present of importance. With the approximate series formulae
adapted to other spectra, the hydrogen constant may be used without disadvantage
in ordinary calculations.
SPARK SPECTRA.
The series of enhanced lines which are especially developed in spark spectra,
as first clearly shown by Fowlerf for Mg, Ca, and Sr, are characterised by the
appearance of the series constant with four times its ordinary value. Such series,
* In a discussion of data relating to the fine structure of the lines, R. T. Birge has deduced
the value 109677-7 0-2- for hydrogen, and 109736-9 0-2 for a nucleus with infinite mass. Phys.
Rev.. 17, 589 (May, 1921).
J Bakerian lecture. Phil. Trans., A. 214, 225 (1914).
Applications of Bohr's Theory. 65
as in ionised helium, are therefore to be attributed to the ionised elements ; that is,
two electrons are to be supposed removed by the exciting source, and the enhanced
series to be produced when one of them returns, the central system then having a
net charge of two units. When the second electron returns its interaction is with a
central system having only one.unit charge, and the ordinary arc series are developed ;
the atom as a whole is then neutral. The two spectra are as different as if they
belonged to two different elements, and since the systems producing them cannot
co-exist, there are no lines arising from combinations of the terms of the arc and
spark series.
As a general conclusion from Bohr's theory, it would thus appear that all series-
having N for the series constant are produced by neutral atoms, while those having,
4:N for the constant have their origin in ionised atoms. If three electrons were
removed by the exciting source, the return of one of them while two remained detached
would be marked by the appearance of series having 9AT for the series constant, and
so on.
It should be observed that the energy necessary to produce the enhanced
lines varies from element to element. In Ca, Sr, Ba, for example, these lines are
strongly developed even in the ordinary arc, though they are relatively much
strengthened in the spark (see Plate IV.). In many elements, including the alkali
metals, on the other hand, such lines do not appear at all under the stimulus of the arc.
A possible connection between the limits of the principal series of enhanced
lines and the limits of the principal series of singlets in the arc spectra of the elements
of Group II. has been noted by E. Fues ; * namely, that the former are about double
the latter. He gives the following data in illustration :
Poo (=1-5S)
TEOO (=l-5a)
1-55
1-5(7
The ratios for Zn and Cd, with the limits shown in the tables which follow (147,544
and 140,226 respectively), are 0-514 and 0-517, in closer agreement with the remaining
three values.
GRAPHICAL REPRESENTATION OF SERIES SYSTEMS.
Since the wave numbers of the spectral lines always appear as differences of
pairs of terms, the whole set of series and combinations may be very conveniently
represented by plotting the " terms " which give rise to them. The various lines
wUl then be represented by differences between the terms taken two by two. Such
diagrams obviously have no necessary connection with any particular theory of
spectra, but they are especially instructive when the terms are regarded as repre-
senting the stationary orbits of Bohr's theory.
Thus, for hydrogen, in place of drawing the orbits as in Fig. 9, it is convenient
to plot the terms N/m 2 as in Fig. 11 (m being an integer), and to regard them as re-
presenting small portions of the successive orbits, although they are not to the true
scale of radii. Following a suggestion made by Birge,f the logarithms of the terms
have been plotted, and not the terms themselves, as this has the advantage of
* Ann. d. Phys., 63, 19 (1920).
t In a paper by Foote and Meggers, Phil. Mag., 40, 80 (1920).
Mg
61,660
121,270
Ca
49,300
95,700
Sr
45,900
88,850
Zn
75,760
159,000
Cd
72,540
151,000
0-509
0-515
0-518
0-477
0-480
66
Series in Line Spectra.
CHAP. IX.
opening out the higher terms as compared with the lower. Regarding the lines as
representing the non-radiating orbits, the nucleus is situated away to the right
of the diagram, and the actual spectral lines correspond to the fall of electrons from
orbits on the left to orbits on the right. By this method the three series of lines
which would be required to represent the known spectrum of hydrogen are reduced
to a single series of term values.
This simplification is of greater importance in connection with more complex
spectra, as will appear from the examples given in Fig. 12. In all cases the terms
plotted are those of the sharp, principal, diffuse and fundamental series, and these are
distinguished by making the lines of different lengths. The two values for the
terms of the principal series in doublets, or three terms in the case of triplets, are
usually too close to be conveniently represented separately, and they have been
indicated in the diagrams by breaking the corresponding lines into two or three equal
portions, as the case may be. Similarly, the fact that there are sometimes two or
three values of the diffuse series terms, arising from the presence of satellites, has
been indicated by appropriate breaks in the upper portions of the lines.
The first diagram represents the orbit terms for the doublet system of sodium.
The falls from the n orbits to the innermost orbit, la, give the principal series, con-
sisting of pairs with diminishing separation. The falls from the a and d orbits to
;
3-0 4-0
FIG 11 TERMS OF THE HYDROGEN SPECTRUM (log
the two adjacent orbits represented by \n and In 2 , yield the constant separation
pairs of the sharp and diffuse series respectively ; falls from the 9 orbits to the orbit
26 give the fundamental series consisting of single lines. It will be seen that the
various combinations can be considered in the same way. The orbits shown in the
sodium diagram are 51 in number, and the lines which are actually represented in
the tables by the various combinations of these terms are 98.
The second diagram represents in a similar manner the triplet system of mag-
nesium. Here there are two sets of orbits, one corresponding to the triplets and
the other to the singlets. There are no satellites. In the triplet system, the Ip
orbits lie inside the Is orbit ; but the innermost orbit is that represented by IS.
Inter-combinations between the two sets of orbits have been found to exist, as will
appear from the tables.
The third diagram represents the doublet system of ionised magnesium, closely
resembling the system of sodium. The term 1$ is not certain, but analogy with
calcium, strontium and barium suggests that it may exist. Also, according to
Fowler's analysis, the observed series of fundamental type (which includes A4481)
has its limit at 2<5, and the separations of its constituent lines are out of step with the
fundamental series of the other alkaline earth elements. The real fundamental
series possibly has 1<5 for limit, and its lines in the extreme ultra-violet ; but the
absence of the lines Id ln li2 which appear in the other elements of the group, throws
doubt on this interpretation. This diagram is of special interest in connection with
the fact that while some of the enhanced lines of magnesium occur quite strongly
Applications of Bohr's Theory.
6 7
I0o-
5ar 4<r 3or 2<r la-
On
lOn
5n 4n 3n 2n
In
\
j
lililjii
56 43 36
HJLJ
26
Na
Log(A-v)2-5
3-0
3-5 4-0 4-5 5-0
Log(A-v)2-5
i
3-0 3-5 4-0 4-5 5-0
i i i i i i i i i i i i i i i i i i i i i
<Ss Zs 5* 5s 4s 3s 2s Is
a
11.
'dtldlOd9d 8d 7d 6d
5p 4p 3p 2p 1p
\5d 4d 3d 2d(
4f\\ 3f\
1ZDHD10D3D 8D TD 6D
5D 4D 3D
2D
**v
3P 2P
fP
5S 4-S 3S 2S IS
3a- 2(T Iff
Sir
2n In
36
26 i6i Mg-\
6<p
*
4<y 3cx
1
X,og(A-v)4"0
4-5 &0
Log(A-v)2-5
3 'P , , 3 \ 5 , , ^ , . . *; 5
5s 4s 3s 2s Is
7d ffd
ff 6
T
5d 4d 3d\ 2i
ii i
/ 5f 4-f ' 3f
2p Ip
l\ Id
>
\
II
61
5 1 5F 4F IF
3D 21
i
ID
10P 9P 8P IP
6P 5P 4P 3P 2P
IP
Is 33 2S IS
4<r 3or
2<r
la-
In
5 ,
T
f
5
48 38
f 4cp
3q>
f
5r+
r./^_-.\ ,-/..
1
1 '
4.5 5-0
FIG. 12. ^TERMS OF THE SPECTRA OP Na, Mg, Mg+, Sr, Sr+.
F 2
68 Series in' Line Spectra. CHAP. ix.
in the arc in air (see introduction to tables of magnesium series), there are others,
belonging to the same series system, which only occur under spark conditions, or
their equivalent in the arc in vacua* It was previously somewhat difficult to under-
stand why the line 4481 (26-89) did not appear simultaneously with lines like A 2795,
2802 (Iff I:r 1)2 ) in the arc in air, sinci all the lines belong to series with 4AT for
constant. In the light of Bohr's theory, as illustrated by the diagram, it would appear
that in the arc in air the second electron is not removed to an indefinitely great
distance from the nucleus, but only to a distance which is something less than the
radius of the orbit corresponding to the term 89. Under these conditions, there
could be no combinations involving 89 or any of the terms to the left of 89 in the
diagram. Under spark conditions, however, the stimulus is sufficient to remove two
electrons to "infinity," so that the entire system of enhanced lines will be produced
when one of the electrons returns. The return of the second electron would, of course,
render the atom neutral, and the arc series would be developed.
The fourth diagram represents the triplet system of strontium, which is similar
to that of magnesium, except that satellites are present in both the diffuse and fun-
damental series.
The last of the diagrams, for ionised strontium, is similar to the corresponding
diagram for magnesium, except that satellites occur in the diffuse terms, and that
the term 1<5 is certainly indicated by the observations. Since there are two values
for Id, falls from the 9 orbits to Id will yield doublets in the fundamental series.
In each case, of course, there may be other combinations of terms, or orbits,
besides those which give rise to the four main series. Some of the combinations,
however, are more probable than others, and these probabilities have been embodied
by Bohrf in the so-called ' ' selection principle."
IONISATION POTENTIALS AND SPECTRAL SERIES.
Experiments on the ionisation potentials of gases and vapours have an important
bearing on Bohr's theory and upon the interpretation of some of the changes of
spectra under different experimental conditions. In such experiments, the gas or
vapour is bombarded by electrons from a glowing filament, and the electrons are
accelerated by an adjustable electric field. The energy of the bombarding electrons
is known from the potential difference through which they fall. Thus, if the potential
difference is indicated by V and the velocity of the electron by u,{ we have
In the case of hydrogen, Bohr's theory gives the negative energy corresponding
to the different stationary orbits as
W T ^1
where r is the integer defining the orbit. This is equal to the energy required to
remove the electron to an infinite distance from the nucleus.
* As a simple working hypothesis, it may be supposed that in air a large amount of energy
is required to separate two electrons from the nucleus, while in the arc in vacuo a smaller amount
of energy suffices on account of the greater freedom of movement of the electrons.
t Zeit. f. Phys., 2, 423 (1920). See also Sommerfeld's book, p. 387.
t Since 1 volt =10 8 e.m.u. = 1/300 e.s.u., and e/m = l-767X 10 7 e.m.u. =5-301 X 10" e.s.u.,
the velocity corresponding to 1 volt will be about 5-9X 10 7 cm./sec.
Applications of Bohr's Theory. 69
V When the electron passes from one orbit to a smaller one, it is assumed that the
difference of energies is radiated as a quantum, hn, of frequency n ; thus
C\ 9 _ _ _ .A . -I 1 .
so that
n
H A \r^ 1
or, if v be the corresponding wave-number, and c the velocity of light,
VTT^^M/J^ /I 1 \ /"I ~i\
-J, I- rruO / JL J-\ HT/-*- J-\
which is the formula already quoted for hydrogen.
We thus have
W,=chN . i.
and WTl -W r
where AT is the Rydberg constant (in wave-number).
For series spectra in general, using the Rydberg formula for simplicity, we shall
have
W W =chN~
For comparison with the results of ionisation experiments, the work necessary
to remove the electron from one orbit to another is most conveniently expressed in
terms of equivalent volts, by putting W T1 W r2 =eV, where V is the potential
difference through which the bombarding electron must fall to acquire the corres-
ponding amount of energy. We thus get the general expression
or (in volts)* 7=
8102
If v be the wave-number of the spectral line which is produced by the return of
the electron from orbit T 2 to T I( we have finally
V=--
8102
Since the ionisation potential corresponds to the removal of an electron from the
innermost orbit to infinity, T 2 in this case = 00 , and the ionisation potential will be
given by substituting for v the limit of the series which extends furthest into the
ultra-violet.
In the case of hydrogen, the innermost orbit, is given by r 1 =l f and v=-.N/] 2
=109678-3. Hence, the theoretical value of the ionisation potential of hydrogen
h 3X10 10 X6-545X10-2 7 X3()0= 1
e 4-774 XlO- 10 8102
70 Series in Line Spectra. CHAP. ix.
atoms is 13-5 volts. The experimental determinations are of this order, but are
complicated by the fact that energy is required to dissociate the molecules before the
atoms can be ionised.
The potential difference corresponding to the removal of an electron from the
i nnermost orbit to the next one has been called the " resonance potential " or " radia-
tion potential." The return of the electron to its normal positidn would then be
followed by the emission of a single line, as observed by McLennan* and others in
some elements. In hydrogen the wave-number of the resonance line would be
N ( ^i) =82,258, and the resonance potential 82,258/8102=10-1 volts.
\JL A I
In the elements of Group I. the innermost orbit is that represented by the limit
of the principal series ; that is, by the term l<j (=1-5 sof Ritz and Paschen). The
second orbit is "represented by the term In^ (2p of Ritz and Paschen), and the frequency
of the resonance line is that of the first principal line, l<j \n (see Na, Fig. 12). Hence,
in Group I.,
Caesium, as observed by Foote and Meggers, f furnishes an interesting example.
Here we find la=31,405, and la Ijr 1 =ll,732. The theoretical ionisation poten-
tial of caesium is therefore 3-876 volts, in remarkable accordance with the experimental
value 3-9 volts. Similarly, the calculated resonance potential is 1-448 volts, in close
accordance with the observed 1-5 volts. Similar results have also been obtained for
sodium, potassium, zinc and cadmium. J
In the triplet systems of Group II., which also include a singlet system (see Mg
and Sr, Fig. 12), the innermost orbit connected with the arc spectra is indicated by
the limit IS of the principal series of singlets, and we accordingly have
8102
The second orbit is represented by the term Ip 1 of the triplet system, but the
resonance line actually observed is the combination 15 lp 2 (=l-5S 2p 2 of Paschen)
Thus, in this group
^ 1S-1_ 2
8102
In mercury the resonance line 15 Ip 2 is the well-known line in the ultra-violet
A2,536, or v39,410. The resonance potential of mercury is consequently 39,410/8102
=4-9 volts. A second resonance potential corresponds with the line 15 IP,
==Al,849=v54,066, its magnitude being 6-7 volts. The term 15,=84,177, is the
highest in the system of arc series, and the ionisation potential of mercury is accor-
* Proc. Roy. Soc., A. 92, 305 (1916).
t Phil. Mag., 40, 80 (1920).
J Tate and Foote, Phil. Mag., 36, 64 (1918).
Applications of Bohr's Theory. 71
dingly 10-4 volts. _ These values are in close accordance with experimental deter-
minations.*
In calcium, two resonance potentials, and the ionisation potential, have been
determined experimentally by Mohler, Foote and Stimson ;f namely, 1-90, 2-85
and 6-01 volts. The corresponding theoretical values are
First resonance IS l/> 2 =A6572-78=vl5210-3 ; 7=1-887 volts.
Second , IS !P=>l4226-73=v23652-4 ; 7=2-918 volts,
Ionisation IS =A2027-56 = i49304-8 ; 7=6-081 volts.
The calcium series are similar to those of strontium illustrated in Fig. 12, and
it will be observed that there is a r.ref rential tendency for the electron to occupy
orbits associated with principal series.
Helium is of considerable interest in this connectien. Bohr's theory gives
the total energy of the neutral helium atom as 6-13 times that of hydrogen.J so that
the potential difference corresponding to the energy required to remove both electrons
to infinity will be 6-13 X 13-5=82-7 volts. When the atom has already lost one
electron, the energy necessary to remove the remaining electron is definitely given
by the theory as four times that required for hydrogen, the equivalent in volts,
therefore, being 54-0. This also follows from our formula, since the highest possible
limit is 4N 1 /1 2 =438,892, which, divided by 8,102, =54-2 volts. For the first
ionisation the theory accordingly gives the ionisation potential as 82-7 54-0=28-7
volts. It is not yet possible to predict the spectral lines of the neutral atom, but the
theory thus points to 28-7x8,102, =v232,530, =A430 as the highest limit in the
helium spectrum.
Experiments appear to show that the first ionisation actually occurs at 25-5
volts, and the first radiation at about 20 volts. The innermost orbit would thus
correspond to a series limit in the region of 25-5 x 8,102 =v206, 600, =A4844, and
a resonance line would be expected at about 20 x8,102=v!62,040, =^605^4.
Experimental evidence of the probable existence of such frequencies in the spectrum
of helium is furnished by the work of Richardson and Bazzoni|| on the high-frequency
limits of the spectrum of this gas. The^highest frequency thus determined was
found to lie between A470 and A420, and probably nearer to the latter value, in
general agreement with A430 for the limit of the s-ries calculated from Bohr's
theoretical value of the ionisalion potential.
Indirect evidence of the existence of lines in the far ultra-violet is also afforded
by the fact that none of the known lines of helium appear as absorption lines until
the gas is submitted to an electric discharge. This is also the case with the Balmer
series of hydrogen and suggests that the limit of the so-called principal series of
helium does not represent the innermost, or normal, orbit. In the alkali metals,
the lines of the principal series are readily reversed at low temperatures, and the
innermost orbits are represented by the limits of these series.
* Franck and Hertz, Verb. d. D. Phys. Ges., 15, 34 (1913). Davis and Goucher, Phys.
Rev., 10. 84 (1917).
t Phil. Mag., 40, 73 (1920).
j Phil. Mag., 26, 489 (1913).
Horton and Davies. Prpc. Roy. Soc., A. 95, 408 (1919) ; Phil. Mag., 39, 592 (1920) ;
Compton and Lilly, Astrophys. Jour., 52, 1 (1920).
i| Phil. Mag., 34, 285 (1917).
72 Series in Line Spectra. CHAP. ix.
The excitation of the enhanced lines of helium, corresponding to the second
ionisation, has been found to require a potential difference of 80 volts, in good
agreement with the theoretical value.*
It will be gathered that a very important field of research has been opened up
by these investigations of the connection between spectral series and the resonance
and ionisation potentials. They not only provide valuable tests of theories of the
origin of spectra, but may help in the detection of series in spectra which have not
yet been resolved. In a doublet system (compare caesium, p. 70) the limit of the
principal series, and the first line, could be calculated with fair approximation from the
observed values of the ionisation and radiation potentials, and thence all the lines
of the series ; from the principal series, the sharp series could also be calculated
approximately from the Rydberg relations. Similarly, the principal series of
singlets in a triplet system could be calculated from the ionisation potential and the
second resonance potential, if it be established that the examples given above are
typical.f
SPECTRAL SERIES AND THE PERIODIC TABLE.
The analysis of spectra into their component series is not yet sufficiently complete
to permit a full discussion of the relation between the spectra and the positions of
the elements in the periodic classification, but there are several points of interest
in this connection.
In the first place, it is to be observed that all the elements of the same group
give series of the same type, so far as they are known. Omitting the inert gases,
and referring first to the " arc " spectra yielded by neutral atoms, the elements
of Group I. present doublet systems, those of Group II. triplets, and those of
Group III. doublets. The remaining groups have not yet been completely sorted out
into series. In Group IV., probable series lines have only at present been identified
in silicon, which gives triplets in the arc. In Group V. no series have yet been
traced. Oxygen, sulphur, and selenium of Group VI., however, give triplets.
The interesting point is that doublets and triplets appear to alternate with
each other through the first six groups. Since the number of the group is supposed
to indicate the valency (and also the number of electrons in the outer ring), it would
seem that elements of even valency yield triplets, while those of odd valency give
rise to doublets. The only known exception is manganese, which gives triplets
in the arc, whereas doublets would be expected according to the rule stated ; the
triplets, however, have not the same simplicity as those which occur in Group II.,
and there appears to be some doubt as to the number of electrons in the outer ring
(Sommerfeld, p. 304).
The elements of Group II., which give triplets in the arc, give series of enhanced
doublets in the spark. Those of Group III., so far as the series are known, give
doublets in the arc, and evidence of the occurrence of triplets in the spark spectra
of Al, Sc, Y, has been found by Popow. Elements of Group I., which give doublets
in the arc, give spark spectra which have not been resolved into series, as in most
of the inert gases.
Thus, so far as these observations permit deductions, the spark spectrum of
* Rau. Sitz. Ber. d. Phys. Med. Ges. zu. Wurzburg (1914), p. 20 ; Compton and Lilly, loc. cit.
t Since the above was written, an important " Report on Photo-electricity, including
Ionising and Radiating Potentials," by Prof. A. L,. Hughes, has been issued by the National
Research Council, Washington (Bulletin, No. 10, 1921).
Applications of Bohr's Theory.
73
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fa op
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74 Series in Line Spectra. CHAP. ix_
an element has the same character as the arc spectrum of the element adjacent
to it in the preceding group of the periodic table. This relation is explicable on
the supposition that the loss of an electron from the outer ring reduces the valency
of the element by 1 and so displaces it to the preceding group. Attention was first
directed to this relation by Kossel and Sommerfeld,* who have called it the
displacement law, from analogy with the displacement law in radio-activity.
Further evidence in support of this " law " is given by certain unpublished:
observations made by the author. In Group IV., definite series of enhanced doublets,
with 4JV for constant, have been identified in carbon and silicon. There is evidence
also of a "second-step" ionisation in each of these elements (C + + and Si ++ ) giving
triplets and possibly representing a displacement of two places to the left in the table ; .
and of a "third-step" ionisation (C + + + and Si + + + ) represented by a system of
doublets and corresponding to a possible displacement of three places to the left. A
final test of these suggestions requires the extension of the observations into the far
ultra-violet so as to permit calculations of the series constants, which should be 9N
and 16JV respectively. In Group V. there are doublets among the spark lines of
nitrogen which -possibly represent the second-step ionisation, N + + . In Group VI.
the second, or spark, spectrum of oxygen shows several doublets which perhaps
represent O+. In Group VII. fluorine and chlorine show triplets under spark,
conditions, which, however, have not yet been arranged in series.
These observations are summarised in the accompanying table of the elements,
in which it is to be understood that d ? and t ? indicate that the evidence is not
complete.
On theoretical grounds Kossel and Sommerfeld also suggested a possible
numerical relation between the spark spectrum of an element and the arc spectrum
of the element which precedes it in the periodic table. Since the doublet separation
in the subordinate series is determined by the difference of limits I7i 1 ln 2 , the fact
that the series constant for the ionised elements is four times that for neutral atoms
suggested that the spark doublets of Group II., for example, would have approxi-
mately four times the separation of the doublets in the arc spectra of corresponding
elements of Group I. They gave the following figures in support :
Spark series, Av. Arc series, A^'. Ratio, Av/Av'.
Mg+ 91-5 Na 17-21 Mg+ : Na=5-3
Ca+ 223 K 57-90 Ca+ : K=3-9
Sr+ 800 Rb 237-71 Sr+ : Rb=3-4
Ba+ 1691 Cs 554-10 Ba+ : Cs=3-I
Zn+ 872 Cu 248-1 Zn+ : Cu=3-5>
Cd+ 2484 Ag 920-6 Cd+ : Ag=2-7
The ratios show a systematic decrease with increase of atomic weight, but the
question will doubtless be further investigated. Similar data were also given com-
paring the imperfectly known spark triplets of Group III. with the arc triplets of'
Group II., showing ratios ranging from 2-2 to 5-0.
An attempt to trace further numerical relations between the series of the ionised !
elements of Group II. and the neutral elements of Group I. has been made by Fues,f
on the ground of Sommerfeld's theoretical deductions (" Atombau," pp. 295, 511). In
the extended Ritz formula, where the denominator is [m-{-a-}-a(m, a}-{-a'(m, a) 2 -+...] 2 -
* Verb. d. D. Phys. Ges., 21, 240 (1919).
t Ann. d. Phys., 63, 1 (1920).
Applications of Bohr's Theory. 75
for arc spectra, and [w+a*+ct*(w, a*) +...] 2 for enhanced series, it is considered that
in a first approximation a* for a singly-ionised atom of atomic number Z should
have twi.c2 the value of a for the neutral atom of atomic number Z i. In the
sharp series a=a, and in the principal series a=n, and with the Ritz numeration,
having w=l-5,... in the sharp series, and m=2, 3,... in the principal series, the
constants for some of the spectra are as follows :
a, a* n lt %*
Na +0-15 +0-15
Mg+ +043 +0-305
K +0-325 +0-29
Ca+ +0-70 +0-50-15
Rb +0-31 +0-36
Sr+ -0-815 +0-610-15
Cs +0-45 +0-45
Ba+ +0-93 +0-75
It will be seen that the relation is in some cases approximately fulfilled, but would
not hold for the sharp series if integral values were assigned to m. Investi-
gations of this nature are evidently of importance m connection with theories of
spectra, and may perhaps give indications as to the best type of series formula.
The question of the relation of the spectral series to the grouping of the elements
in the periodic table calls for much further investigation of the spectra which have
not yet been resolved into series. So far as the inquiry has gone, however, the
results are very suggestive as to the kind of series to be expected in the spectrum of
an element, and may be of considerable assistance in guiding further research.
APPENDIX I.
Calculation of Formula Constants.
Probably the most generally useful formulas are those of Ritz and Hicks, and
it will suffice to indicate the methods of determining the constants in the case of
the latter, namely
N
v=A
V
From the observational data it will be advisable, as a rule, to choose the wave-
numbers of the two least refrangible lines, and one of the most refrangible, since
the former have most effect on the second term and the latter have the greatest
influence on the limit. In all cases an approximate value of the limit should first
be obtained by reference to Rydberg's interpolation table, as explained on p. 28.
When an approximate value of fi is also required, it may be obtained from the
same source.
Successive Approximation.
Let v v v. 2 , v 3 be the wave-numbers of three lines selected for the determination
of constants, and let m, m+p, m-\-q be the corresponding order-numbers. Further,
let
/~N~~ /~N~~ I N
vn/^f a ; (tn-\-p)\y =0 ; and (m-{-q).y i ~ c
Then a value of A has to be found which satisfies the relation
p(c-b)-(q-p)(b-a)=pq(q-p)
Beginning with the approximate value of A determined from Rydberg's table, a
few trials will lead to the true value. We then have
and
a=a m(m+/t)=b (m-\-p}(m+p+[jL)=c (
When three consecutive lines are selected, ^>=1 and q=2, and the relation to
be satisfied by trials of A becomes
(c -b) -(ba) =2
Hicks's Method.
A more direct solution has been given by Hicks.* An approximate value of A
having been determined as before, the series is supposed given by
N
v=A+x
a v
)
m/
* Phil. Mag., 30, 734 (1915).
Appendix I.
77
where x is the correction to the limit, and x, JJL, a are to be determined from three
successive wave-numbers v. Binomial expansion gives
, a VN
m+ t u-\ =
m (A
Differencing,
VN
+#)* (A v)
VN
x = (m-\-d m )y m x (say)
Ifct.
whence
x =
and fj, and a are then easily calculated. Hicks gives the following example from a
series of oxygen lines in which the three consecutive wave-numbers are 10791-32,
16233-52, and 18753-65. The limit is 23,194 +*.
V (1) 10791-32
16233-52
18753-65
fff-V
(2)
12402-68
6960-48
4440-35
(3)
4-0935156
4-37978
3-8426392
4-75610
3-6474172
3-04893
(4)
0-9465921
0-0002397
1-1974685
0-0005703
1-3926907
0-0011196
>(5)
0-4732960
0-0001198
0-5987342
0-0002851
0-6963453
0-0005592
2-973693
Av
1-947386
0-961066
2-908452 0-009974
0-971040
3-879492
Q.Q09974 =13 . 00
0-0007674
3-969484 4-969873
0-0002396
0-0006157
0-0008553 0-0007674
0-0013831
0-0022384
A =23194-00+13-00=23207-00
(13x0-0006157)
0-008004
0-953062
a=l-947386-13 x 0-0002396-2^
1-909238
0-038148
v=23207-00-iV fm+0-953062
0-003114
1-906124
1-909238
0-038148
L
m
In each of the above main columns the first number is v, the second (Av),
the third log. (Av), the fourth log. N/(Av) obtained by subtracting the third
from log. N (taken as 5-0401077 in the above example), the fifth is half the fourth,
and the sixth is VNlVAv, or (m-\-d m ). The third is then subtracted from the
78 Series in Line Spectra,
fifth and written down on the right, being the log. of N*/(A v)* ; below this is the
antilog., which, divided by two, gives y m .
The decimal parts of VU!v / (Av) at the bottom of the main columns are
next multiplied by the respective integers m (in this case 2, 3, 4) and differenced
twice. Similarly with the y terms, the work being on the right. The constants
are then readily determined.
A valuable feature of this method is that if the limits of error of the observations
be known, their effects on the values of the constants can readily be found by
calculating dx, d/j,, 3a.
When the term fi/m 2 is introduced into the original formula, four lines are
necessarily to be used ; the d m , y m are then to be multiplied by m 2 , and differenced
three times. Then
a = A (m*d J x A (m 2 y m ) (2m + 1 ) ft
fi =m 2 d m m 2 y m xma m 2 /j,
When wave-numbers are derived. from data on the international scale the value
of N should be taken as 109678-3, or log. AT=5-0401278.
The Differential Method.
The differential method is generally applicable to series formulae. In the case
of the Hicks formula we have
Approximate values of A and JLI being determined from Rydberg's table, and
a being supposed zero, the values of Av, being the differences between the observed
and calculated wave-numbers, are obtained for the three lines selected for the
determination of constants. The values of A^4, A^w, and Aa (=a in this case) can
then be determined from the three resulting linear equations. If a be large, it will
be necessary to recalculate the constants, including an approximate value of a in
the first equations when the AV are calculated.
When it is desired to investigate the value of N, four lines must be used, and a
similar procedure adopted, with four equations of the form
AW 2N /. , Aa\
/ . . ay /
( m+n+-} (
\ m) \
/. , a
( AJM +
\ m /
m
If a term /?/w 2 be introduced into the original formula, the procedure is similar
but rather more complex.
The differential method is obviously adapted for a least square solution, in
which all the observed lines may be utilised in the calculation of constants. The
numerical work involved, however, is rather laborious, and there is not much point
in forcing a series of observations into an imperfect formula.
Appendix I. 79
Determination of Limits in Special Cases.
In the case of series which do not closely follow the formulae of Ritz or Hicks,
other methods of determining the limits have to be adopted. In a communication
to the author, Prof. Saunders has explained that his procedure is first to make some
reasonable assumption as to the limit (say, from a graphical construction), and then
to calculate the values of \m-\- [A-{-f(m)\ from the corresponding terms (A v) for
the later lines. The values of [fjt-\-J (m}} are then plotted against m, and if the
curve shows an inflexion another limit is tried. By successive trials the limit is thus
obtained within a few units if several members of the series have been observed.
The result can often be checked by other series relationships, as, for instance, that
the sharp and diffuse series must have the same limit, or that the first term of the
principal series must correspond with the limit of the sharp series. Combination of
terms from different systems also gives an important check, as in the case of
IS Ip 2 . Saunders's plan is to adjust the limits so as to satisfy as many as possible
of these conditions.
The method adopted by Nicholson in the case of helium (see p. 34) would
probably also be useful in this connection, since it is possible to use all the lines of a
series in calculating the limits.
APPENDIX II.
TABLES FOR COMPUTATIONS.
TABI,E I. Corrections to reduce Wave-lengths from Rowland's scale to the international scale.
Region.
Subtract.
Region.
Subtract.
Region.
Subtract.
X 8800-8300
0-35
X 6500-6050
0-21
X 3450-3250
0-14
8300-8200
0-31
6050-5500
0-22
3250-3125
0-13
8200-8000
0-30
5500-5400
0-21
3125-2950
0-12
8000-7700
0-29
5400-5375
0-20
2950-2800
0-11
7700-7400
0-28
5375-5325
0-19
2800-2625
0-10
7400-7200
0-27
5325-5300
0-18
2625-2475
0-09
7200-7000
0-26
5300-5125
0-17
2475-2300
0-08
7000-6850
0-25
5125-4550
0-18
2300-2150
0-07
6850-6750
0-24
4550-4350
0-17
2150-1950
0-06
6750-6570
0-23
4350-4150
0-16
6570-6500
0-22
4150-3450
0-15
The corrections from 8800 to 7000 are as given by Meggers ; the remainder are as given by
Kayser. At 10.000A the correction will be about 0-43A.
TABI.E IL\. Correction to Vacuum of Wave-lengths in Infra-Red.
The following corrections have been calculated from the Washington formula for 15 C.
and 760 mm. It is not certain that the formula is accurately applicable to this region.
X in air.
Add
X (jz-1)
Diff.
X in air.
Add
X (,i-l)
Diff.
10,000
2-74
15,000
4-10
0-27
1-35
11,000
3-01
20,000
5-45
0-27
2-73
12,000
3-28
30,000
8-18
0-27
2-73
13,000
3-55
40,000
10-91
0-28
2-72
14,000
3-83
50,000
13-63
0-27
2-73
15,000
4-10
60,000
16-36
Appendix II.
TABI.E II. Correction to Vacuum of Wave-lengths in Air at 15 C. and 760 mm.
81
X in air.
Add
X (tt-1)
DifE.
X in air.
Add
X (n-1)
Diff.
X in air.
Add
X (jx-1)
Diff.
2000
0-6512
4500
1-2581
7400
2-0350
89
264
270
50
0-6601
4600
1-2845
7500
2-0620
94
265
271
2100
0-6695
4700
1-3110
7600
2-0891
96
265
270
50
0-6791
4800
1-3375
7700
2-1161
100
265
270
2200
0-6891
4900
1-3640
7800
2-1431
102
266
271
50
0-6993
5000
1-3906
7900
2-1702
104
267
270
2300
0-7097
5100
1-4173
8000
2-1972
107
266
271
50
0-7204
5200
1-4439
8100
2-2243
109
267
270
2400
0-7313
5300
1-4706
8200
2-2513
222
267
271
2500
0-7535
5400
1-4973
8300
2-2784
229
267
270
2600
0-7764
5500
1-5240
8400
2-3054
233
268
271
2700
0-7997
5600
1-5508
8500
2-3325
238
267
271
2800
0-8235
5700
1-5775
8600
2-3596
241
268
271
2900
0-8476
5800
1-6043
8700
2-3867
245
268
270
3000
0-8721
5900
1-6311
8800
2-4137
247
269
271
3100
0-8968
6000
1-6580
8900
2-4408
249
268
271
3200
0-9217
6100
1-6848
9000
2-4679
252
269
271
3300
0-9469
6200
1-7117
9100
2-4950
253
269
27]
3400
0-9722
6300
1-7386
9200
2-5221
255
269
271
3500
0-9977
6400
1-7655
9300
2-5492
256
269
271
3600
1-0233
6500
1-7924
9400
2-5763
257
269
272
3700
1-0490
6600
1-8193
9500
2-6035
259
269
271
3800
1-0749
6700
1-8462
9600
2-6306
259
270
271
3900
1-1008
6800
1-8732
9700
2-6577
260
269
271
4000
1-1268
6900
1-9001
9800
2-6848
262
270
271
4100
1-1530
7000
1-9271
9900
2-7119
262
270
272
4200
1-1792
7100
1-9541
10000
2-7391
262
270
4300
1-2054
7200
1-9811
263
269
4400
1-2317
7300
2-0080
264
X vac.
= X Tac . X air =X a ,- r (p. 1).
82
Series in Line Spectra.
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S 03
PART II.
TABLES OF SERIES LINES.
CHAPTER X.
EXPLANATION OF TABLES.
The construction of the tables of spectra which follow may be gathered from the
descriptions of series which have already been given, but a brief summary of the main
points may not be superfluous.
The wave-number of a series line usually appears as the difference of two wave-
numbers, one of which is the limit of the series to which it belongs. The lines of
any one series are represented by the differences between the limit and a number of
terms forming a sequence, the sequence being of the form A/7f/(w)] 2 , where N is the
Rydberg constant as determined from hydrogen, and f(m) is of the form m plus
i fraction. The fractional part for successive lines is not constant, but varies with m,
and the fraction may be represented approximately by the terms (ju+a/m) of
the Hicks formula, or by the corresponding terms of other formulee.
When the limit of a series has been ascertained, the actual values of the terms of
the sequence can be determined, independently of formulae, by subtracting the wave-
numbers of the observed lines from the wave-number representing the limit. Other
terms of the sequence may be approximately calculated by the use of a formula
when required.
The limit of a series appears as one of the terms of the sequence of another series.
Thus the four chief series are represented by
Limits.
Terms.
p(m)
= Is
mp
s(m)
= IP
ms
d(m)
= IP
md
f(m)
= 2d -
mf
As expressed in the combination principle, other series, or other lines, may appear
corresponding to other combinations of terms from the various sequences ; as
2s mp, 2pmf, and so on. For the analysis of a spectrum, whereby it is sought to
associate as many lines as possible in a connected system, the terms of the four chief
series are first determined, and afterwards utilised in a search for combinations.
The procedure which has been adopted in recent years has accordingly been to rely
upon formulae mainly for the determination of the limit, or limits, of one of the chief
series. The limits of the other chief series are then obtained by the aid of the
Rydberg-Schuster and Runge laws, as illustrated on p. 24, and when these have been
determined, the terms are derived by subtracting the wave-numbers of the observed
lines from the respective limits.
In the tables, the wave-lengths, intensities, and wave-numbers of the observed
lines of the four chief series are first given, followed by the separations in the case of
doublets and triplets, and finally by the terms. Singlet, doublet and triplet series
are distinguished respectively by capital, Greek and small letter abbreviations.
Single lines which are derived by combination from doublet or triplet terms, however,
are necessarily indicated by the symbols of the series from which they originate.
Combinations cannot conveniently be represented by single letters, but their relations
to the main series are readily shown by differences such as 2<5 m n, 15 mp, and so on.
The components of pairs and triplets, and the structure of members of the diffuse
88 Tables of Series Lines. CHAP. x.
series, are indicated by appropriate groupings of the lines. Unrecorded components
or satellites are indicated, where necessary, by a dash ( ). When two or more lines
are available for the determination of a term the mean has been taken. When no
intensity is stated it may usually be assumed, except for infra-red lines, that the
intensity is low.
The wave-lengths from A1000(X4 to the ultra-violet are on the international scale
unless otherwise stated. When the original determinations were on the Rowland
scale they have been corrected by Table I. In the calculation of wave-numbers,
the wave-lengths were corrected to vacuum by the Washington tables (Table II.)
and the reciprocals taken.
Wave-lengths in the infra-red greater than 1000(M are on Rowland's scale, unless
otherwise stated, as the correction to the international system has only a slight effect
on the wave-numbers. In view of the uncertainty as to the corrections to vacuum,
the published wave-numbers have been adopted.
In the examples of formulae which have been introduced, the series constant has
been taken throughout as 109678-3, except for helium. Bohr's theory suggests a
special value for each element, depending on the atomic weight (see p. 64), but the
range is small, and the accuracy with which the lines are represented would scarcely
be affected, if at all.
In the compilation of many of the tables, much assistance has been derived from
reports on the admirable work carried on under the direction of Prof. Paschen which
have been given by Dunz* and Lorenser.f
Man*\ B ' Dunz> " Bearbeitu ng unserer Kenntnisse von den Serien." Dissertation, Tubingen
(191 1).
t E. Lorenser, " Beitrage zur Kenntnis der Bogenspektren der Erdalkalien." Dissertation
Tubingen (1913).
CHAPTER XI.
HYDROGEN AND HELIUM.
The spectra of hydrogen and helium have unusual features, and it will be con-
venient to refer to them apart from the general groups of elements.
HYDROGEN.
H. At. wt.=l; At. No.=l.
In the vacuum tube spectrum of hydrogen there are usually two spectra super-
posed, one called the primary spectrum, which includes the Balmer series ; and the
other called the secondary spectrum, consisting of a great number of comparatively
faint lines. The latter appears to consist, in part at least, of the components of a
band spectrum, but it has not yet been completely analysed, and is not considered in
the appended table.
The primary spectrum, as already explained (p. 14), does not form an
ordinary system of series, but is represented closely by the formula
v=109678-3f
Vwh 2 m z
When m l =l, the formula gives lines in the Schumann region observed by Lyman!
w x =2 gives the Balmer series, and m 1 =3 gives a series in the infra-red which was
predicted by Ritz and partially observed by Paschen.
The lines of the Balmer series designated H a , H^, are very close doublets,
the separations in wave-length being respectively 0-14A and 0-08/1, according to
Michelson, the less refrangible components being the stronger. In a recent
Paper, Merton* has described experiments on mixtures of hydrogen and helium,
which show that each of these lines probably consists of three components, which
exhibit great variations in their relative intensities under different conditions. The
exact nature of these .changes has not been completely determined, but the results
are probably not inconsistent with Sommerfeld's theory of the fine structure of the
lines.
Careful measurements of the first six lines of the Balmer series in an unresolved
condition have been made by W. E. Curtis (p. 27), who found that the "centres
of gravity " of the lines could not be represented within the limits of error by the
simple formula given above.
The formula,
r_ _!_ l I
L(2-0-00000383) 2 (w+0-00000210) 2 J
was found by Curtis to represent the six observed lines with no error exceeding
0-OOL4, and the remaining lines with errors which probably do not exceed those of
observation. The wave-lengths tabulated below have been calculated from this
formula, and are the values in I.A. units (i.e., in air at 15C. and 760 mm.). In
calculating the infra-red and ultra-violet series, it has been assumed that they may be
regarded as combinations derived from terms of the Balmer series.
Paschen's wave-lengthsf for the first four lines of the Balmer series are 6562-797,
* Proc. Roy. Soc., A. 97, 307 (1920).
t Ann. d. Phys., 51, No. 7 (1916).
v=109678-28
Tables of Series Lines.
CHAP. XI.
4861-326, 4340-465, 4101-735. A discussion of these, in conjunction with Curtis's
measures, has led H. Bell* to suggest 109677-9 as the value of the Rydberg constant N.
In an extension of Bohr's theory, J. Ishiwaraf has given a formula for the hydro-
gen series which is written
a w 2 -
where the theoretical value of ci=3-942 xlO* 5 . From Curtis's wave-lengths for
the first six lines of the Balmer series, Ishiwara found the mean value of 2V to be
109678-05. The individual values (decimal parts) were 0-06, 0-01, 0-00, 0-04, 0-07,
0-10, showing an appreciably smaller range than those deduced from the simple
Balmer formula.
H. BAI.MER SERIES.
H. INFRA-RED SERIES.
L,imit=;4 =27419-674.
L,imit=J = 12186-46.
m
\,I.A.
V
Av
m X air. X vac. v A v
1
109,677-82
4 i 18751-05 18756-17 5331-58 6854-88
2
27419-512
5 i 12818-11 12821-61 7799-33 4387-13
3
6562-793
15233-216
12186-458
' _
4
4861-327
20564-793
6854-881
5
4340-466
23032-543
/ 4387-131
Paschen's observed values, on Rowland's scale,
6
4101-738
24373-055
3046-619
are 18751-3, 12817-6; these give 1^=5331-53
7
3970-075
25181-343
2238-331
and i/ 8 = 7799-67.
8
3889-052
25705-957
1713-717
9
3835-387
26065-61
1354-06
10
3797-900
322-90
1096-77
H. UI/TRA-VIOI.ET SERIES.
11
70-633 -
513-24
906-43
Limits =109677-82.
12
KA.154
Afte.O^
7fil -fi4
;
13
tJ\J XJ^
34-371 s
-> i .IHI
\j\jfj \j*j
770-68
QAA.AO
t Ul \J^
648-99
~ ~(1 KQ
m X vac. v A v
15
Ai ati
11-973
ODU'Uy
932-21
OOirOo
487-46
2 1215-68 82258-31 27419-51
16
03-855
991-24
428-43
3 1025-83 97481-36 12186-46
17
-| Q
3697-154
m r KT
27040-16
Q1 1 i
379-51
4 972-54 102822-94 6854-88
lo
19
91-557
86-834
81-lb
27115-85
338-51
303-82
The wave-lengths, in vacuo, as observed by
20
82-810
45-47
274-20
Lyman, are 1216-0, 1026-0. 972-7.
21
79-355
70-96
248-71
Mfflikan finds 1215-7 for the first line.
22
76-365
93-07
226-fiO
23
24
25
26
73-761
71-478
69-466
67-684
27212-35
29-26
44-19
57-42
. ' ' ' M
207-32
190-41
175-48
162-25
NOTE. The provisional wave-lengths given by
Wood for the nine lines of the Balmer series first
observed by him in the laboratory spectrum are
27
66-097
69-23
150-44
as follows :
28
64-679
79-78
139-89
"\ D "i T A
29
63-405
89-26
130-41
X ri. A.I.A.
30
62-258
97-81
121-86
3722-12 ... 3721-97
31
61-221
27305-54
114-13
12-22 ... 12-07
32
33
60-280
59-423
12-55
18-94
107-12
100-73
03-92 ... 03-77
3697-35 ... 3697-20
34
58-641
24-79
94-88
91-72 ... 91-57
35
57-926
30-14
89-53
86-99 ... 86-84
36
57-269
35-05
84-62
82-96 ... 82-81
37
56-666
39-55
80-12
79-46 ... 79-31
GO
45-981
27419-674
3676-44 ... 76-29
i
* Phil. Mag., 40, 489 (1920).
t Math. & Phys. Soc., Tokyo, Series 2, 8, 179 (1915).
Hydrogen and Helium.
HELIUM.
He. At. wt.=4; At. No. =2.
The line spectrum of helium, as observed ordinarily in vacuum tubes, consists
of a system of singlet series and a system of doublets. The doublets are very close,
the wave-number separation being about 1-02, so that in the principal series only
the first member has been resolved, and only the earlier members of the sharp and
diffuse series. The doublets are somewhat unusual, inasmuch as in the sharp and
diffuse series the stronger component is on the more refrangible side, while the first
principal line has its stronger component on the side of greater wave-length. The
weaker components are also unusually faint in comparison with the chief lines.
The majority of the measurements are by Runge and Paschen.* but the more
recent interferometer values determined by Merrill at the Bureau of Standards,
Washington,! have been substituted for 21 lines ; the greatest error in these values
is believed not to exceed 0-003 A. In the case of doublets, the Washington values
refer to the stronger components, and the wave-lengths of the companion lines have
been adjusted to show the same separations as those indicated by Runge and Paschen's
values. The infra-red wave-lengths are by Paschen. J The last two lines in the
principal series of doublets are due to Schniederjost.
It should be noted that the resolution of the spectrum into two systems of series
was regarded by some as indicating the presence of two gases, which were distin-
guished as helium and parhelium, giving the doublet and singlet systems respectively.
There is now no reason to believe that helium is other than a single element, but the
name " parhelium " has to some extent survived. In connection with his work on
stellar spectra, Lockyer re-named this pseudo-element " asterium." The doublet
and sin let systems are also sometimes distinguished as He I. and He II. respectively.
The following Hicks formula has been calculated from the three lines of the
sharp series of singlets measured at Washington :
=27175-17
109723-2
w-fO-862157-
0-010908N
m
As will be seen from the following list of the differences " observed minus cal-
culated " wave-numbers, the formula represents all but the first line with considerable
accuracy. Lines marked with an asterisk were used in the calculation of constants.
m
C ( Ai/)
m
C (Ay)
m
C ( Ay)
1
16-4
5
+0-10
9
+0-49
2
0-00*
6
+0-14
10
not observed.
3
0-00*
7
+0-52
11
0-02
4
0-00*
8
+0-35
12
+ 1-85
The later lines were probably less accurately measured than the earlier ones in
consequence of their low intensities.
For the doublet system, the following formula for the stronger components of
* Astrophys. Jour., 3, 4 (1896).
t Astrophys. Jour., 46, 357 (1917).
J Ann. d. Phys., 2,7, 537 (1908) ; 29, 628 (1909).
Zeit. f. Wiss. Phot., 2, 265 (1904).
Tables of Series Lines.
CHAP. XI.
the diffuse series has been calculated from the first, third and fifth lines as measured
at Washington :
109723-2
=29223-88
W+0-996982 +
0-001 695\ 2
m
giving the following residuals :
m
C(Av)
m
O C( Ay)
m
O C( Av)
2
+0-02*
8
0-08
14
+0-08
3
0-06
9
0-22
15
+0-33
4
0-00*
10
0-08
16
+0-30
5
+0-02
11
+0-09
17
1-7 ?
6
0-00*
12
+0-13
18
+ 1-2
7
0-00
13
+0-01
The limits of other main series were deduced by the application of the Rydberg-
Schuster and Runge laws. All the observed lines are either included in the main
series of singlets or doublets or are accounted for as combinations.
Several combination series are observed in the helium spectrum when the gas
is subjected to strong electric fields. The first of these was recorded by Koch,*
and others have been observed by Merton,f Stark J and Liebert. The wave-lengths
of most of these lines have only been roughly measured, and the wave-
lengths calculated from the combinations have therefore been inserted in the tables
for comparison with the observations.
Besides the line spectrum, there is an interesting band spectrum of helium, which
is well developed under appropriate experimental conditions. || It was found by
Fowler^j that the heads of some of the stronger bands, in contrast with all other
known band spectra, are arranged in accordance with the laws of line-series. There
is, however, no apparent relation between the band- and line-series, except that the
main series of bands runs nearly parallel to the principal series of helium doublets.
Thus, a displacement of the latter towards the red by a wave-number interval of
4159 would nearly superpose it on the stronger heads of the main set of bands.
IONISED HELIUM (He + ).
Under the action of strong discharges, as already mentioned .helium yields
another system of lines for which the series constant has rather more than four times
the value deduced from hydrogen. Otherwise the series resemble those of hydrogen,
and can be represented closely by an equally simple formula, namely,
where N' has the value 109723-22 as compared with 109678-3 for hydrogen.
* Ann. d. Phys., 48, 98 (1915).
t Proc. Roy. Soc., A. 95, 30 (1918).
j Ann. d. Phys., 56, 577 (1918).
Ann. d. Phys., 56, 600-617 (1918).
|| W. E. Curtis, Proc. Roy. Soc., A. 89, 146 (1913). E. Goldstein, Verb. d. Deutsch. Phys
Gesell., 15, 402 (1913).
Tj Proc. Roy. Soc., A. 91, 208 (1915).
Hydrogen and Helium.
93
HELIUM, DOUBLET SYSTEM.
PRINCIPAL,, la nm.
la=38454-71.
DIFFUSE. ITT m8.
l7T 2 = 29222-85 ; 1^ = 29223-88.
X, Int.
V
Av
m
r 2(1
X, Int.
V
A,,
m
wS
*10829-09\, 2nm
*10830-30/ (200)
9231-86
9230-83
1-03
(1)
29222-85
29223-88
5875-960 (1)
f5875-618 (10)
17013-79
17014-78
0-99
(2)
12209-10
f3888-646 (10)
f3187-743 (8)
25708-63
31361-12
(2)
(3)
12746-08
7093-59
4471-689 (1)
t4471-477 (6)
22356-66
22357-72
1-06
(3)
6866-16
f2945-104 (6)
33944-75
(4)
4509-96
2829-06 (4)
2763-80 (2)
35337-05
36171-40
(5)
(6)
3117-66
2283-31
4026-358 (1)
1 4026- 189 (5)
24829-34
24830-39
1-05
(4)
4393-49
2723-18 (1)
36710-92
(7)
1743-79
2696-13 (1)
2677-1 (1)
37079-21
37342-7
(8)
(9)
1375-50
1112-0
3819-753 (1)
f3819-606 (4)
26172-30
26173-31
1-01
(5)
3050-57
2663-2 (1)
37537-5
(10)
917-2
2652-95
2644-84
37682-67
37798-22
(11)
(12)
772-04
656-49
3705-139 (1)
f3705-003 (3)
26981-90
26982-88
0-98
(6)
2241-00
SHARP. ITT wo.
l7T 2 =29222-85 ; 17^= 29223-88.
3634-37 (1)
3634-24 (2)
27507-27
27508-26
0-99
(7)
1715-62
X, Int.
Av
m
wo
3587-42 (1)
3587-28 (2)
27867-26
27868-35
1-09
(8)
1355-53
-10829-09|
10830-10J 1 '
9231-86
9230-83
1-03
(1)
38454-71
7065-677 (1)
|7065-185 (5)
14149-03
14150-01
0-98
(2)
15073-87
3554-57 (1)
3554-44 (1)
3530-50 (1)
28124-79
28125-81
28316-53
1-02
(9)
(10)
1098-07
907-35
4713-366 (1)
f4713-143 (3)
21210-34
21211-35
1-01
(3)
8012-53
3512-50 (1)
3498-63 (1)
3487-72 (1)
28461-64
28574-47
28663-85
(11)
(12)
(13)
762-24
649-41
560-03
4120-981 (1)
f4120-812 (3)
24259-24
24260-25
1-01
(4)
4963-63
3478-95 (1) 28736-11
3471-78 (1) 28795-45
3465-89 (1) 28844-39
(14)
(15)
(16)
487-77
428-43
379-49
3867-62 (1)
3867-46 (2)
25848-40
25849-46
1-06
(5)
3374-42
3461-2 ? (1) 28883-4
3456-7 (1) 28921-0
(17)
(18)
340-5
302-9
3732-99 (1)
3732-85 (1)
26780-58
26781-59
1-01
(6)
2442-29
FUNDAMENTAL,. 28 my.
28 = 12209-10.
3652-12 (1)
3652-00 (1)
27373-58
27374-48
0-90
(7)
1849-40
X, Int.
V
A,
m
mcp
18684-2 (3)
5350-71
(3)
6858-39
3599-46 (1)
3599-32 (1)
27774-05
27775-11
1-06
(8)
1448-77
12784-6 (1)
7819-89
(4)
4389-21
3562-98 (1)
28058-41
(9)
1165-47
* Measures in I.A. (Paschen). X 10830 is the
3536-81 (1)
28265-96
(10)
957-92
chief component.
3517-33 (1)
28422-56
(11)
801-32
f Interferometer measures, Bureau of Stand-
3502-32 (1)
28544-37
(12)
679-51
ards, Washington.
3490-62 (1)
28640-04
(13)
583-84
3481-4
28715-8
14)
508-1
94
Tables of Series Lines.
HELIUM, DOUBLET SYSTEM Continued.
CHAP. XI.
COMBINATIONS.
X obs.
V
v calc.
X obs.
X calc.
v calc.
17002-55
5879-87
27^ 38=5879-92
% 3586-55
3589-85
iTCi STC =27848-38
X calc.
*3809-05
3809-08
la 28=26245-61
...
4275-81
la 2o = 23380-84
*3166
3164-79
lo3S = 31588-55
3283-97
la 3a = 30442-18
*2936
2935-03
lo48=34061-22
f2986
2985-00
la 4o = 33491-08
*2824
2823-70
lo58=35404-14
J2851
2849-77
la 5o = 35080-29
*2761
2760-57
1068 = 36213-71
j-2777
2776-00
lo 6a = 36012-42
*2722
2721-09
1 _7S = 36739-09
f2732
2731-04
lo 7a = 36605-31
$6059-8
6067-09
17^271 = 16477-80
* Stark's " diffuse principal " series ; X 3809
$4518-59
4517-43
iTti 371=22130-29
previously observed by Paschen.
$4045-87
4045-16
l7C 1 47t = 2471 3-92
f Stark's " sharp principal " series.
$3829-85
3829-42
I7r 1 57r = 2610 6-22
$ Stark's "near sharp" (fastscharfe) series;
$3711-15
3710-85
17^671=26940-57
measures by Liebert. Koch's " third subor-
$3636-75
3637-96
ITU! 7rc =27480-09
dinate " series.
HELIUM, SINGLET SYSTEM.
PRINCIPAL. 15 mP.
DIFFUSE. IP mD.
15 = 32032-51.
1P = 27175
17.
X, Int.
v
m
mP
X, Int.
v
m
mD
20582-04 (20)
4857-34
(1)
27175-17
t 6678-149 (6)
14970-08
(2)
12205-09
f 5015-675 (6)
19931-95
(2)
12100-56
f 4921-929 (4)
20311-57
(3)
6863-60
t 3964-727 (4)
25215-30
(3)
6817-21
f 4387-928 (3)
22783-41
(4)
4391-76
t 3613-641 (3)
27665-06
(4)
4367-45
4143-77 (2)
24125-84
(5)
3049-33
3447-594 (2)
28997-46
(5)
3035-05
4009-27 (1)
24935-17
(6)
2240-00
3354-52 (1)
29801-99
(6)
2230-52
3926-53 (1)
25460-59
(7)
1714-58
3296-76 (1)
30324-11
(7)
1708-40
3871-80 (1)
25820-49
(8)
1354-68
3258-30 (1)
30682-04
(8)
1350-47
3833-56 (1)
26078-04
(9)
1097-13
3231-20 (1)
30939-35
(9)
1093-16
3805-75 (1)
26268-60
(10)
906-57
3211-50 (1)
31129-13
(10)
903-38
3784-88 (1)
26413-44
(11)
761-73
3196-68 (1)
31273-45
(11)
759-06
3768-80 (1)
26526-14
(12)
649-03
(12)
3756-09 (1)
26615-88
(13)
559-29
3176-5? (1) 314/2-4:
(13)
560-1
COMBINATIONS.
SHARP IP wiS
1P = 27175-17.
X
V
v calc.
X, Int.
v
m
mS
19090-58
5236-78
2P3D =5236-96
20582-04 (20)
4857-34
(IX?,
32032-51
X/VKo
t 7281-349 (3)
t 5047-736 (2)
f 4437-549 (1)
4168-97 (1)
4023-99 (1)
13729-94
19805-35
22528-65
23980-00
24843-96
(3)*'.
(4) -
(5)
(6)
13445-23
7369-82
4646-52
3195-17
2331-21
6635
4910-6
4384-3
4143-2
6631-84
4910-61
4383-25
4141-32
IP 2P= 15074-61
IP 3P = 20357-96
IP 4P = 22807-72
IP 5P = 241 40-12
3935-91 (1)
3878-18 (1)
3838-09 (1)
25399-92
25778-02
26047-26
(7)
(8)
(9)
1775-25
1397-15
1127-91
930-15
$ ...
t -.
$ ...
5378-59
4053-56
3650-46
1525 = 18587-28
1535=24662-69
1545 = 27385-99
3787-49 (1)
26395-24
(11)
779-93
$ 3468
3466-74
1555 = 28837-34
3770-57 (1)
26513-69
(12)
661-48
* 5043
5042-15
IS 2D =
= 19827-42
FUNDAMENTAL. 2D mF.
|| 3974
3972-04
IS 3D =25168-91
2D = 12205-1.
|| 3618
3616-82
15 4D = 27640-75
1C & 7~> 9QQ&Q.1Q
X, Int.
v
m
mF
|| 3356
3355-59
15 6Z> =29792-51
18693-4 (2)
5348-0
(3)
6857-1
12792-2 (1)
7815-1
(4)
4390-0
* Merton, Proc. Roy. Soc., A. 98, 258 (1920).
J Stark's " sharp-princip
il " series
f Interferometer measures, Bureau of Stan-
Observed by Merton, Stark, and Liebert.
dards, Washington.
|| Stark's " diffuse-principal " series.
Hydrogen and Helium.
95
Wj=3 gives a strong series of which A4686 is the first member, and of which seven
lines were observed; m x =4 gives a fainter series with several lines in the visible
spectrum, including the " Pickering lines " ; and w 1 =2 gives a series in the
Schumann region, of which two members have been observed by Lyman.* There
was at first some confusion as to the origin of these lines, but they may now be
certainly attributed to ionised helium (p. 62).
The fine structure of these lines has been studied by Paschen.f Wave-lengths
of the lines have been determined by Fowler, Evans.J and Paschen, as in the
following table. The values of Fowler and Evans have been corrected to the inter-
national scale, and those of Paschen are for the chief components of the complex
lines observed by him. Paschen's values are entitled to greatest weight.
Fowler.
Paschen.
Fowler.
Evans.
Paschen.
Lyman.
4685-81
4685-808
6560-21
6560-130
3203-17
3203-165
5410-29
5411-67
5411-551
1640-2
2733-24
2733-345
4859-342
1215-1
2511-22
2511-249
4541-13
4541-72
4541-612
2385-39
2385-440
4339-81
4338-694
2306-12
2306-215
4200-14
4199-79
4199-857
2252-81
4100-049
The values tabulated below have been calculated from the general formula, m
being given integral values, and the constant 4AT having been calculated from the
observed line 4685-81.
He+ (CALCULATED VALUES).
" 4686 " SERIES.
,/ = 4x 109723-22 ( "\
\3 8 m*J
Limit=yl =48765-87
" PICKERING " SERIES.*
i/ = 4X 109723-22 (- ]
\4 2 m 2 /
Limit=27430-80.
X, I. A. (air). v m
Av
X, I.;4.(air).i v
m
Av
4685-81
3203-16
2733-34
2511-25
2385-46
2306-18
2252-72
21335-07
31210-16
36574-40
39808-87
41908-17
43347-44
44376-94
(4)
(5)
(6)
(7)
(8)
(9)
(10)
27430-80
17555-71
12191-47
8957-00
6857-70
5418-43
4388-93
10123-72
6560-16
5411-57
4859-36
4541-63
4338-71
4199-87
4100-08
4025-64
3968-47
3923-51
3887-47
3858-10
3833-83
3813-53
3796-36
3781-71
9875-09
15239-33
18473-80
20573-10
22012-37
23041-87
23803-59
24382-93
24833-80
25191-75
25480-17
25716-38
912-14
26076-19
215-03
333-57
435-58
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
17555-71
12191-47
8957-00
6857-70
5418-43
4388-93
3627-21
3047-87
2597-00
2239-25
1950-63
1714-42
1518-66
1354-61
1215-77
1097-23
995-22
" LYMAN " SERIES.
/I 1\
/=4X 109723-22 (- )
\2 2 m 2 }
Limit = 109723-22.
X, I. A. vac.
V
m
Av
1640-49
1215-18
1084-98
921-39
60957-35
82292-42
92167-51
108531-75
(3)
(4)
(5)
(6)
48765-87
27430-80
17555-71
12191-47
* The original " Pickering " or " ( Puppis "
series included only alternate lines, beginning
with 5411.
* Nature, 104, 314, 565 (1919).
f Ann. d. Phys., 50, 901 (1916).
j Phil. Mag., 29, 284 (1915).
CHAPTER XII.
GROUP IA. THE ALKALI METALS.
The chief series in the arc spectra of the alkali metals consist of doublets, the
separations of which increase with the atomic weight. There is also a general
displacement of corresponding series in the different elements towards the red as
the atomic weight increases. Lines of the principal series are easily reversed, and
were traced towards their limits by Bevan* in his experiments on the absorption
of the metallic vapours.
The allotment of the lines to the respective series is essentially as given by
Dunz in his Tubingen dissertation. In the principal series, the first pair appears
with + sign in all the metals of the group, and the limits of the sharp and diffuse
series consequently lie on the red side of the limits of the respective principal
series. The fundamental series lie still further to the red.
The numeration of the diffuse series, following Rydberg, is based upon potassium,
in which case the sharp and diffuse series are nearly coincident and the adjacent
members have been assigned the same numbers. There are then no lines with
order-number less than 2 in the diffuse series, negative members corresponding to the
order-number 1 not having been recorded.
In the Rydberg formulae for the principal series, ju is >1 except in the case of
lithium ; in the sharp and diffuse series [t is always < 1. In the fundamental series
the order-numbers have been chosen so as to make ju nearly unity.
References to sources of data are given in connection with each element, but
to avoid repetition it may be stated that the observations of Meggersf and Meissner J
in the red have been utilised as far as possible.
Enhanced lines have been observed in each of the elements except lithium, but
no series have yet been identified.
LITHIUM.
Li. At. wt.=7-0 ; At. No. =3.
The arc spectrum of lithium is characterised by well-marked series, of which
the principal has the first line in the red and the other members in the ultra-violet,
whilst the brighter parts of the subordinate series are in the visible region, and the
fundamental series in the infra-red. The system consists of close doublets, as in the
other alkali metals ; but in the ordinary arc they are very diffuse, so that the compo-
nents are not separated except in the case of the first principal line. In vacuum
tubes, however, five of the lines have been resolved into their components by
N. A. Kent, who made use of a powerful echelon grating. Kent's results are as
follows :
X
AX
A*
Series
8126
0-225^4
0-340
a
6708
0-151
0-336
7T
6103
0-115
0-309
s
4972
0-084
0-339
a
4603
0-070
0-328
S
* Proc. Roy. Soc., A. 83, 421 (1910) ; 85, 54 (1911) ; 86, 320 (1912).
t Scientific Papers, Bureau of Standards, Washington, No. 312 (1918).
j Ann. d. Phys., 50, 713 (1916).
Astrophys. Jour., 40, 337 (1914).
The Alkali Metals.
LITHIUM.
97
PRINCIPAL, la WTT.
la=43486-3.
DIFFUSE. 1 TT m8.
ITC= 28582-5.
X, Int.
v
m
mn
X, Int.
v
m,
wS
6707-85 (10.R)
3232-61 (8R)
2741-31 (6R)
2562-50 (5.R)
2475-29 (4#)
2425-68 (3R)
2394-4B (IR)
73-8
59-3
48-4
40-4
34-2
28-9
25-1
21-8
19-2
17-0
15-1
13-5
12-1
11-0
09-9
08-9
08-2
07-4
06-82
06-40
05-82
05-36
04-94
04-58
04-24
03-95
03-68
03-41
03-19
02-98
02-78
02-54
02-33
02-15
14903-8
30925-9
36468-1
39012-7
40387-1
41213-0
41750-0
42113-6
372-7
569-1
714-6
828-0
925-6
995-6
43056-9
105-1
146-0
181-4
211-3
237-4
258-0
276-4
297-4
310-5
325-5
336-4
344-3
355-2
363-8
371-7
378-5
384-9
391-3
395-4
400-5
404-7
408-6
412-4
416-9
420-9
424-3
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
(22)
(23)
(24)
(25)
(26)
(27)
(28)
(29)
(30)
(31)
(32)
(33)
(34)
(35)
(36)
(37)
(38)
(39)
(40)
(41)
28582-5
12560-4
7018-2
4473-0
3099-2
2273-3
1736-3
1372-7
1113-6
917-2
771-7
658-3
560-7
490-7
429-4
381-2
340-3
304-9
275-0
248-9
228-3
209-9
188-9
175-8
160-8
149-9
142-0
131-1
122-5
114-6
107-8
101-4
95-0
90-9
85-8
81-6
77-7
73-9
69-4
65-4
62-0
6103-53 (10.R)
4602-99 (QR)
4132-29 (8)
3915-0 (6)
3794-7 (5)
3718-7 (3)
3670-4 (1)
16379-4
21719-0
24192-9
25535-5
26345-1
26883-5
27237-3
(2)
(3)
(4)
(5)
(6)
(7)
(8)
12203-1
6863-5
4389-6
3047-0
2237-4
1699-0
1345-2
FUNDAMENTAL. 28 m<p.
28 = 12203-1
X
v
m
m 9
18697-0
12782-2
5347-0
7821-3
(3)
(4)
' 6856-1
4381-8
COMBINATION. ITC WTT.
lTr=28582-5
X
v
m
v calc.
6240-1
4636-1
4148-0
*3921-65
16021-0
21563-9
24101-2
25492-3
(2)
(3)
(4)
(5)
16022-1
21564-3
24108-9
25483-3
COMBINATION. 2u ma.
27t = 12560-4.
X
v
m
v calc.
24467-0
13566-4
4086-1
7369-5
(3)
(4)
4085-2
7372-6
COMBINATION. 2TT mS.
2 TC = 12560-4.
X
v
m
v calc.
17551-6
12232-4
5696-0
8172-8
(3)
(4)
5696-9
8170-8
OTHER 14 COMBINATIONS.
X v
v calc.
SHARP. ITT mo.
l7t=28582-5.
4601-4 21726-5
19290 5182-6
26875-3 3719-9
40475 2470-0
7-436^ 1344-4
ITT 39 =
28 STT
2<T 2TC
= 21726-4
ci 04,. Q
X, Int.
v m
ma
= 3720-1
6707-85 (lOfl)
8126-52 (10)
4971-93 (Ir)
4273-28 (5r)
3985-79 (3r)
*3838-15 (lr)
14903-8 (1)
12302-0 (2)
20107-3 (3)
23394-7 (4)
25082-1 (5)
26046-9 (6)
43486-3
16280-5
8475-2
5187-8
3500-4
2535-6
3949 = 2474-3
4858= 1342-6
- Unclassified.
X v
* There is some doubt about these lines.
23990-8 4167
98 Tables of Series Lines. CHAP. xii.
The variations in Av are believed to be real. It seems probable that the
a and n pairs are equal, while the smaller values for the d pairs are due to normal
close satellites.
Combinations are numerous, and in view of the uncertainties in the wave-
lengths, the calculated are in satisfactory agreement with the observed positions.
The combinations entered as 3545 and 4<5 5(5 were respectively given by Dunz
as 4A^>-iV/5 2 (=3cp-2V/5 2 ) and AT/5 2 -AT/6 2 .
Lines 2-7 of the principal series are from observations by Huppers,* and 8-41
-from Be van. The estimated possible error in Be van's values is 0-3/1, but the error
jn relative positions is probably much smaller. Other lines are from Paschen,
Kayser and Runge, and Saunders.
The principal series is represented fairly well by the formula
n^rn) =43486-3 AT/(w+0-951125+0-007766/w) 2
the residuals being
m 123456 10 15
O-C(Av) 0-0 0-0 -1-9 -2-9 -3-9 -4-2 -2-8 +1-6
m 20 25 30 35 40
C(Av) +1-0 +2-1 0-1 1-1 0-0
SODIUM.
Na. At. wt. =23-00; At. No. =11.
-,
The arc lines of sodium form a system of pairs, of which the well-known strong
lines in the yellow are the first of the principal series. Other members of the n series
lie in the ultra-violet, but o? and d are almost entirely in the visible spectrum. The
fundamental series lies in the red and infra-red.
The principal series has been traced in the absorption spectrum as far as the 57th
member by Wood and Fortrat,f who measured the positions of the lines on the
international scale with great accuracy ; the wave-lengths tabulated are as given by
them, and have been re-reduced to wave-numbers in vacuo with the . aid of the
Washington tables. The following formulae have been calculated :
n^(m}= 41449-00 AV(w+M48066 0-031200/w) 2
For or! the residuals are
m 12345 6 7 10
C(Av) 0-00 +1-43 0-00 0-33 +0-08 0-11 0-26 0-39
m 15 20 30 35 40 45 50
C(A") 0-38 +0-18 +0-22 0-25 0-10 0-04 0-01
m 54 55 56 57
O-C(Av) -0-01 -0-24 -0-81 -1-34
It is clear that the simple formula does not accurately represent the series,
.although the residuals rarely exceed a few hundredths of an angstrom. Hicks has
* Zeit. f. Wiss. Phot., 13, 46 (1914).
f Astrophys. Jour., 43, 73 (1916).
JAstrophys. Jour., 44, 231 (1916).
The Alkali Metals.
Na DOUBLETS.
99
PRINCIPAL, la m-K.
la=41449-00.
I-RINCIPAI.. la WTC (continued).
la = 41449-00.
X, Int.
V
A,
m
WZ7T 1)2
X, Int.
V
Av
m
tn7T 1>2
5889-963(8^)
16973-35
17-18
(1)
24475-65
2414-872
41397-46
(45)
51-54
95-930(10fl)
956-17
24492-83
746
9-61 ,
49-39
627
41401-66
47-34
3302-34 (1R)
30272-86
5-49
'(2)
11176-14
518
3-53
45-47
02-94 (8R)
267-37
11181-63
411
5-37
43-63
313
7-06
(50)
41-94
2852-828(5^)
35042-66
2-49
(3)
6406-34
218
8-69
40-31
53-031 (QR)
040-17
6408-83
131
41410-19
38-81
050
1-57
37-43
2680-335(4^)
37297-70
1 '^0
(4)
4151-30
13-971
2-93
36-07
80-443(5fl)
296-20
A tj\f
4152-80
910
3-97
(55)
35-03
873
4-61
34-39
2593-828
38541-54
1-47
(5)
2907-46
837
5-22
33-78
93-927
540-07
2908-93
2543-817
39299-20
n.aa
(6)
2149-80
43-875
298-31
\J Oi7
2150-69
SHARP. ITC ma.
2512-123
39794-92
1-31
(7)
1654-08
17^ = 24475-65; lTC 2 = 24492-83.
12-210
793-61
1655-31
X, Int.
V
A,,
m
wa '
2490-733
40136-72
(8)
1312-28
75-533
64-397
383-14
565-60
(9)
(10)
1065-86
883-40
5889-963(87?)
95-930(10^)
16973-35
956-17
17-18
(1)
41449-00
55-915
705-69
(11)
743-31
49-393
44-195
814-08
900-87
(12)
(13)
634-92
548-131
11404-2
382-4
8766-34
8783-13
16-79
(2)
15709-50
40-046
970-41
(14)
478-59
36-627
33-824
41027-90
075-14
(15)
(16)
421-10
373-86
6 160- 725 (8r)
54-214(8r)
16227-37
244-54
17-17
(3)
8248-28
31-433
41115-53
i
(17)
333-47
29-428
27-705
149-46
178-67
(18)
(19)
299-54
270-33
5153-645(6)
49-090 (5w)
19398-34
415-51
17-17
'(4)
5077-31
26-217
41203-91
(20)
245-09
24-937
23-838
225-65
244-35
223-35
204-65
4751-891(4n)
48-016(3w)
21038-37
055-55
17-18
(5)
3437-28
22-856
261-07
187-93
21-997
21-233
275-70
288-72
(25)
173-30
160-28
4545-218(4w)
41-671(3w)
21995-00
22012-18
17-18
(6)
2480-65
20-520
41300-88
149-12
19-922
19-380
11-07
20-34
137-93
128-66
4423-31 (4w)
19-94 (3)
22601-16
618-40
17-24
(?)
1874-49
18-893
28-67
120-33
454
062
36-17
42-86
(30)
112-83
106-14
4344-8 (3)
41-5 (2)
23009-6
027-1
17-5
(8)
1466-0
17-695
49-11
99-89
362
058
54-83
60-03
94-17
88-97
4290-6 (2)
87-5 (2)
23300-3
317-1
16-8
(9)
1175-5
16-779
64-81
(35)
84-19
518
271
69-27
73-50
79-73
75-50
4252-4 (2)
49-3
23509-5
526-6
17-1
(10)
966-1
046
77-35
71-65
15-838
651
80-91
84-12
(40)
68-09
64-88
4223-3
20-3 (2)
23671-4
688-2
16-8
(11)
804-4
474
87-15
61-85
305
147
90-05
92-75
58-95
56-25
4201-0
4198-3 (2)
23797-1
812-4
15-3
(12)
679-5
006
05-16
53-84
H2
100
Tables of Series Lines.
Na DOUBLETS Continued.
CHAP. XII.
DIFFUSE. ITT m8.
COMBINATION. ITT WZTT.*
171! = 24475-65 ; lTU 2 = 24492-83.
X, Int.
V
A,
m
m8
X
V
v calc.
5532-0
27-5
18071-6
086-5
IT?! 371! = 18069-3
l7C 2 37C 2 = 18084-0
8194-82 (10.R)
83-30 (SR)
12199-48
216-64
17-16
ta
12276-18
5688-222 (10)
82-675 (8)
17575-30
592-47
17-17
"(3)
6900-35
4918-2
13-8
20327-0
345-2
ITT! 471! = 20324-4
I7t 2 47i 2 = 20340-0
4982-867 (6r)
78-608 (5r)
20063-20
080-34
17-14
(4)
4412-47
4632-9
29-2
21578-7
596-0
l7r 1 57C 1 = 21568-2
iTCi 57C 2 = 21583-9
4668-597 (4r)
64-858 (3f)
21413-73
430-89
17-16
15)
3061-92
4472-3
4372
22353-6
22866
iTij 67^1 = 22325-9
iTCi 77Ti=22821-6
4497-724 (2w)
94-266 (2w)
22227-11
244-25
17-14
(6) 2248-56
OTHER Na COMBINATIONS.
> Int
4393-45
90-14
22754-77
771-96
17-19
(7) 1720-88
5675-70(3z>)
17614-1
iTti 39 = 17615-3
4324-3
01.0
23118-7
16-6
(8)
1357-2
70-18(3w)
631-2
l7U 2 39 = 17631-5
4975-9 (Iv)
20091-3
iTUi 49=20085-3
4276-5
73-4
23377-0
394-0
17-0
(9)
1098-7
72-8 (lv)
j-4665-0
103-8
21430
l7T 2 49 = 20102-5
ITT! 59 = 21434-1
4241-6
tia.fi
23569-3
15-6
(10)
907-1
60-0
453
l7U 2 59=21451-3
22056-9
4532-5
2cj 27ti= 4533-4
4215-6
23714-7
22084-2
4526-9
2a 27U 2 = 4527-9
198
15-7
(11)
761-7
.
3-418[x
2925
27T! 3a= 2927-9
4195-5
92-6
23828-3
844-7
16-4
(12)
647-7
5-430 (Ji
9-048(ji
9-085[jL
1841
1104-9
1100-5
3037^= 1841-9
28 2^= 1100-0
28 27T 2 = 1094-5
4180-0
77-0
23916-6
933-8
17-2
(13)
559-0
23361-0
23391-0
50230
4279-5
4273-9
1990
27t 2 38= 4281-3
27C! 38= 4275-8
STUj 48= 1993-9
4168
23985
(14)
491
40449
7-443[jL
2471-6
1343-2
8949 = 2470-0
4959 1348-9
3427-1(1)
29170-8
la 28 =29172-8
FUNDAMENTAI,. 28 WKp.
o5J i OO7R.1 a
Unclassified Lines of Na.
X
V
Av
m
5
18459-5
5415-81
(3)
j 6860-37
X v
12677-6
7885-81
(4)
, 4390-37
calc.
(5).
3041-5
7418-0 13477-0
7409-7 13492-1
* The lines of this series are very faint, and the
7377-1 13551.-7
wave-lengths uncertain ; this is often called
7369-1 13566-4
the L,enard series.
3345-0 29886-8
f Also 8 2 (5).
The Alkali Metals. 101
drawn attention to the sudden increase of the residuals beyond w=54, and has
suggested that the last three lines may not belong to the n series.
The lines of cr from m=3 to mS, and of <5 from m=3 to m=7 are as determined
by S. Datta* from photographs of the spectrum of the sodium vapour lamp designed
by Lord Rayleigh, in which the lines are very sharply denned. <5(2) are from observa-
tions by Meggers, <r(2) from Paschen, and the remainder are as obtained by Zicken-
drahtf in the vacuum arc.
The combinations are almost entirely as given by Dunz from the work of Paschen.
A40449 is entered by Dunz as 89 N/5 2 , and A7-443/* as W/5 2 N/6 2 . Exner and
Haschek's line at A3427-1 has been included as a previously unrecognised combination.
POTASSIUM.
K. At. wt.=39-10 ; At. No. =19.
The arc lines of potassium form a doublet system similar to that of sodium.
The first and second n pairs, in the red and violet respectively, are developed in the
Bunsen flame spectrum. Be van observed to the 24th member of the n series in the
absorption spectrum, and the lines from 7r(10) are as given by him. The wave-
lengths of the principal pairs 2 4, of the cr pairs 4 10, of the <5 pairs 4 10, and of
the combination pair la 26, are as determined by S. Datta from observations with
Lord Rayleigh's vapour lamp, in which the lines were much less diffuse than in air.
The limits calculated from the cr pairs by Datta are 21963-06 and 22020-77,
from which the limit of n becomes 35005-88. With this limit, the lines n^l) and
jr 1 (2) lead to- the formula
:7 r 1 (w)=35005-88-Ar/(m-fl-296281-0-061661/w) 2
giving the following residuals :
m 123 4 5 10 15 20
O-C(A.v) 0-00 0-00 -2-80 +2-34 -0-76 -1-2 +4-0 0-0
m 21 22 23 24
O-C(Av) -0-6 +0-2 +0-8 -0-2
The presence of a satellite in 6(2) is strongly suggested by the combination
Iff 26, which was clearly resolved and accurately measured by Datta. The less
refrangible component of the combination is the stronger, and it would thus appear
that the chief line in 6^2) is abnormally placed on the less refrangible side of the
satellite. The terms 26' and 2(5 entered in the table have been derived from the lines
.(Icr 26') (la iTtj) and (la 2(5) (la \n^, thus eliminating errors of measure-
ment of 6(2). The structure of <5(2) is probably as follows :
A calc. v calc. AV A obsd,
1st chief line 11771-5 8492-80
2-74 ill 771 -7^
Satellite 11767-9 8495-54 J '* )
2nd chief line 11688-3 . 8553-25 11689-76
The combination la 26 ,d' further suggests that the fundamental series should
consist of pairs with Av=2-74.
*Proc. Roy. Soc., A. 99, 69 (1921).
t Ann. d. Phys., 31, 233 (1910).
102
Tables of Series Lines.
K DOUBLETS.
CHAP. XII.
PRINCIPAL. Id rnn.
10 = 35005-88. f
SHARP. ITT mo continued.
17^=21963-06; l7t 2 =22020-77.
>, Int.
V
A,
.m
W7U 1)2
X, Int.
V
A,,
m
mo
7664-94 (10.R)
99-01 (10.R)
13042-82
12985-11
57-71
(1)
21963-06
22020-77
5099-180 (3R)
84-212 (2R)
19605-54
663-28
57-74
(6)
2357-51
4044-140 (8R)
4047-201 (6jR)
24720-18
701-49
18-69
^2)
10285-70
304-39
4956-043 (IR)
41-964 (lit)
20171-61
229-24
57-63
(7)
1791-49
3446-722 (8R)
29004-70
8.1 K
"(3)
6001-18
4863-61
49-88
'20555-16
613-33
58-17
(8)
1407-7
47-701 (6R)
28996-55
A v
6009-33
3217-01 (6R)
31075-88
4-83
>)
3930-00
4800-16
4786-89
20826-82
884-58
57-76
(9)
1136-2
17-50 (412)
071-05
3934-83
3102-03 (4R)
32227-61
2-29
(5)
2778-27
4754-54
41-62
21026-70
083-97
57-27
(10)
936-6
02-25 (2R)
225-32
+- it/
2780-56
3034-82 (4ff)
32941-3
(6)
2064-6
2992-21 (2R)
33410-4
(7)
1595-5
^
63-24 (IR)
737-1
(8)
1268-8
DIFFUSE. ITT mS.
42-7 (Iff)
972-5
(9)
1033-4
IT?! = 21963-06; lTU 2 = 22020-77.
27-9
34144-2
(10)
861-7
x
if
Ai/
m
m8
16-5
277-7
728-2
07-5
00-3
2894-5
383-8
469-1
538-1
622-1
536-8
467-8
*11771-73
689-76
8492-64
8552-19
59-6
V(2)
13467-528'
470-268
89-6
85-8
82-8
596-7
642-4
678-4
(15)
409-2
363-5
327-5
t6965-0 (1)
t 36-0 (1)
14353-6
413-6
60-0
^(3)
7608-3
80-2
77-8
75-7
709-7
738-6
764-0
(20)
296-2
267-3
241-9
5832-31 (IR)
12-71 (6J?)
17141-13
198-91
57-78
(
V*)
4821-89
74-0
72-4
71-0
784-6
803-9
820-9
221-3
202-0
185-0
5359-521 (5R)
42-974 (4R)
18653-20
711-00
57-80
>)
3309-81
69-9
834-2
(24)
171-7
5112-204(3^)
5097-144 (2R)
19555-61
613-38
57-77
(6)
2407-42
SHARP. ITT mo.
17^=21963-06; lTU 2 = 22020-77.
4965-038 (IR)
50-816 (IR)
20135-23
193-08
57-85
(7)
1827-76
* , Int.
V
A,
m
ma
7664-94
99-01
13042-82
12985-11
57-71
(i)
35005-88
4869-70
56-03
20529-46
587-23
57-77
(8)
1433-57
12523-0
434-3
7983-16
8040-10
56-94
k>
13980-28
4805-19
4791-08
20805-0
866-3
61-3
(9)
1156-3
6938-98 (8)
11-30 (7)
14407-37
465-08
57-71
'-(3)
7555-69
4759-31
45-58
21005-6
066-4
60-8
(10)
955-9
5802-16 (&R)
5782-77 (5R)
17230-20
287-97
57-77
V)
4732-83
* The terms 28 are calculated from the com-
bination la 28,8' (see text).
f Roughly measured from reproduction in the
5339-670 (4R)
23-228 (4R)
18722-56
780-40
57-84
'(SI
3240-44
Paper by Meggers. The lines are abnormally
faint.
The Alkali Metals.
K DOUBLETS Continued.
103
FUNDAMENTAL. 28^9.
28 = 13470-3.
K COMBINATIONS continued.
X
"
v calc.
X v Ay
m | mq>
8-510[X
8-452[ji
31395
31596-8
6-203{Ji
6-236LI
7-426(ji
*3650
*3062
1174-8
1182-9
3184-5
3164-0
1611-6
1603-1
1346-3
27390
32649
37^ 48= 1179-3
37r 2 48= 1187-4
28 27T 1= 3184-6
28 27r 2 = 3165-9
38371!= 1607'!
38 37t 2 - 1599-0
15166-3 6591-8
11027-1 9066-1
9600-04 10413-8
8905-44 11226-0
8504-3 11755-5
j (3)
(4)
(5)
(6)
(7)
6878-5
4404-2
3056-5
2244-3
1714-8
K COMBINATIONS.
X
v
v calc.
4959 - 1347-7
4642-172 (2)
41-585 (1)
27065-6
27215-0
6-431(ji
36626-4
36372-7
37354-3
37075-6
21535-62
538-36
3693-7
3673-5
1554-4
1547-3
2729-5
2748-6
2676-5
2696-4
lc22
la 22
2a 2r
2<j 27i
3a 37i
3a 37i
27^3
27T 2 3
27^3
27T 2 3
= 2
: i
2 =
1535-62
538-36
3694-6
3675-9
1554-5
1546-4
2730-0
2748-7
2677-4
2696-1
lo3S =27397-6
ICT 60 =32648-4
Unclassified Lines of K.
X
v
CT^
CT =
8=
8=
40115-5
*4600
*4120
*3580
2492-1
21733
24265
27925
* Approximate wave-lengths of faint lines
observed by Datta.
It should be noted that several of the calculated combinations agree less closely
with the observed values than is shown in the works of Paschen and Dunz. In order
to secure better agreement, Paschen assumed a higher value for the wave-length of
jr 2 (2) than that given by Kayser and Runge, and he explained that unless such?
correction were made the discordances of the corresponding combinations were
greater than the probable errors of his infra-red measurements. Paschen's assumed
wave-length has not been confirmed by Datta.
The intensities are as given by Kayser and Runge, except for the pair at 4642.
RUBIDIUM.
Rb. At. wt. -85-45; At. No. =37.
The arc lines of rubidium form a pair system resembling those of sodium and
potassium, but with wider separation. The wave-lengths of the principal series
from 1 3228 onwards have been taken from the list of absorption lines given by
Bevan. 'Other wave-lengths are by Meggers, Kayser and Runge, Paschen, and
Randall.
The satellites in <5 would appear to be somewhat abnormal. A satellite is clearly
indicated in (5(3), and the smaller separations of other d pairs also suggest the presence
of satellites in the usual positions. In (5(2), however, only two lines have been
recorded, and these show the same separation as the a pairs. The real absence of a
104
Tables of Series Lines.
CHAP. XII.
Rb DOUBLETS.
PRINCIPAL, la WOT.
10 = 33689-1.
DIFFUSE. ITC mS.
17^ = 20872-6; l7T 2 =21110-2.
X, Int.
V
A*
m
mn lr ..
X, Int.
V
&y
m
wS',8
15290-3
6538-3
-(2)
14334-3
7800-29(107?)
12816-5
237-fi
(M-
20872-6
237-7
'"*>
7947-64 (8R)
578-9
fclt* 9 \f
/&'
21110-2
14754-0
6776-0
4201-82 (8fl)
23792-5
77-5
(2)
9896-6
15-56 (7R)
715-0
9974-1
7759-61 (1)
12883-7
3-0
(3)
7988-9
57-83 (8)
886-7
7985-9
3587-08 (5R)
27869-9
Q.n
(3)
5819-2
237-6
91-59
834-9
OtJ \J
5854-2
7619-12 (8)
13121-3
3348-72 (32?)
29853-6
1 9-3
(4)
3835-5
50-89 (5R)
834-3
3854-8
(4)
5002-4
6298-50(10)
15872-4
5000-2
3228-05
30969-5
10-3
(5)
2719-6
29-13
959-2
2729-9
6206-48 (8)
16107-8
3157-56
31660-9
K.ft
(6)
2028-2
58-12
655-3
tj i/
2033-8
(6).
3409-6
5724-19 (4r)
17464-9
3407-7
3112-83
32115-8
(7)
1573-3
3082-27
434-3
(8)
1254-8
5647-96 (3r)
700-6
60-50
664-9
0)
1024-2
44-21
839-8
(10)
849-3
32-08
971-1
(H)
718-0
(6)
2468-2
22-60
33074-5
(12)
'614-6
5431-62 (2r)
18405-6
2467-0
15-04
157-4
(13)
531-7
08-91
225-0
(14)
464-1
5362-75 (2r)
642-0
03-99
279-4
(15)
409-7
2999-84
325-5
(16)
363-6
96-39
363-8
(17)
325-3
(?)
1868-8
93-40
397-1
(18)
292-0
5260-3
19005-0
1867-6
91-00
423-9
(19)
265-2
88-82
448-3
(20)
240-8
5195-7
241-4
86-89
469-9
(21)
219-2
85-33
487-4
(22)
201-7
83-93
503-1
(23)
186-0
(8)
1464-6
82-56
518-5
(24).
170-6
5150-8
19409-1
1463-5
81-39
531-6
(25)
157-5
80-40
542-8
(26)
146-3
5088-8
19645-6
79-50
552-9
(27)
136-2
78-69
562-0
(28)
127-1
77-98
570-0
(29)
119-1
(9)
1182-7
77-27
33578-0
(30)
111-1
5075-8
19695-9
1176-7
16-8
927-5
The Alkali Metals.
Rb DOUBLETS Continued.
105
SHARP. ITT ma.
FUNDAMENTAL. 28 my.
17^=20872-6;
l7r 2 =21110-2.
28 = 14334-3.
X, Int.
V
A,
m
ma
X
v \* in
M9
7800-29(10^)
7947-64(8^)
12816-5
578-9
237-6
(1)
33689-1
13443-7
10081-9
7436-7 ... (3
9916-1 , ... (4
) / 6897-6
) 4418-2
8873-6
11266-3
(5
) 3068-0
13666-7
OO7. A .
7314-6
'7CCO.K
237-9 j
'(2)
13557-9
8274-6
12081-9 ... (6
) 2252-4
Rb COMBINATIONS.
7408-37 (10)
7280-22 (10)
13494-5
732-1
237-6
'(3)
7378-1
X
V
v calc.
27319-8
3659-4
2o 27t! =
= 3661-3
6159-84 (5)
6070-95 (2)
16229-
467-
7
3
237-6
(*)
4642-9
27909-8
38511-4
3582-0
2595-9
2a 27T 2 =
27T 2 3d =
= 3583-8
= 2596-0
6-436[i
1553-3
3a 3K!=
= 1558-9
5654-00
5579-2
17681-
918-
7
7
237-0
(5)
3191-2
6-567{A
22533-0
1522-3
4436-7
3o 37T 2 =
28 27U 1 =
= 1523-9
= 4437-7
22936-7
4358-7
28 27C 2 =
= 4360-2
5391-0
. 22-9
18544-3
781-5
237-2
(6)
2328-5
5165-18
52313-4
19355-0
1911-1
la 28 =19354-8
27C! 38 = 1910-7
12924-1
7735-4
2a ST^! =
= 7738-7
5233-8 .
5170-8
19101-3
334-0
(7)
1773-8
12986-6
46190-1
7698-2
2164-4
2a 37i 2 =
38 37Ui =
= 7703-7
= 2166-7
4-637(Jt
2156-1
38 37T! =
= 2166-7
5133-3
19475-
2
(8)
1397-4
4-696jj
I
2129-0
38 37r 2 =
= 2131-7
Unclassified Lines of Rb.
X
V
39866-9
2507-7
7-428[z
1345-9 ,
7-269fz?
1375-3
(
Note. Meggers has found that aline observed by Bder. andValenta at X7060is due to barium;
also that the line measured as X8521 by Eder and X8513 by Lehmann belongs to caesium.
satellite in <5(2) is further suggested by the fact that only single lines have been
recorded in the fundamental series, and also by the combination ICT 2<5, which only
appears as a single line.
The general arrangement of the series is as given by Dunz, who adopted the
combinations indicated by Paschen and Randall. For the first two of the unclassified
lines Dunz suggested the combinations (3? -AT/5 2 ) and (N/5 z -N/&), giving wave-
numbers 2506-1 and 1340-5 respectively ; in this connection it may be observed that
The limit adopted for n is the mean of two closely accordant values deduced
by Hicks and Johanson, corrected to the international scale. From this and the
first two lines the Hicks formula is
=33689-1 -AT/(w+l-365753-0-073450/w) 2
io6 Tables of Series Lines. CHAP. xn.
This represents the lines very closely, as will appear from the following residuals :
m 1 2 3 4 5 6 10 15 20 25 30
C(&v) 0-0 0-0 +0-3 +0-1 0-5 +0-1 +0-8 0-0 0-5 +0-3 +0-4
CAESIUM.
Cs. At. wt. =132-8; At. No. =55.
The arc spectrum of caesium is generally similar to those of the other alkali
metals, the main differences being that the characteristic pairs have a wider separation,,
and that satellites in the diffuse series are well-marked. Observations have been
very numerous, but the wave-length determinations in many cases still leave much
to be desired ; they could probably be improved by observations of the vacuum
arc.
The series are tabulated in accordance with Dunz, but the more recent data
for the red lines given by Meggers and by Meissner have been incorporated. Bevan's
observations have been adopted for the principal series from the third pair onwards ,.
and the wave-numbers have been re-calculated. The wave-lengths for the
fundamental series, and for the two unclassified pairs having the same separation,.
are from Meissner.*
The limit adopted for the principal series is that given by Bevan, which, with.
and ^i(2), gives the formula
The residuals are
m 1 2 3 4 5 10 15 20 25 30 31
O-C(Av) 0-0 0-0 -0-7 +0-1 -0-1 +1-5 -0-2 +0-2 -0-3 +1-3 +1-0-
Bevan considered the possible errors in his wave-lengths to be about 0-2/4,.
and the residuals are within this limit throughout.
* New measures of lines in the red have since been published by Meissner (Ann. d. Phys.
65, 378, June 1921)
The Alkali Metals.
107
Cs DOUBLETS.
PRINCIPAL la mn.
l<i = 31404 : 6.
DIFFUSE. ITT mS.
17^ = 19672-3; lTU 2 = 20226-3
X, Int.
V
Ay
m
W7r ll2
X, Int.
V
Ay
m
wS', 8
8521-12 (lOfl)
8943-46 (lOtf)
11732-3
178-3
554-0
(1)
19672-3
20226-3
36127-0
34892-0
2767-3
2865-2
97-9
(2)
16905-0
16807-1
554-1
4555-26 (8)
21946-5
181-4
(2)
9458-1
30100-0
3321-4
93-16 (6)
765-4
9639-2
3876-39 (6)
88-65 (4)
25789-9
709-3
80-6
(3)
5614-7
5695-3
9208-40 (1)
9172-23 (2)
10856-7
899-5
42-8
(3)
8815-6
8772-8
7 of. 6 7
554-0
3611-52 (4)
27681-3
4.K.1
(4)
3723-3
8761-35 (5)
11410-7
17-41 (2)
636-2
^cf J.
3768-4
3476-88
80-13
28753-2
726-4
26-8
(5)
2651-4
2678-2
6983-37 (5)
73-17 (10)
14315-8
336-7
20-9
(4)
5356-5
5335-6
554-0
3398-14
29419-5
17-1
(6)
1985-1
6723-18 (10)
14869-8
3400-00
402-4
2002-2
3347-44
48-72
29865-0
853-6
11-4
(7)
1539-6
1551-0
6217-27 (1)
12-87 (8)
16079-8
091-2
11-4
(5)
3592-7
3581-1
553-6
3313-16
30174-0
Q.n
(8)
1230-6
6010-33 (7)
16633-4
14-04
166-0
O V
1238-6
3288-56
89-13
30399-8
394-5
5-3
(9)
1004-8
1010-1
5847-64
44-7
17096-2
104-8
8-6
(6)
2575-7
2567-5
554-9
3270-44
30568-1
(10)
836-0
5663-8
17651-1
3256-66
697-5
(11)
707-1
45-91
799-2
(12)
605-4
37-47
879-5
(13)
525-1
(7)
1936-1
30-58
945-3
(14)
459-3
5635-22
17740-6
1931-7
25-00
998-8
(15)
405-8
20-23
31044-7
(16)
359-9
5465-9
18290-2
16-34
082-3
(17)
322-3
12-91
10-07
115-5
143-0
(18)
(19)
289-1
261-6
(8)
1508-3
07-67
166-3
(20)
238-3
5502-9
18167-3
1505-0
05-53
187-1
(21)
217-5
03-69
205-0
(22)
199-6
5340-96
718-0
02-02
221-3
(23)
183-3
00-60
3199-34
98-14
235-2
247-5
259-2
(24)
(25)
(26)
169-4
157-1
145-4
(9)
1208-6
1207-5
5414-2
18464-8
97-17
268-7
(27)
135-9
96-09
279-2
(28)
125-4
5256-79
19017-7
95-31
286-9
(29)
117-7
94-48
93-83
295-0
31301-4
(30)
(31)
109-6
103-2
5350-8
18683-6
(10)
996-4
988-7
5198-8
19229-9
4
(11)
828-5
\
5303-8
18849-2
\ x /
823-1
5153-8
19397-8
io8
Tables of Series Lines.
Cs DOUBLETS Continued.
CHAP. XII.
SHARP. ITT mo.
li^ = 19672-3; l7t 2 =20226-3.
FUNDAMENTAL. 28 my.
28 = 16807-1; 2S' = 16905-0.
X, Int.
V
A,
m
ma
X, Int.
V
A
m
wcp
8521-12
8943-46
11732-3
11178-3
554-0
(1)
31404-6
10124-1
025-4
9874-8
9972-0
97-2
(3)
6932-6
14694-8
13588-1
6803-3
7357-4
554-1
(2)
12868-9
8079-24(8r)
16-90(8*')
12374-0
471-8
97-8
(4)
4433-1
7944-11 (6)-
7609-13 (5)
12584-5
13138-5
554-0
(3)
7087-8
7280-34(6r)
28-85(6r)
13731-9
829-7
97-8
(5)
3075-2
6586-94 (5)
6354-98 (4)
15177-4
731-4
554-0
(4)
4494-9
6871-10(4w)
25-1 1(4)
14549-7
647-7
98-0
(6)
2257-4
6034-6
5839-11
16566-5
17121-2
554-7
(5)
3105-5
6628<78
(6586-07) *
15081-6
179-3
97-7
(7)
1725-5
5746-15
5568-7
17398-1
952-6
554-5
(6)
2274-Q
6472-9
32-0
15444-7
542-9
98-2
(8)
1362-3
5574-2
5407-3
17935
18488
553
(7)
1738
6366-2
26-8
15703-5
801-5
98-0
(9)
1103-6
6289-2
15896-0
51-1
992-8
96-8
(10)
911-6
Unclassified Lines of Cs.
6232-2
16041-3
(11)
765-8
X, Int. v
Av
Cs COMBINATIONS.
8053-35 (2v) 12413-8
07.0
X
v calc.
7990-68 (2v) 511-1
29318-3 3409-9
2d 27^=3410-8
7270-70 (40) 13750-1
7219-70 (4v) 847-2
97-1
30962-9 3228-8
42202-3 2368-9
39180-1 2551-6
2a 27T 2 =3229-7
2^30 =2370-3
27t 2 3a =2551-4
7-425(Ji 1346-4
7-lll{i? -1405-9
6-931(JL 1442-4
39398-5 2537-5
6-807(X 1468-6
7-193[JL 1390-2
13605-2 7347-8
13761-2 7264-9
3a 37^ = 1473-1
3o 37T 2 = 1392-5
28 271! = 7349-0
28' 27r 2 = 7265-8
5209 (1) 19192
1
* Calculated X ; line obscured by a(4).
CHAPTER XIII.
GROUP IB. COPPER, SILVER AND GOLD.
These elements, like the alkali metals which form the first branch of Group I.,
yield spectra containing doublets. The separations of the pairs, however, are
greater in proportion to the atomic weights than in the first sub-group. Thus silver,
with atomic weight 108, gives a doublet separation of 920, while caesium with atomic
weight 133 gives a separation of 554. In these elements the typical series are not
at all well developed, and there are many lines which remain unclassified. The chief
lines of copper and silver were classified by Kayser and Runge, and by Rydberg, and
several combinations have since been noted by Dunz. As in the spectra of the alkali
metals, the first principal pair occurs with positive sign in the principal series.
Extensive discussions of the three spectra in relation to the " oun " have been
givei by Hicks.* With the aid of the theories of linkages and summation series
which he has developed, Hicks has sought to associate a large number of lines with
those belonging to the typical series. Some of the individual illustrations, as Hicks
acknowledges, are doubtless merely numerical coincidences. It is largely by the
indiscriminate association of spark with arc lines that his results have been obtained,
and this is in direct opposition to our knowledge of the spark spectra of other elements
in which series are well developed.
Among the more recent observations of the spark spectra of the three elements
are those by Eder,f covering the region A2080 /1 855.
COPPER.
Cu. At. wt.=63-56; At. No.=29.
Measures of the arc spectrum of copper have been made by Kayser and Runge
and others, and more recently, in Kayser's laboratory, by HuppersJ and by
Hasbach, who give wave-lengths on the international scale. Wave-lengths on the
new scale have also been given by Meggers in the region /8683 A6415.
The lines are very numerous, and only a small percentage has been identified
as representing the typical series or tiieir combinations. As shown by Rydberg, 'j
however, there are many triplets and paHrs having approximately constant difference -
of wave-number, but these have no obvious relation to the separations in the main
series.
The principal series of doublets is apparently represented by a characteristic
strong pair in the near ultra-violet, showing appropriate Zeeman patterns ; but there
is no very convincing representation of the second or succeeding pairs. The position
of the second pair was calculated by Randall^ as 2025-73, 202442 (Rowland scale),
but Kayser and Runge observed only one line, at 2025-08(2^). Two lines in this
region have since been photographed by Rubies, and Dr. M. Catalan** has suggested
* Phil. Mag., Cu39, 457 ; Ag38, 301 ; Au 38, 1 (1919).
t Zeit. f. Wiss. Phot., 14, 135 (1914).
+ Zeit. f. Wiss. Phot., 13, 59.
Ibid. 399 (1914).
j| Astrophys. Jour., 6, 239 (1897).
If Astrophys. Jour., 34, 1 (1911).
** An. Soc. Esp. Fis. y Quim., 15, 432 (1917).
no Tables of Series Lines. CHAP. xm.
that they may correspond with the principal pair. The wave-lengths are 2025-1,
2024-11, giving wave-numbers 49364-7, 49389-8, and a separation of 25-1. The
probable combinations involving the term 2jr, however, suggest a separation of 33,
and it is doubtful whether the second pair is really represented in the spectrum. In
any case, there would seem to be an unusually rapid fall in intensity in the principal
series.
The series are here tabulated as in the memoir of Dunz, except that Hasbach's
wave-lengths have been substituted and the wave-numbers re-calculated ; the
calculated 7i(2) lines have also been slightly modified. The meaning of the term
" x " is not clear, but it may be noted that its value approximates to N/(l-5) 2 .
By extrapolation from the terms 2(5, 26', Hicks has calculated the terms 1<5 and
16' as 28382-9 and 28410-0, and has suggested that the true fundamental series has
these wave-numbers for limits. By extrapolation from 3<p( =6880) he similarly found
12257-1 as the value of a possible term 29 ; terms for higher orders were also cal-
culated, and he was thus able to compute the whole series from m1 to w=10.
The actual representatives suggested for this series, however, include two spark
lines and one " displaced " line, and in four instances only one component is given.
It seems probable, therefore, that the terms 1<5 have no real existence, and that the
first pair of the fundamental series is represented by the tabulated infra-red lines
observed by Randall.
The constant difference lines to which attention was directed by Rydberg are
too numerous "for reproduction here, but it may be noted that they comprise :
6 triplets with Av 129-5, 50-6
6 pairs 129-5
10 pairs 50-6
7 triplets 680,212
5 pairs 680
8 pairs 212
Some of the lines are used more than once in forming the combinations.
A consideration of these pairs and triplets, using the probably more accurate
values of Hasbach, suggests that some of the supposed constant differences are
merely approximate numerical coincidences, though a majority may be sufficiently
exact to be significant.
Huppers has also attempted to identify constant-difference pairs, and has
suggested a considerable number of pairs with separations averaging about 248,
79, 50 and 16. Most of these, however, are far from exact, and as spark lines have
also been introduced, the results do not seem entitled to much weight. The whole
question is worthy of further investigation.
There are numerous other lines which do not appear either in the regular series
or in the constant difference groups.
The spark spectrum of copper shows a multitude of lines, but regular series
have not been traced. It may be remarked that the Cu and Cu+ lines are perhaps
but imperfectly distinguishable in the existing tables, as enhanced lines occur
quite prominently in the arc if observed near the poles.
The spark spectrum in the Schumann region has been observed by Handke,*
.and the vacuum-arc spectrum by McLennan. f
* Quoted in Lyman's book, and by McLennan.
t Proc. Roy. Soc., A. 98, 105 (1920).
Copper, Silver and Gold.
Cu DOUBLETS.
ill
PRINCIPAL, la mn.
la = 62308-0.
FUNDAMENTAL. 28^9.
28 = 12365-9; 28' = 12372-8.
X, Int.
V
A,
m
^ 1)2
X
V
Aj/ ! m mq>
3247-55 (10-ff)
73-97(10.ff)
30783-6
535-2
248-4
(1)
31524-4
772-8
18229-5
194-7
5484-1
94-6
! (3) 6880-0
J[2024-331
J[2025-67]
[49383-0]
[ 350-3]
32-7
(2)
[12925-0]
[ 957-7]
(4) [4400-0]
(5) [3056-0]
SHARP. ITC mo.
17^=31524-4; l7T 2 = 31772-8.
X, Int.
V
A,
m
mo
3247-55
73-97
30783-6
535-2
248-4
,|1)
62308-0
Cu COMBINATIONS.
8092-76 (10)
7933-19 (10)
12353-3
601-8
248-5
??"
19171-1
X, Int.
V
v calc.
4530-84 (6r)
4480-38 (6y)
22064-8
313-5
248-7
9459-5
16008-5
16653-4
6245-0
6003-2
2o 271! = 6246-1
27C! 3 8' =6004-2
3861-75 (3w)
25-05 (3)
25887-7
26136-]
248-4
(4)
5636-7
4056-7 (2n)
4015-8 (In)
24643-7
894-6
iTCj 39 = 24644-4
17C 2 39=24892-8
3652-40 (In)
27371-5
l7T 2 49 = 27372-8
DIFFUSE. ITC m8.
3512-12 (4n)
28464-7
ITT! 59=28468-4
l7T 1 = 31524-4; lTC 2 = 31772-8.
X, Int.
V
A*
m
mS',8
2369-88 (6)
2238-43 (2w)
42183-4
44660-3
#39 =42182-6
x 49 = 44662-6
5220-04 (6)
18-17 (10)
19151-6
158-5
6-9
248-3
(2)-
12372-8
lt 365-9
t5782-16 (8)
J5700-25 (6)
17289-8
538-2
x l7T 2 = 17289-8
#1:1! = 17538-2
5153-23 (8)
19399-9
*2768-89 (3)
36104-9
x 2TC 2 =36104-9
66-39 (8)
137-6
x 27T! = 36137-6
4063-30 (4w)
62-69 ()
24603-6
607-3
3-7
(3)
<- 6920-8
; 17-1
2723-95 (2)
36700-5
#28 = 36696-7
248-5
4022-67 (6w)
24852-1
# = 49062-6.
(4)
4415-5
* Used in calculation of 27^, 27: 2 .
3687-5 (3)
27111-0
13-4
t Used in calculation of x.
% Calc. from combinations x 27T.
3654-3 (3w)
27357-3
SILVER.
Ag. At. wt. =107-88; At. No. =47.
The arc spectrum of silver includes only a moderate number of lines, some
of which are of great intensity. Kayser and Runge's list contains several lines which
are not given by Exner and Haschek as appearing in the arc. Further measures
112
Tables of Series Lines.
Ag DOUBLETS.
CHAP. XIII.
PRINCIPAL, la WTT.
lo=61095-9.
DIFFUSE. ITT mS.
17^ = 30623-0 ; l7T 2 = 31543-6
X, Int.
&
m
Wi,i
X, Int.
v
A,
m
m y, 8
3280-66 (10J?)
3382-86 (lOfl)
[2061-19]
[2069-85]
30472-9
29552-3
48500-1
297-2
920-6
202-9
(1)
(2)
30623-0
31543-6
12595-8
12798-7
5471-51 (6)
} 65-45(10^2)
J5209-08(10fl)
4212-60
10-71 (8B)
4055-31 (6k)
18271-4
291-7
19191-9
23731-7
742-3
24652-1
20-3
920-5
10-6
920-4
(2)
(3)
(4)
(5)
(6)
(7)
(8)
12351-6
331-3
6891-4
6880-7
4394-3
4388-6
3040-2
3035-9
2224-6
1698-3
1337-3
SHARP. ITT mo.
17^=30623-0; l7t 2 = 31543-6.
X, Int.
v
A
m
mo.
3280-66 (107?)
3382-86 (10R)
8273-73
7688-12
4668-52 (8r)
4476-12 (6r
3981-72 (Qr)
3841-15 (2r)
3709-96 (If)
*3587-25
<*i
*3568-31
*3487-53
*3435-87
30472-9
29552-3
12083-1
13003-5
21414-1
22334-5
25107-7
26026-5
26946-8
27868-6
28016-5
28665-5
29096-4
920-6
920-4
920-4
918-8
921-8
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
61095-9
18540-0
9209-0
5516-2
3675-6
2606-5
1957-5
1526-6
3810-71 (2)
3682-30 (2)
26234-4
27149-3
3623-85 (In)
*3507-35
27587-1
28503-4
*3520-35
*3409-76
28398-2
29319-2
Ag COMBINATIONS. ITT 27r.
*3456-25
*3349-66
*3413-66
28924-8
29845-2
29285-7
X, Int.
v calc.
f5545-64 (4y)
f5276-2 (If)
t5333-31 (*)
18027-2 iTCx 27C 1 = 18027-2
18947-8 17^27^=18947-8
18744-9 l7C 2 27T 2 = 18744-9
Ag COMBINATIONS. ITI w^p.
FUNDAMENTAL. 28^9.
28=12331-3; 2S' = 12351-6.
X
v v calc.
X
v
Av
m
>9
4212-60
4055-31
3810-71
3682-30
3681-6
23731-7
24652-1
26234-4
27149-3 )
154-1 j
IT^ 3<p 2
3731-2
4651-8
6236-8
7157-4
ITT, 39 = 2
17^49 = 2
l7T 2 49=2
18382-3
307-9
12551-0
5438-6
5460-7
7965-4
22-1
1
(3)
(4)
6891-8
4386-2?
"Observations by Catalan.
fUsed in calculation of 27r x and 27U 2 .
JFabry & Perot's wave-lengths are 5465-489,
5209-081.
Calc. from combinations ITT 27T. Catalan's
observed XX are 2061-7, 2070-3.
Ag COMBINATIONS. 2o 71.
X
v v calc.
16819-5
17415-7
5943-9 20277! =5944-2
5740-4 2c 27C 2 =5741-3
Copper, Silver and Gold.
on the new scale have been made by Kaspar,* and by Frings.f Measures in the
ultra-violet beyond ^2983 have also been given by HuppersJ ; the suggested series
in this region, however, are probably fictitious. The majority of the lines are some-
what nebulous, and high precision in the measurements is scarcely to be expected.
The series are here tabulated in accordance with the memoir by Dunz, chiefly
using Kayser and Runge's wave-lengths, but they have been extended towards the
violet as indicated by Catalan. The adopted limit has been calculated from the
sharp series.
The spark spectrum of silver is much more complex than the arc spectrum, but
many of the lines are of low intensity. No series have yet been traced. Hicks, ! |
however, has made an extensive investigation of the lines in connection with his
theory of linkages. New measures of the spark lines have been made by Frings,.
Wagner, <; and Eder.**
GOLD.
Au. At. wt. =197-2; At. No. =79.
Series have not yet been very clearly traced in the spectrum of gold. Two"
pairs of lines of equal separation and appropriate to a doublet system of this element
were noted by Rydberg, together with a possible diffuse pair and satellite. The
latter, however, are probably not significant. An additional pair has since been found
through Lehmann's observations!! in the extreme red, showing a line which pairs
with one in the orange. The discussion of the spectrum by Hicks also suggested
further pairs, but spark lines are involved in some of them, and there is probably only
one (4811, 4065) which is real.
Measures of the arc spectrum en the international scale have been made in
Kayser's laboratory by Quincke ; +t whose values have been adopted for the lines
mentioned below, except for Lehmann's line 7509. The four most probable pairs
are :
X, Int.
V
A
7509-5
5837-396 (4)
13312-8
17126-19
3813-4
6278-179 (4)
5064-616 (2n)
15923-79
19739-34
3815-55
4811-611 (4n)
4065-080 (6)
20777-27
24592-85
3.815-58
2427-978 (HXR)
2675-953 (lOfl)
41174-02
37358-78
3815-22
* Zeit. f. Wiss. Phot., 10, 53 (1912).
t Ibid., 15, 165 (1915).
i Zeit. f. Wiss. Phot., 13, 51 (1914).
An. Soc. Esp. Fis. y Quim., 15, 222 (1917).
II Phil. Trans., A. 217, 374 (1918).
*[ Zeit. f. Wiss. Phot., 10 (1912).
** Zeit. f. Wiss. Phot., 13, 20, and 14, 137.
ft Ann. d. Phys., 39, 75 (1912).
+J Zeit. f. Wiss. Phot., 14, 249 (1915).
H4 Tables of Series Lines. CHAP. xm.
The very strong pair in the ultra-violet has usually been regarded as the first
of the principal series, analogous with those of Ag and Cu, but Hicks argues against
this supposition on the ground that the wave-lengths are not in step with 3280,
3382 for Ag and 3247, 3274 for Cu. It may be remarked, however, that the first
principal Li pair is similarly out of step with those of Na and K.
The first pair in the list is assigned to the sharp series by Lehmann and Hicks,
forming <r 1 (2) and cr 2 (2) ; the line 5837 gives a Zeeman resolution in accordance with
this supposition. The second pair, in association with a line A523O306(lw), or
v!91 14-03, is described by Hicks as an inverse set of the diffuse type. The third
pair is assigned to the sharp series by Hicks, who also places the limit for o^ at 29470.
Assuming the fourth pair to be the first principal, the limit of the principal series
would thus be 70664.
The spark spectrum of gold comprises a very large number of lines, but typical
series have not been identified.
CHAPTER XIV.
GROUP HA. THE ALKALINE EARTH METALS.
Apart from beryllium, which requires further investigation in the region of
short wave-lengths, the arc spectra of these elements include a triplet system and a
system of singlets. There are combinations in each system, and also a certain
number of inter-combinations, of which IS Ip 2 is of considerable importance in
adjusting the limits in the two systems so as to yield accurate combinations.
In each of the triplet systems the limit of the principal series lies on the less
refrangible side of the limits of the subordinate series, and the first principal line
appears with negative sign in the principal series and with positive sign in the sharp
series. In the formulae for the sharp series, Rydberg's ^ has to be given a value >1
in order that m=l may give the first line. The diffuse series differ from those of the
alkali metals in exhibiting lines corresponding to m1 (except in the case of Mg)
when IJL is put <1. The numeration of the diffuse series also differs from that
adopted in the alkalis, and is possibly not altogether satisfactory. In the alkalis,
lines of the diffuse series were assigned the same numbers as the lines of the sharp
series to which they were nearest, but to do this in the alkaline earth metals would
require either that the first diffuse triplet should be numbered zero, or that the first
sharp and principal triplet should be given the order-number 2. That the actual
first d triplets have been recorded is indicated by their connection with the
/ series.
In the singlet systems, the component series are arranged in the same way as
in lithium, and the chief difference lies in the appearance of lines corresponding to
m1 in the diffuse series, except in the case of magnesium.
The enhanced lines form systems of pairs, having 4AT for the series constant,
and showing no simple relations to the arc series. These are tabulated under the
headings "ionised Mg " (Mg+), &c. In each case the arc is a sufficient stimulus
to excite some of the enhanced lines quite strongly, but these lines are more especially
developed in the spark (see Plate IV.).
MAGNESIUM.
Mg. At. wt. =24-32; At. No. =12.
The infra-red lines are from observations by Paschen. Of the remaining lines,
most of the wave-lengths are from a paper by Fowler and Reynolds,* but a few are
from measures by Lorenser and by Meggers. In the case of the triplets the limits
adopted for the subordinate series are as calculated by Fowler and Reynolds, cor-
rected to the international scale.
The less refrangible components of the triplets are represented approximately
by the following formulae :
Sl (m) =39760-5 N/(w-|-l-376546 0-062064/w) 2
di(m) =39760-5 N/ (m +0-832086 0-008310/w) 2
* Proc. Roy. Soc., A. 89,]137 (1913).
12
n6
Tables of Series Lines.
Mg TRIPLETS.
CHAP. >:iv.
PRINCIPAL . 1 s m p .
ls=20474-5.
DIFFUSE. Ip md.
1^=39760-5; l 2 = 39801-4 ; l 8 = 39821-3.
X, Int.
v
Av
m
Pw
X, Int.
v
Av m md
5183-67 (10)
72'-70 (9)
19286-0
326-9
40-9
'i
39760-5
39801-4
3838-29 (10) 26045-9
32-31 (10) 086-6
40-7
20-1
(2)
13714-7
67-38 (8)
346-8
39821-3
3229-36 (9)
106-7
3096-91 (9)
32280-9
41-1
15023-3
6654-5
4..1
7^(2)
13820-0
92-97 (8)
322-0
19-8
(3)
7479-5
032-7
50-4
~t i
824-1
91-07 (6)
341-8
032-7
50-4
824-1
f
2851-65 (8)
35057-1
39-6
7657-5
13055-5
53)
7419-0
48-43 (7)
096-7
20-5
(*)
4704-1
46-77 (6)
117-2
6318-55
15822-6
/(4)
4651-9
6319-08
821-3
*
4653-2
2736-53 (7)
36531-8
40-0
33-54 (6)
571-8
19-8
(5)
3229-3
5782-10
17290-0
7j(5)
3184-5
32-06 (5)
591-6
SHARP. Ip ms.
1^=39760-5; l 2 = 39801-4 ; 1^ = 39821-3.
2672-43 (6)
69-56 (5)
68-14 (4)
37408-1
448-3
468-2
40-2
19-9
(6)
2352-9
X, Int.
v Av
m
ms
2632-88 (5)
37970-0
4.1 -ft
5183-67 (10)
72-70 (9)
19 l 8 'o 40-9
19-9
(1)
20474-5
30-04 (4)
28-63 (4)
38011-0
031-3
T-L \J
20-3
(7)
1790-3
67-38 (8)
346-8
2606-64 (4)
38352-1
40-5
3336-69 (8)
32-14 (7)
29961-2
30002-1 ir"'l
(2)
9799-3
03-89 (3)
02-50 (2)
392-6
413-1
20-5
(8)
1408-5
29-9 * 6)
021-9
i
\ /
2588-28 (3)
38624-2
2942-10 (6)
33979-4
85-54 (2)
665-1
(9)
1136-4
38-56 (5)
34020-2 '
(3)
5781-3
84-23 (2)
684-7
36-88 (4) 039-8
2574-93 (3)
38824-4
40-4
* [2781-33
* 78-17
35943-6
984-3
40-7
19-9
(4)
3817-0
72-25 (2)
70-87 (1)
864-8
885-7
20-9
(10)
936-1
* 76-63]
36004-2
2564-91 (2)
38976-0
41-1
2698-13 (5)
95-18 (4)
37051-7
092-3
40-6
19-7
(5)
2709-1
62-21 (1)
60-87 (1)
39017-1
037-5
20-4
(11)
784-2
93-75 (3)
2649-02 (4)
112-0
37738-6
40-6
2557-20 (2)
54-61 (1)
39093-5
133-1
39-6
(12)
667-6
46-17 (3)
44-78 (2)
779-2
799-1
19-9
(6)
2022-1
2551-13 (2)
48-47 (1)
39186-5
227-4
40-9
(13)
574-0
2617-48 (3)
14-65 (2)
38193-3
234-6
41-3
(7)
1567-0
COMBINATIONS.
X
v v calc.
2595-92 (2) 38510-4
93-19 (1) 551-0
40-6
(8)
1250-3
15768-3
15759-1
6340-2 2pi 3^ = 6340-5
6343-9 2p 2 3^ = 6344-6
* Calculated lines, the real lines being
10969-8
9113-5 2p! 4^=9115-9
obscured.
10963-2
9119-1 2^>, 4^ = 9120-0
The Alkaline Earth Metals.
117
Mg TRIPLETS Continued.
FUNDAMENTAL. 2d m/. 2^ = 13714-7.
COMBINATION, lp 2p.
X
V H
*' mf
X
v
v calc.
14877-1
10812-9
6719-9 (
9245-7 (-
J) 6994-8
i) 4469-0
3854-11
3848-09
. 3844-97
3854-53
3848-78
25939-0
979-6
26000-6
25936-2
974-9
Ifa 2p! =25940-5
lp z 2/> 1 =25981-4
1^32^1=26001-3
COMBINATION 1 . lp m/.
X
-
v
v calc.
Ip^pl^lll-t
3051
2833
2729
32766
35288
36633
l^ 1 _4/ = 35291-5
Mg SINGLETS.
PRINCIPAL. 1 5 m P.
15=61672-1.
DIFFUSE. IP mD.
lP=26620-7.
X, Int.
v
m
mP
X. Int.
V
m
mD
2852-11 (10-ff)
2025-82
1828-1
35051-4
49346-6
54702
(1)
(2)
w ;
26620-7
12325-5
6970
8806-75 (8)
5528-42 (8r)
4703-00 (8r)
4351-91 (7y)
4167-39 (6r)
4057-63 (5r)
3986-79 (4y)
3938-43 (3r)
3904-02 (2r)
3878-58 (1)
3859-24 (1)
11351-8
18083-3
21257-1
22972-0
23989-1
24638-0
25075-8
25383-7
25607-4
25775-3
25904-5
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
15268-9
8537-4
5363-6
3648-7
2631-6
1982-7
1544-9
1237-0
1012-3
835-4
716-2
SHARP. IP mS.
!P=26620-7.
X, Int.
' v
m
mS
2852-11 (10-ff)
11828-8
5711-09 (4)
4730-16 (2)
4354-36 (1)
35051-4
8451-7
17504-9
21135-0
22959-1
(1)5-
(2)
(3)
(4)
(5) ,
61672-1
18169-0
9115-8
5485-7
3661-6
Unclassified Lines of Mg.
X, Int.
v
COMBINATION. 25 mP.
25 = 18169-0-
23991-3 (15)
23977-1 (8)
23963-6 (5)
17073-1
11054-2? (15)
7800-4 (1)
7779-9 (1)
6332-26 (2)
6021-70 (1)
2782-98 (6)
81-52 (6)
79-84 (6)
78-29 (6)
76-76 (6)
4167-0
4169-5
4171-9
5855-6
9043-9
12816-4
12850-1
15787-8
16602-0
35922-1
941-0
962-7
982-7
36002-5-
X
v
v calc.
11828-8
*17108-1
8928-97
- 8451-7
5843-6
11196-4
2S !P=-8451-7
25 2P= 5843-5
25 3P= 11199
COMBINATION. IP mP.
X
v
v calc.
4511-2
4250-8
4106-6
4018-1
22160-9
23518-4
24344-2
24880-4
lp_4P|=22162-6
IP 5P- =23528-3
IP 6Pt=24351-5
IP 7Pf=24885-2
* J chanson includes this in the Rydberg series
as IP+ID, giving ID =32464-3.
f These are terms calculated by Lorenser.
The lines were observed by Fowler, and are all
faint and diffuse.
I Used in calculation of 15. This line occurs
in the flame spectrum and is strong in the electric
furnace at low temperatures.
These closely represent a (s) triplet, but .other
lines are probably involved.
Mg INTER-COMBINATIONS.
X V
v calc.
J4571-15 (4)
12083-2
9257-9
3043-75
2768-47
2765-34
21870-7
8273-7
10798-6
32844-7
36110-3
36151-2
15 l a =21870-7
2D3f = 8274-1
2D 4/ =10799-9
Ip 3 3P=32850-8
\p-i- 5Z>=36111-8
lp 2 5D =36152-7
ii 8 Tables of Series Lines. CHAP. xiv.
The residuals C(Av) are as follows :
m 1 2 3 456789 10 11 12 1.3
s 0-0 0-0 0-5 0-8 0-8 0'6 -0-8 0-5
d 0-0 0-0 2-0 2-3-1-7 2-0 2-0-1-5 -1-2 1-0 0-80-7
In the formula for s, /m has been put >1 so that m=\ gives a positive value, in
accordance with the occurrence of the p series on the less refrangible side of s. If jn
were < 1 the formula would suggest a p series in the ultra-violet, but this has not
been observed.
Direct calculation of the limit for the diffuse series of singlets gave 26619-2, and
thence, by adding the wave-number of the first principal line, 61670-6 for the limit
of the principal series. The limits adopted, however, have been derived from the
combination IS l 2 =21870-7, which gives 61672-1 for IS, and thence 26620-7
for IP.
The combinations have been taken from the works of Dunz and Lorenser.
Attention has already been drawn (p. 37) to the difficulty of representing the
singlet D series by a formula.
IONISED MAGNESIUM (Mg+).
The enhanced lines of magnesium have been the subject of an extended in-
vestigation by Fowler.* The spectrum is remarkable for the fact that some of
the enhanced lines appear conspicuously in the ordinary arc in air while others
associated with them in their series relations only appear in the spark, or in the
equivalent conditions in an arc in vacuo (see also p. 66). The lines which appear
in the arc in air are U 2936, 2928, 2802, 2795, 2798, 2790, constituting three pairs
with a separation in wave-number of 91-5. Two pairs of like separation have been
observed in the spark by Lyman at 1753-6, 1750-9, and 1737-8, 1735-0 ; it is not
certain that these appear under ordinary arc conditions.
In the spark in air the majority of the arc lines are present, but the first three
pairs above mentioned are strengthened, and there is an intense broad line at
A4481 (see PI. IV.), together with feeble indications of other extremely nebulous lines,
including one about A3105. As observed in the arc in vacuo, ^4481 becomes well-
defined, and many other lines appear which are probably so diffuse in the spark
as to escape detection. Among the additional lines are a number of doublets having
a separation of 30-5, and two series of single lines. Under the conditions of the
vacuum arc, the line 4481 is revealed as the leader of a strong series which extends
far into the ultra-violet ; with high resolution, the first three members have been
shown to be very close doublets, having the stronger components on the more re-
frangible sides, and a constant separation Ai> of 0-99. The other members of the
series are too close for resolution with the grating. This series is of the fundamental
(<P) type.
The doublets of separation 91-5, the first of which appears in the arc, as well
as in the spark, have been arranged in principal (n), sharp (a), and diffuse (6) series.
Most of the members of the series lie in the Schumann region, outside the range
of the observations at present available ; their positions, however, can be calculated
with considerable certainty from the data given by the parallel series of doublets
having separation 30-5. The possible associated fundamental series, given by
* Phil. Trans., A. 214, 225 (1914).
The Alkaline Earth Metals. 119
Id my (where Id is about 110830 and 89 about 27467), would lie in the Schumann,
region, and has not been recorded (see also p. 66).
The doublets with separation 30-5* may be regarded as forming a secondary
system, based upon the second member of the main principal series, which the
calculations prove to have an identical separation. The a and d series of this second
system are well marked, but the n series has only been partially observed. The
" 4481 " series is the fundamental series of this secondary system. The more
refrangible (stronger) members of these pairs are closely represented by the formula
,() =49777-07. *X109678.3
rm + 0.994112 + - 007190 T
m J
in which the constants have been calculated from the first, second, and eighth lines.
The differences C, in wave-number, for the eight lines are 0-00, f 0-01,-f 0-35,
-0-32, 0-58, 0-17, 0-11, and 0-00. f Notwithstanding their small magnitude,
the residuals are sufficiently systematic to show that the formula is not exact. The
largest residual is equivalent to 0-03^4 . The unresolved lines have been regarded
as consisting of two components, separated by 0-99, and since in the resolved lines
the more refrangible components have about twice the intensity of the less refrangible,,
the observed wave-numbers have been increased by 0-33 for comparison with the
formula. As in most fundamental series, it will be noted that the value of /j, approxi-
mates to unity. The fact that this series consists of doublets indicates the presence
of a satellite in the d doublet 2798, 2791, with which it is connected. The satellite
has not been directly observed, but its presence is indicated by the wider separation
of the chief lines as compared with the other doublets of the same system. The
arrangement is unusual, as the chief line is displaced to the red side of the presumed
satellite, but this accords with the greater intensity of the more refrangible com-
ponents of the 4481 series.
A combination series 3d my is well marked, and the calculated values do not
differ greatly from the observed, though the differences are fairly systematic.
The series 3ym<p is apparently represented, and is of special interest because
the calculated values show a clearly systematic deviation from the observed. The
terms involved depend upon observations of great accuracy, and the combinations
are independent of the adopted value of the limit of the 4481 series.
The separation 14-1 of the third n pair re-appears in the combination
26-3n 1>2 .
Formulae for the individual series were given by Fowler, and served to justify
the arrangement of the lines adopted in the accompanying table. All the observed
enhanced lines are included in the scheme. In drawing up the table, the limits
49777-0 and 49776-0 have been adopted for the " 4481 " series, and all the other
limits have been derived from these with the aid of observed lines, whether occurring
in the main series or in combinations. Thus, starting with 2<5=49777'0, we have
In 1= 2d+d(2) =49777-0+35729-44=85506-44 ; and 10=1^+^(1) =85506-44 +
35760-97=121267-41.
* These have sometimes been designated the " FP " (Fowler and Payn) doublets- of
magnesium.
f Used in calculation of constants.
I2O
Tables of Series Lines.
Mg + DOUBLETS.
CHAP. XIV.
PRINCIPAL, lo mis.
10 = 121267-41.
COMBINATION, TC TYPE. 2o WITT.
2o=51462-2.
X, Int.
V
Av
m
W7T 1)2
X, Int.
v
Av
m
m7t ll2
2795-523 (50)
2802-698 (50)
1239-9*
1240-4*
1026-0*
1026-1*
35760-97
35669-42
80651-3
80620-8
97469-0
97454-9
i
91-55
30-5
14-1
(1)
(2)
(3)
85506-44
597-99
40616-1
646-6
23798-4
812-5
2936-496 (35)
2928-625 (35)
9217-4*
43-4*
3613-80 (4)
15-64 (3)
2790-33*
90-92*
34044-25
34135-74
10846-1
10815-6
27663-82
27649-75
35827-5
35819-9
91-49
30:5
14-07
7-6
(1)
(2)
(3)
(4)
85506-45
597-94
40616-1
646-6
23798-4
812-5
15636-7
644-3
SHARP. ITT mo.
17^=85506-44; lTT 2 = 85597'99.
X, Int.
v Av
m
mo.
COMBINATION, 8 TYPE. 27i mS.
27^=40616-1 ; 27u a = 40646-6.
2795-523 (50)
35760-97
35669-42
34044-25
34135-74
57027
57115
91-55
91-49
88:
(1)
(2)
(3)
121267-4
51462-2
28481-2
2802-698 (50)
2936-496 (35)
28-625 (35)
1753-6
50-9
X, Int.
v
Av
m
r8
*
*
7896-37
77-13
4390-585 (10)
84-643 (8)
3538-86 (6)
35-04 (5)
3168-98 (3)
65-94 (2)
2967-87 (1)
65-19 (0)
9130-4
9160-9
12660-6
12691-5
22769-64
22800-50
28249-6
28280-1
31546-8
31577-1
33684-4
33714-9
30-5
30-9
30-86
30-5
30-3
30-5
(2)
(3)
(4)
(5)
(6)
(?)
(8)
49777-0
27955-3
17846-3
12366-5
9069-4
6931-7
5471-7*
DIFFUSE. ITT m8.
1^ = 85506-44; l7t 2 = 85597-99.
X, Int.
v Av
m
mS, 8'
2797-989 (40)
t
90-768 (40)
1737-8
35-0
35729-44
35730-43
35821-90
57546
57639
0-99
91-46
93:
(2)
(3)
49777-0
776-0
27960 :
COMBINATION, o TYPE. 27r wo.
27^=40616-1 ; 27r 2 =40646-6.
X, Int.
v Av m ; ma
28 "1
COMBINATION, <p TYPE. 2 ' r~ m( ?
2S'=49776-0 ; 28=49777-0.
*
*
4433-991 (8)
27-995 (7)
3553-51 (5)
49-61 (4)
3175-84 (2)
3172-79 (1)
2971-70 (1)
2969-02 (0)
12134-9
12165-4
22546-74
22577-27
28133-2
28164-1
31478-6
31508-9
33640-9
33671-3
30-5
30-5
30-9
30-3
30-4
(3)
(4)
(5)
(6)
(?)
(8)
28481-2
18069-3
12482-7
9137-6
6975-2
5500-8*
X, Int.
v Av
m
mq>
4481 -327 \
81-129/ (1
3104-805 \
04-713/ (30)
2660-821 \
60-755 / (1U
+2449-573 (6)
J2329-58 (5)
J2253-87 (4)
{2202-68 (3)
2166-28 (2)
22308-58
22309-57
32198-83
32199-79
37571-22
37572-15
40811-08
42912-93
44354-35
45385-03
46147-60
0-99
0-96
0-93
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
27467-4
17577-2
12204-8
8965-6
6863-8
5422-3
4391-7
3629-1
3049-0*
* Calculated lines or terms,
t Probable satellite.
J Not resolved ; 49776-7 adopted for limit.
The Alkaline Earth Metals.
121
Mg+ DOUBLETS Continued.
COMBINATION. 38 w 9.
38=27955-3.
COMBINATION. 89 w 9 (?)
39=27467-4.
X, Int.
v obs.
v calc.
m
X, Int. v obs;
v calc.
m
6346-67 (5)
15752-0
15750-5
(5)
6545-80 (5)
15272-8
15262-6
(5)
5264-14 (5)
18991-2
18989-7
(6)
5401-05 (5)
18509-8
f 8501 -8
(6)
4739-59 (5)
21093-0
21091-5
(7)
4851-10 (5)
20608-2
20603-6
(?)
4436-48 (5)
22534-1
22533-0
(8)
4534-26 (4)
22048-1
22045-1
(8)
4242-47 (4)
23564-6
23563-6
(9)
4331-93 (3)
23078-0
23075-7
(9)
4109-54 (3)
24326-8
24326-2
(10)
4193-44 (2)
23840-1
23838-3
(10)
4013-80 (2)
24907-0
24906-3
(11)
4093-90 (1)
24419-7
24418-4
(11)
COMBINATION. 28 3TT 1)2 .
28=49776-7.
X, Int.
v obs.
v calc.
Av
3848-24 (7)
25964-0
25964-2
3850-40 (6)
25978-6
25978-3
14-6
CALCIUM.
Ca. At. wt. =40-07; At. No. =20.
The arc spectrum of calcium includes a system of triplets and a system of
singlets. Lines of a doublet system also occur in the spectrum of the arc, but these
ibelong to ionised calcium (Ca +) and will be considered separately.
Data relating to the arc lines have been collected and much extended by Saunders,*
.and the series are tabulated as given by him. Many of the adopted measures were
'made by Crew and McCauley,f who used the vacuum arc, and others were made by
_A. S. King in the course of his work with the electric furnace. Preliminary observa-
tions of the infra-red region were provided by H. M. Randall. A valuable set of
wave-lengths has also been given by Holtz.J
The p series of triplets lies in the infra-red, and has only been partially recorded ;
'but the s, d, and / series are well marked in the visible and ultra-violet regions. In
the d series, the separations of the satellites from the chief lines show marked irregu-
larities, the usual shrinkage continuing only to the fourth member, after which the
separations increase ; the satellites, however, show constant separations from the
third line characteristic of the triplet, and it is therefore the chief components which
are abnormally displaced. Reference has already been made to the difficulty of
representing the d series by formulae (p. 42). The separations in the / triplets
show the usual correspondence with those of the satellites of the first d triplet.
There are indications that the triplets of the / series have satellites, as in the case of
ibarium, but the lines are too close for measurement in any but the first.
The P series of singlets begins with the well-known flame line 4226A, and all
the lines are easily reversed, except the second, which is abnormally faint. This
does not reverse, as is also the case with the corresponding lines in Sr and Ba, but
* Astrophys. Jour., 52, 265 (1920).
t Astrophys* Jour., 39, 29 (1914).
j Zeit. Wiss. Phot., 12, 201 (1913).
122
Tables of Series Lines.
Ca TRIPLETS.
CHAP. XIV.
PRINCIPAL . 1 5 mp .
ls = 17765-l.
FUNDAMENTAL. 1 d mf.
1^=28933-5; l^'=28955-2 ; ld"=28968-8.
X, Int. v
Av
m
#!...,
X, Int.
V
Av
m
mf
6162-18(9) 16223-6
105-9
33988-7
4585-92 (2)
21799-7
(3)
7133-9
- 6122-22(8) 329-5
52-2
(1)
34094-6
85-87 (6)
799-5
- 6102-72(8) 381-7
146-9
21-5
4581-41 (5)
21821-2
13-6
19856-3 5034-8
19-9
*12730-3
4578-57 (4)
21834-8
19935-2 5014-9
(2)
750-2
4098-55 (4)
24392-1
21-5
(4)
4541-5
f!0987-3
7-8
6777-8
94-94 (3)
413-6
13-7
f 979-5
4-0
(3)
85-6
92-65 (2)
427-3
t 975-5
89-6
3875-81 (4)
25793-9
21-8
(5)
3139-5
72-55 (3)
815-7
13-5
fl 3422-4
(4)
4342-7
70-51 (2)
829-2
SHARP. Ip ms.
1^=33988-7; l/> 2 =34094-6 ; l/> 8 = 34146-9.
3753-37 (1)
50-35 (1)
48-37 1)
26635-3
656-8
670-9
21-5
14-1
(6)
2298-1
X, Int.
V
Av m
ms
\ /
3678-24 (2)
27179-4
21-6
(7)
1754-1
6162-18 (9)
22-22 (8)
16223-6
329-5
105-9
52-2
(1)
17765-1
75-31 (2)
73-45 (1)
201-0
214-8
13-8
02-72 (8)
381-7
3628-60
27551-2
22-1
(8)
1382-3
3973-72 (4)
57-05 (5)
25158-4
264-3
105-9
52-2
(2)
8830-3
25-69
24-11
573-3
585-3
12-0
48-90 (3)
316-5
3594-08
27815-7
21-8
(9)
1117-7
3487-61 (5)
74-77 (3)
28664-9
770-9
106-0
52-1
(3)
5323-8
91-26
89-49
837-5
851-3
13-8
.
68-48 (2)
823-0
3568-91
28009-6
24-3
(10)
923
3286-06 (3)
30423-1
105-8
66-12
033-9
13-9
74-66 (2)
528-9
52-1
(4)
3565-6
64-35
047-8
69-09 (1)
581-0
3550-03
28158-5
23-5
(ID
774
3180-52 (2)
69-85 (1)
31432-5
538-3
105-8
52-1
(5)
2556-2
47-38
45-58
182-0
196-3
14-3
^
64-62 (1)
590-4
Oil 7. *(* /I \
3535-55
28273-8
(12)
660
oil /*OO (1)
ojJUbo'o
105-9
07-39 (1)
02-36 (0)
172-2
224-4
52-2
(6)
1922-4
* Terms calculated from combination Id 2p
are 12729-4, 12749-5, 12756-4.
3076-99
67-01
62-05
32490-1
595-6
648-5
105-7
52-7
(7)
1498-6
t Calculated, not observed.
J Probably belongs to d series.
See also d series.
3049-01
32788-2
105-8
39-21
894-0
1200-3
J34-52
944-8
3028-97
33005-2
19-37
110-1
10 ^ 9 (9)
982-5
3014-01
33168-9
(10)
819-8
The Alkaline Earth Metals.
Ca TRIPLETS Continued.
123
DIFFUSE, ipmd.
1^=33988-7; l 2 =34094-6 ; 1^=34146-9.
X, Int.
V
Av
m
md", d', d
X, Int.
V
Av
m
md", d', d
19917-3
5019-6
11-3
(1)
28969-1
(7)
1848-9
864-3
771-1
32-9
55-1
J. tl O
22-2
955-2
933-5
3109-51
3108-58
32150-3
159-9
9-6
38-7
28-8
105-6
105-4
19506-8
5125-2
452-6
39-5
14-3
3099-34
32255-7
52-1
19310-3
5177-3
3095-29
32298-0
4456-61(3)
22432-4
0.7
(2)
11556-4
(8)
1551-2
55-88(5)
436-1
> i
K.K
552-6
3081-55
32441-9
7-7
47-0
54-77(9)
441-7
o u
547-0
80-82
449-6
39-1
105-9
105-4
4435-67(8)
22538-3
3-7
3071-97
32543-2
4-1
34-95(9)
542-0
71-58
547-3
52*1
52-6
4425-43(9)
22590-4
3067-01
32595-8
3644-99(0)
27427-3
1 .7
(3)
6561-4
(9)
1272-7
44-76(3)
429-0
It
2-8
59-7
3055-55
32718-2
2-3
70-7
44-40(7)
431-8
56-9
55-32
720-5
68-2
106-0
105-1
3630-97(2)
27533-3
1-6
30-75(6)
534-9
3045-75
32823-3
52-0
3624-11(6)
27585-3
3041-05
32874-0
3362-28(0)
29733-3
1-4
(4)
4255-5
(10)
1045-4
62-13(2)
734-7
i.a
54-0
61-92(6)
736-5
A O
52-2
3034-52
32944-8
105-8
3350-36(2)
29839-1
1 -1
50-20(5)
840-6
i CF
3024-93
33049-2
52-2
3344-51(5)
29891-3
3020-15
33101-5
(5)
3002-4
3018-55
33119-1
(11)
869-6
3226-13(1)
30988-1
2-4
00-6
25-88(5)
990-5
%
2998-2
105-8
3006-22
33254-9
(12)
733-8
3215-33(1)
31092-2
1-7
15-15(3)
093-9
52-3
2996-67
33360-8
(13)
627-9
3209-93 (3)
31144-5
2988-98
33446-7
(14)
541-0
(6)
2268-2
3151-28(1)
50-75(4)
31724-1
729-4
5-3
64-5
59-3
2982-89
33515-2
(15)
473-5
106-0
3141-16(0)
31826-3
3-8
40-78(2)
830-1
52-4
.3136-00(2)
31878-7
124
Tables of Series Lines.
Ca TRIPLETS Continued.
CHAP. XIV.
COMBINATIONS. Id mp.
COMBINATION. 2d mf. ',
' X, Int.
V
v calc.
X
V
v calc.
6169-58(3)
16204-1
\d-2p! = 16204-1
22655-9
4412-9
2d 3/ = 4413-1
6161-31(2)
225-9
ld'2p j = 225-8
624-6
19-0
2d' 3/ = 4418-7
6156-08
239-7
Id"2p 1 = 239-4 610-0
21-8
2d"3f = 4422-5 ,
6169-03(2)
205-6
Id' 2p 2 = 205-7
i
i
6163-75(2)
ftl flA.J_A/^M
219-5
91 9. A
Id" 2p 2 = 219-3
1/7" 9>i 91 9. A.
14278
7002
2d 4/ = 7005-5
4512-28(1)
22155-7
ld 3p!= 22155-7
07-85(0)
177-4
Id' 3pi= 177-4
05-00
191-4
Id"3p 1 = 191-0
COMBINATION. 2pwd. , ,
09-45(0)
06-62
07-42
169-6
183-5
179-5
Id' 3p 2 = 169-6
Id" 3^2= 183-2
1^" 3 3 = 179-2
X i Possibly part of incom-
16200-0 pletely observed group
162-2 J" of six lines of combina-
4065-44
24590-8
144-8 J tion2p 3d.
nd 4/>! = 24590-8
4062-49
608-7
?ld' 4j = 24612-5
Ca SINGLETS.
PRINCIPAL. IS mP*
15=49304-8.
DIFFUSE. IPmD.
!P=25652-4.
X. Int.
v
m 1 mP
X, Int.
v
m
mD
4226-73(10^)
f2721-65
2398-58(2)
2275-49(1)
2200-78(1)
2150-78(1)
2118-68
2097-49
2082-73
2073-04
2064-77
23652-4
36731-8
41678-8
43933-3
45425-0
46480-5
47184-7
47661-3
47998-9
48223-2
48416-3
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
25652-4
12573-1
7625-9
5371-4
3879-6
2824-6
2120-3
1638-2
1305-9
1071-6
888-5
7326-10(8)
5188-85(3)
4685-26(2)
4412-30
(-1802-9)
13646-1
19266-9
21337-7
22657-7
(1)
(2)
(3)
(4)
(5)
27455-3
12006-3 ,
6385-5
4314-7
2994-7
FUNDAMENTAL. ID mF. J
ID =27455-3.
X, Int.
v
m
mF
4878-13(5)
4355-10(5)
4108-55(1)
3972-58(1)
3889-14(1)
3833-96
3795-62
3767-42
20494-0
22955-3
24332-7
25165-6
25705-5
26075-5
26339-0
26536-0
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
6961-3
4500-0
3122-6
2289-7
1749-8
1379-8
1116-3
919-3
SHARP. IP mS.
!P=25652-4.
X, Int.
v
m
mS
4226-73(10^)
10345-0
5512-98(4)
4847-29(2)
4496-16
4312-31
4203-22
4132-64
4084-5
23652-4
9664-2
18134-0
20624-4
22235-1
23183-0
23784-7
24190-9
24476
rof
(2)f
(3).V
(4)
(5)
(6)
(7)
(8)
(9)
49304-8
15988-2
7518-4}
5028-0
3417-3
2469-4
1867-7
1461-5
1176
COMBINATION. ID mP.
X, Int.
v
v calc.
6717-69(5)
5041-61(3)
4526-94(4)
4240-46(2)
4058-91(0)
3946-05(0)
3871-54
(1803)
14882-0
19829-5
22083-9
23575-8
24630-4
25334-8
25822-3
]
]
'
WIP= 1802-9
ID 2P 14882-2
* Formerly known as SL,1 (81,=" single
line"). A strong series.
t Abnormally faint.
' j Formerly known as SL3.
Formerly known as SL/2. Faint and diffuse
in air, but of medium strength in vacuum arc.
LD 3P = 19829-4
ID 4P= 22083-9
W5P =23575-7
LD 6P =24630-7
LD7P =25335-0
LD 8P=25817-1
The Alkaline Earth Metals.
125
Ca SINGLETS Continued.
COMBINATION. IS mD. *
Unclassified Triplets and Pairs of Ca.
X
V
v calc.
X, Int. v
Av
4575-43
2680-36
2329-33
2221-91
21849-9
37297-6
42918-0
44992-6
IS ID =21849-5
IS 2D 37298-5
IS 3Z> 42919-3
IS 4D 44990-1
4318-648(9)
4298-989(8)
89-363(9)
5601-283(5)
5594-464(8)
90-109(5)
5270-272(5)
64-237(3)
60-375(1)
7202-161(2)
7148-123(3)
4302-525(9)
4283-008(9)
3006-864(5)
2997-309(4)
6499-648(4)
93-789(8)
6471-659(4)
62-576(9)
6455-606(3)
49-811(7)
5602-829(5)
5598-484(8)
5588-746(9)
81-973(6)
5265-559(5)
61-701(3)
23148-91
254-76
306-96
17848-11
869-87
883-79
18969-08
990-84
19004-77
13880-89
985-83
23235-66
341-53
33247-58
353-57
15381-20
395-08
15447-72
469-44
15486-15
500-05
17843-18
857-03
17888-15
909-85
18986-07
999-99
105-85
52-20
21-76
13-92
21-76
13-93
104-94
105-87
105-99
13-88
21-72
13-90
13-85
21-70
13-92
COMBINATION. IS mS.
X
V
v calc.
2392-22
2257-40
2177-8
41789-8
44285-5
45883
IS 35=41786-4
1545=44276-8
1555=45887-5
OTHER COMBINATIONS.
X, Int.
V
v calc.
7645-25(1)
4929-25
13076-9
20281-4
3412
8359
19935-2
IP 2P = 13079-3
IP 4P=20281-0
25 2P= 3415
25 3P= 8362
ID 35 = 19936-9
Ca INTER-COMBINATIONS.
X
V
v calc.
6572-78(3)
2734-82
3761-70
15210-3
36554-9
26576-2
lSl^ 2 = 15210-2
IS 2/> 2 = 36554-6
Ip 2 35=26576-2
Possibly also ID 2p lt lD2p 3 , !D3p 3
Other Unclassified Lines of Ca.
X, Int. v Av
* Faint and diffuse except in vacuum sources ;
last two wave-lengths difficult to determine.
6439-086(9) 15525-87
5857-476(8) 17067-48
5349-470(5) 18688-25
5262-238(3) 18998-05
4307-738(7) 23207-53
4298-989(8) 23258-17
3000-865(4) 33311-50
126 Tables of Series Lines. CHAP. xiv.
the line must belong to the series, because its " term " enters into combinations
which appear in the spectrum (see also p. 40). The terms quoted for the P series
are averages from P itself and the combination IDmP. Saunders remarks that the
courses of the S and D series would have been difficult to trace but for the existence
of parallel combination series. In the D series it should be noted that the suggested
first line has a negative frequency ; it seems necessary to suppose its existence in
order to give an appropriate connection with the F lines. Support for the selected
F series is given by the close approach of the terms to those of hydrogen (i.e., ^
is nearly unity), which is a general feature of such series.
The limits chosen by Saunders have been adjusted to accord with the inter-
relations indicated by the various series and combinations, and are believed to have
been found with considerable precision.
In addition to combinations in each of the two groups of series, there are
lines which result from combinations of terms taken from the singlet and triplet
systems. As Saunders remarks, this points to a close relation between the two
systems.
There are several interesting triplets and pairs which have not been found to
belong to the regular system, although their separations are identical with those
observed in the series. These and the brighter unclassified single lines have been
included in the tables, as further investigation of possible series or combinations is
very desirable.
The intensities shown in the table are those given by Crew and McCauley, as
photographed in the vacuum arc. The intensities of the additional lines observed
by Saunders have not been stated, but it may be assumed that all the lines for which
no intensities are quoted are of low intensity.
IONISED CALCIUM (Ca+).
The enhanced lines of calcium form a system of pairs, of which but few occur
outside the Schumann region. The well-known H and K lines form the principal
pair. Crew and McCauley's wave-lengths have been adopted in the range which
they cover, and the remainder are as given by Lyman, except 6(1), in which case
the wave-lengths are the means of the values given by Meggers and Meissner. The
separation of the main pairs is 222-85, and that of the narrower fundamental pairs,
as indicated by the satellite separation in 6 (1) is 60-85.
The limit 70325-29 was calculated by a Hicks formula from the less refrangible
components of the first three CT pairs, giving the formula :
Ol (m) =70325-29 -4JV/(w+l-205543-0-064899/w) 2 .
The C ( Av) equal +0-01,* +0-04,* 0-00,* 18, 24. As shown by Hicksf
a more accurate representation of the series is obtained by putting / u>l, and the,re
is the additional advantage that m=l then gives the first pair. The first pair of
6 occurs with negative sign, and this also is given by m=\, when ju, in that series
is taken to be greater than unity. No combination lines have yet been
recognised.
* Used in calculation of constants.
f Proc. Roy. Soc., 91, 452 (1915).
The Alkaline Earth Metals.
Ca + DOUBLETS.
127
PRINCIPAL.
lo mn.
DIFFUSE. ITC m8.
lo=95739-70.
17^ = 70325-29 ; lTU 8 = 70548- 14.
X, Int. v
Av
m
nci,.
X, Int.
V
Av
m
w8', 8
3933-664(10fl) 25414-41
3968-465(10^?) 191-56
222-85
(1)
70325-29
548-14
8498-00 (8)
8542-15 (10)
11764-25
703-44
60-85
222-89
(1)
82089-52
028-73
QfJfJO.l 1 /Q\
KA] .Ofi
SHARP. ITT mo.
17^ = 70325-29; I7r 2 = 70548-14.
3181-283 (6)
79-340(10)
58-877(10)
31424-80
443-99
647-69
19-19
222-89
(2)
38900-47
881-30
X, Int.
V
Av
m
wo
3933-664(10.ff)
25414-41
191-56
222-8
(1)
95739-70
8-61
222-89
(3)
23017-56
008-95
3968-465(10^)
2112-763 (2)
47316-34
03-239 (2)
530-58
3736-903 (9)
06-022 (9)
26752-55
975-46
222-91
(2)
43572-71
1815-0
55096
(4)
15232
07-8
316
2208-606 (3)
2197-791 (3)
45263-26
485-97
222-71
(3)
25062-10
1680-5
59506
(5)
10815
74-1
733
1851-3
43-8
54016
236
220
(4)
16310
FUNDAMENTAL. 18 m<$.
1698-9
58861
18 = 82029 ; l8'=82090.
92-4
59087
226
<J>)
11463
X
V
Av m
m<p
1840-2
54341
65
(3)
27686
38-0
406
1555-1
64304
66
(4)
17723
53-5
370
1434-3
69720
58
(5)
12311
33-1
778
1370-6
72960
(6)
9060
69-1
73040
STRONTIUM.
Sr. At. wt. =87-63; At. No. =38.
The arc spectrum of strontium is generally similar to that of calcium, consisting
of a system of triplets and a system of singlets. The separations of the components
05! the triplets are greater than those of Ca in approximate proportion to the squares
of the atomic weights, and corresponding triplets are displaced to the red with
respect to those of Ca.
The chief line of the singlet system is 1 4607, which is the only line of Sr developed
in the bunsen flame, and is the leader of the P series. As in the case of Ca, the
intensities in P are somewhat irregular, and the series cannot be represented by a
simple formula.
Measurements of the arc and spark lines on the international system have been
made by Hampe,* covering the region 7070 to 2428,4 . Observations by Lorenser and
* Zeit. Wiss. Phot., 13, 348 (1914).
128
Tables of Series Lines.
Sr TRIPLETS.
CHAP. XIV..
PRINCIPAL. lsmp.
ls = 16897-8.
FUNDAMENTAL. Id mf (continued).
1^=27617-2 ; ld'=27717-7 ; 1<T =27777-6.
A, Int.
v ' Av m
mp 1(2 ,3
\ v
Av
m
mf. f, f
7070-10(10)
6878-35(10)
6791-05(5)
" 14 IS1 394 - 2
- 72l'-2 186 ' 8
(1)
31038-0
432-2
619-0
4087-46
70-88
61-08
24458-2
557-8
617-1
99-6
59-3
(5)
3160-5
59-9
59-0
20263
4933-8
(2)
*11964-0
3950-65
25305-1
1 1 n i.i i
(6)
2314-5
9597-0
10417-1 (3)
t6480-7
35-10
405-1
1UU U
58-0
12-6
26-14
4.fi*>* I
12-1
SHARP. | \p ms.
1^ = 31038-0; l^ 2 =31432-2; l 3 =31619-0.
-' /, Int. v
Av m
ms
3867-2
25851-2
(?)
1766-0
7070-10)7) j 14140-2
,
6878-35 (7) 534-4
186-8
16897-8
DIFFUSE, ip md.
6791-05(6) j 721-2
1/> 1 =31038-0 ; l/> 2 = 31432-2 ; 1/> 3 = 31619-0.
4438-04 (4) i 22526-2
004.0
X, Int.
v Av
m
md", d', d
4361-71 (4) ! 920-4
(9\
1 /* 1 '
8511-8
4326-44(3) j 23107-2
186-8
(3260-4)
"f\ (\
(1)
27777-6
30109-7
3320-3
:>9-y
717-7
3865-46(4) 25862-8
3Q4.-5
29225-0
3420-8
LOO-5
617-2
07-38(4) ! 26257-3
Ov*T <J /O\
187-0
5174-9
394-2
3780-46 (3) 444-3
27355-3
3654-6
' i
26914-5
3714-5
59-9
3628-37 (2) 27552-7
3577-33 (1) 945-9
393-2
187-4
(4)
3485-7
26023-6
3841-6
187-0
53-5 ; 28133-3
j
3504-27(2) | 28528-5
3456-52 (1) 922-6
34-28(1) ' 29109-9
394-1
187-3
(5)
2509-4
4971-65 (3)
67-93 (4)
62-24 (QR]
20108-5
123-5
146-6
15-0
23-1
(2)
10929-5
,914-5
89-1-4
FUNDAMENTAL. Id mf.
1^=27617-2 ; lrf'=27717-7 ; ld"=27777-6.
4876-06 (6)
72-49 (6)
20502-7
517-7
394-2
15-0
A, Int.
v
Av
m
mf", /', /
186-6
4832-08 (6)
20689-3
4893-12
20431-2
1 x
(3)
7186-0
92-69 (2)
433-0
1 o
84-2
92-03 (6)
435-7
"
81-5
4033-19 (0)
24787-3
4.Q
(3)
6250-7
100-5
32-39 (3)
792-2
7
45-8
4869-19 (3)
20531-7
1f\
-
30-39 (4)
804-5
12-3
33-5
68-74 (4)
533-6
9
394-2
59-7
3970-05 (3)
25181-5
1-Q
4855-08 (4)
20591-4
69-27 (3)
186-4
X <J
186-9
A K*7 1 O
3940-81(4)
25368-4
4337-89
23046-2
1-0
(4)
4571-3
70-9
* The terms calculated from combinations
37-70 (4)
047-2
70-0
ld2p are 11963-8, 12068-4, 12109-8. These
values are further justified by combinations
4319-12
23146-4
0-5
ID Ip.
19-03 (3)
146-9
f The probable terms calculated from com-
59-0
binations Id 3p are 6479-1, 6510-2, 6525-0.
4308-13 (2)
23205-4
The Alkaline Earth Metals.
Sr TRIPLETS Continued.
129
DIFFUSE. lpmd (continued). 1^! = 31038-0; l 2 = 31432-2 ; 1 3 = 31619-0.
X, Int.
v
Av
m md", d', d
X
v
Av
m md", d', d
(4)
4072-0
(6) 2134-7
3706-74 26970-2
6-1
67-5
3458-47
28906-3
4tl
31-7
05-90(3) i 976-3
61-7
57-98
910-4
1
27-6
;
3653-91 (2)
27360-2
4-8
53-26 (3)
365-0
3411-94
29300-5
186-9
3629-12 (3)
27547-1
3390-67
29484-3
(5)
2869-8
3401-23
29392-8
(7) 1 645-2 (d)
^48-66
28171-7
66-3
OtJTtO \J\J
48-09 (4)
28176-2
4-5
61-8
COMBINATIONS. Id mp.
X, Int.
v v calc.
3500-11
28562-4
3499-68 (4)
28565-9
3-o
6386-51 (6)
15653-6
Id 2p 1 = 15653-6
186-8
45-76 (4)
754-2
Id' 2p l = 754-1
3477-37 (0)
28749-2
21-77 (0)
814-0
Id" 2p 1 = 814-0
88-25 (6)
649-3
Id' 2p 2 = 649-3
63-93 (5)
709-1
Id" 2p z = 709-2
80-74 (5)
667-8
ld"2p a = 667-8
4729-48 (In)
21138-1
Id 3/> 1 =21138-l
07-1 (Ow)
238-6
Id' 3p 1 = 238-6
14-0 (Ow)
207-5
Id' 3p 2 = 207-5
04-0 (Ow)
252-6
Id" 3 3 = 252-6
Sr SINGLETS.
PRINCIPAL. ISmP*
15=45936-5.1
DIFFUSE. lPmD.
1P=24238-1.
X, Int.
v
m
mP
X, Int.
v
m
mD
4607-34 (10J?)
2931-88 (2)
2569-50 (2)
2428-11 (2)
2354-32 (1)
2307-4 (1)
2275-48 (1)
53-34 (1)
37-4 (1)
25-9 (1)
21698-4
34097-8
38906-4
41171-8
42462-1
43325-5
43933-3
44364-8
44680-8
44911-5
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
24238-1
11838-7
7030-1
4764-7
3474-4
2611-0
2003-2
1571-7
1255-7
1025-0
7621-54 (5)
5543-32 (5)
(1547-9)
13117-1
18034-7
(1)
(2)
(3)
(25786-8)
11121-0
6203-4
FUNDAMENTAL. ID mF.%
l> = 25786-8.
X, Int.
\t
m
mF
5156-07 (4)
4678-30 (4)
4406-11(1)
4252-97 (1)
19389-2
21369-3
22689-4
23506-4
(3)
(4)
(5)
(6)
6397-6
4417-5
3097-4
2280-4
SHARP. IP mS.
1P=24238-1.
X, Int.
v
m
mS
* Formerly known as S.I,, (single line) No. 1.
t Limit derived from inter-combination
IS l 2 = v!4504-3.
\ Formerly known as S.L/. 3.
4607-34 (10)
11242-3?
5970-10 (3)
5165-46(2)
21698-4
8892-5
16745-5
19354-0
(1)
(2)
(3)
(4)
' 45936-5
15345-6
7492-6 ;
4884-1
K
130
Tables of Series Lines.
CHAP. XIV.
Sr SINGLETS Continued.
COMBINATION. ID wP.*
1 T\ OCTOC.O
Unclassified Triplets and Pairs of Sr.
X, Int.
v
Av
X, Int.
v m v calc.
4876-32 (6)
20501 6
7167-24 (6)
13948-5 (2) 13948-1
4784 39 (4)
895-5
393-9
5329-82 (5)
18757-2 (3) 18756-7
4741-99 (5)
21082-3
186-8
4755-47 (2)
21022-5 (4) 21022-1
4480-54 (2)
22312-5 (5) 22312-4
4811 -87 (6#)
20776-2
4313-18(1)
23178-2 (6) 23175-8
4722-27 (6)
21170-3
394-1
4202-81 (1)
23787-0 (7) 23783-6
COMBINATION.
4531-35 (4)
4451-80 (3)
22062-3
456-5
394-2
X
v
v calc.
3366-34 (5)
29697-3
4961-48 20149-7
IS l>=20149-7t
22-24 (5)
30091-5
186-9
01-74(5)
30278-4
Sr INTER-COMBINATIONS.
3351 -26 (6#)
29831-0
v
v calc.
394-2
07-55 (4)
30225-2
6892-62 (6) 14504-3
15-1^ = 14504-3
6446-70 (1)
15507 5
1 Sfi-8
7309-47 (6) 13677-1
ID 2/> 3 = 13677-0
6369-96 (6)
694-3
JL <J\J O
7287-44 (1)
7232-24 (6)
718-5
823-2
lD2p a = 13718-4
lD2p 1 = 13823-2
7438-29 (2)
05-83 (2)
13440-3
499-2
58-9
Unclassified Lines of Sr.
6643-58 (4)
15048-0
X, Int.
v
17-28 (5)
107-8
59-8
20704-8
4828-5
6546-82 (4)
15270-4
9643-7
10366-3
04-02 (6)
370-9
100-5
7673-11 (6)
13029-0
7408-08 (3)
13495-1
6546-82 (4)
15270-4
7362-59 (1)
13578-5
21-29(1)
330-2
59-8
7348-48 (1)
13604-5
7153-08 (4)
13976-1
5693-00(0)
17560-6
Kfl A
6550-28 (5)
15262-3
73-80 (0)
620-0
59-4
6465-78 (1)
15461-8
6408-49 (9)
15600-0
5540-11 (5)
18045-2
5847-82 (1)
17095-7
21-83(6)
104-9
59-7
5816-77 (2)
17186-9
5767-05 (2)
17335-1
5534-80 (5)
18062-5
5556-32 (1)
17992-5
5504-17 (5)
163-0
100-5
Kt\ Q
5521-30 (1)
18106-7
5486-12 (5)
222-8
59-8
5225-11 (5)
19133-0
4412-62 (3)
22655-9
5480-84 (7)
18240-3
4140-36 (2)
24145-7
50-91 (6)
340-5
100-2
4051-0 (1)
24678-3
3962-62 (2)
25228-7
5256-90 (6)
19017-3
1 (\f\ K.
3371-00 (1)
29656-3
29-27 (5)
117-8
1UU-5
3330-01 (4)
30021-3
12-97 (2)
177-6
59-8
3200-1
31240-0
3199-0 (2)
31250-8
5238-55 (6)
19084-0
KQ.7
3190-1 (2)
31338-0
22-20 (5)
143-7
oy- /
3189-3 (2)
31345-8
2549-54 (1)
39210-9
3182-3 (1)
31414-7
2435-55
41046-0
72-2 (I)
514-7
100-0
2408-74
41502-9
2138-60?
46744-7
* Formerly known as S.I/. 2.
2047-28?
48829-6
t Used for calculation of ID.
The Alkaline Earth Metals. 131
by Meggers have also been utilised in drawing up the tables. Other measures, with
the vacuum arc as a source, have been communicated to the author by Prof. Saunders,
who has also given valuable suggestions as to the allocation of many of the lines.
The p series is at present very imperfectly known, but it has been possible to
calculate the probable terms with the aid of certain combinations. The presence of
satellites in the /series is very clearly shown.
For the least refrangible components of the sharp series of triplets the formula
from the first three lines is
s 1 (w)=31037-98-AT/(w+l-631561-0-083879/w) 2 ,
giving residuals Av= 1-1 and 2-9 form =4 and 5. The three limits have therefore
been adopted as 31038-0, 31432-2 and 31619-0 in accordance with the triplet separa-
tions.
The limits for p, d and /have been derived in the usual way.*
Limits for the singlet system have been based upon the combination IS Ip 2 ,
except in the case of F, for which the limit depends upon the probable combination
IS-1D.
As in calcium, there are numerous triplets and pairs which do not fall into the
regular systems, and many lines for which places have not been found. These have
been tabulated to facilitate further investigations.
Intensities have been inserted when available, and it may generally be assumed
that the lines are faint when no intensity numbers appear, except for infra-red lines.
IONISED STRONTIUM (Sr+).
The enhanced lines of strontium form a pair system analogous with those of
calcium and barium. As in the case of those elements, the arc is a sufficient stimulus
to develop the lines, but they are relatively more important in the spark, where the
ordinary arc lines tend to disappear. (See PI. IV.)
Only one pair of the principal series has been identified. Using the limits
calculated for the <r pairs, TTOO (=lcr) is found to be =88,952, and the Rydberg
formula indicates a second n pair in the region of /1810 with Av about 300. No
such pair has been noted, and it would seem that the simple Rydberg formula is
not sufficiently exact to predict its position.
The sharp series is very closely represented by the formula
<7 1 (w)=64435-80-4]V/(w+l-304298-0-083489/w) 2 ,
giving errors 0-0 for the first three lines, and C(Av) = +3-5 (or AA= 0-15,4) for
* NOTE. Since the above was written, a further communication from Prof. Saunders indi-
cates the observation of many additional lines in extension of several of the series, and new limits
are given as follows :
l 1= 31026-9 Is =16887-1 1P=24227-1
lp, =31421-1 l<f'=27766-0 15=45925-6
1^3=31607-8 ld'=27706-3 !Z>=25776-3
Id =27606-0
As the investigation is not completed, and the combinations and general arrangement of
the series are not affected, it has not been thought necessary to adjust the tables to the new
limits. Some of the new data, however, have been incorporated.
K 2
132
Tables of Series Lines.
CHAP. XIV.
the fourth. With the same limit, and calculating from 6 (2) and d (3), we get the
formula
<5 1 (w)=64435-80-4Ar/(w+l-560163-0-106710/w) 2 .
This represents dj_ (4) very closely, but extrapolation to d l (1) gives 8447 in place of
9959. The error, however, is considerably smaller than with the formulae previously
given by Lorenser and Fowler, in which case p was put < 1.* Johanson has applied
his formula! to this series, and with the limit 64323-3 adopted from the a series he
finds =2-563879, & = 3-805663, N being taken =4x109675. This gives residuals
(AA) 0-04 0-0,J 0-0,} -1-2, -1-4.
Sr+ DOUBLETS.
PRINCIPAL, lc wir.
lo = 88952-47.
DIFFUSE.
17^ = 64435-80;
ITT mS.
I7i 2 = 65237-26.
X, Int.
V
Av
m
m7T 1)2
X, Int.
V
Av
m mS',8
4077-71 (10)
4215-52 (9)
24516-67
23715-21
801-46
(1)
64435-80
65237-26
10038-0
10328-0
10915-4
3474-90 (3)
64-47 (7)
3380-72 (6)
2324-52
22-39
2282-05
1994-31
1963-74
*1847-0
* 20-0
9959-42
9679-80
9158-85
28769-60
28855-21
29571-04
43006-40
43045-86
43806-70
50126-3
50906-5
54142
54945
279-62
800-57
85-61
801-44
39-46
800-30
(1)
(2)
(3)
(4)
(5)
74395-66
115-60
35666-20
580-59
21429-98
389-94
14330-8
309-5
10293
SHARP. ITI mo.
iTtj =64435-80; ITT, = 65237-26.
X, Int. v
Av
m
mo
4077-71 (10.K) 24516-67
4215-52 (9R) 23715-21
4305-46 (5) 23219-81
4161-81 (3) 24021-26
2471-63 40446-92
23-59 41248-56
2051-76 48722-98
18-53 49524-96
801-46
801-45
801-64
801-98
(1)
(2)
(3)
(4)
88952-47
41215-99
23988-79
15712-56
FUNDAMENTAL.
18 = 74115-60; IS'
IS m<p.
= 74395-66.
X, Int.
V
Av
m
w<p
2165-92
52-84
*1778-8 (9)
69-8 (8)
*1 620-7 (5)
13-3 (4)
*1538 ? (1)
46154-84
46435-60
56217
56503
61702
61985
65020
280-76
286
283
(3)
(4)
(5)
(6)
27960-4
17896
12412
9096
Unclassified Lines.^
X
*1560-8?(1)
*1532-3?(1)
V
64070
65261
* X vacuum, f Not certainly Sr+.
* Phil. Trans., A. 214, 237 (1914).
f See p. 36.
Used in calculation of constants.
The Alkaline Earth Metals. 133
BARIUM.
Ba. At. wt. =1374; At. No. =56.
A careful study of all the available data for the arc lines of barium has recently
been made by Saunders,* who has revised the previously recognised series, and has
identified additional combinations. The / series is remarkable for the presence of
satellites, which are generally similar to those occurring in the d series. Both the
/ and d series show curious irregularities in the satellite separations ; the data show,
however, that the normal triplet separations are maintained by the satellites through-
out, and that it is the chief lines which are subject to irregular displacements. There
are also irregularities in the intensities of the lines in some of the series. No simple
formula of ordinary type will represent the series with reasonable accuracy.
The data chiefly used by Saunders in addition to his own special observations
were obtained by King, Randall, Meggers and Eder. Observations of the arc and
spark spectra, and comparisons with previous records, have also been given by
Schmitzf for the region / 7,060 to 2,214, and by George J for the region I 7,060
to 8,210.
The tables which follow are a re-arrangement of those given by Saunders, but
in some cases the lines have been differently numbered. Thus, in the /series, since
H usually approaches unity in these series, the first triplet has been called (3) in place
of the (1) assigned by Saunders.
The intensities in the barium spectrum have been very incompletely recorded ;
Kayser and Runge's estimates have been adopted so far as possible. Many lines
remain unclassified.
IONISED BARIUM (Ba+).
The enhanced lines of barium form a pair system, with satellites, similar to
those of Mg, Ca, and Sr. The leading members of the series were recognised by
Ritz, and additional members were subsequently traced by Saunders. The series
are here given according to Lorehser, except that the new wave-lengths determined
by Schmitz have been utilised as far as possible. Lines in the Schumann region
are from observations by Lyman.
Hickshas adopted the same sets of lines, except for the first member of the d
series, for which he has selected, as an inverted d set,
X (Rowland) v Av
5853-91 (107?) 17077-96 ]
6148-6 (ft) 16190-53 f 1690-59
6497-07 (6R) 15387-37 J
The first line, however, is unduly strong, and the suggested satellite is not only
misplaced, but has a separation out of the usual proportion. The infra-red lines
assigned by Lorenser are doubtless correct, as they show a satellite separation in
agreement with Av of the related fundamental series.
* Astrophys. Jour., 51, 23 (1920).
f Zeit. Wiss. Phot., 11, 209 (1912).
} Ibid., 12, 237 (1913).
Proc. Roy. Soc., A. 91, 455 (1915).
134
Tables of Series Lines.
Ba TRIPLETS.
CHAP. XIV.
PRINCIPAL. Ismp.
DIFFUSE. Ip md.
ls = 15869-3.
1^=28514-8 ; l 2 =29392-8 ; 1^ = 29763-3.
X, Int.
v
Av
m
mp t , M
X, Int.
v
Av
m
md", d', d
7905-80(7)
7392-44(7)
7195-26(6)
12645-5
13523-7
13894-3
878-2
370-6
(1)
28514-8
29392-8
763-3
22313-4
23255-3
25515-7
4480-6
4299-0
3918-2
181-6
380-8
878-0
d)
32995-6
814-1
433-0
20712-0
21477-2
4827-0
4655-1
171-9
72-2
(2)
11042-3
214-2
27751-1
29233-9
3602-6
3421-1
181-5
370-7
*4582-9
286-4
30933-8
3231-9
f!0189-l
10272-9
10326-
9812-1
9732-0
9682-4
80-1
49-6
(3)
6057-2
137-3
186-9
5818-91 (4n)
5800-30(67?)
17180-7
235-8
55-1
67-4
(2)
11333-9
279-0
5777-70(107?)
303-2
211-6
878-2
5535-93
18058-9
55-0
5519-12(87?)
113-9
SHARP. Ip ms.
370-7
l/> 1 =28514-8; l/> 2 = 29392-8 ; l/> 3 = 29763-3.
5425-55(87?)
18429-6
x
Av
m
WlS
(3)
6320-1
4493-66 (4w)
22247-6
23-0
\ /
267-3
7905-80(7)
12645-5
878-2
4489-00 (4i>)
270-6
244-2
7392-44(7)
13523-7
Q7A. A
(1)
15869-3
7195-26(6)
13894-3
O l\J "D
4332-96(4w)
23072-6
52-8
4323-63 (4w)
125-4
4902 -90 (6r)
20390-5
87C.9
370-7
4700 -45 (6r)
21268-7
o / o &
370-5
(2)
8124-3
4264-43(4w)
23443-3
461 9-98 (4r)
21639-2
(4)
4067-5
4239-56(2y)
23580-9
878-4
4087-31 (In)
24459-3
14-5
\ /
55-4
4087-31 (In)
24459-3
370-4
(3)
4934-0
4084-87(lw)
473-8
41-0
4026-30
24829-7
3947-51
25325-4
12 2
3975-32(2*')
25148-3
S7C.Q
3945-61
337-6
3841-15
26026-6
O / O'O
(4)
3366-5
370-6
3787-23
26397-1
9R1 Irt.Q
370-5
3890-57
25696-0
9000.7
3704-23
ZD1 1U O
26988-5
878-2
(5)
2404-5
3898-58
25643-3
27-7
(5)
ZoOO /
71-4
1
'
OOQJ..Q.1
671-0
JQ.O
OO.7rt ort
3771-93
26504-1
17-4
*o o
3769-48
521-5
COMBINATIONS.
O7in An o^O7y.7
370-6
X v
v calc.
3719-92
^UO IV 4
4674-97 21390-5
ld2p l = 21390-7
3789-72
26379-9
6)
2137-1
34-8
4593-16 21771-5
Id'2p 1 = 21771-8
3788-18
390-6
10-7
24-2
[obscured]
Id' 2p 1 = [21953-3]
4629-63 21600-0
Id' 2p 2 = 21599-9
3667-93
27255-7
2-4
4591-07 21781-4
Id" 2/> 2 = 21781-4
3667-60
258-1
4606-38 21709-0
3790-27 26376-9
Id"2p 3 = 21709-2
ld3p! = 26375-8
;(3618-72)
26227-44 3812-8
2d 3/ = 3813-0
7)
3721-17
26865-7
1649-1
* Calculated wave-number.
3720-85
868-0
2-3
1646-8
f Provisionally placed.
% Masked by a line of iron impurity.
3603-40
27743-7
The Alkaline Earth Metals.
Bi TRIPLETS Continued.
135
FUNDAMENTAL. Idmf. 1^=32433-0; ld'=32814-l ; l<T = 32995-6.
X, Int.
V
Av
m
mf, f, f
X, Int.
V
Av m
/*,/',/
3997-92
25006-1
U.i
(3)
7426-8
(8)
1415-4
95-66(6)
020-2
i
U.o
7412-8
13222-28
31025-1
3-3
07-8
93-40(107?)
034-4
m
7398-6
21-63
031-4
01-6
381-1
381-3
3937-88(6)
25387-3
1 Q.Q
3183-96
31398-6
7-8
35-72(87?)
401-2
lo-y
83-16
406-4
1 O
181-5
182-0
3909-92(87?)
25568-8
3165-60
31580-6
3596-33
27798-3
O A A
(4)
4634-6
(9)
1134-2
93-20(4r)
79-67(47?)
822-7
927-7
24-4
105-0
4610-4
4505-3
3193-97
93-91
31300-2
300-8
0-6
32-8
32-2
381-1
383-2
3547-70
28179-5
3155-67
31680-1
30
44-66(67?)
203-6
24-1
t 55-34
683-4
3
181-6
181-3
3524-97(67?)
28361-1
-
3137-70
31861-4
*O/4 Ol A Q
>( i-> 1 Q Q
IK\
001 O.Q
lift}
932-9
V 0425i**o
21-01
20-32(47?)
zyzicvy
222-9
228-8
4-0
5-9
()
> 1O O
10-1
04-2
f3173-72
t 73-69
31499-7
500-0
0-3
(IV)
oo 1 ? 1 -? on
OftHAA o
381-2
381-8
oo77-39
76-98(47?)
^yboo-o
603-9
3-6
3135-72
31881-5
181-6
181-9
3356-80(67?)
29781-9
3117-94
32063-4
IR\
OQfCl .0
(11)
781-7
3323-06
30084-3
(V)
.)'! ^J
48-7
\ /
22-80(4r)
086-7
2-4
46-3
3158-54
31651-1
381-0
380-5
3281-77
81-50(4*)
30462-8
465-3
2-5
3121-02
32031-6
181-8
f3262-30(2r)
30644-6
/7\
1790-5
(12)
664-7
f3262-24
61-96
30645-2
647-8
2-6
(' 1
88-0
85-2
3146-90
31768-3
380-8
380-6
3222-44
t 22-19
31023-6
026-0
2-4
3109-63
32148-9
181-4
3203-70
31205-0
* Much too strong ; perhaps not a member
of this series.
3137-80
31860-6
(13)
572-4
t These lines somewhat doubtful, as they
are not clearly resolved.
% This may not belong to the series ; triplet
3130-6
31934
(14)
499
irregular.
Tables of Series Lines.
CHAP. XIV.
Ba SINGLETS.
PRINCIPAL. 15 mP.
15=42029-4.
DIFFUSE. IPmD.
!P=23969-2.
1
X, Int.
V
m
mP
X
v
m
mD
5535-53(107?)
3071-59(6/2)
2702-65(47?)
2596-68(47?)
2543-2
*2500-2
*2473-l
18060-2
32547-2
36989-9
38499-5
39308
39985
40423
(1)
(2)
(3)
(4)
(5)
(6)
(7)
23969-2
9482-2
5039-5
3529-9
2721
2044
1606
15000-4
?9831-7
P6233-59
P5267-03
P4877-69
?4663-60
6664-9
10168-8
16038-2
18981-4
20496-6
21437-5
(1)
(2)
(3)
(4)
(5)
(6)
30634-1
13800-4
7931-0
4987-8
3472-6
2531-7
COMBINATION. 2 5 mP.
SH,
1
nS.
P=23969-2
X, Int.
v
m
v calc.
X, Int.
v m
mS
(2)
(3)
(4)
[6917-2]
11359-9
12869-5
8799-70(2)
7766-80(2)
11360-9
12871-8
5535-53(107?)
13207
18060-2 (1)
7569-8 (2)
42029-4
16399-4
OTHER COMBINATIONS.
FUNDAMENTAL. 17J> mF.
ID =30634-1.
X, Int. v v
calc.
X, Int.
V
m
mF
J9527-0 10493-6 IP 2F= 10494-0
3900-37(4w) 25631-5 1525=25630-0
5826-29(87?)
4080-93
3789-74
17158-9
24497-4
26397-7
(2)
(3)
(4)
13475-2
6136-7
4254-4
Ba INTER-COMBINATIONS.
COMBINATION. ID mP.
X, Int.
v
V
calc.
X, Int.
V
m
v calc.
7911-36(6)
3244-20
11304-20
$4284-90
3599-40 (6)
3413-84
12637-1
30816-6
8844-1
23331-2
27774-9
29284-3
15 1/> 2 = 12636-6
15000-4
4726-46(87?)
$3905-98(2)
3688-35(2)
6664-9
21151-7
25594-7
27104-5
(1)
(2)
(3)
(4)
6664-9
21151-9
25594-6
27104-2
15 2p 2 30815-2
1^'_1P = 8844-9
Id' 2P=23331-9
Id' 3P=27774-6
\d e 4P=29284-2
COMBINATION. IS mF.
X, Int.
V
m
v calc.
* Not positively identified as belonging to
this series,
f Very faint line.
$ Abnormally faint.
This series is strong at low temperatures.
3501-12(107?)
2785-26(8w)
2646-50
28554-3
35893-0
37774-8
(2)
(3)
(4)
28554-2
35892-7
37775-0
The less refrangible components of the second, third, and fourth pairs of the.
sharp series lead to the formula
a 1 (w)=58712-5-4AT/(w+l-438086-0-108104/w) 2
This gives the first line as 22099-4 in place of the observed 219524, and the
fifth as 48057 in place of the observed 47999.
The limits assigned to the fundamental series follow the usual rules, but are
considerably different from those independently calculated from the observed lines,
namely, 71120-5 and 71696-4.
The Alkaline Earth Metals.
Ba+ DOUBLETS.
137
PRINCIPAL, lo mis.
lo = 80664-9.
DIFFUSE
17^ = 58712-5
ITC m8.
; 17^ = 60403-4
X, Int.
V
Av
m
W7T 1)2
X, Int.
V
Av
m
wS',8
4554-04 (lOfl)
4934-10 (9R)
21952-4
20261-5
1690-9
(1)
58712-5
60403-4
10035-6
10652-4
9961-8
9385-1
576-7
(1)
68674-3
097-6
1 fiftQ-1
SHARP. ITT wo.
12084-8
8272-7
17^ = 58712-5; IK Z = 60403-4.
X, Int.
V
Av
m
wo
4166-02 (4)
4130-68 (8J?)
23997-0
24202-3
205-3
(2)
34715-5
510-2
4554-04 (10.R)
4934-06 (9R)
21952-4
20261-5
1690-9
(1)
80664-9
3891-79 (QR)
25687-9
1690-9
4899-97 (8)
4524-95 (7)
20402-6
22093-5
1690-9
(2)
38309-9
2641-39 (4)
2634-80 (7)
37847-5
37942-2
94-7
(3)
20865-8
770-3
2771-35 (6)
2647-28 (4)
36072-8
37763-4
1690-6
(3)
22639-8
2528-51 (5)
39536-8
1689-3
2286-11
2201-1
43728-9
45420
1691
(4)
14983
2235-4
44721
54
(<i\
13991
2232-7
44775
938
2082-7
47999
IK\
10714
1691
v '
2154-0
46412
FUNDAMENTAL. 18 w<p.
18 = 68097-6 ; l8' = 68674-3.
2054-9
48649
(5)
10109
X, Int.
V
Av
m
>9
1987-7
50294
064
2335-25 (8R)
2304-21 (8R)
42808-8
43385-5
576-7
(3)
25288-8
Unclassified Pair.*
X, Int.
v
Av
1869-2
53499
1849-5
54068
(<*)
14602
5853-70 (8)
17078-5
1690-9
6496-90 (8)
15387-6
1694-3
59021
1677-9
59598
(6)
9077
* Zeeman effect is of 8 type.
RADIUM.
Ra. At. wt.=226-4 ; At. No. =88.
Measurements of the spark spectrum of radium, between wave-lengths 6487
and 2709, were made by Runge and Precht,* of the arc and spark by Exner and
Haschek,f and of the spark spectrum by Crookes.J The spark spectrum may, of
course, include arc lines, just as the arc often includes spark lines.
The series of arc lines have not yet been satisfactorily traced. Analogy with
the other elements of the alkaline earth group indicates that a triplet system and a
* Ann. d. Ph., 14, 418 (1904).
t Wien, Ber., 120, HA, 967 (1911).
j Proc. Roy. Soc.. 72, 295, 413 (1903).
138
Tables of Series Lines.
CHAP. XIV.
system of singlets may be expected. Hicks* has attempted to find the triplets,
and has suggested an arrangement which gives separations 2050 and 832 ?, but the
relative intensities and general fragmentary character of the suggested triplets
leave the question very doubtful. A further attempt has been made by the Misses
Anslow and Howell,f who proceeded on the basis of Av=about 3060 for the separa-
tion of the extreme components of the triplets as deduced from the spectra of calcium,
strontium and barium. Attention is drawn to a number of possible triplets with
A^, Av 2 =2016-64 and 1036-15, giving 3052-79 for the extreme members. These
intervals, however, are averages, and the individual differences seem to vary more
than the probable errors of measurement. The wave-numbers were not corrected
to vacuum in this investigation, but when this correction is made the results are
not sufficiently improved to establish confidence. Furthermore, the intensities of
the components of the triplets are irregular, and the suggested satellites call for
further investigation.
There is a strong line in the flame spectrum at 1 4825-94 LA.
IONISED RADIUM (Ra+).
Some of the lines of the spark spectrum were identified by Ritz as forming
pairs analogous with corresponding pairs of Ca, Sr, and Ba.l These may now be
certainly regarded as enhanced lines, although their behaviour in the arc has not
been investigated. The lines are not sufficiently numerous to permit the calculation
of satisfactory formulae, but by assuming the constant for these series to be 4iV,
and using a simple Rydberg formula, the limit for the less refrangible components
of the sharp series is found to be about 57863. Hicks, however, has found reason
to believe that the true limit is nearer to 56653-23, and this has been adopted in the
following table for the known lines of Ra+ :
Ra+ DOUBLETS.
PRINCIPAL . 1 a WTT .
lo = 82862-05.
SHARP. ITC ma.
1 71! = 56653 -23 ; l7T 2 = 61510-44.
X, Int. 1 v
Av
m
m^,,
X, Int.
v
Av
m
ma
3814-43 (100)
4682-18 (50)
26208-81
21351-61
!
' 4857-21
(1)
56653-23
61510-44
3814-43 (100)
4682-18 (50)
5813-63 (15)
4533-16 (10)
26208-82
21351-61
17196-20
22053-50
4857-21
4857-30
(1)
(2)
82862-05
39456-98
DIFFUSE.
17^=56653-23 ;
l7T 2 = 61510-44.
X, Int.
v | Av
m
mS',8.
4436-32 (20)
4340-67 (50)
3649-60 (50)
22534-90 z
23031-46
27392-49
L96-56
4857-59
(2)
34118-1
33621-77
Fues gives the limits as la=80,000, 1^=53785, Ijr 2 =58645.
* Phil. Trans., A. 212, 64 (1913).
t Proc. Nat. Acad. Sci., Wash., 3, 409 (1917).
J Phys. Zeit., 16, 521 (1908).
Ann. d. Phys., 63, 17 (1920).
CHAPTER XV.
GROUP HB. ZINC, CADMIUM, AND MERCURY.
The elements zinc, cadmium, and mercury form a second branch of Group II.
of the periodic system, and their spectra have a general resemblance to those of the
alkaline earth metals, which form the first branch. Thus, the arc spectrum in each
case comprises a triplet system and a singlet system, with combinations and inter-
combinations. The spectra of the ionised elements have not been completely investi-
gated, but it is probable that they yield doublets as in the case of the alkaline earth
metals.
The elements, zinc, cadmium, and mercury, however, while showing the usual
atomic weight relationship among themselves, are not united in this way with the
alkaline earth metals.
The sharp and diffuse series of triplets were identified by Rydberg, and by
Kayser and Runge, and the work of Paschen* subsequently led to a knowledge of the
principal series and of the single line systems, in addition to numerous combinations.
A further important contribution was made in Paschen's laboratory byK. Wolff, f
who traced the principal series of singlets in the Schumann region, and obtained wave-
lengths which appear to be of remarkable accuracy.
The spectra of zinc and cadmium in the Schumann region have also been observed
by McLennan, Ainslie and Fuller .J
The most complete lists of wave-lengths are those given by Kayser and Runge.
These have been supplemented in the ultra-violet for Zn and Cd by Huppers and
by Eder.||
A partial revision of wave-lengths for Zn and Cd, based on photographs of vacuum
arc spectra, has been made by Saunders, ^j and the new wave-lengths have been
adopted in the tables which follow.
ZINC.
Zn. At. wt. =65-38; At. No. =30.
The wave-lengths of the principal series of triplets, and of all the lines less
refrangible than A4810, have been adopted from the observations by Paschen. For
the sharp and diffuse series the revision and extension by Saunders have been
utilised. The remaining wave-lengths are mostly from the lists of Kayser and Runge
and of Huppers, except in the region of short wave-lengths. The adopted limits of
the series are as determined by Saunders.
Apart from lines which are probably due to impurities of lead and tin, there are
yeryfew tabulated lines which do not find places in one or other of the series. The
combination line 1S2D, at 1601-09, has not previously been recognised as such.
The " single line " spectrum of zinc, as observed by McLennan,** is represented
by the prominent line A 3075-88, being the inter-combination IS Ip 2 .
* Ann. d. Phys., 29, 625 (1909) ; 30, 747 (1909) ; 35, 860 (1911) ; 40, 602 (1913).
t Ann. d. Phys., 42, 825 (1913).
I Proc. Roy. Soc., A. 95, 316 (1919).
Zeit. Wiss. Phot., 13, 46 (1914).
|| Ibid., 13, 20 (1914) ; 14, 137 (1915).
If Privately communicated.
** Proc. Roy. Soc., A. 91, 485 (1915).
140
Tables of Series Lines.
Zn TRIPLETS.
CHAP. xv.
PRINCIPAL. Is mp.
Is =22094-4.
DIFFUSE. lp md.
l 1 =42876-3 ; Ip 2 =43265-2 ; l 3 =43455-0.
X, Int.
V
Av
m
W^LZ.S
X, Int.
V
Av
m
md", d', d
-4810-53(1 OR)
20781-9
QQQ. Q
(1)
42876-3
3345-96(4)
29878-2
4.-O
(2)
12997-6
-4722-16(107?)
21170-8
OOo 5:
1 8Q.fi
43265-2
45-51(87?)
882-2
* V
K.J.
994-2
-4680-20(107?)
360-6
lO*7 C
455-0
44-91(107?)
887-6
ij t
988-7
389-4
13054-89
7657-9
Kfi O
(2)
14436-5
3302-91(87?)
30267-6
0.9
151-50
01-7
DO'Z
O.7
492-7
02-56(87?)
270-8
O ^
197-79
7575-0
O i
519-4
190-3
3282-28(87?)
30457-9
6928-33(8)
14429-5
01 .1
(3)
7664-9
38-48(6)
408-4
1 J.
1 <I-S
86-0
43-22(4)
398-6
1 17 O
95-8
(3)
7187-0
2801-07(7)
35690-2
2-9
85-9
5772-00(10)
17320-2
10-3
(4)
4774-2
00-90(8)
692-4
2
83-9
75-43(8)
309-9
A. 7
84-5
77-02(6)
305-2
T 9
89-2
2770-95(67?)
36078-0
1 .-
70-84(87?)
079-5
I O
5308-51(8)
18832-4
K.K
(5)
32620
190-2
10-11(6)
826-8
O U
2-6
67-6
2756-43(67?)
36268-2
10-84(4)
824-2
70-2
md
5068-53(4)
69-49(2)
19724-1
720-4
3-7
1 i
(6)
2370-3
74-0
2608-55(87?)
2582-38(87?)
38323-0
712-4
389-4
i QQ.F;
(4)
4553-3
69-98(0)
718-5
i <a
75-9
69-80(67?)
901-9
ioy c
SHARP. Ipms.
2515-81(6)
39737-6
(5)
3138-7
l^ 1 =42876-3; l 2 =43265-2 ; 1 3 =43455-0.
2491-48(6)
40124-7
387-1
1 QQ O
X, Int.
V
Av
m
ms.
79-74(4)
314-6
loy-B
4810-53(107?)
4722-16(107?)
20781-9
21170-8
388-9
189-8
df
22094-4
2463-47(4)
40-11(4)
*
40580-8
969-3
388-5
(6)
2295-5
4680-20(107?)
360-6
/
3072-07(107?)
35-81(107?)
18-38(8y)
32541-9
930-6
33120-7
388-7
190-1
(2)
10334-4
2430-79(1)
08-13(1)
2397-15
41126-4
513-4
703-5
387-0
190-1
(7)
1749-9
2712-48(87?)
2684-06(87?)
70-44(6r)
36855-8
37245-9
435-8
390-1
189-9
(3)
6020-5
2409-06
2386-80
76-01
41497-4
884-3
42074-4
386-9
190-1
(8)
1378-9
2567-80(6r)
42-32 (6r)
30-09(2r)
38932-2
39322-4
512-4
390-2
190-0
(4)
3944-1
2393-85
71-78
60-96
41761-0
42149-5
342-7
388-5
193-2
(9)
1115-3
2493-32(4w)
40095-1
2382-22
419"64-8
10)
911-5
69-38(2r)
485-3
390-2
(5)
2781-2
60-96
42342-7
57-80(ly)
674-5
190-2
2374-36
42103-7
U)
707-6
2449-72(1)
40808-3
26-63(1)
41196-8
388-5
190-1
(6)
2068-0
2367-72
42221-9
12)
654-4 '
15-48(1)
386-9
2421-82
2399-23
41278-7
667-3
388-6
f7^
1 PiQ7.fi
FUNDAMENTAL. 2d m/.
2^ = 12988-7; 2d' = 12994-2 ; 2rf"=12997-6.
88-30
858-0
190-7
\'i
1 O7 i \J
X
V
Av
m
mf
2402-82
41605-5
(8)
1270-8
16498-6
4QO.^
6059-5
RAAO.fi
3-1
/q\
fiQOl .0
* Observations discordant, and enhanced line
rrt/V O
483-7
WDA \J
6065-0
2-4
M*J
D5/O1 O
Involved.
(4)
;4442-3]
Zinc, Cadmium and Mercury.
Zn TRIPLETS Continued.
141
COMBINATION. 1 p mf.
l 1 =42S76-3 ; l 2 =43265-2 ; 1 3 =43455-0.
COMBINATIONS.
X
V
v calc.
X, Int.
V
v calc.
24045-7
13792-4
13784-8
10979-4
3515-ll(lw)
4157-6
7248-4
7252-4
9105-5
28440-5
oy, .,0,. A-\ c;o-O
2781-23 (4w)
51-39 (2)
36-86 (2w)
2600-94 (2n)
2575-06 (2n)
62-61 (2n)
35944-1
36334-6
527-4
38436-1
822-4
39011-0
l^ 1 _3/== 35945-0
1 2 3/=36333-9
lp 3 3/=36523-7
1^47=38434-0
l/> 2 4/ = 822-9
1 3 4/=39012-7
2p l 3d' = 7250-6
2p 1 3d =7252-6
Is 2d =9105-7
\p! 2pj, =28439-8
,
Zn, SINGLETS.
PRINCIPAL. 1.
S mP.
6-8.
Zn.
INTER-COMBINATIONS.
1S = 757
X, Int.
V
v calc.
X, Int.
v
m
mP
15682-1
6239-22 (6)
6238-00 (8)
||3075-88 (872
4292-86 (2)
t!632-ll (4)
6375-0
16023-2
16026-4
32501-6
23288-0
61270-4
2D 3/
IP 2d"
IP 2d'
IS Ip 2
1 2 25
15 -2 Pl
^077.0
* 2138-61 (8R)
t 1589-76 (10)
t 1457-56 (8)
t 1404-19 (4)
t 1376-87 (2)
46745-1
62902
68608
71215
72629
(1)
(2)
(3)
(4)
.(5)
29021-7
12857-9J
7160-6}
4559-1J
3141-7|
= 16024-1
= 16027-5
= 32501-6
=23286-5
= 61274-1
SHARP. IP mS.
!P=29021-7.
Unclassified Lines of Zn.
X, Int.
v
m
mS
X, Int.
v
2138-61 (BR)
11055-4
5182-0 (5)
4298-38 (2)
3965-7
3799-4
46745-1
9043-0
19292-2
23258-0
25209-2
26312-3
(1)
(2)
(3)
(4)
(5)
(6)
75766-8
19978-7
9729-5
5763-7
3812-5
2709-4
10970-7
7478-75 (6)
6470-98 (4)
6102-17 (2)
6022 (1)
P4101-79 (2)
3739-97 (4)
2623-78 (1)
P2393-81
P2063-8
9113-2
13367-5
15449-3
16383-1
16601
24372-8
26730-6
38101-6
41761-7
48438
DIFFUSE. IP mD.
!P=29021-7
X. Int.
v
m
mD
6362-37 (10)
4629-88 (Br)
4113-6
3883+2
15713-1
21592-8
-24302-5
25746^13
(2)
(3)
(4)
(5)
13308-6
7428-9
4719-2
327613
McL/ennan, Ainslie
Wolff. and Fuller.
X vac.
v
X vac.
v
COMBINATION. 25 mP.
25 = 19978-7.
1649-87 (5)
1486-20 (5)
1476-01 (2)
1474-67 (3)
1450-82 (1)
60610-8
67285-7
67750-2
67811-8
68926-5
1510-4 (1)
1491-5 (1)
1486-2 (6)
1478-5 (2)
1477-6 (4)
1451-1 (4)
1445-0 (3)
66207
67047
67286
67636
67677
69915
69204
X
v
m
mP
11055-4
14039-5
7799-33 (6)
6479-24 (5)
5937-67 (3)
5654-39 (1)
5485-98 (1)
9043-0
7120-8
12818-1'
15429-6
16837-0
17680-5
18223-2
(1)
(2)
(3)
(4)
(5)
(6)
(?)
29021-7
12857-9
7160-6
4559-1
3141-7
2298-2
1755-5
* Eder's X in. spark is 2138-55.
f Wolff X vac.
j Determined from combination 25 mP.
New values by Saunders.
|| Used for calculation of 15.
COMBINATION.
X, Int.
v
v calc.
t 1601-09 (4)
62457 5
IS 2D = 62458-2
142
Tables of Series Lines.
IONISED ZINC (Zn + ).
CHAP. XV.
Certain pairs of lines in the spectrum of zinc, with a mean separation of 876,
were noted by Rydberg, and further attention was directed to them by Paschen, who
also observed their behaviour in the magnetic field.
The lines in question are definitely enhanced lines, and there can be no doubt
that they originate in the ionised element. The magnetic resolutions suggest that
one of the pairs is of the principal, and the other of the sharp series type. A third
pair, in the orange, noted by Paschen as having the same separation, gives a magnetic
resolution of the diffuse series type. On the basis of N for the series constant,
Paschen assigned one pair to 0-5a ln vz and the other to ln l>2 1-5(7, in the
notation of Ritz. When 4JV is adopted for the series constant, and in the notation of
this Report, these become respectively ICT l7i l>2 and l7r 1)2 2<r. The lines are too
few to permit a trustworthy calculation of limits, but approximate values, as shown
below, have been derived by the use of Rydberg's table, with 4JV for constant.*
Zn+ DOUBLETS.
PRINCIPAL. ICT WTU.
10 = 147,544.
SHARP. ITT ma.
17^ = 98190 ; l7C 2 = 99062.
X '
V
Av
m W7i 1(2
X
V
Av
m
wa
*2025-49 <
61-96
19354-7
18482-5 /
872-2
m 98190
99062
2025-49
61-96
f2558-01
02-03
49354-7
48482-5
39081-1
955-7
872-2
874-6
(1)
(2)
147,544
59.109
Unclassified Pair, Diffuse Type.
X
V
Av
6214-65
5894-43
16086-6
960-5
873-9
* X Eder.
f X Huppers.
There are numerous other enhanced lines of zinc, especially in the ultra-violet,
and further investigation of the series is needed. Attention should be specially
drawn to the pair of lines 4923-98(10) and 4911-63(10), with wave-numbers 20303-1
and 20354-2. There is an analogous pair in cadmium, and since they do not occur
in the true arc spectrum, f it is possible that they correspond with 4481 of magnesium,
and may be members of a series of the fundamental type.
CADMIUM.
Cd. At. wt.=112-4; At. No. =48.
The authorities for wave-lengths are generally the same as for zinc, and the
adopted limits are as communicated by Saunders.
The "single line" or "resonance" spectrum, as observed by McLennan, is
represented by the combination line !SIp 2 , 43261-04.
* Fues gives lTT 1 = 109650, lTC 2 = 110,520, l<r = 159,000 (Ann. d. P., 63, 18, 1920).
t Fowler and Payn, Proc. Roy. Soc., 72, 255, Plate 14 (1903).
Zinc, Cadmium and Mercury.
Cd TRIPLETS.
143
PRINCIPAL. 1 s mp .
ls=21054-7.
DIFFUSE. Ipmd.
l/> 1 =40711-5 ; l/> 2 =41882-6 ; l/> 3 =42424-5.
X, Int.
V
Av
m
/l.M
X, Int.
V
Av
m
md", d', d
5085-88 (10#)
19656-8
1171-1
(1)
40711-5
3614-43 (4)
27659-0
11-8
(2)
13052-4
4799-91 (lOfl)
20827-9
541-9
41882-6
12-89 (SR
670-8
18-2
13040-7
4678-19 (10 J?)
21369-8
42424-5
10.51 (10R
689-0
13022-5
1171-1
13979-22
7151-6
174-1
(2)
13903-1
3467-61 (SR
28830-1
11-9
14327-99
6977-5
70-7
14077-2
66-18 (10.R
842-0
14474-62
6906-8
14147-9
542-2
3403-60(10^
29372-3
7346-2 (10)
13608-7
71-5
(3)
7446-0
85-0 (9)
537-2
25-4
7517-5
98-9 (5)
511-8
7542-9
2981-89 (1)
33526-0
6-2
(3)
7185-3
81-34 (4fl
532-2
8-0
7179-5
6099-18 (8)
16391-1
33-1
(4)
4663-6
80-63 (8R
540-2
7171-3
6111-52 (6)
358-0
12-5
4696-7
1171-3
6116-19 (4)
345-5
4709-2
2881-23 (1R
34697-3
5-5
80-77 (8R
702-8
5598-77 (6)
17856-1
18-8
(5)
3198-6
542-1
5604-68 (4)
837-3
6-9
3217-4
2836-90 (8fl
35239-4
5605-85 (2)
830-4
3224-3
5339-50 (1)
18723-2
(6)
2331-5
(4)
4549-9
2764-19 (2R
fJO.QQ /fiT?
36166-2
1 7H.9
4546-3
AKA 1 .0
SHARP. \p ms.
uo oy ^u/i
1 /U ^
40*1 o
1^=40711-5; l^ 2 = 41882-6; l/> 3 =42424-5.
2677-64 (Sd
37335-2
X, Int.
V
Av
m
ms
2639-50 (6.R;
37874-6
5085-88 (10 R)
19656-8
1171-1
4799-91 (10J?)
20827-9
541-9
(1)
21054-7
2660-40 (4r)
37577-2
(5)
3139-2
4678-19 (lOfi)
21369-8
2580-27 (2w)
38744-1
3138-5
44-72 (2w)
39285-3
3134-5
3252-52 (8r)
30736-5
1170-6
3133-19 (8r)
31907-1
541-2
(2)
9975-6
2602-18 (2)
38417-8 j
(6)
2294-5
3080-93 (6r)
32448-3
2525-30 (In)
39587-3
2491-16
40129-9
2868-26 (6r)
34854-1
1171-3
2775-00 (6r)
36025-4
541-8
(3)
5857-3
2565-88
38961-3
(7)
1751-3
2733-88 (4y)
567-2
2491-16
40129-9
57-87
40673-4
2712-40 (6r)
36857-1
1168-0
2629-06 (4r)
38025-1
541-5
(4)
3856-6
2541-64
39332-9
(8)
1379-3
2592-14 (2r)
566-6
2468-25
40502-2
35-58
41045-5
2632-25 (2f)
37979*1
1170-6
2553-53
39149-7
541-3
(5)
2732-9
2524-68
39597-1
(9)
1114-3
2518-70
691-0
2452-22
40767-1
19-90
41311-4
2585-07
38672-1
1173-8
2508-91
39845-9
541-8
(6)
2037-6
2512-37
39791-0
10)
920-3
2475-25
40387-7
2440-51
40962-6
2554-51
39134-7
1171-1
2502-99
39940-3
U)
771-6
2480-28
40305 ;8
(7)
1576-8
2431-73
41110-5
2495-88
40054-0
12)
658-1
2533-91
39452-9
1173-3
25-04
41223-9
2460-72
40626-2
(8)
1257-0 1
2490-23
40144-8
13)
566-7
,
144
Tables of Series Lines.
Cd TRIPLETS Continued.
CHAP. XV.
FUNDAMENTAL. 2d mf.
OTHER COMBINATIONS.
nj I OAOO K 9/7' 1 QO4.O r
2d" 13052-4
a loVirir t> , ^a lou^tu /
X, Int.
v
v calc.
X v
m mf
14852-9
6730-4
2pi 3d 6731-8
16482-2 6065-5
14474-6
6906-8
2p 2 3d = 6905-9
16433-8 6083-4
(3) 6957-1
14329-6
6976-8
2/> 3 3d = 6976-6
16401-5 6095-4
14354-5
6964-6
2p 3 3d"= 6962-6
3729-06 (4r)
26808-8
\pi 2/^ 1 = 26808-4
11630-8 8595-6
(4) 4445-1*
3005-41 (lr)
33263-7
l Pi 3p 1 = 33265-5
OpTQK.^Q ft o*\
27804-7
17) 27> 2780^-4.
COMBINATION. lp mf.
2903-13 (1)
34435-9
Ip2 3pi = 34436-6
X, Int.
v
v calc.
2908-74 (lr)
34369-1
1^23^2 = 34365-1
2961-48 (4u)
2862-30 (2v)
33757-1 lp 1 3f= 33754-4
34926-7 Ipt 3/ = 34925-5
* The term 4/ is somewhat uncertain.
2818-73 (Iw)
35466-5 1
p z 3/ = 35467-4
2756-78 (3)
36263-5 1
p 1 4f = 36266-4
2670-66 (3w)
37432-9 lp a 4/ = 37437-5
2632.26 (2)
37978-9 l^> 3 4/ = 37979-4
Cd SINGLETS.
PRINCIPAI,. IS mP.
15 = 72538-8.
DIFFUSE. IPmD.
!P=28846-6.
X, Int.
v
m
mP
X, Int. v
m
mD
2288-02 (10.R)
43692-2
(1)
28846-6 J6438-47 (10) 15527-4
(2)
13319-2
*1669-29 (10)
59905-7
(2)
12633-2 4662-51 (8r) 21441-7
(3)
7404-9
*1526-85 (8)
65494-3
(3)
7044-6
f4140-5 24144-9
(4)
4701-7
*1469-39 (6)
68055-5
(4)
4483-4
J3905-1 25600-3
(5)
3246-3
*1440-18 (3)
69435-8
(5)
3103-1
*1423-23 (1)
70262-7
(6)
2276-2
COMBINATION. 2S mP.
SHARP. IP mS.
25 = 19229-3.
!P=28846-6.
X, v
m mP
X, Int. v m
mS
10394-7 9617-3
(I) 28846-6
2288-02(107?) 43692-2 ; (1)
10394-7 9617-3 (2)
72538-8 15154-8 6596-8
19229-3 8200-2 12191-5
(2) 12632-5
(3) 7037-8
5154-68 (6r)
19394-5 13}
9452-1 6778-10 14749-3
(4)
4480-0
4306-82 (4n)
23212-5
( 4 )
5634-1
6198-22 16129-2
(5)
3100-1
3981-77 (2r)
25107-4
(5)
3739-2
5895-8 16956-5
(6)
2272-8
t3818-5
26180-9
(6)
2665-7 5715-8 17490-5
(7)
1738-8
t3723-2
26851-0
(7)
1995-6
P5598-06 17858-4
(8)
1380-9?
COMBINATIONS.
* ^ rror. TXr,Off
X
v
v calc. f Saunders.
* 1688-58(2)
59221-4
J The fundamental line of the international
IS !Z)=59219-5 system of wave-lengths.
39086-9
2557-7
3P 4P= 2557-8 1 XPaschen (Trans. Int. Sol. Union, 4,81, 1913).
Zinc, Cadmium and Mercury.
Cd SINGLETS Continued.
145
Cd INTER-COMBINATIONS.
Unclassified Lines of Cd. ^f
X, Int.
v v calc.
X, Int.
V
15713-5
11268-4
6329-97(8)
6325-19(10)
4615-39
4614-17
4114-5
'5297-64(2)
*1942-29(6)
f3261-04(10)
*1710-51(3)
*1537-83(1)
4413-06(6)
3082-68
7132-1
6031-39
5568
5324
3649-59(2;-)
3499-94 (4r)
6362-2
8872-0
15793-5
15805-4
21660-6
21666-3
24297-4
18871-1
51485-6
30656-2
58462-1
65026-7
22653-7
32429-6
14017-3
16575-3
17954-8
18777-7
27392-5
28563-7
2D 3/= 6362-1
2D 4/= 8874-1
IP 2d" = 15794-2
IP 2^ = 15805-9
IP 3<T=21661-3
TfP Id' 21fifi7-4.
J15257-3
6128-66 (2)
5783-93 (4)
5637-22 (5)
4615-75 (2)
4511-34(5)
6552-4
16312-3
17284-5
17734-3
21658-9
22160-2
IP 4d" = 24296-7
IP 4^ = 24300-3
IP 2s = 18871-0
IS ls = 51484-l
IS 1^2=30656-2
IS 2 2 =58461-6
IS 3^2 = 65021-3
1^225=22653-3
l^ 2 3S=32430-5
X v Av
3298-97 (4) 30303-6
2748-61 (2) 36371-3
2657-00 (2) 37625-2
2654-55 (1) 37660-0
2329-27 (10) 42918-6
2267-48 (5) 44088-2
2239-86 (5) 44631-7
Is 4P= 16574-7
Is 5P=17954-6
Is 6P=18781-9
Ip 1 2> = 27392-3
lp 2 2D =28563-4
X
V
1| 2306-61 (5)
2262-29 (1)
2230-40 (1)
2170-04 (1)
43340-3
44189-3
44820-9
46067-7
* X vac., Wolff,
t Used in calculation of IS.
{ Dr. Catalan has suggested that this may be
the combination 2p 2 3 2 , giving v = 6559-7.
The wave-number is 352-6 lower than that of
the line 15 Ip 2 .
|| The wave-number is 351-9 lower than that
of the line IS IP.
Tf Other lines in the Schumann region have
been recorded by McLennan, Ainslie and Fuller
(Proc. Roy. Soc., A. 95, 330, 1919).
X vac.
V
*1993-07 (1)
*1682-12 (1)
*1647-78 (2)
*1571-40 (1)
50173-8
59448-8
60687-7
63637-5
IONISED CADMIUM (Cd+).
The spectrum of ionised cadmium is similar to that of zinc, and Paschen has
suggested that one pair belongs to the principal and another to the sharp series.
Limits have been calculated by the Rydberg formula on the supposition that the
series constant is 4AT ; but they can only be regarded as roughly approximate.* The
wave-lengths of the principal and sharp pairs are by Huppers ; those of the unclassi-
fied pair by Eder.
* Fues gives 17^ = 103,880, Irc 2 = 105,350, lo = 150,500.
146
Tables of Series Lines.
Cd+ DOUBLETS.
CHAP. XV-
PRINCIPAL, la WTT.
la = 140225-7.
SHARP. ITT WIG.
17^ = 93607-2; l7T 2 =96090-0.
X, Int.
V
Av
m WTC 1)2
X, Int.
V
Av
m
mo
2144-39 (SR)
2265-04 (8R)
46618-5
44135-7
2482-8
93607-2
96090-0
2144-39 (8R)
2265-04 (8R)
2748-61 (10)
2573-0 (10)
46618-5
44135-7
36371-3
38853-4
2482-8
2482-1
(1)
(2)
140225-7
57236-2
Unclassified Pair of Cd+.
X
V
Av
2321-13 (8)
2194-60 (4)
43069-3
45552-1
2482-8
As in the case of zinc, enhanced lines are numerous, more especially in the ultra-
violet. The pair of lines 5378-24 (10), 5337-54 (10), wave-numbers 18588-3 and
18730-0, corresponds with the 4924 pair of zinc. The separations of the two pairs
are approximately proportional to the squares of the atomic weigh ts.
Observations of the spark spectrum of cadmium in the Schumann region have
lately been published by McLennan.* .
MERCURY.
Hg. At. wt. =200-4; At. No. =80.
The wave-lengths for mercury are taken from Cardaun,f Eder and Valenta,J
Kayserand Runge,{ Paschen, Stiles,|| Wiedmannlj and Wolff.** The series arrange-
ment is mainly due to Paschen. In addition to the lines given, there are nearly 300
which have not yet been classified. Under certain conditions, mercury yields also
a " rich line spectrum," which was first observed by Eder and Valenta.tf
A large number of the mercury lines, even the sharp ones, are resolvable, under
high dispersion, into several components. J{ In general, only the mean wave-lengths
are included in the tables.
The limits Is of the principal series of triplets and 2S of the singlet series 2S mP
have been taken from Wiedmann, and corrected to the International Scale. The
other limits have then been calculated from observed lines.
The Hicks formula is found to be inadequate to express the series of mercury
except for the higher members. Generally speaking, for values of m lower than 5>
the formulae are not even approximately applicable.
* Proc. Roy. Soc., A. 98. 106 (1920).
t Zeit. f. Wiss. Phot., 14, 89 (1915).
J Kayser : Handbuch der Spektroscopie, 6.
Ann. d. Phys., 29, 662 (1909) ; 30, 750 (1909) ; 35, 869 (1911) ; Jahrb. d. Rad. u. Elek.,
8, 178.
|| Astrophys. Jour., 30, 48 (1909).
U Ann. d. Phys., 38, 1041 (1912).
** Ann. d. Phys., 42, 835 (1913).
ft Denk. Wien Akad., 61, 401 (1894).
tj Cardaun, loc. cit. Wendt, Dissert. Tubingen, 1911. Janicki, Ann. d. Phys., 39, (1912).
Nagaoka and Takamine, Proc. Phys. Soc., Vol. XV. (1912), &c., &c.
Zinc, Cadmium and Mercury.
147
Wiedmann has adopted a more complex grouping for the diffuse triplet series
than that given here. Each member of the series, according to his arrangement,
consists of one of the tabulated diffuse triplets (excluding the third chief line) together
with the corresponding member of the combination series IpmD. He then calls
attention to a remarkable relation between this series on the one hand, and an
association of the diffuse singlet series with the combination series IP md", d' ,
on the other. The wave-number differences between corresponding members are
found to be constant throughout the series, as shown in the following table for the
first two members. With the present classification of the series, however, this
relation is a necessary consequence, the constant differences being represented by
-\A i p *
lPi> 9t a J-t
m
Diffuse Singlets and IP md",d'.
Wave
Number
Differences.
Diffuse Triplets, as given by
Wiedmann.
X
V
V
X
10025-7
27290-2
3663-28
5790-66
17264-5
14656-5
31921-0
3131-84
16424-0
33688-5
2967-52
10025-8
27293-2
3662-88
2 i
5789-69
17267-4
14656-5
31923-9
3131-56
16423-8
33691-2
2967-28
10025-8
27353-3
3654-83
5769-60
17327-5
14656-5
31984-0
3125-66
10025-9
33021-2
3027-48
4347-50
22995-3
14656-7
37652-0
2655-13
10025-9
33041-6
3025-62
3 J
4343-64
23015-7
14656-8
37672-5
2653-68
16424-1
39439-8
2534-77
10026-0
33065-1
3023-47
4339-23
23039-1
14656-7
37695-8
2652-04
All the measures given in the tables are on the International Scale except those
of Wolff in the extreme ultra-violet. The infra-red measures of Paschen have been
adjusted in accordance with his correction of their original values. f
* Since the above was written it has been shown by II. Dingle (Proc. Roy. Soc., A. 100, 167)
that it is possible to regard the spectrum as exhibiting a system of quadruplet series, the separa-
tions in the subordinate series being respectively 10025-2, 4630-6, 1767-3. The suggested quad-
ruplat system includes all the terms of the tabulated triplet and singlet systems, with the excep-
tion of those of the sharp series of singlets.
t Ann. d. Phys., 36, 197 (1911).
L 2
148
Tables of Series Lines.
Hg TRIPLETS.
CHAP. XV.
PRINCIPAL . 1 s mp .
ls=21830-8.
DIFFUSE. Ip md.
lp 1 =40138-3; l 2 = 44768-9 ; l 3 =46536-2.
X, Int.
V
Av
w
*.*
X, Int.
V
Av
m
md", d', d
5460-74(10)
18307-5
4630-6
(1)
40138-3
3662-88 (4r)
27293-2
60-1
(2)
12845-1
4358-34(10)
22938-1
1767-3
44768-9
3654-83 (6)
27353-3
35-1
12785-0
4046-56(10)
24705-4
46536-2
3650-15(10)
27388-4
12749-9
4630-7
11287-15(10)
13673-09(6)
8857-3
7311-7
1545-6
145-5
(2)*
12973-5
14519-1
3131-56 (7)
3125-66 (8)
31923-9
31984-0
60-1
13950-76(2)
7166-2
14664-6
1767-3
2967-28 (5)
33691-2
6907-53(10)
14473-0
356-6
(3)
7357-8
7082-01(4)
14116-4
20-2
7714-4
70 92 -20 (Ir)
14096-2
*
7734-6
3025-62 (2)
33041-6
2
(3)
7096-5
3023-47 (4)
33065-1
*"O
7073-2
5803-55(4r)
17226-1
1 R4-0
(4)
4604-7
3021-50 (5)
33086-6
21-5
7051-7
t5859-32(4y)
17062-1
I VJTt \f
07.1
4768-7
4630-9
5872-12(2)
17025-0
Oil
4805-8
2653-68 (4)
37672-5
09.0
2652-04 (5)
37695-8
4O O
5354-05 (4y)
18672-4
Iflfi.O
(5)
3158-4
1767-3
J5384-70(3r)
18566-1
1UO o
U.Q
3264-7
2534-77 (4)
39439-8
5389-01(1)
18551-2
9
3279-6
5120-65(3r)
19523-4
fifi-9
(6)
2307-4
2805-42 (1)
35635-0
(4)
4502-7
5138-09(1)
19457-2
DO t
7.R
.
2373-6
2804-46 (2)
35647-1
10. K
4491-0
5140-10(1)
19449-6
I O
2381-2
2803-48 (4)
35659-6
lAtj
4478-7
4631-6
4980-82(3f)
20071-5
(7)
1759-3
2482-72 (3)
40266-6
11-5
4991-5(2)
20028-5
1802-3
2482-01 (4)
40278-1
1767-2
2378-34 (3)
42033-8
4890 -27 (2r)
20443-2
27-7
(8)
1387-6
4896-9 (1)
20415-5
~ ' t
1415-3
/ K\
3110-2
2699-50 (In)
37033-1
Q.Q
**
3104-5
4827-1 (2)
20710-7
21 -Q
(9)
1120-1
2698-85 (3)
37042-0
o &
3096-3
4832-2 (1)
20688-8
^ i \j
1142-0
4632-1
2399-74 (2)
41658-9
2399-38 (3)
41665-2
6-3
1767-0
2202-09 -(2n)
43425-9
Pi
V
Av m
m Pl
4782-1 (1)
20905-6
1(10)
925-2
2639-93 (3n)
2352-48 (In)
37868-8
42495-8
(6)
2279-4
2273-1
4748-1 (1)
21055-2
(11)
775-6
2258-87 (1)
44256-8
2269-5
4722-8 (1)
21168-0
.(12)
662-8
2603-15 (2n)
38403-8
(7)
4701-8 (1)
21262-5
(13)
568-3
2323-30 (In)
43029-5
1739-4
4685-3 (1)
21337-3
(14)
493-5
* Paschen hesitates between this triplet and
(12390-7), 13950-76, (?), the latter being indicated
4672-7 (1)
21394-8
(15)
436-0
by a formula. The line IS 2p z , however, after-
wards discovered by Wolff, indicates that the
4662-4 (1)
21442-3
(16)
388-5
above triplet is the true one.
t Has satellites X5860-10 and X5868-08.
4653-4 (1)
21483-8
(17)
347-0
j Has satellite X5385-79.
Zinc, Cadmium and Mercury.
Hg TRIPLETS Continued.
149
SHARP. Ip ms.
1/^ = 40138-3; l 2 = 44768-9 ; l 3 = 46536-2.
FUNDAMENTAL. 2d mf.
2^ = 12749-9 ; 2d' = 12785-0 ; 2d" =
= 12845-1.
X, Int.
v
Av
m
ms
X, Int.
v
m
mf
5460-74(10)
4358-34(10)
4046-56(10)
3341-48 (6)
2893-60 (5)
2752-78 (4)
2925-41 (4)
2576-29 (3)
2464-06 (2)
2759-70 (3)
2446-90 (2)
2345-43 (1)
2674-99 (2)
2379-99 (1)
18307-5
22938-1
24705-4
29918-3
34549-1
36316-4
34173-4
38804-2
40571-6
36225-3
40856-1
42623-5
37372-5
42004-6
4630-6
1767-3
4630-8
1767-3
4630-8
1767-4
4630-8
1767-4
4632-1
4630-8
<tf
(3F
(4)
(5)
(6)
(7)
21830-8
10219-9
5964-7
3912-8
2765-0
2057-5
1590-3
17193 (1)
17108-5(1)
16938-9 (2)
12020-2 (1)
5814-8
5843-5
5902-0
8317-2
(3)
(4)
6939-9
4433-6
*11886-6(1)
8410-6
COMBINATION. Ipmf.
X, Int.
v
v calc.
3011-05 (In)
2462-60 (1)
2524-71 (Ir)
2799-83 (2)
2478-1 (1)
2374-02 (2n)
33201-4
37830-5
39596-9
35706-1
40342-1
42110-2
!/>! 3/ = 33198-4
1 2 3/=37829-0
1^3 3/ = 39596-3
Ip i 4/ = 35704-7
1 2 4/=40335-3
lp 3 4/=42102-6
2625-24 (2)
2340-60 (1)
38080-7
42711-5
OTHER COMBINATIONS.
X, Int.
v
v calc.
3680-01 (5)
3050-46 (In)
3085-29 (In)
3144-48 (2r)
3305-09 (Ir)
2672-67 (In)
3135-76 (2n)
36258 (2)
23263 (3)
22489 (3)
27166-1
32772-5
32402-5
31792-6
30247-7
37404-9
31881-0
2757-3
4297-6
4445-4
\p v 2pi =27164-8
l/>i 3i =32780-5
Ip 1 Sp 3 = 32403-7
1^2 2/>! = 31795-4
Ip 2 2p 2 = 30249-8
1^3 2^3=31871-6
2p 1 2s = 2753-6
2p 2 2s = 4299-2
2p 3 2s = 4444-7
2593-41 (1)
38548-0
* Stated by Paschen to be a double line with
separation =10 A.U.
Hg SINGLETS.
PRINCIPAL. ISmP.
15 = 84178-5.
SHARP. IP mS.
!P=30112-8.
X
v
m
mP
X, Int.
v
m
mS
*1849-57
54065-7
(1)
30112-8
1849-57
54065-7
(1)
84178-5
*fl402-72
71290-6
(2)
12887-9
10139-67 (24)
9859-7
(2)
20253-1
4916-04 (4r)
20335-9
(3)
9776-9
4108-08 (2n)
24335-4
(4)
5777-4
DIFFUSE. lPmD.
3801-67 (2)
26296-8
(5)
3816-0
IP ^01 1 9-S
* X vac Wolff
X, Int.
v
m
mD
t Paschen obtains this
line by assuming
"xi ^'iTn-fis as tVif>
r.-1iii /-vf 9^
9lP T
5790-66 (lOr)
17264-5
(2)
12848-3
the truth of this, however, and the value of 2P
4347-50 (6)
22995-3
(3)
7117-5
which it gives leads to a line for Is
2P which
3906-40 (4n)
25591-8
(4)
4521-0
has not been observed, and
which is unexpect-
3704-22 (1)
26988-6
(5)
3124-2
edly close to Is 2p^ It is probable, therefore,
3592-97 (1)
27824-4
(6) ,
2288-4
that X1402-72 and X13570-68 do not take part
3524-27 (2)
28366-7
(7)
1746-1
in the above series, but are combination lines,
3478-98 (1)
28736-4
(8)
1376-4
associated by the fact that
their wave-number
3447-22 (1)
29001-0
(9)
1111-8
difference is equal to IS 2S.
150
Tables of Series Lines.
Hg SINGLETS Continued.
CHAP. XV,
FUNDAMENTAL 2D mF.
2D = 12848-3.
COMBINATION. 2S mP.
25=20253-1.
X, Int.
V
m
mF
X, Int.
v
m
iPt
16918-3 (2)
*11886-6 (1)
5909-2
8410-6
(3)
(4)
6939-1
4437-7
10139-67 (24)
13570-68 (?) (4)
6716-45 (?) (5)
6234-35 (8)
J5803-55 (4r)
5549-28 (3r)
5393-50 (2)
5290-1 (2)
5218-9 (2)
5165-8 (1)
5128-9 (1)
9859-7
7366-9 (?)
14884-8 (?)
16035-8
17226-1
18015-4
18535-8
18897-9
19155-7
19352-2
19492-0
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
30112-8
12886-2 (?)
5368-3 (?)
4217-3
3027-0
2237-7
1717-3
1355-2
1097-4
900-9
761-1
COMBINATION. IP mF.
!P=30112-8.
X
V
v calc.
4313-3 (1 v)
3893-89 (In)
23177-7
25674-2
IP 3P=23173-7
IP 4P=25675-1
* Stated by Paschen to be a double line with
separation=10 A.U.
f Used in calculation of Principal series.
J This line occurs also as Is 4/>,. It is very
diffuse, and is considered by Paschen to arise
:rom both sources.
Hg INTER-COMBINATIONS.
COMBINATION. lp mD.
!/>!= 40 138-3 ; l/> z =44768-9 ; l/> 3 =46536-2.
COMBINATION. IP md.
!P=30112-8.
X, Int
v
v calc.
X, Int.
v
v calc.
3663-28 (5)
3131-84 (7)
2967-52 (1)
3027-48 (2)
2655-13 (4)
*
27290-2
31921-0
33688-5
33021-2
37652-0
lp!2D =27290-0
Ip 2 2> = 31920-6
lp t 2D = 33687-9
lp! 3Z> = 33020-8
1 2 3>=37651-4
5789-69 (2)
5769-60 (lOr)
17267-4
17327-5
IP 2d"= 17267-7
IP 2d' = 17327-8
IP 3d"= 23016-3
IP 3d' = 23039-6
IP 4d"= 25610-1
IP 4^' = 25621-8
IP 5d"= 27002-6
IP 5d' = 27008-3
IP 6rf"= 27833-4
<
4343-64(2)
4339-23 (4)
23015-7
23039-1
2806-84 (1)
2483-83 (2)
2379-46
2700-92 (1)
2400-52 (0)
35616-9
40248-6
42013-8
37013-7
41645-4
Ip 3 AD J9418-7
lp 1 4D = 35617-3
lp z 4> = 40247-9
Ip 3 4Z)=42015-2
Tp!5D =37014-1
\p z 5D =41644-7
3903-64 (2)
3901-90 (2)
25609-9
25621-3
3702-36 (1)
3701-44(1)
27002-3
27008-8
Lp 3 oJJ 4d41/-0
3591-48(1)
3590-95(1)
27835-9
27840-0
COMBINATION. Ip 2 mS.
X
v
v calc.
IP 6d' 27839-7
IP Id' = 28373-4
IP 8d' =
2536-52 (lOw)
4077-83 (7r)
2856-94 (1)
2563-90 (1)
39412-6
24515-9
34992-4
38991-7
lp z 1S = 39409-6
Ip 2 2S= 24515-8
lp z 3S= 34992-0
\p z 4S= 38991-5
3523-00(1)
28377-2
* Probably hidden by strong diffuse line
X2536-52 (v=39412-6).
3477-85 (1)
28745-5
Zinc, Cadmium and Mercury,
Hg INTER-COMBINATIONS Continued.
COMBINATION. 15 mp 2 .
COMBINATION
LINE.
X, Int.
V
v calc.
X, Int.
v
v calc.
2536-52 (10)
"1435-63
39412-6
69655-8
lSl^ 2 = 39409-6
IS 2^2 = 69659-4
17071-54(2)
5856-2
2p l 3D=5856-0
COMBINATION.
Is mP.
COMBINATION. IP ms.
X
U
v calc.
X
V
v calc.
12070-23 (1)
?
6072-63 (5)
5675-86 (5)
5316-69 (3w)
5102-42 (2u)
4970-13 (10)
4883-1 (1)
4822-3 (1)
8282-7
?
16462-9
17614-5
18803-6
19593-1
20114-7
20474-6
20731-3
Is 1P= 8282-0
Is 3P= 16462-5
Is 4P= 17613-5
Is 5P= 18803-8
Is 6P= 19593-1
Is 7P= 20113-5
Is 8P= 20475-6
Is 9P= 20733-4
12070-23 (1)
5025-56 (3)
4140-03 (1)
3815-84(1)
8282-7
19892-8
24147-9
26199-3
IP ls= 8282-0
IP 2s = 19892-9
IP 3s = 24148-l
lP_4s = 26200-0
* X vac.. Wolff.
IONISED MERCURY (Hg+).
The enhanced lines of mercury do not appear to have been investigated in
relation to possible series. Rydberg, however, noted a pair of lines in the ultra-
violet which appeared to be analogous with the pairs of ionised zinc and cadmium
which have already been mentioned. The wave-lengths of these lines as given by
Cardaun are shown below, together with the wave-numbers and separation.
;., int.
v
Av
2847-83 (8)
2224-82 (3)
35104-16
44933-44
9829-3
These lines have been found to give Zeeman resolutions of the type of D 2 and
DI of sodium, and possibly represent a principal pair. They are among the enhanced
lines identified as such by Steinhausen.
For the pairs of Zn, Cd, Hg, the values of Av divided by the squares of the
atomic weights are respectively -204, -197, -246.
CHAPTER XVI.
GROUP IIlA. SCANDIUM, YTTRIUM, AND RARE EARTHS.
Series in the elements of this sub-group have not yet been clearly identified.
From analogy with previous groups it would be expected that the arc spectra would
resemble the elements of Group Hie., and give series of doublets. The spark spectra,
on the other hand, might show triplets. The difficulty of analysing the spectra is
increased by the fact that the (enhanced) lines of the ionised elements are well
developed even by the stimulus of the electric arc, and that the two spectra have
only been partially separated in most cases.
Hicks has stated* that he has found evidence of doublet series of 5 and D types
in Sc, Y, La and Yb, but details have only been given for Sc. A tentative arrange-
ment of the possible two series of this elementf suggested the limits Ijr 1 =37950 for
the sharp series, and ICT =22282 for the principal series, with the doublet separation
Av=320-8.
The question of constant differences in some of these spectra has been investi-
gated by Paulson, but the details are too extensive for quotation.
Probably the most important contribution to the analysis of the spectra is that
of Popow,| who based his results on observations of the effects of a magnetic field
which were made in Paschen's laboratory at Tubingen.
Popow did not succeed in identifying any complete series, but only some com-
bination groups, which will be best understood by reference to the corresponding
combinations of calcium or strontium. The combinations in question are those
indicated by Id 2p. Being connected with a triplet system, each term has three
values, but of the nine possible combinations only six appear. In the form adopted
by Popow, the strontium group, with our notation and numeration, would be repre-
sented thus :
15668 2p s
41
15649 60 15709 2p 2
105 105
15654 100 15754 w 15814 2^
Id U' U"
The^> and d terms may here be regarded as co-ordinates, and 15649, for instance,
is to be read as ld'2p z . The differences Id' Id, Id" Id' give the separations
of the fundamental series ; 2p 1 2p 2 , 2p 2 2p 3 give the separations in the second
member of the principal series.
Scandium (Sc. At. wt.=44'l ; At. No. =21). A combination group of this
type, according to Popow, is composed of the lines :
^ (Rowd.) v
2563-30 (2) 39000-8
60-35 (3) 045-6
55-90 (2) 113-7
52-46 (3) 166-2
45-24 (2) 276-99
40-94 (1) 344-05
* Phil. Trans., A. 212, 34 (1913).
f Hicks, Phil. Trans., A. 213, 409 (1914).
I Ann. d. Phys., 45, 163 (1914).
Scandium, yttrium and Rare Earths.
The suggested arrangement is as follows :
153
39166-23
d
110-76
39045-57
231-42
39276-99
d'
68-11
39000-80
112-88
39113-68
230-37
39344-05
d"
P2
Pi
In terms of the Ritz equation, Popow designates the group as 3^' 3p', which
becomes l(?2)d 2p in' the notation of the present report.
It is of importance to note that, according to the tables of Exner and Haschek,
the lines in question are probably of the enhanced type.
Yttrium (Y. At. wt.=88-8; At. No. =39). Two groups are given by Popow
for Yttrium, designated respectively 3d'2p J and 3^ 3p j . The wave-numbers are
23196-67
2d
22730-31
871-22
404-86 23601-53
204-96
204-64
22604-07
331-20
22935-27
870-90
23806-17
2d"
30832-61
2d
404-84
31077-98
159-47
31237-45
204-86
204-85
31207-57
75-27
31282-84
159"46
31442-30
2d"
It may be deduced that the separations of the narrow triplets of the fundamental
series are probably 405 and 205, while those of the first member of the principal series,
and therefore the main separations in the subordinate series, would be 870 and 331.
Lines of the first group are included among the enhanced lines given by Lockyer ;
those of the second group were not within the range of his investigation, and the
observations of Exner and Haschek merely indicate that with one exception the lines
are strong in both arc and spark.
Lanthanum (La. At. wt. =139-0 ; At. No. =57). The following group for
lanthanum is given by Popow as the combination 3d i 3p J :
29953-03
2d
29568-35
1043-44
30611-79
2d'
696-43
696-62
29889-59
375-19
30264-78
1043-63
31308-41
2d"
The separation A^ (=658-76) is here smaller than 6d (=696-6), whereas in the
other elements considered it is greater. An irregularity in the arrangement of the
154 Tables of Series Lines. CHAP. xvi.
satellites in the related diffuse triplets is therefore suggested, if the combinations
have been correctly identified.
The available evidence does not very strongly point to the above lines being of
the enhanced type, but Exner and Haschek's observations suggest that two of the
lines are enhanced. In the visible spectrum the only enhanced lines tabulated as
such by Lockyer are H192-5 and 4099-7.
From the data for Sc and Y, Popow deduces the formulae
0-529 log A^>=log A -0-395
0-652 log dp=\og A -0-305
where A=Ai. wt. ; &P=p 2 pi', dp = =Pzp-i
He then calculates that for Al, A_/>=92, <5^>=53-5, which do not compare favour-
ably with the separations of the probable triplet, 128, 64. It may be observed, how-
ever, that in the atomic weight relation Al belongs to the Ga, In, Tl sub- group, and
agreement need not be expected with the elements of the first sub-group. At alt
events, in the first and second groups the sub-groups do not show a common atomic
weight relation.
The general result of the discussion of the three elements is to suggest that the
enhanced lines probably form triplet series.
Of the " rare earths " having atomic numbers ranging from 57 to 71, many have
been examined by Paulson* for " constant differences." Numerous lines of this-
class have been found, but it is scarcely possible to give any useful summary of the
results. Europium, however, is possibly of special interest, as in some arrangements
of the periodic table it is suggested that this element should fall in Group II., between
Cd and Hg. Paulson finds four pairs of strong lines with separation 1669-7, and
twelve weaker pairs with the same separation. Hicks, t on the other hand, considers
that the spectrum consists of triplets, having separations 2631 and 1004, the limit
of the sharp series (Sjoo ) being 40364. The diffuse series suggested by Hicks, how-
ever, is very imperfect, and the question cannot be considered settled one way or
the other.
As bearing on the place of gadolinium in the periodic table, Hicks thinks it
probable that this element falls in Group IIlB., between indium and thallium, on
the ground that there is a large number of doublets of separation about 5000. No-
details are given, and this separation does not appear among those noted by Paulson.
There are no data relating to the spectrum of actinium.
* Astrophys. Jour., 40, 298 (1914). See also p. 26.
f Phil. Trans., A. 212, 59 (1913).
CHAPTER XVII.
GROUP IIlB. THE ALUMINIUM SUB-GROUP.
The arc spectra of the elements Al, Ga, In, and Tl, forming a sub-group of
Group III. of the periodic table, present series of doublets. The subordinate series
were early identified by Rydberg and by Kayser and Runge, and the principal series
were afterwards found by Paschen. The series have a general resemblance to those
of the alkali metals, but the separations are greater as compared with the increase of
atomic weights. Also, in these spectra the first principal pair occurs with negative
sign, and the other members of the principal series lie on the red side of the sub-
ordinate series, whereas in the alkali metals the principal series lie on the more
refrangible side of the sharp and diffuse series. As in the case of the alkali metals,
there are very few lines which have not been placed in one or other of the four main
series, or are to be accounted for as combinations.
The spectrum of boron probably lies mainly in the region of short wave-lengths,
and complete series have not yet been traced.
Little progress has been made in the detection of regularity in the spark spectra
of these elements.
BORON.
B. At. wt. =11-0; At. No. =5.
The arc spectrum of boron in the region ordinarily observed is of remarkable
simplicity, consisting of a close pair of lines in the ultra-violet, for which wave-
lengths have been given by several observers. The values from Rowland's measures
are :
"k v Av
2497-73 (KM?) 40024-3
96-78 (8R) 039-6
Rydberg was probably right in supposing this to be the first pair of the sharp
and principal series, but the formulae which he suggested for the series depended
upon the use of spark lines, and are probably therefore of no significance.
Dr. M. A. Catalan * has recently drawn attention to a second pair of arc lines,
observed by Sr. Pifia de Rubies, which have a separation practically identical with
that of the original pair, namely
A v Av
2089-49 47843-2
88-84 58-1
An extension of the observations into the region of shorter wave-lengths would
seem to be necessary for the calculation of formulae, but meanwhile the observations
are of interest as indicating the separation in the doublets constituting the series.
As many as seventeen lines were observed in the spark. spectrum by Eder and
Valenta, but, with specially pure material, only three lines were found byCrookes,f
two of which form the pair at /2497, while the third has the wave-length 3451-35.
* An. Soc. Espanola Fis. y Quim., 15, No. 38 (1917).
t Proc. Roy. Soc., A. 86, 36 (1911).
156
Tables of Series Lines.
Al DOUBLETS.
CHAP. XVII.
PRINCIPAL, la mTT.
lc = 22933-27.
DIFFUSE. ITC m8.
ln l =48168-84; l7T 2 = 48280-91.
X, Int.
v
Av
m
mn 1>2
X, Int. v [ Av
m
m8', 8
3961-540(107?)
25235-60
m-01
(1)
48168-87
3092-843(67?)
32323-36
1-33
(2)
15845-49
3944-032(107?)
347-61
\J 1
280-88
92-716(107?)
324-69
844-15
112-04
13125-36
7616-
79
J K.OO
(2)
15316-48
3082-159(107?)
32435-40
13151-65
01-
67
1 1
331-70
6696-064 (3)
14930-03
_
(3)
8003-24
2575-411(37?)
38817-13
4-49
(3)
9351-71
98-734 (3)
924-08
09-19
75-113(107?)
821-62
47-22
112-07
5557-08 (In)
17990-08
2-82
(4)
4943-19
2567-997(107?)
38929-20
57-95 (In)
987-26
46-01
*5105-14
19582-
7
2-0
(5)
3350-6
2373-360(27?)
42121-49
4-04
(4)
6047-37
* 05-64
580-
7
\J
52-6
73-132(87?)
125-53
)0
43-31
SHARP. In ma.
2367-064(87?)
42233-52
L'o
iTTj =48168-84 ;
I7r 2 =48280-91.
X, Int.
v
Av
yft win
2269-212(27?)
44054-51
2.^1
(5)
4114-33
3961-540(107?)
44-032(107?)
25235-60
347-61
112-01
(i)
22933-27
69-093(47?)
2263-453(47?)
056-82
44166-58
Ol
112-07
12-09
2660-393(107?)
52-484(107?)
37577-28
689-31
112-03
(2)
10591-58
2210-046(27?)
45233-78
(6)
2935-96
2378-408 (3)
72-084 (3)
42032-08
144-14.
112-06
(3)
6136-76
04-627(27?)
344-95
35-06
2174-028(17?)
45983-10
(7)
2187-09
2263-731 (2)
44161-16
68-805(17?)
46093-82
85-74
57-999 (2
273-2-5
112-09
(4)
4007-67
" v \ /
2150-59 (1)
46484-2
(8)
1684-3
*f2204-66 (4)
45344-3
45-39 (1)
596-9
2199-64 (1)
447-7
(5)
2833-2
\ /
2134-70 (1)
46830-2
(9)
1336-9
Al COMBINATIONS.
29-44 (1)
945-8
X, Int. v
v calc.
*2123-38 (1)
47079-9
(10)
1091-0
21166-3 4723-23
271! 2a =4724-90
* 18-52 (1)
187-8
21098-2 4738-47
27T 2 2a =4740-12
16752-2 5967-76
27^ 38 =5969-26
FUNDAMENTAL. 28 my.
16720-5 5979-07
27T 2 38' =5979-99
28 = 15844-8.
X v Av
m
m
* 2426-14(4r) 41205-2
iKi 89 =41206-3
* 19-56(21-) 317-2
I7t 2 39 =41318-3
11255-5 8882-2
(3)
6962-6
* 2312-48(2) 43230-4
iTCj 47UJ 43225-7
8774-7 11393-3
(4)
4451-5
* 2231 -20 (lr) 44804-9
iTTj 57T! =44818-3
Unclassified Lines of Al.
* 25-70(lr) 915-7
l7T 2 5TC 2 =44928-3
X, Int.
v
X
v
* Kayser and Runge (other lines by Paschen or
Griinter) .
3066-16 (4)
32604-6
2321-57 (2)
43060-7
t Confused with a 8 line.
64-30 (4)
624-4
J19-05 (2)
107-9
t This and three following lines are given as arc
lines by K.R., butHuppers records them only in the
aark.
59-93 (2)
57-16 (5)
54-70 (4)
671-0
700-6
726-9
17-48 (2)
14-98 (2)
13-53 (2)
137-1
183-7
210-7
Satellites not seen beyond this.
50-08 (4)
776-6
The Aluminium Sub-Group. 157
ALUMINIUM.
Al. At. wt.=27-l ; At. No. =13.
An excellent series of measures of the lines constituting the arc spectrum of
aluminium was made by Kayser and Runge, and it is still necessary to make use of
their determinations of some of the fainter lines. Wave-lengths of arc and spark lines
on the new scale have been determined over a long range (6929-2129) by R. Griinter,*
and in the region more refrangible than A3200 by W. Huppers.f Measures in the
region 2500-1850 have also been given for the spark by Eder.J
The vacuum arc spectrum in the Schumann region has been observed by
McLennan, but no connection of the lines with the established series has been
recognised. It should be observed that the vacuum arc usually develops spark lines,
so that the true arc lines in this region, if any, are not known.
Reference has already been made (p. 39) to the abnormal arrangement of the
satellites, and to the difficulty of representing the diffuse series by a simple formula.
The adopted limits are based upon those calculated by Dunz for the sharp
series.
IONISED ALUMINIUM (A1+).
Enhanced lines of aluminium are numerous and well marked, but no series
have yet been traced. The most recent measures are those of Griinter, which
extend from the red to the ultra-violet. The spark lines in the Schumann region
have been tabulated, and a photograph reproduced, by Lyman.||
In connection with Kossel and Sommerfeld's " displacement law " (p. 74),
according to which the ionised elements of the Al sub-group should exhibit triplet
series, it should be noted that Popow^j had previously directed attention to the
following triplets, which may represent Al + :
X vac.
V
Av
1765-7 (8)
56635
122
61-9 (8)
757
61
60-0 (8)
818
1725-0 (10)
21-2 (9)
57971
58099
128
64
19-3 (9)
163
The second triplet is quite isolated, but the first occurs as part of a group of
five lines, and some doubt is thrown upon its assignment to Al + by the fact that
McLennan did not observe the third line in the vacuum arc.
GALLIUM.
Ga. At. wt.=69-9 ; At. No. =31.
Very few lines have been observed in the spectrum of gallium, but it is possible
that the records are incomplete in consequence of difficulty in obtaining material
for experiment. While the spectrum was almost unknown, Rydberg made an
* Zeit. f. Wiss. Phot., 13, 1 (1914).
t Ibid., 13, 46.
j Ibid., 13, 20 ; 14, 137 (1915).
Proc. Roy. Soc., A. 95, 323 (1919).
!| " Spectroscopy of the Bxtreme Ultra- Violet."
Tf Ann. d. Phys., 45, 166 (1914).
158
Tables of Series Lines.
CHAP. XVII.
interesting calculation of the formulae for the subordinate series by interpolation
from the constants for related elements. For the limits of the subordinate series he
deduced 47390 and 48222, and the calculated positions of some of the lines were
not very widely different from those subsequently observed. Our knowledge of
the series has been extended by Paschen and Meissner,* whose observations have
been utilised in the table which follows. All the known arc lines are included in
the table.
Exner and Haschek have recorded nine lines which are special to the spark
spectrum in the region A4172 to /2450, and other spark lines were recorded in the
visible spectrum by the discoverer of gallium, Lecoq de Boisbaudran.f
Ga DOUBLETS.
PRINCIPAL, la mit.
10 = 23591-5.
DIFFUSE. ITT mS.
lTT 1 =47553-8 ; l7T 2 =48379-8.
X, Int.
V
Av
TO
mn lt2
X, Int
V
Av
m
wS', 8
4172-06 (30 R)
4033-03 (3OR)
*[11940]
*[12096]
6396-89
6413-77
5353-81
59-8
23962-3
24788-3
[8373]
[8265]
15628-3
587-2
18673-1
652-2
826-0
41-1
20-9
(1)
(2)
.(3)
(4)
47553-8
48379-8
[15218]
[15326]
7963-2
8004-3
4918-4
39-3
2944-18 (5.ff)
43-66 (IOR)
2874-24 (IOR)
33955-4
961-4
34781-6
6-0
826-2
(2)
(3)
13598-3
592-4
7577-1
68-7
2500-18 (2R)
2450-10 (2R)
39985-1
STl.
40802-7
COMBINATION.
SHARP. ITT ma.
lTT 1 =47553-8 ; l7T 2 = 48379-8.
X
V
v calc.
X, Int.
V
Av
m
TOO
3020-49 (3)
33097-6
lTC 2 27T 2
qonru
4172-06 (30)
4033-03 (30)
2719-66 (3)
2659-84 (2)
23962-3
24788-3
36758-5
37585-1
826-0
826-6
(1)
(2)
23591-5
10795-0
* Calculated lines.
INDIUM.
In. At. wt. =-114-8 ; At. No. =49.
The sharp and diffuse series of indium doublets were identified by Kayser and
Runge, and by Rydberg, and the principal series by Paschen and Meissner. $ The
limits adopted for the subordinate series are those determined from the sharp series
by Johanson. These lead to a limit for the principal series which is almost identical
with that calculated independently by Paschen and Meissner (22294-9). As in
aluminium, the satellite in the first diffuse pair is abnormally close to the chief
line.
The wave-lengths, other than for the principal series, are due to Kayser and
Runge. The infra-red region has not been observed, and the fundamental series
* Ann. d. Phys., 43, 1223 (1914).
t Comptes Rendus, 82, 168 (1876).
{ Ann. d. Phys., 43, 1223 (1914).
The Aluminium Sub-Group.
In DOUBLETS.
159
PRINCIPAL, la WTI.
1(1=22294-8.
DIFFUSE. ITT mS.
17^=44455-3 ; l7T 2 =46667-9.
X, Int.
V
Av
m
m*i,,
X, Int.
V
Av
m
m8', 8
4511-27 (10.R)
4101-72 (SR)
22160-5
24373-1
2212-6
(1)
44455-3
46667-9
3258-52 (QR)
56-03 (IOR)
30679-9
703-4
23-5
2212-5
(2)
13775-4
751-9
(2)
[14519]
[14811]
3039-34 (1QR)
32892-4
6847-77 (8)
6900-37 (6)
14599-3
488-0
111-3
(3)
7695-5
7806-8
2713-95 (QR)
10-28 (IOR)
36835-8
885-7
49-9
2212-5
(3)
7619-5
7569-6
5209-75 (5)
28-27 (4)
17509-1
452-5
56-6
(4)
4785-7
4842-3
2560-16 (SR)
39048-3
5253-97 (3)
62-38 (2)
19027-9
18997-5
30-4
(5)
3266-9
97-3
2522-99 (4R)
21-36 (SR)
39623-6
649-2
25-6
2212-3
(4)
4831-8
06-1
5017-5 (1)
23-0 (0)
19924-7
902-9
21-8
(6)
2370-1
91-9
2389-56 (SR)
41835-9
4878-8 (0)
20491-1
(7)
1803-7
2430-7 (IR)
29-68 (IR)
41127-9
145-2
17-3
2210-7
(5)
3328-3
10-1
SHARP. ITU ma.
17^=44455-3 ; l7C 2 =46667-9.
2306-7 (IR)
43338-6
(6)
2443-6
45-4
X, Int.
V
Av
m
WCT
4511-27 (IOR)
4101-72 (IOR)
22160-5
24373-1
2212-6
(1)
22294-8
2379-66 (IR)
42009-9
2932-60 (6R)
2753-87 (6R)
34089-4
36301-8
2212-4
(2)
10366-0
2260-5 (IR)
44224-3
m8'
2601-75 (6R)
2460-06 (6R)
2468-01 (4R)
2340-22 (QR)
2399-25 (4R)
2278-2 (Ifl)
*2357-6 (IR)
2241-5 (Ifl)
38424-2
40637-0
40506-2
42717-9
41667-0
43880-6
42403-1
44599-1
2212-8
2211-7
2213-6
(3)
(4)
(5)
(6)
6031-0
3949-5
2787-8
2068-8
2230-8 (IR)
2211-1 (IR)
2197-4 (IR)
2187-4 (IR)
2179-9 (IR)
44813
45212
45494
45702
45859
(7)
(8)
(9)
(10)
(11)
1855
1456
1174
966
809
In COMBINATIONS.
X, Int.
V
v calc.
2720-00 (2)
2565-50 (2)
2572-62 (2r)
36753-9
38967-1
38859-3
ITT! 37T 1 = 36759-8
l7T 2 37^=38972-4
l7T 2 37T 2 =38861-1
2218-2 (IR)
2199-9 (1J?)
45068
45442
(7)
(8)
1600
1226
2666-23 (2)
37495-0
iTt! 3<p = 37495-0f
* X possibly in error.
t 3cp assumed=6960-3, which is a probable
value.
i6o
Tables of Series Lines.
CHAP. XVII.
In DOUBLETS Continued.
Unclassified Lines of In.*
\ Int.
V
X, Int.
V
4108-84 (\R)
3610-50 (1 ?)
3261-06 (2 ?)
3186-79 (1)
3066-30 (\R)
51-19 (1)
51-07 (4)
2957-02 (2R)
24330-9
27689-1
30656-0
31429-6
32603-1
764-7
765-9
33808-0
2858-19 (1)
58-08 (1)
36-90 (3R)
2775-36 (1)
2470-57 (2 ?)
34976-9
978-2
35239-4
36020-7
40464-2
* All except the last are from Exner and
Haschek. *
has accordingly not yet been identified. As in other elements of this sub-group,
nearly all the arc lines have been classified. Only one of Kayser and Runge's lines
is outstanding, but twelve faint lines given by Exner and Haschek do not appear
to be capable of explanation as combinations.
The spark spectrum shows some characteristic lines, but possible series have
not been investigated. Rydberg, however, called attention to two pairs of lines
having a separation Av=7926, according to Hartley and Adeney's wave-lengths.
The more accurate measures by Exner and Haschek, however, do not confirm the
equality of the separations. The lines in question are (in I. A.) :
A, Int.
V
Av
3835-0 (3n)
2941-28 (10)
26068-3
33988-9
7920-6
2890-24 (4)
2350-76 (1)
34589-0
42526-4
7937-4
Measures of the spark spectrum on the international scale have been made by
Schulemann,* covering the region A7455 2264, and giving a large number of lines
not recorded by other observers. For the above pairs, his values give the separations
as 7922-74 and 7937-84.
THALLIUM.
Tl. At. wt. =204-0; At. No. =81.
The series spectrum of thallium is well developed, and consists of widely-
separated pairs, so that while one component of the first principal pair lies in the
green, the other is in the ultra-violet. Thallium is remarkable for the easy reversal
of most of the series lines.
The most complete measures of the arc spectrum are those of Paschen, and
Kayser and Runge, whose wave-lengths have been adopted from the red to A2129.
Beyond this, the only published wave-lengths of the series lines are those determined
by Cornu.f which are subject to considerable uncertainty. A list of wave-lengths
from 3229 to 2210 has been given by Huppers,J but is too incomplete for our present
purpose. The series are tabulated as given by Dunz, with the figures corrected to the
international system, and a few additional combinations. The limits of the sub-
* Zeit. f. Wiss. Phot., 10, 263 (1912).
t Jour, de Phys., (2) 5, 93 (1886).
j Zeit. f. Wiss. Phot., 13, 74 (1914).
The Aluminium Sub-Group.
Tl DOUBLETS.
161
PRINCIPAL, la mn.
lcr=22786-7.
DIFFUSE. ITT mS.
lTC 1 =41471-5; l7T 2 =49264-2.
X , Int.
V
Av
m
WTC 1>2
X, Int.
V
Av
m
mS', 8
5350-46 (\OR) 18684-8
7792-7
(1)
41471-5
3529-43 (8R)
28325-2
82-0
(2)
13146-2
3775-72 (10J2)
26477-5
49264-2
19-24 (10.R)
407-2
064-3
11513-22
13013-8
8683-3
7682-1
1001-2
(2)
14103-4
15104-6
2767-87 (10 R)
36118-2
7793-0
6549-77 (8)
15263-5
372-7
(3)
7523-2
2921-52 (QR)
34218-8
37-5
(3)
7252-8
6713-69 (6)
14890-8
7895-9
18-32 (10 R)
256-3
15-2
5527-90 (4)
83-98 (2)
18085-0*
17903-4
181-6
(4)
4701-7
4883-3
2379-58 (8R)
42011-3
7792-5
5109-47 (2)
19566-1
IAJ..O
(5)
3220-6
2710-67 (45)
36880-4
19-6
(4)
4591-6
36-84 (I)
461-8
1U4 o
3324-9
09-23 (SR)
900-0
71-5
7791-6
4891-11 (2)
4906-3 (2)
20439-6
376-3
63-3
(6)
2347-1
2410-4
2237-84 (6R)
44672-0
4760-6 (1)
20999-9
QA.fi
(7)
1786-8
2609-77 (4R)
38306-1
11-5
(5)
3165-8
68-5 (1)
965-1
O*
1821-6
08-99 (6fl)
317-6
53-9
7791-9
4678-1 (3)
4617-2 (2)
21370-2
21652-1
(8)
(9)
1416-5
1134-6
2168-61 (4:R)
46098-0
4574-6 (1)
4547-9 (0)
21853-7
21982-0
(10)
(U)
933-0
804-7
f2552-98 (ZR)
52-53 (QR)
39158-1
165-1
7-0
(6)
2314-7
06-4
SHARP. ITC ma.
7790-0
17^=41471-5 ; l7t 2 =49264-2.
2129-33 (IR)
46948-1
X, Int.
V
Av
m
ma
2517-41 (4#)
39711-4
(7)
mo
1760-1
J2105-0
47491
5350-46 (107?)
3775-72 (10.R)
18684-8
26477-5
7792-7
(1)
22786-7
2493-91 (2R)
40085-6
(8)
1385-9
2088-7
47861
\ /
3229-75 (10.R)
2580-14 (8R)
30953-2
38746-0
7792-8
(2)
10518-3
2477-49 (Ifl)
40351-2
(9)
1120-3
2077-2
48126
\ v l
2826-16 (8R)
2315-93 (QR)
35373-3
43166-0
7792-7
(3)
6098-2
2465-46 (IR)
2069-1
40548-0
48315
(10)
923-5
2665-57 (2w)
2207-06 (4#)
37504-3
45295-0
7790-7
(4)
3968-2
2456-45 (IR)
2062-2
40696-9
48476
(U)
774-6
2585-59 (4fl)
2152-01 (IR)
38664-4
46453-5
7789-1
(5)
2808-9
2449-49 (IR)
2057-2
40812-5
48594
(12)
659-0
2538-18 (2R)
12119-1
39386-5
47174-6
(6)
2085-0
2443-92 (IR)
2053-8
40905-8
48675
(13)
565-7
2507-94 (IR)
2098-4
39861-3
47640-1
(7)
1610-2
2439-50 (1.R)
40979-6
(14)
491-9
2487-48 (IR)
2083-1
40189-2
47989-9
(8)
1282-3
FUNDAMENTAL. 28 mcp.
28=13064-3; 28' = 13146-2.
2472-57 (IR)
OHTO.Q
40431-5
<4Q9JiV.9
(9)
1040-0
X
V
Av
m
my
-U /Z o
*2461-93 (IR)
*&6'.\J-*
40606-2
(10)
865-3
16340-3
16123-0
6118-2
6200-7
82-5
(3)
6945-8
*2453-79 (1.R)
40741-0
(U)
730-5
*2447-51 (IR)
*2442-16 (IR)
40845-5
40935-0
(12)
(13)
626-0
536-5
11594-5
11482-2
8622-4
8706-8
84-4
(*)
4440-7
* More refrangible components not recorded.
t Satellites not observed beyond this pair.
(5)
[3077-0]
J This and smaller wave-lengths may be much
in error.
9170-7
10901-3
(6)
2244-9?
M
l62
Tables of Series Lines.
Tl COMBINATIONS.
CHAP. XVII.
COMBINATIONS lo mS.
lo=22786-7.
COMBINATIONS 2^ mS.
X
v
v calc.
X, Int.
v
v calc.
51057-9
14592-6
12736-4
10496-4
9512-4
9136-1
8376-1
14515-5
10492-5
1958-0
6851-0
7849-4
9524-5
10509-7
10942-6
11935-5
6887-3
| 9528-1
10292-3
6420-45 (1)
5488-79 (2)
5093-28 (1)
9713-4
15570-9
18213-9
19628-2
lo 28= 9722-4
1038 = 15571-5
1048 = 18215-2
lo_58 = 19632-8
27^38' =
27t 2 38' =
2^48' =
2rr 2 48' =
1958-4
= 6850-6
= 7851-8
= 9511-8
= 10513-0
COMBINATIONS nm mo.
27T 2 58' =
= 10937-6
= 11938-8
X
v
v calc.
27TJ 38 -
= 6888-2
27889-6
21803-0
12491-8
7-023 \L
5-559[z
3584-6
4585-3
8003-7
1423-5
1798-6
2:r 1 2o = 3585-1
27T 2 2o = 4586-3
27T! 3o-8005-2
27T! 48 =
= 9531-9
COMBINATIONS 38 my.
37^30 = 1425-0
37T 2 3o 1797-7
X
v
v calc.
3-505 p
3-568[z
2781
2803
38 49=2774-5
38' 49=2812-1
COMBINATIONS ITT ;WTT.
X, Int.
v
v calc.
Unclassified Lines of Tl.
*3652-95 (In)
2945-04 (4r)
f2719-10 (1)
2977-93 (lr)
f2843-27 (1)
2416-70 (lr)
27367-3
33945-5
36766-1
33570-6
35160-5
41366-1
l7T 1 27r 1 =27368-1
iTij 37T! =33948-3
l7T 1 4TC 1 = 36769-8
iTTj 3ru 2 = 33575-6
lTT 2 27^ =35160-8
l7T 2 37t 2 =41368-3
X
v
X
v
7-117(z
3-92865 {Jt
3-92155
2-70276?
2-70237
2-13979
2-04858
1-45978
1-16907
3230-6 (1)
2210-73 (2R)
1404-7
2544-7
2549-3
3698-9
3699-4
4672-1 !
4880-1 ;
6848-5
8551-4
30945-1
45219-8,
J2671-10 (2w)
2669-95 (1)
2577-67 (1)
2532-71 (In)
2530-80 (In)
2512-59 (1)
2434-05 (1)
2417-01 (2)
37426-7
37442-8
38783-1
39471-6
39501-3
39787-5
41071-3
41360-8
COMBINATIONS ITT my.
X, Int.
v
v calc.
2895-41 (4)
2362-08 (2v)
2700-2 (2n)
34527-3
42322-7
37023-3
iTTi 39 = 34525-7
I7t 2 39 = 42318-4
iTtj 49 = 37030-8
COMBINATIONS 2o mn.
2o = 10518-3.
* Not given by Dunz.
t Given by Huppers.
j This and succeeding lines are given by
Huppers, not by Kayser and Runge. The
first, second, fifth, and seventh are given
in spark by Eder and Valenta.
X
v
v calc.
33393-2
38131-0
2993-8
2621-8
2o STTJ =2995-1
2o37T 2 =2622-4
ordinate series were calculated by Dunz from the sharp series. It will be seen that
nearly all the lines are included in the recognised series.
The enhanced lines do not appear to have been investigated for series relation-
ships. The vacuum-arc and spark spectra in the region A1908 to A1477 have been
observed by McLennan.*
The sharp series is not well represented by most of the ordinary formulae. For
wave-numbers on the Rowland system, however, Johanson has obtained a fair
agreement by his formula (see p. 36) with the constants A =41469-33 ; ^=2-261774 ;.
a=l-672006: b = 1-937964.
* Proc. Roy. Soc., A. 98, 108 (1920).
CHAPTER XVIII.
ELEMENTS OF GROUPS IV. AND V.
ELEMENTS OF GROUP IV.
There are no published records of the discovery of typical series in the spectra
of any of the elements of this group. Constant difference groups, however, were
found by Kayser and Runge in the spectra of lead and tin which have been verified
with remarkable accuracy in Kayser's laboratory by Klein* and Arnolds f
respectively. In the arc spectrum of lead there are 10 lines differing in wave-number
by 10807-4:3 from 10 other lines, and these, again, by 2831-2 from other more
refrangible lines. Similarly, for the arc lines of tin there are 10 sets of three lines
for which the separations are 5185-43 and 1735-84.
In the spectrum of tin LohuizenJ has suggested two groups of parallel series,
which he has called " translation series." Thus, he gives six series with limits
45307-40, 50494-43, 50926-14, 52330-66, 53507-27, 53924-00, for all of which the
terms " mx " are given by ]V/(w+l-651360 657-42^- 1 ) 2 ; and three series having
limits 43825-00, 49012-03, 50748-26, with the variable terms given by
JV/(w-f-l-384406+446-70A~ 1 ) 2 . The number of lines in a series ranges from three
to five.
In germanium (Ge. At. wt.=72-5; At. No. = 32) Paulson finds three triplets
with separations of 1416, 903, and two pairs with a separation equal to the sum
of these.
Constant difference pairs have also been noted by Paulson among the arc lines
of titanium, with separations of 71, 64, 779, or 1166. Only a small proportion of
the lines of this element are included.
As regards the remaining elements of Group IV., carbon and silicon, some
unpublished results obtained by the writer are of interest and may be briefly
mentioned.
Carbon (C. At. wt. = 12-0 ; At. No. = 6). The arc spectrum of carbon shows only
one line, A2478, in the whole range of spectrum from the extreme red to A2000.
It is possible that there may be other arc lines in the Schumann region, but the
spectrum has not been obtained under conditions which permit them to be
distinguished as such with certainty. Observations in this region have been made
by Wolff, McLennan,|| and Millikan.^
In the spark spectrum of carbon, C + , the writer has established doublet series
for which Ar=10-8 and which have 4Af for the series constant as in other series of
ionised elements. With greater energy, a triplet is developed near A4647, having
Av=13-0, 5-5 ; this may possibly represent C++, or the second-step ionisation, but
it has not yet been possible to prove this by establishing the triplet as a member
of a system of series having $N for constant. With the greatest energy, as Merton**
* Zeit. f. Wiss. Phot., 12, 16 (1913).
t Ibid., 13, 313 (1913).
J Proc. Roy. Acad. Amsterdam, April, 1912.
Ann. d. Phys., 42, 837 (1913).
|| Proc. Roy. Soc., A. 95, 272, 327 (1919).
|j Astrophys. Jour., 52, 59 (1920).
** Proc. Roy. Soc., A. 91, 498 (1915).
M2
164 Tables of Series Lines. CHAP. xvm.
has shown, certain other lines are developed in the carbon spectrum which correspond
with lines in the spectra of Wolf-Rayet stars. The wave-lengths of the most
prominent of these are 5812 and 5801, forming a pair with Av=31-4. This may
perhaps represent a third-step ionisation, but the evidence for this is not complete.
Silicon (Si. At. wt. =28-3; At. No. = 14). Lockyer has shown that successive
spectra are developed in this element as the energy of excitation is increased, and he
has designated them Si I., Si II., Si III., and Si IV., the first representing the arc
spectrum. These observations, however, covered too restricted a range of spectrum
for the investigation of series, and have been extended by the writer.
Evidence has been obtained that the arc spectrum, Si I., includes a system of
triplets, in which Av=146, 77. There is a diffuse triplet, with a normal set of
satellites, a normal sharp triplet, certain other triplets not yet classified, and a
number of pairs having separations of 146 or 77. Series formulae have not been
calculated, but the lines in question are undoubted arc lines.
The spark spectrum, Si II., shows a system of doublets in which Av=60-0.
The principal, sharp, and diffuse series are well represented in the spectrum under
suitable conditions of experiment, and the series constant for them is definitely 4AT.
The doublets are therefore to be assigned to ionised silicon, Si + .
Additional triplets associated with that observed in Si III. by Lockyer have
been obtained, but not yet in sufficient number to allow of the definite calculation
of the series constant. It is not improbable, however, that the triplets represent
the second-step ionisation, for which the constant would be 9AT, and they may be
provisionally assigned to Si ++ .
Lockyer's Si IV. was represented by a well-known pair in the violet. The
separation Av is 164, and three other pairs with the same separation have now been
found in the ultra-violet. Further observations in the Schumann region may
establish the character of these pairs, but meanwhile it may be supposed possible
that they represent the third-step ionisation, Si + + + .
It should be noted that the separations of the doublets and triplets in the
successive spectra of silicon are related to the corresponding separations in carbon
in very close proportion to the squares of the atomic weights.
These observations of carbon and silicon are of special interest in connection
with Kossel and Sommerfeld's displacement law to which reference has already been
made (p. 74).
ELEMENTS OF GROUP V.
No series have been identified in any of the elements of this group. Constant
difference lines, however, were noted by Kayser and Runge in the spectra of arsenic,
antimony and bismuth, and in other elements of the group by Paulson. In all
cases, the constant separations refer to pairs of lines, two or more separations being
involved.
It is scarcely possible to summarise the data usefully, and reference must be
made to the original sources.*
In the case of nitrogen, it should be observed that Stark and Hardtkef have
obtained a spectrum which they have described as the arc spectrum. The more
familiar line spectrum thus becomes the probable spark spectrum, N+. Prior
to Hardtke's work, certain lines developed under a more powerful stimulus were
* Kayser's Handbuch, Vol. II., and Paulson's papers previously quoted,
t Ann. d. Phys., 56, 363 (1918.)
Elements of Groups IV. and V.
165
obtained by Lockyer, Baxandall, and Butler, and described as the enhanced lines of
nitrogen. This spectrum was afterwards described more completely by Fowler,*
and should, perhaps, be considered to represent the second-step ionisation, or N++.
The matter is of some importance in connection with Kossel and Sommerfeld's
suggestive displacement law, and the following particulars of pairs of lines may be
quoted :
A LA.
V
Ar
Probable principal pair
/ 4097-33 (10)
\4103-39 (8)
24399-30
363-22
36-08
Probable diffuse pair
(4641-91 (3)
\ 40-65 (10)
I 34-17 (8)
21536-84
542-70
572-83
5-86
35-99
Possible sharp pair ...
(4867-14 (4)
\ 58-82 (3)
20540-23
575-40
35-17
The measures of the last pair are less satisfactory than those of the first two.
* Monthly Notices R.A.S.,80. C92 (1920).
CHAPTER XIX.
GROUP VI. OXYGEN, SULPHUR, AND SELENIUM.
Our knowledge of the series lines of the elements of this sub-group is due to Runge
and Paschen.* Each element shows two distinct line spectra, which are well known
under the names of the " compound line " and " elementary line " spectra. These
names were assigned to the oxygen spectra by Schuster, f and were adopted by
Kayser for the corresponding spectra of sulphur and selenium. The two spectra are
developed respectively by uncondensed discharges and condensed discharges of
moderate intensity, and the names given by Schuster were based upon the sup-
position that complex and simplified molecular groupings were involved in the two
cases. The compound line spectra were distinguished as the " series spectra " of
the respective elements by Runge and Paschen.
When powerful condensed discharges are employed, a third system of lines is
produced in oxygenj and sulphur, ^ and it would seem convenient, provisionally,
to follow the plan adopted by Lockyer in the case of silicon, and to distinguish the
compound line, the elementary line and the third line spectra by adding I, II, III to
the chemical symbol of the element, as 0. I, O. II, O. Ill, &c. In general terms,
the three spectra have been described as the arc, spark and super-spark spectra.
Intermediate stages may be readily obtained by suitable adjustment of the gas
pressure, diameter of capillary tube and intensity of discharge.
It is only in the first line spectra that series have at present been identified.
OXYGEN.
O. At. wt. =16-00; At.No.=8.
The compound line, or O. I, spectrum of oxygen exhibits a system of narrow
triplets, and a system which was at first described as consisting of doublets. The
latter, however, were only partially resolved, and the separation was only given for
one line of the sharp series, namely :
A6046-348 (7) =vl 6534-34
A6046- 120 (2) =4 6534-97
Since most other spectra which show triplets also show singlet series, but never
doublets, it is possible that the oxygen series in question may really consist of single
lines. ] | They have been entered as singlets in the table.
The first principal triplet shows separations Ar=3-4, 2-7, according to the
* Ann. d. Phys., 61, 641 (1897) ; Astrophys. Jour., 8, 70 (1898).
t Phil. Trans., 170, 41 (1879).
J Fowler and Brooksbank, Monthly Not. R.A.S., 77, 511 (1917).
Lockyer, Proc. Roy. Soc., A. 80, 55 (1907).
II See also Sommerfeld, Ann. d. Phys., 63, 224 (1920). Recent investigations by Dr. Cataliin,
however, have suggested that the members of this system may be very narrow triplets.
Oxygen, Sulphur and Selenium.
167
measures of Runge and Paschen ; the more recent determinations by Meggers and
Kiess* are
A
V
Av
7771-928
74-138
75-433
12863-28
859-62
857-49
3-66
2-13
and the intervals are thus brought into closer accordance with the separations of
the triplets of the subordinate series. It may be recalled that the principal triplet
occurs in the solar spectrum, and has its origin in the solar atmosphere.
The limits given in the tables have been adapted from those calculated for the
sharp series by Dunz. The fundamental series should be in the infra-red, where
observations have not yet been made.
Among the unclassified lines of O. I are two " inverted " wider triplets, with mean
separations 7-7 and 12-6, which Hicksf has suggested may be united with /5037 of
the D series in a " new diffuse series," for which he has calculated the limit 22926.
A considerable number of lines of O. I have been observed in the ultra-violet by
Schniederjost.J but their relation to the established series, if any, has not yet been
traced. The wave-lengths of these lines are included in the table of unclassified lines.
In the spectrum of O. II, six pairs of lines, with separation Av=179-9,have been
identified by the writer, but the series arrangement remains to be discovered.
O "SINGLETS.
PRINCIPAL. IS mP.
15 = 33043-3.
DIFFUSE. IP mD.
!P=21207-2.
X, Int.
V
m
mP
X, Int. v
m \ mD
8446-38
11836-1
(1)
21207-2
11287-3 1 8857-2
(2)
12350-0
4368-30 (10)
22885-8
(2)
10157-5
7002-22 (4) 14277-3
(3)
6929-9
3692-44 (7)
27074-7
(3)
5968-6
5958-53 (<od) 16778-0
(4)
4429-2
5512-71 (5d) 18134-9
(5)
3072-3
SHARP. IPmS.
5275-08(4) 18951-8
(6)
2255-4
!P = 21207-2. 3 lg>
5130-53 (3) 19485-8
(?)
1721-4
X, Int.
v m
mS
5037-16 (2n) \ 19846-9
4972-87 (In) ! 20103-5
()
(9)
1360-3
1103-7
8446-38
11836-1
(1)\
33043-3
-
13163-7
7594-7
(2)
' 13612-5
7254-05 (2)
13781-6
(3)
7425-6
6046-34 (Id)
16534-4
(4)
4672-8
5554-94 (6d)
17997-0
(5)
3210-2
5299-00 (5)
18866-3
(6)
2340-9
5146-06 (5)
19426-9
(7)
1780-3
5047-70 (2n)
19805-5
(8)
1401-7
4979-55 (In)
20076-6 (9)
1130-6
* Scientific Papers, Bureau of Standards, Washington, No. 324, p. 644 (1918).
f Phil. Trans., A , 213, 368 (1914).
J Zeit. . Wiss. Phot., 2, 266 (1904).
Tables of Series Lines.
CHAP. XIX.
O TRIPLETS.
PRINCIPAL. 1* mp.
DIFFUSE. \p md.
ls = 36069-0.
1/^=23205-8 ; l 2 =23209-2 ;
X, Int.
Av
in
.
lp 3 =23211-9.
Pl'2'3
.
,
7771-97 (10)
12863-2
3-4
(1)
23205-8
' n '
V
V
YYl
m
74-01 (8)
859-8
2-7
209-2
[9266-57]
10788-5
"""^
75-68 (6)
857-1
211-9
9263-88
791-7
y 2 )
12417-3
3947-33 (10)
25326-5
1-2
(2)
10742-5
47-51 (7)
325-3
0-6
743-7
6158-20 (10)
16234-0
3.0
47-61 (4)
324-7
734-3
56-78 (8)
K K f\(\ t r 7\
237-8
o
2-1
(3)
6971-7
SHARP. Ip ms.
55-99 (7)
239-9
l^ 1 =23205-8 ; l 2 =23209-2 ;
l 3 =23211-9.
5330-66 (10)
29-59 (7)
18754-2
68-0
3-8
21
(4)
4451-5
X, Int.
V
Av
m
ms
28-98 (6)
60-1
1
7771-97
12863-2
4968-76 (6)
20120-2
3-6
74-01
859-8
3-4
2m
(1)
36069-0
67-86 (5)
123-8
1-9
(5)
3085-7
76-68
857-1
7
67-40 (4)
125-7
11300
8847-3
4773-76 (5)
20942-0
294
8852-0
(2)
14358-5
72-89 (4)
945-8
1-6
(6)
2263-9
294
8852-0
72-54 (3)
947-4
6456-07 (9)
15485-0
4655-36 (4)
21474-6
3.1
54-55 (7)
63-69 (6)
488-7
490-7
3-7
2-0
(3)
7720-8
54-56 (3)
54-23 (2)
478-3
479-8
i
1-5
(7)
1731-4
5436-83 (8)
35-78 (6)
18388-0
391-5
3-5
2-1
(4)
4817-9
4577-66 (3)
76-79 (2d)
21839-1
843-3
(8)
1367-1
35-16(5)
393-6
4523-53
22100-5
1 Ultl- 1
5020-13 (5)
19914-3
3-1
22-78 (d)
104-1
1 1UO 1
19-34 (4)
917-4
2-2
(5)
3291-9
18-78 (3)
919-6
4803-00 (4)
20814-5
3-5
02-20 (3)
818-0
1-7
(6)
2391-6
01-80 (2)
819-7
4673-70 (3)
21390-4
72-75\
72-75/ (3d)
394-7
394-7
(7)
1815-7
4589-89 (3)
21780-9
88-98\. 2 ,.
785-3
(8)
1425-1
8o'98 J
785-3
Oxygen, Sulphur and Selenium.
169
O TRIPLETS Continued.
Unclassified Lines of O. I.
(Runge & Paschen.)
(Schniederjost.)
X, Int.
f V
Av
X, Int.
X
X
6266-85 (1)
15952-6
2897-31 (2w)
2672-79 (1) i
2352-53 (2)
64-57 (1)
958-4
7.9
95-26 (3)
38-90 (2)
25-26 (3)
61-47 (3)
966-3
12-4
83-82 (4)
07-42 (2)
2299-86 (3)
56-60 (1)
978-7
81-74 (2)
2577-84 (2) j
14-55 (2)
5995-48 (4)
16674-6
58-70 (1)
50-55 (1)
2189-92 (2)
92-45 (3)
683-0
-i
2786-07 (1)
04-58 (2)
37-5 (1)
50-60 (5)
800-4
53-37 (1)
2474-37 (2)
12-3 (1)
5410-76 (3)
18476-6
7-4
23-47 (1)
45-97 (3)
08-59 (4)
(\A. 07 /q\
484-0
AQfi.7
12-7
08-08 (1)
19-56 (3)
4233-32
23615-5
Oxygen Lines in infra-red* (Kiess).
22-78
674-4
X, Int.
V
Av
17-09
706-4
3830-26
25-07
23-56
26100-5
135-9
146-3
8233-05 (<1)
30-05 (<1)
21-84 (1)
12142-83
147-25
159-39
4-42
12-14
2883-84
34665-9
7952-22 (<1)
12571-66
2-18
50-84 (1)
573-84
5-15
* Pop. Ast.,29, 19(1921).
' 47-58 (2)
578-99
7481-27 (<1)
13363-04
3-64
79-23 (<1)
366-68
4-74
76-58 (1)
371-42
SULPHUR.
S. At. wt. =32-07 ; At. No. = 16.
The compound line spectrum of sulphur (S. I) is found only in vacuum tube
observations. Nearly all the lines are included in a system of triplets resemtling
those of O. I, but having a wider separation. Some of the earlier members of the
series have not yet been observed. The limits of s and d have been adapted from
those given by Dunz.
It should be noted that the p series is not indicated by Dunz, and that the first
p triplet, which lies in the infra-red and outside the range of the observations, has
been calculated from the Rydberg relations. Thus, the limit lp l having been
determined from the d series, we have
Observed p^
.. ^=1-336781
=2p 1 = 9850-7
=15-2^=21297-0
ls=31147-7
=20085-5
Calculated ^(1) =11062-2
170
Tables of Series Lines.
CHAP. XIX.
The position thus assigned to ^(l) depends solely upon the Rydberg formula,
and is probably not exact, but it might have been sufficiently near to suggest a
combination which would have indicated the necessary correction.
S TRIPLETS.
PRINCIPAL. Is mp.
Is = [31 147-7].
DIFFUSE. \p md.
1^ = 20085-5; l 2 = 20103-4; l 3 =20114-7.
X, Int. v
Av
m
pi,*,s
X, Int. v
Av I m
wftt
[11062-2]
[ 044-3]
[ 033-0]
4694-18 (TO) 21297-0
95-51 (8) 291-0
96-31 (6) 287-4
17-9
11-3
6-0
3-6
(1)
(2)
20085-5
103-4
114-7
F9850-7]
[ 56-7]
[ 60-3]
6757-16 (7)
48-83 (6)
43-69 (5)
6052-75 (7)
46-01' (6)
41-95 (5)
5706-22 (8)
00-36 (7)
5696-80 (6)
5506-98 (5)
01-56 (3)
5498-16 (3)
5380-99 (4)
75-78 (3)
72-62 (2)
5295-69 (4)
90-72 (4)
87-71 (2)
14795-1
813-3
824-6
16516-9
535-3
546-4
17519-9
537-9
548-8
18153-7
171-6
182-9
18578-8
596-8
607-7
18878-0
895-8
906-5
18-2
11-3
18-4
11-1
18-0
10-9
17-9
11-3
18-0
10-9
17-8
10-7
(4)
(5)
(6)
(7)
(8)
(9)
5290-2
3568-3
2565-7
1931-8
1506-8
1207-8
SHARP. Ip tns.
1^ = 20085-5 ; l 2 = 20103-4 ; l 3 = 201U-7.
X, Int.
v
Av
m
ms
6415-47 (4)
08-11 (3)
03-49 (2)
5889-86 (2)
83-52 (2)
79-57 (1)
5614-26 (5)
08-65 (4)
05-30 (3)
5449-78 (3)
44-37 (2)
15583-0
600-9
612-2
16973-6
991-9
17003-3
17806-9
824-7
835-3
18344-3
362-5
17-9
11-3
18-3
11-4
17-8
10-6
18-2
(4)7
(5)
(6)
(7)
4502-5
3111-6
2278-9
1741-1
Unclassified Lines of S continued.
X, Int.
v
Av
6175-80 (1)
73-56 (1)
*5279-02 (6)
78-64 (5)
78-14 (3)
16187-8
193-6
18937-6
939-0
40-8
5-8
1-4
1-8
Unclassified Lines of S.
X, Int. v
Av
7241-7 (2) 13805-1
6538-60 (1) 15289-6
36-33 (1) 294-9
6396-69 (1) 15628-8 '
94-89 (1) 633-2
5-3
4-4
* Compare with isolated triple group in Se.
SELENIUM.
Se. At. wt.=79-2; At. No. =34.
The compound line spectrum of selenium (Se I.) generally resembles the
corresponding spectrum of sulphur. In the diffuse series of triplets, however,
many of the brighter components are accompanied by fainter lines or satellites
which are not arranged in the normal way. The first line of a triplet appears to
Oxygen, Sulphur and Selenium.
Se TRIPLETS.
171
PRINCIPAL. Ismp.
DIFFUSE. Ipmd.
Is = [30699-0].
l/> 1 = 19267-7; l 2 = 19371-4 ; l 3 = 19416-2.
X, Int.
V
Av
m
>P\, 2, 3
X, Int.
V
Av
m
md
[11431-3]
(1)
19267-7
7061-88(5)
14156-7*
(4)
5112-5
r
327-6]
371-4
103-5
4
L
r
282-8]
416-2
7013-98(3)
14253-3
L
10-58(3)
260-2*
4731-04(10)
39-28(9)
21131-9
095-2
36-7
U-4-
(2)
[9567-1]
[9603-8]
6990-71(4d?)
14300-8*
40-6
42-58(8)
080-8
^
[9618-2]
6325-60(6)
15804-4
(5)
3462-1
SHARP. \p ms.
25-2 (1)
805-4*
103-7
lp! = 19267-7 ;
l/> 2 = 19371-4; 1^3 = 19416-2.
6284-30(3)
15908-3
X, Int.
V
Av
m
ms
83-98(1)
909-1*!
45-3
6746-42(6)
6699-55(6)
14818-6
922-3
103-7
44-8
(4)
4449-1
6269-07(3)
66-15(4)
15946-9
954-4*
79-49(5)
967-1
6177-66(3)
38-30(2)
16182-9
286-6
103-7
44-1
(5)
3085-0
5961-86(5)
61-5 (1)
16768-7
769-7*
103-5
(6)
2498-2
21-74(2)
330-7
5925-09(1)
16872-7
5878-66(2)
42-88(2)
27-68(1)
17006-0
110-0
154-7
104-0
44-7
(6)
2261-5
24-91(4)
5909-27(2)
06-88(2)
873-2*
16917-9*
924-7
44-7
5700-10(3)
17538-7
103-3
5666-73(3)
52-40(3)
642-0
686-7
44-7
(7)
1729-3
5753-30(7)
52-09(2)
17376-5
380-2*
(7)
1887-9
103-4
t Unclassified Lines of Se I.
5718-3 (1)
18-06(7)
17482-9
483-6*
X, Int.
V
Av
K'7(\A.QRt'y\
1 7^9^-8
44-2
6831-04(5)
14635-0
o i(jt'yo(o)
03-64(4)
X i Qo o
527-8*
6701-06(1)
14918-9
6283-33(2)
15910-8
6135-31(1)
16294-6
5617-83(5)
17795-5*
(8)
1472-2
5866-31(2)
17041-8
5374-08(10)
18602-7
14-6
5528-42(4)
18083-3*
(9)
1184-3
5369-85(10)
18617-3
15-5
103-9
5365-40 (8)
18632-8
5496-85(3)
18187-2*
* Lines tabulated for diffuse series by
Dunz.
to t
5464-61(3) 18294-5
(10)
973-2
oome ot tne lines tauuiateu unuer
diffuse series should possibly be included
under this head.
172 Tables of Series Lines. CHAP. xix.
have a satellite on the more refrangible side, while the second has a satellite on the
less refrangible side ; the third line in three of the triplets also has a companion of
nearly the same brightness as itself.
The normal triplet separations of the sharp series are found in the diffuse series,,
as shown in the table, but a satisfactory interpretation of the relationships of the
remaining components has not been reached. The observations of d(4) may be
considered incomplete, as are also those of ^(8), d(9), and ^(10). Those of ^(5),.
^ 1 (6), and d^(l] suggest that in the first member of the triplet the satellite occupies
the normal position, while the chief component is abnormally displaced to the red.
A similar abnormal displacement is shown by d z (5), but d z (G) and d z (l} show the
chief line in the normal position and the satellite displaced to the red. The third
member in d(5) and d(l] has its companion on the red side, but in d 3 (6) the
companion is on the violet side. There is no very marked regularity in the
separations of the chief lines and their companions.
The limits of s and d have been adopted from Dunz, with a small correction
for the change to the international scale. The limit of the principal series has been
calculated as in the case of sulphur.
The vacuum arc spectrum of selenium in the region A2296 A1432 has been
observed by McLennan.*
OTHER ELEMENTS OF GROUP VI.
Constant difference pairs have been noted by Paulson in molybdenum and
tungsten, but no regular series have been recognised. Some of the spectra are
extremely complicated.
Proc. Roy. Soc., A. 98, 103 (1920).
CHAPTER XX.
ELEMENTS OF GROUPS VII. AND VIII.
Elements of Group VII. Little progress has been made in the analysis of the
spectra of the elements of this group.
Measures of fluorine of sufficient accuracy do not extend over a large range,
and further investigations are much to be desired. There are some narrow triplets
in the spectrum, which are produced under experimental conditions suggesting that
they may belong to the ionised atoms.
Chlorine, according to Paulson, shows a few triplets with Av about 67, 41, and
some pairs with one or other of these separations, or their sum. The proper classi-
fication of the lines as arc or enhanced lines calls for further experimental investigation.
Paulson has found numerous constant difference pairs in bromine and iodine.
The arc spectrum of manganese, as shown by Kayser and Runge, appears to
include a system of triplets, of which they recognised five members. The wave-
lengths given below are from an extensive investigation of the manganese arc spec-
trum by Fuchs.* The members of the first diffuse triplet are involved in groups of
lines, and it is doubtful which of the components should be taken. Several are
entered in the table, and the Av correspond with the lines marked with an asterisk.
The entire spectrum contains many hundreds of lines, and the series call for further
investigation.
A few constant difference pairs, and two narrow triplets with separations 14-2
and 8-7 have been noted by Paulson.
Mn TRIPLETS.
SHARP. \p ms.
l/>! =41224-4 ; 1 2 =41398-1 ; l 3 =41527-2.
DIFFUSE. \p md.
1^ = 41224-4; 1 2 =41398-1 ; l 3 =41527-2.
X, Int.
V
Av
m
ms
X, Int.
V
Av
m
md
4823-52 (10)
20726-0
173-7
3570-10(41?)
28002-4*
(2)
13222-4
4783-43 (8)
20899-7
129-1
(2)
20498-4
3569-80(87?)
28004-8
4754-05 (10)
21028-8
3569-50(67?)
28007-1
173-1
3548-17(47?)
28175-5*
3178-51 (8w)
31452-2
m.7
3548-02(47?)
28176-7
3161-06 (4)
31625-9
i
1 2Q-2
(3)
9772-2
129-0
3148-19 (4)
31755-1
I &o
3532-11(57?)
28303-6
3532-00(57?)
28304-5*
3531-84(47?)
28305-8
2940-40(6w)
33999-0
172-2
(3)
72266
2925-59(6n)
34171-2
128-6
2914-62(8w)
34299-8
2726-15(4n)
36670-9
173-1
W
4554-4
2713-35(3w)
36844-0
127-6
2703-98(3w)
a6971-6
Elements of Group VIII. No series have been detected in any of the elements of
this group, but Paulson has found many constant difference groups, the details of
which are too extensive for quotation. ,
* Zeit. f. Wiss. Phot., 14, 239, 263 (1915).
CHAPTER XXT.
THE INERT GASES.
In addition to helium this group of elements includes neon, argon, krypton,
xenon and niton (radium emanation). The spectra are very complex, and it is only
in the case of neon that series arrangements have been disentangled. In argon,
krypton and xenon, however, it has been found possible to arrange many of the lines
in groups showing constant differences of wave-number.
The spectra of neon, argon, krypton and xenon have been discussed at great
length by Hicks,* following his own special methods, but the results cannot be briefly
summarised.
NEON.
Ne. At. wt. = 20-2; At. No. = 10.
The first extensive measures of the lines of neon were made by Baly,f who
observed more than 800 lines in the region A 7000 to A 3500. Accurate measures
of the lines in the less refrangible part of the spectrum have since been made by
Meissner,} and also of many lines in this region by Burns, Meggers and Merrill,
many of which are interferometer determinations. Several hundreds of lines have
also lately been accurately measured by Paschen.
Watson || was the first to note that many of the strong lines of neon could be
arranged in groups of three or four, having constant wave-number separations.
These are exhibited with remarkable accuracy by the Washington measures. Fifteen
groups of such lines were found, of which seven are complete quadruplets ; five lack
the second member, one lacks the third, and in two the second and fourth members
are wanting. Three examples may be quoted :
X, Int.
Vj- 4 AV
8082-45 (3)
7438-902 (6)
7245-167 (8)
7032-413 (9)
12369-09
13439-149
13798-507
14215-957
1070-06
359-36
417-45
7024-049 (3)
6532-883 (4)
6382-991 (8)
6217-280 (4)
14232-885
15302-958
15662-316
16079-765
1070-073
359-358
417-449
6717-043 (5)
6266-495 (7)
6128-44 (3)
5975-534 (4)
14883-402
15953-481
16312-87
16730-282
1070-079
359-39
417-41
Two sets of apparent doublet series were traced by Rossilf with separation about
* Phil. Trans., A. 220, 335-468 (1920).
t Phil. Trans., A. 202, 183 (1904).
J Ann. d. Phys., 51, 115 (1916) ; 58, 333 (1919). Phys. Zeit., 17, 549 (1916).
Scientific Papers, Bureau of Standards, Washington, No. 329 (1918).
|| Astrophys. Jour., 33, 399 (1911).
If Phil. Mag., 26, 981 (1913).
The Inert Gases.
167 and converging to the same limits near 24105 and 24272. Several additional series
were afterwards recognised by Meissner. All these are included in a masterly analysis,
of the neon spectrum which has been set forth by Paschen in two recent papers.*
The spectrum differs from those which have previously been described in having an
extraordinarily large number of series. Thus, Paschen finds four series of s terms,,
ten of p terms, and twelve of d terms. f The values of the first terms, with Paschen's
notation, are as follows :
s terms.
p terms.
d terms.
l-5s 2 = 38040-731
2p! = 20958-718
3s 1 =11493-777
l-5s 3 = 39110-808
2 2 = 22891-003
3s x ' =11509-498
l-5s 4 = 39470-160
2/> 3 = 23012-015
3! " =11519-257
l-5s s = 39887-610
2 4 =23070-944
3s x '" = 11520-818
*!-5s 3 l-5s 2 = 1070-077
2^5 = 23157-342
3rf x =12228-051
l-5s 4 l-5s 3 = 359-352
2p 6 = 23613-586
3di ' =12229-816
l-5s 5 l-5s 4 = 417-450
2 7 = 23807-852
3d 3 =12292-853
2p 8 =24105-229
3d s =12322-259
2/> 9 =24272-411
3^4 =12337-323
2/> 10 = 25671-654
3^ 4 ' =12339-151
3d s =12405-233
3d e =12419-875
* These are the constant difference values previously noted.
The possible number of combinations is thus very large, but not all of them appear
in the spectrum. For example, of the 40 possible principal series l-5s mp, 30 are
actually observed, and there are similarly 30 sharp series ; of the possible 120 series of
diffuse type, 72 have been identified.
A large number of these series were found to be represented with remarkable -
accuracy by the Ritz formula : namely the 72 series :
l-5s 2 ^
l-5s 4 / mpQ
2^> 6 - 9 |
i-io
md.
md/
md*
-md s
J -ws 4
j- -ws 5
l-5s 2 - 6 -
L
l-5s 2
l-5s 4 [ mp s
l-5s 5 J
l-5s
Owing to the inter-relations between these series, it is sufficient to calculate one
limit. The one selected by Paschen was l-5s 5 , and the adopted value was the mean
from the four series l-5s 5 mp 6 ^ 9 . The terms 2p 6 ~ 9 thus became known, and it
was then possible to calculate md-^, md^', md 2 , md s , md^, md^, md 5 , md 6 , w 4 ,.,
ms & , l-5s 2 , l-5s 3 . Then from md 2 , &c., the remaining 2p terms were found ; namely
*Ann. d. Phys., 60, 405 (1919) ; 63, 201 (1920).
f In the first paper, four series terms designated s/, s/', s
s type, but in the second paper these are classed as of d type.
i'" were considered to be of
176 Tables of Series Lines. CHAP. xxi.
2p lt 2,3,4,5, 10- Thus, all the limits and terms of the above series could be determined,
namely :
2^1-5 2^> 6 _9 2/> 10 l-5s 2 1'5* 3 l-5s 4 , 5 3d Sd^' 3^ 2 -4 3^ 4 ' 3^ 5 , 6
"r6-9 **OS 4 ,j 4 1 4 1 4 2 -4 4 4 4:*5>6
These terms being known, the following combination lines were found to exist :
2i-8io 1-5*2 1-5*2.4 2i l-5s 2>4 -2p 3 l-5s 8 - 5 2 5
2^2.5.7.10 1-5*3 1-5*2-5 2^2 1-5*2,4.5 2 ^4 I'SSjj.g 2/> 10
The lines thus indicated were the first lines of additional series, and it was natural
to take the limits of such series as 2/> 1 _ 8 , 10 , l-5s 2 , 4 , &c. When this was done, however,
the terms of the new series did not follow any known type of series formula. With
limits calculated independently, from the actual lines, the series were nevertheless
of the ordinary type. Two alternatives were therefore open : (1) to preserve the
limits indicated by the combination principle and to assert the series to be abnormal;
(2) to calculate the limits from the Ritz formula and to abandon or modify the combi-
nation principle. In his first paper Paschen adopted the first alternative and pro-
posed new types of formulae ; in the second paper he adopted the second alternative.
Besides the above, the following 28 series were also found :
The terms ms^, ms^', ms^", wSj"" are new and do not arise from the combination
principle. There appears, therefore, to be no obvious reason why A should be identified
with any of the known terms. Paschen, however, called it 2p and again got " abnor-
mal " series. The only justification for this procedure seems to be that the limits
calculated by the Ritz formula were identical with those of some of the series for
which the above alternatives were open. As before, the second alternative was finally
adopted.
The main points in the above arguments may be illustrated by the following
numerical calculations :
1.5; 5 =39887-610-05 (from the 4 Ritz type series l-5s 5 w 6 _ 9 )
First lines of l-5s 5 w., 7 , g are v=46274-02, 16079-76, 15782-38
.-. 2/> 6 =23613-59 ; 2/> 7 =23807-85 ; 2^ 8 =24105-23
First lines of l-5s g m^ e>7>8 are v=U27-U, 14232-88, 13935-51
23613-59+14427-14=38040-73
l-5s = mean of
23807-85+14232-88= -73
=38040-73
24105-23+13935-51= -74
First lines of l-5s 4 w/> 6 , 7 , 8 are 15856-57, 15662-31, 15364-93
23613-59+15856-57=39470-16 \
l-5s 4 = mean of
23807-85+15662-31= -16 1=39470-16
24105-23+15364-93= -16 J
Jirst lines of 2/> 4 ws 4 , 5 are 16399-22, 16816-67.
/ 39470-16-16399-22=23070-94 )
of \ 39887 . 61 _ 16816 . 67= . 94 } =23070-94.
The Inert Gases. 177
If there be a combination line l-5s 2 2/> 4 , its wave-number should be
r=38040-73-23070-94=14969-79.
There is a line in this position, and it is the first member of the series :
14969-79
27819-95
32490-07
34708-57
35939-3
This series is accordingly designated l-5; 2 w/> 4 where l-5s a =38040-73. In
this form, however, the series is abnormal, and in his first paper Paschen represented
it by the formula
109694-8*
- "=38040-73-- 0^746753 ~ .
(^w -0-0232537 + +0-06 1 229 \e m '-)
If the entire Ritz formula for the series be calculated, however, the limit being
regarded as unknown, the limit is found to be 38821-10, and the series is well repre-
sented. The relative accuracy of the two formulae is indicated by the following
residuals 0C.
5 6
0-00 3-50
+0-21 -3-42
When the Ritz limit 38821-10 is adopted, the values of the terms for the above
lines are 23851-31, 11001-15, 6331-03, &c., and these naturally follow the Ritz
formula. If, however, the limit l-5s a (=38040-73) be adopted, then, since 38821-10
=38040-73+780-37, these terms would be decreased by 780-37, and would become
23070-94, 10220-78, 5550-66, &c. These do not obey the Ritz formula, and in order
to make them do so they must be increased by 780-37. Paschen actually adopts
l-5s 2 for the limit, and the terms mp^ are calculated accordingly ; for comparison
with the Ritz formula, he then uses terms " (mp^ reduced," which are equivalent
to w/> 4 +780-37. And similarly for the other series of this character.
Altogether, there are 48 series with the limits thus displaced by about 780
units, 2 with displacements of about 730, 4 with 763, 2 with 40, and 4 with
displacements of 10 units. That is, the limits calculated by the Ritz formula
differ by these amounts from those indicated by the combinations which give
the first lines of the series. The significance of these displacements is not yet
understood.
Besides these 60 " abnormal " series, there are the 72 normal series previously
indicated.
* This is Paschen's value for the series constant of neon calculated in accordance with the
quantum theory.
N
m
2
3
4
Av
(Paschen)
+0-01
0-00
+5-83
Ai>
(Ritz)
0-00
-0-12
0-12
178
Tables of Series Lines.
CHAP. XXI.
The following table shows the wave-lengths, intensities, and classification of
some of the well-known strong lines of neon, together with the Zeeman effects
when known :
X
Int.
Series.
Zeeman type.
6717-042
6266-495
5852-488
2
15
50
1 -5s 2 2p 5
l-5s s 2p s
Normal triplet.
6074-337
5400-556
10
50
l-5s t 2p a
l-5s t 2p 1
3/2 Normal triplet.
3/2
6506-527
15
l-6s t 2pi
6402-246
20
l-5s & 2p s
6334-428
5975-534
10
12
l-5s 5 2p g
1-5*, 2/> 5
A second spectrum of neon, developed under the action of a condensed dis-
charge, has been observed by Merton,* but no investigations of series in this
spectrum have been published.
ARGON.
A. At. wt.=39-9; At. No. = 18.
Two spectra are given by argon. That obtained with the uncondensed dis-
charge has its strongest lines in the less refrangible regions, and is called the " red
spectrum," while that developed by the condensed discharge has its brightest lines
in the blue, and is called the " blue spectrum."
Rydbergf found that most of the lines between A4702 and A2967 in the red
spectrum could be arranged in quadruplets having constant separations, and the
same arrangement was afterwards found by PaulsonJ to extend to the less refrangible
parts of the spectrum. If the first line of each quadruplet be designated A, and
succeeding ones B, C, D, it results that
B=A+ 846-47
C=A +1649-68
D=A +2256-71
A 1= =846-47
A 2 =803-21
A 3 =607-03
Some of the " quadruplets " are incomplete, exhibiting only two or three
members, and no simple regularity of intensities is evident. Neither Rydberg nor
Kayser and Runge succeeded in tracing anything of the nature of the typical series
spectra.
* Proc. Roy. Soc., A. 89. 447 (1914).
t Astrophys. Jour., 6, 338 (1897).
t Phys. Zeit., 15, 831 (1914).
More accurate determinations of the wave-lengths and separations have since been pub-
lished by Meggers (Scientific Papers, Bureau of Standards, Washington, No. 414, 1921).
The Inert Gases.
179
Groups of lines in the blue spectrum, some of them incomplete, were also found
by Paulson.* These may be represented by the following expressions :
B=A+ 84449
C=A +2455-82
D=A +2605-37
=4 +2759-34
A!= 844-49
A 2 =1611-33
A 3 = 149-55
A 4 = 153-97
There are also numerous pairs of lines in the spectrum having the differences
AJ, A 2 , A 3 , A 4 , or C A, DA, &c.
A preliminary analysis of the spectrum of argon, following the methods adopted
by Paschen for neon, has been made by Nissen.f
KRYPTON.
Kr. At. wt. =-82-9; At. No. =36.
The original determinations of krypton lines by BalyJ have recently been supple-
mented by some very accurate measurements in the region A8929-6421 made by
Merrill at Washington. A first inspection of the latter measures revealed three
additional pairs of the type discovered by Paulson. || The eight pairs are given by
Merrill as follows :
X, Int.
Av
X, Int.
Av
8776-73 (3)
8104-33 (7)
945-06
5870-90 (10)
5562-23 (6)
944-96
8298-07 (6)
7694-53 (8)
945-00
4502-39 (9)
4318-58 (8)
945-06
8190-02 (6)
7601-55(20)
944-97
4463-71 (10)
4283-01 (4)
944-95
5879-84 (1)
5570-28 (10)
944-99
4453-95 (10)
4273-99 (10)
945-04
Paulson has also indicated five pairs having a mean separation Av of 4732-9.
Krypton exhibits two spectra, one produced without condenser in the discharge
circuit, and a second when the condenser is introduced. The above lines occur in
the condensed discharge.
XENON.
Xe. At. wt. =130-2 ; At. No. =54.
The sources of data for xenon are the tables of Baly and Merrill, the latter
extending from /9163 to A5823.
The strongest lines in the red end are 8231-62 and 8280-08, which are believed
to be good standards of wave-length in the extreme red.
* Astrophys. Jour., 41, 75 (1915).
t Phys. Zeit., 21, 25 (1920).
t Phil. Trans., A. 202, 183 (1904).
Sc. Papers, No. 345 (1919).
|| Ann. d. Phys., 45, 428 (1914).
180 Tables of Series Lines. CHAP, xxi,
Paulson* has drawn attention to four " triplets," having separations Ar of
about 3685 and 760. The intensities in these groups, however, show no regularity,
and three of the triplets have the wider separation on the more refrangible side.
An interesting feature of the spectra of neon, argon, krypton and xenon has been
noted by Merrill, namely, the tendency of the lines to form large groups occurring
in positions which are apparently related to the atomic weights. Merrill photo-
graphed the spectra with small dispersion, and the displacement of the groups to
the red with increase of atomic weight is thus very clearly indicated. Thus, there
are groups beginning at A 5850 in Ne, A6970 in A, A7590 in Kr, and A8230 in Xe.
There are comparatively blank spaces on the more refrangible sides of each of these
groups. Correspondence between individual lines of the different elements, however,
is not clear.
NITON. (Radium Emanation.)
Nt. At. wt. =222-4 ; At. No. =86.
The spectrum of the radium emanation was first studied by Ramsay, and after-
wards more completely by Rutherford and Royds,t and again by Royds.J Wave-
lengths extending from 6079 to 3005 are thus available, but there is no record of
any attempt to trace regularity in the arrangement of the lines.
* Astrophys. Jour., 40, 307 (1914).
t Phil. Mag., 16, 313 (1908). '
j Proc. Roy. Soc., A. 82, 22 (1908). Phil. Mag., 17, 202 (1909).
A further investigation of this spectrum over the range XX3982 to 7450 has since been
made by Nyswander, I^ind, and Moore (Astrophys. Jour., 54, 285, 1921).
INDEX TO AUTHORS.
Adeney, 160.
Ainslie, 139, 141, 145.
Angstrom, 1.
Anslow, 46, 49, 138.
Arnolds, 163.
Balmer, 9, 10, 12, 14, 27, 63, 89, 90.
Baly, 174, 179.
Baxandall, 165.
Bazzoni, 71.
Bell, 49, 90.
Benoit, 1.
Bergmann, 15, 23.
Bevan, 96, 98, 101, 103, 106.
Birge, 33, 44, 64, 65.
Bohr, 25, 28, 38, 59-71, 88, 90.
Boisbaudran, 7, 158.
Brauner, 54.
Brooksbank,166.
Burns, 174.
Butler, 165.
Cardaun, 146, 151.
Catalan, 109, 112, 113, 145, 155, 166.
Compton, 71, 72.
Cornu, 160.
Crew, 121, 126.
Crookes, 137, 155.
Curtis, 12, 14, 27, 28, 64, 89, 90, 92.
Datta, 101, 103.
Davies, 71.
Davis, 71.
Dewar, 7, 8, 9, 10, 11.
Dingle, 147.
Dunz, 88, 96-113, 118, 157, 160, 162, 167-
172.
Eder, 109, 113, 133, 139, 141, 145, 157.
Bder & Valenta, 6, 105, 146, 155, 162.
Evans, 63, 95.
Exner & Haschek, 4, 6, 101, 111, 137, 153,
154, 158, 160.
Fabry & Perot, 1, 112.
Foote, 65, 70, 71.
Fortrat, 98.
Fowler, 3, 4, 24, 31, 61, 64, 74, 92, 118,
163-166.
Fraiick, 71.
Frings, 113.
Fuchs, 173.
Fues, 33, 65, 74, 138, 142.
Fuller, 139, 141, 145.
George, 133.
Goldstein, 92.
Goucher, 71.
Grunter, 39, 156, 157.
Hagenbach, 6.
Halm, 31, 32, 44.
Hampe, 127.
Handke, 110.
Hardtke, 164.
Hartley, 9, 10, 11, 43, 160.
Hasbach, 109, 110.
Hermann, 37.
Hertz, 71.
Hicks, 15, 21, 34, 51-58, 76, 98, 109-1 14,
133, 138, 152, 154, 167, 174.
Holtz, 121.
Horton, 71.
Howell, 46, 49, 138.
Huggins., 7, 9.
Hughes, 72.
Huppers, 98, 109, 110, 139, 145, 156, 157,
160, 162.
Ishiwara, 38, 90.
Ives, 49.
Janicki, 146.
Jeans, 59.
Johanson, 34, 37, 105, 117, 132, 158, 162.
Johnstone Stoney, 7, 11.
Kaspar, 113.
Kayser, 1, 6, 26, 80, 166, 173.
Kayser & Runge, continually quoted.
Kent, 45, 96.
Kiess, 167.
King, 21, 121, 133.
Klein, 163.
Koch, 92, 94.
Konen, 6.
Kossel & Sommerfeld (Displacement
lyaw), 74, 157, 164, 165.
182
Index to Authors.
Lehmann, 105, 113, 114.
Lenard, 100.
Liebert, 92, 94.
Lilly, 71, 72.
Liveing, 7, 8, 9, 10, 11.
Lockyer, 3, 61, 91, 153, 164, 165, 166.
Lohuizen, 36, 163.
Lorenser, 41, 88, 115, 117, 118, 127, 132,
133.
Lyman, 5, 6, 60, 90, 95, 126, 133, 157.
McCauley, 121, 126.
McLennan, 5, 70, 110, 139, 141, 142, 145,
146, 157, 162, 163, 172.
Meggers, 2, 70, 80, 96, 101, 102, 105, 106,
109, 115, 126, 131, 133, 167, 174.
Meissner, 26, 96, 106, 126, 158, 174, 175.
Merrill, 91, 174, 179, 180.
Merton, 4, 89, 92, 94, 163, 178.
Michelson, 1, 89.
Millikan, 5, 60, 63, 64, 90, 163.
Mogendorff, 35, 36.
Mohler, 71.
Moseley, 49.
Nagaoka, 146.
Nicholson, 4, 34, 79.
Nissen, 179.
Paschen, 5, 14, 18, 41, 88, 89, 95; et seq.
See also Runge & Paschen.
Paulson, 26, 27, 35, 36, 49, 152, 154, 163,
164, 172-180.
Payn, 3, 119, 142.
Perot, 1, 112.
Peters, 2.
Pickering, 61, 62, 63, 95.
Planck, 59. '
Popow, 72, 152, 153, 157.
Precht, 45, 46, 48, 137.
Preston, 25.
Quincke, 113.
Ramage, 47.
Ramsay, 180.
Randall, 5, 103, 105, 109, 110, 121, 133.
Rayleigh, 101.
Reinganum, 44.
Reynolds, 37, 115.
Richardson, 71.
Ritz, 14, 18, 23, 32, 46, 74, 89, 133, 138,
142, 176.
Rowland, 1, 80, 88, 155.
Royds, 5, 180.
Rubies, 109, 155.
Rudorf, 46.
Rummel, 31.
Runge, 17, 24, 42, 45, 46, 48, 87, 137.
See also Kayser & Runge.
Runge & Paschen, 91, 166, 167, 169.
Rutherford, 59, 180.
Rydberg, 10-12, 14, 16, 19, 21, 23, 27-30,
43,45, 61, 82-84 ; et seq'.
Rydberg-Schuster (Law), 16, 24, 33, 34,
42, 87, 92.
Saunders, 18, 25, 39, 40, 41, 79, 98, 121,
126, 131, 133, 139, 141, 142, 144.
Schmitz, 133.
Schniederjost, 91, 167, 169.
Schulemann, 160.
Schumann (region), 5, 89, 95, 110, 118,
133, 139, 145, 146, 157.
Schuster, 8, 16, 166.
Shaw, 31, 36.
Silberstein, 59.
Sommerfeld, 33, 59, 68, 74, 166. See also
Kossel & Sommerfeld.
Stark, 92, 94, 164.
Stimson, 71.
Stuhlmann, 49.
Takamine, 146.
Tate, 70.
Vogel, 9.
Wagner, 113,
Watson, 174.
Watts, 6, 46, 47, 48.
Wiedmann, 146.
Wolff, 139, 141, 144, 149, 163.
Wood, 90, 98.
Zeeman, 25, 26, 109, 114, 137, 151.
Zickendraht, 101.
DESCRIPTION OF PLATES.
PLATE; i.
(1) Arc spectrum of sodium, showing principal, sharp and diffuse series. (Quartz
spectrograph.)
(2) Arc spectrum of lithium, showing principal, sharp and diffuse series. (Quartz
spectrograph.)
(3) The sharp and diffuse series of sodium, with components resolved. The
principal pair, AA5896, 5890, is reversed. (Glass spectrograph.)
PLATE II.
The arc spectra of cadmium, zinc, and magnesium (quartz spectrograph). The
triplets of the diffuse and sharp series are marked. There is an impurity of zinc in the
cadmium spectrum, and of cadmium in the spectrum of zinc. The series marked " D "
in the spectrum of magnesium is the Rydberg singlet series. The line X2852 is the first
principal line of the magnesium singlet system. The lines marked at XX 3261, 3076,
and 4571, are the " resonance lines " (IS Ip^ of Cd, Zn, and Mg respectively.
PLATE III.
(a) Corresponding sharp triplets of Zn, Cd, and Hg, showing relative positions in
the spectrum, and the relative separations.
(b) A fundamental triplet of barium, showing the diffuse character of the lines in
the arc in air (lower spectrum), and the presence of satellites in the electric-furnace
spectrum at low pressure (A. S. King, Mt. Wilson Observatory).
(c) A sharp and a diffuse triplet of calcium compared. The fundamental triplet
shown on the plate has separations corresponding with those of the satellites of the
first diffuse triplet, which lies in the infra-red.
PLATE IV.
Arc and spark spectra of the alkaline-earth metals. In each case the arc is below
and the spark above. Typical series lines are marked. The reduced intensities of the
characteristic arc lines, and the enhancement of the spark lines in the spark spectrum
are clearly shown. The increased separations of the arc triplets, and of the enhanced
doublets, with increase of atomic weight should be noted, and also the displacement of
corresponding lines towards the red. The shorter lines in the spark spectra are due
to nitrogen and oxygen. (Thorp-grating spectrograph.)
PLATE V.
(1) The spectrum of helium between X3188 and A7066, showing the arrangement
of the lines in six series. (The two associated fundamental series are in the infra-red.)
(2) The upper spectrum is that of helium with an ordinary uncondensed discharge,
and the lower that obtained with a strong condensed discharge. The latter shows the
line /14686 of He+ very strongly, while the ordinary lines tend to disappear.
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