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http://www.archive.org/details/astrophysicaljou42ameruoft 







The Astrophysical Journal 



THE UNIVERSITY OF CHICAGO PRESS 
CHICAGO, ILLINOIS 



Agrttts 
THE CAMBRIDGE UNIVERSITY PRESS 

LONDON AND EDINBURGH 

THE MARUZEN-KABUSHIKI-KAISHA 

TOKYO, OSAKA, KYOTO 

KARL W. HIERSEMANN 

LEIPZIG 

THE BAKER & TAYLOR COMPANY 

NEW YORK 



T\ 



THE 



ASTROPHYSICAL JOURNAL 



\\\ 



An International Review of Spectroscopy and 
Astronomical Physics 



EDITORS 

George E. Hale Edwin B. Frost 

Mount Wilson Solar Observatory of the Yerkes Observatory of the 

Carnegie institution of Washington University of Chicago 

Henry G. Gale 

Ryerson Physical Laboratory of the 
University of Chicago 

COLLABORATORS 

Joseph S. Ames, Johns Hopkins University; Aristarch Belopolsky, Observatoire de Poulkova; 

William W, Campbell, Lick Observatory; Henry Crew, Northwestern University; 

Charles Fabry, Universite de Marseille; Charles S. Hastings, Yale University; 

Heinrich Kayser, Universit'dt Bonn; Albert A. Michelson, University of 

Chicago; Hugh F. Newall, Cambridge University; Ernest F. Nichols, 

Dartmouth College; Alfred Perot, Paris; Edward C. Pickering, 

Harvard College Observatory; Annibaxe Riccd, Osservatorio 

di Catania; Carl Runge, Universit'dt Gottingen; Arthur 

Schuster, The University, Manchester; Karl 

Schwarzschild, Astrofhysikalisches Obser- 

valoriicm, Potsdam; Frank Schles- 

inger, Allegheny Observatory 



VOLUME XLII 
JULY-DECEMBER, 19 15 





THE UNIVERSITY OF CHICAGO PRESS 
CHICAGO, ILLINOIS 



$% 



I 






Published 
July, September, October, November, December, 191 5 



Composed and Printed By 

The University of Chicago Press 

Chicago, Illinois, U.S.A. 



CONTENTS 



NUMBER I 

PAGE 

Lady Huggixs. Sarah F. Whiting i 

A Theory of Absorption, Fluorescence, and Phosphorescence. 

E. C. C. Baly 4 

On Thlele's ''Phase" in Band Spectra. H. S. Uhler ... 72 

Effective Wave-Lengths of 184 Stars in the Cluster X.G.C. 

1647. Ejnar Hertzsprung 92 

Effective Wave-Lengths of Absolutely Faint Stars. Ejnar 

Hertzsprung in 

Color-Indices in the Cluster N.G.C. 1647. Frederick H. Seares 120 



NUMBER II 

The Eclipsing Yarhble Star 8 Orionis. Joel Stebbins ... 133 

A Study of the Light-Curve of XX Cygni. Harlow Shapley and 

Martha Betz Shapley 148 

The Electric Spark. W. O. Sawtelle . 163 

The Radlvl Velocities of Five Hundred Stars. Walter S. Adams 172 

The Infra-Red Arc Spectrum of Barium. H. M. Randall . 195 

Reviews: Tables for Facilitating the Use of Harmonic Analysis, 
H. H. Turner (O. J. L.), 203; The Sun, R. A. Sampson (P. F.), 
203; LAstronomie, Marcel Move (P. F.), 204. 



XUMBER III 



The Reflecting Power of Metals in the Ultra-Violet Region 

of the Spectrum. E. 0. Hulburt 205 

A Study of the Pole Effect in the Iron Arc. Charles E. St. 

John and Harold D. Babcock 231 



vi CONTENTS 

PAGE 

Stellar Parallax Work at the McCormick Observatory. 

S. A. Mitchell 263 

Xote ox the Dexsities of Secoxd-Type Stars. Harlow Shapley 271 

Review: Galileo's Dialogues concerning Two New Sciences, Henry 

Crew and Alfonso de Salvio (E. P. Hubble) 283 



NUMBER IV 



The Visibility of Radiation in the Red End of the Visible 

Spectrum. Edward P. Hyde and W. E. Forsythe . . . 285 

The Effective Wave-Length of Transmission of Red Pyrome- 
ter Glasses and Other Notes ox Optical Pyrometry. 
Edward P. Hyde, F. E. Cady, and W. E. Forsythe ... 294 

Ox Some Peculiarities of the Residual Radial Velocities of 
Stars of Differext Spectral Classes axd Their Relation 
to the Solar Motion. CD. Perrine 3°5 

The Orbital Elemexts of the Eclipsixg Varlvble SX Dracoxis. 

W. Van B. Roberts 3™ 

Orbital Elemexts of the Eclipsixg Varlvbles TW Axdromedae, 

TU Herculis, axd RS Vulpeculae. John Q. Stewart . . 315 

An Adaptation of the Koch Registering Microphotometer to 
the measuremext of the sharpxess of photographic 
Images. Orin Tugman 3 21 

The Resolvixg Power of Photographic Plates. Orin Tugman 331 

The Variation with Temperature of the Electric Furnace 

Spectra of Cobalt and Nickel. Arthur S. King . . . 344 

Minor Contributions and Notes: Nickel Deposits on Glass 
Mirrors for Ultra- Violet Photography, R. W. Wood, 365; The 
Distribution and Some Possible Characteristics of the Spectro- 
scopic Binaries of Class M, C. D. Perrine, 370; Editorial 
Note, 372. 



NUMBER V 

The Spectroscopic Determixatiox of the Solar Rotation at 

Ottawa. J. S. Plaskett 373 

The Transparency of Aqueous Vapor. F. E. Fowle . . . 394 



CONTEXTS vii 



PAGE 



The Elements of the Eclipsing Systems TV. T\V, TX Cassio- 

peiae and T LeonIs Minoris. R. J. McDiarmid ... 412 

The Structure of the Third Cyanogen Baxd axd the Asso- 
ciated Tails. H. S. Uhler and R. A. Patterson . . . 434 

Ox the Wave-Lengths of Irox Arc Lixes in the Neighborhood 

of the Calcium H and K Lixes. E. G. Bilham . . . 469 

The Spectra of Cathode Metals. Philip Ely Robinson . . 473 

Index 47 o 




LADY MARGARET LINDSAY HUGGIXS 



THE 

ASTROPHYSICAL JOURNAL 

AN INTERNATIONAL REVIEW OF SPECTROSCOPY 
AND ASTRONOMICAL PHYSICS 



VOLUME XLII 



J U LY 1915" NUMBER 1 



LADY HUGGIXS 

By SARAH F. WHITING 

Died on March 24, at 8 More's Garden, Chelsea, England, alter a long 
illness, Margaret Lindsay, widow of Sir William Huggins, in her sixty-seventh 
year. 

The achievements of the Victorian age were all passed in review 
in 1897, the year of Queen Victoria's Diamond Jubilee. In the 
columns of the London papers was a long list of men whom the 
Queen delighted to honor, among them but a scant number from 
the ranks of science, and but one woman even remotely mentioned, 
and that one Margaret Lindsay Huggins. 

Knighthood of the Order of the Bath was conferred upon William 
Huggins "for the great contributions which, with the collaboration 
of his gifted wife, he had made to the new science of astro-physics." 
So it may be said that the wife became Lady Huggins in her own 
right. 

Dr. Huggins was born for research, and under him, as he 
remarked himself, ''the astronomical observatory for the first time 
had also become a laboratory, and the spectroscope attached to the 
telescope had shown that the chemistry of the solar system pre- 
vailed wherever a star twinkled." For thirteen years Dr. Huggins 
worked alone, mapping lines of stars by night and of the elements 
by day. 



2 SARAH F. WHITING 

Meantime, with no aid from the schools, because, as Lady 
Huggins afterward said, " intellectual justice was denied to women," 
a colaborer was being prepared. Margaret Lindsay Murray, of 
Dublin, was as a child a lover of the stars. In her early teens she 
mapped sun-spots with a little telescope of her own construction. 
Fascinated by certain unsigned articles on the spectrum in a maga- 
zine, she made for herself a little spectroscope, and to her joy saw 
the dark lines in the solar spectrum. She also took up photography 
and had attained considerable skill when a happy fate brought to 
her acquaintance the unknown author of the inspiring articles, and 
in 1875 she became the wife of Dr. Huggins. 

Lady Huggins was possessed of the same characteristics as her 
husband. Both were full of enthusiasm and yet displayed cool 
judgment; both were patient, conscientious, exact, resourceful. 
Henceforth her fine qualities of sight and mind were devoted to 
furthering her husband's investigations into the chemistry and 
physics of the heavenly bodies. 

An eighteen-inch reflector and fifteen-inch refractor had been 
purchased by the Royal Society and loaned to the Tulse Hill 
Observatory. In 1876 the dry-plate process was brought to Dr. 
Huggins' notice, the telescopes were fitted with photographic plates, 
and the pair began their pioneer work in photographing the spectra 
of celestial objects. 

The period from 1876 to 1882 was spent in work on the planets to 
gain experience. Then the eighteen-inch reflector was fitted with 
two prisms of Iceland spar and Lady Huggins worked with skill 
guiding the telescope for the long-exposure photographs of the 
ultra-violet spectra of the stars. She was also most successful in 
manipulating the plates. 

Papers were constantly given out from the Tulse Hill Observa- 
tory. Lady Huggins' name appears as joint author of the following : 
"The Photographic Spectra of Uranus, Saturn, and Mars"; "On 
the Spectrum, Visible and Photographic, of the Great Nebula in 
Orion"; "Spectra of Wolf-Rayet Stars in Cygnus"; "Lines in the 
Photographed Spectrum of Sirius"; "Studies of the Spectrum of 
Nova Aurigae"; "Laboratory Studies of the Spectra of Calcium 
and Magnesium under Different Conditions"; "Spectrum of 



LADY HUGGINS 3 

Radium," etc. Meantime the work for the Atlas of Representative 
Stellar Spectra was kept up until this came out in 1899, with its dis- 
cussion of the evolution of the stars and its majestic sequence of 
spectra arranged with the lines of hydrogen and calcium as guides. 

To the perfection of detail of this monumental work, both 
scientifically and aesthetically, Lady Huggins made large contri- 
butions. 

In 1909 appeared the Scientific Papers, under the joint editorship 
of Sir William and Lady Huggins, and in 1906, also edited by her, The 
Royal Society, a reprint of Sir William's addresses given during the 
five years of his presidency of the Royal Society, with history and 
illustrations. The three books just mentioned were in contents 
and finish such fine specimens of book-making that the life of 
Sir William upon which she was engaged was justly awaited with 
anticipation. Her untimely death has interrupted this task, but 
it is to be hoped that it will be put into the hands of a worthy 
literary executor. 

Many American astronomers can testify that Lady Huggins was 
not only a scientist but a most gracious and hospitable home- 
maker. She was mistress of many so-called accomplishments, and 
possessed much accurate knowledge of art and antiquities, as was 
witnessed by her brochure on the Astrolabe and articles in the 
Encyclopaedia Britannica and various archaeological journals. 

She was, together with her friend Miss Agnes Gierke, whose life 
she wrote, made an honorary member of the Royal Astronomical 
Society in 1903. Her genius for friendship was attested by the 
motto with which she was accustomed to head her letters "Dieu ■ — 
et mes amis." An intimate friend writes: " Her loss is keenly felt 
by many and in many ways." 

WmTiN Observatory 
Wellesley College 



A THEORY OF ABSORPTION, FLUORESCENCE, 
AND PHOSPHORESCENCE 

By E. C. C. BALY 

CONTENTS 

Introduction. 

Part I. An Electromagnetic Force Field Theory of Absorption. 

i. The existence of molecular force fields and a theory of chemical reac- 
tion and reactivity. 

2. The opening up of the closed molecular force fields by the action of a 

solvent or of light. Theory of selective absorption. 

3. The opening up of a complex field must take place in stages, each stage 
being differentiated by its power of absorbing definite rays of light. 

4. The stages in the opening up of a complex molecular force field proved 
by the existence of intermediate stages in chemical reactions. 

5. Application of the theory to the explanation of the variation from 
Beer's law. 

6. Application of the theory to fluorescence and phosphorescence and 
the experimental proof. 

Part II. Absorption, Fluorescence, and Phosphorescence in Relation to the 
Energy-Quantum Theory. 

1. The existence of constant differences between the central frequencies 
of absorption bands, which equal the frequency of an absorption band 
in the infra-red. 

2. Application of the Bjerrum principle to absorption-band groups in 
the ultra-violet and visible regions. Experimental proof of its validity 
with absorption, fluorescent, and phosphorescent bands. 

3. Determination of the basis constants -, — 777 from the known absorption 

° (27T 2 /) c 

in the short-wave infra-red region, and the calculation from these of the 
component lines in an ultra-violet absorption-band group. 

4. Calculation of the absorption lines of phenol from the basis constants 
of water and benzene, and of aniline from those of ammonia and 
benzene. 

5. Summary and conclusions. 

INTRODUCTION 

During recent years a number of papers have been published 
describing the absorption spectra of organic compounds, and the 

4 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 5 

majority of these publications have dealt with the constitution of 
the compounds, the assumption being made that there exists a 
definite correlation between the primary structure of a molecule and 
the type of absorption which it exerts. Perhaps the most striking 
papers that have been published on this subject are those by 
Hantzsch, who has established the existence of numbers of series 
of differently colored salts from colorless acids or bases. To each 
differently colored salt he attributed a different formula. Xow 
recent investigations in these laboratories into the problem of light- 
absorption by organic compounds by no means favor the view that 
there is any direct relation between absorption and constitution, if 
such relation is held to mean that, when a colored salt is obtained 
from a colorless acid or base, the parent substance has changed 
its constitution in the salt. The principal outcome of this work is 
the establishment of a definite relation, not between primary struc- 
ture and absorption, but between absorption and chemical reactiv- 
ity. The evidence obtained is so strong that it is necessary to 
formulate a new theory to account for the new phenomena, a theory 
which at the same time must explain all those experimental facts 
that appear to support the absorption-structure relation. 

It is somewhat surprising that in all the work that has appeared 
dealing with the absorption spectra of organic compounds in rela- 
tion to their structure no notice has been taken of the absorption 
exerted by these compounds in the infra-red region of the spectrum. 
There is at hand a series of most accurate measurements of the 
absorption of organic compounds in the infra-red, made by Coblentz 
and others, and it is impossible to doubt that there must exist an 
intimate relation between the absorption bands as exhibited by a 
given compound throughout the whole spectrum from extreme 
ultra-violet to extreme infra-red. In spite of this no attention has 
been paid to infra-red absorption, and it has been attempted entirely 
to decide the constitution from arguments based on absorption 
in the ultra-violet and visible regions alone. 

It is proposed in the present paper in the first place to formulate 
a theory of light- absorption, fluorescence, and phosphorescence, and 
to show how intimate is the connection between these and chemical 
reactivity. In the second place it is proposed to apply the energy- 



6 E. C. C. BALY 

quantum theory to absorption, fluorescence, and phosphorescence 
throughout the whole spectrum, and to show how it is possible to 
calculate the wave-lengths of the lines of any absorption-band 
group in the ultra-violet or visible regions from the wave-lengths 
of the absorption bands in the infra-red. 

PART I. AN ELECTROMAGNETIC FORCE FIELD THEORY OF ABSORPTION 

i. The existence of molecular force fields and a theory of chemical 
reaction and reactivity.- — -It was shown by Humphreys 1 that the 
phenomena of the Zeeman effect and the pressure-shift of spectrum 
lines can be explained by the existence of electromagnetic force 
fields surrounding the atoms. Although so marked a success has 
attended the application of these fields to the phenomena above 
noted, their influence upon the properties of molecules has not been 
considered. It would seem, indeed, that in the existence of molec- 
ular force fields we can find the explanation of the phenomena of 
absorption and fluorescence such as is exerted by compound 
substances. 

Clearly these atomic fields must possess a polar factor as well as 
a quantity factor, and if the general case be considered of a mole- 
cule composed of several atoms of different elements, it is evident 
that the free and independent existence of the several force fields 
must represent a metastable condition. A certain amount of con- 
densation must occur between the force lines of the separate fields 
with the escape of energy and the establishment of a molecular force 
field. There is little doubt that the properties of any molecule will 
depend upon its force field. It is not proposed here to enter into 
a full discussion of how the chemical properties of molecules are 
determined by their force fields, but it is necessary very briefly 
to refer to this side of the problem for the proper understanding of 
what follows. 

If two elementary atoms of opposite type are brought together, 
their respective force fields will condense together with the forma- 
tion of a molecular field, and within this field there will exist a 
potential gradient. If this potential gradient be sufficiently steep, 
one or more electrons will tend to move from one atom to the other, 

1 Astrophysical Journal, 23, 233, 1906. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 7 

with the result that a true compound of the two elements will be 
formed. Similarly, when two molecules of different types arc- 
brought together, their force fields will tend to condense with the 
formation of an addition complex. If the potential gradients within 
this complex be steep enough, there will ensue a rearrangement of 
electrons and the formation of new chemical individuals. In other 
words, a chemical reaction will take place, but if the gradients be 
not sufficiently steep, the addition complex first formed will remain 
as such. We are therefore enabled to recognize a complete grada- 
tion between the condition when a chemical reaction occurs between 
two molecules and the condition when, owing to their force fields 
being exactly the same, the molecules have no mutual action what- 
soever. This recognition of mutual influence between two mole- 
cules when no specific chemical reaction occurs is of great 
importance both in pure chemistry and in the phenomena of 
light absorption. 

Xow when the condensing together of the force lines of the 
several atomic force fields within a given molecule takes place, it 
is possible that owing to the relation between the numbers of the 
force lines the resulting molecular force field may be entirely closed. 
In such a case the reactivity of the molecule will be nil. On the 
other hand, there may be left over, after the maximum possible 
condensation has taken place, an uncompensated balance of force 
lines. In this case the molecule will possess a definite and measur- 
able reactivity. This last condition is doubtless the explanation 
of that property known to chemists as residual affinity, while in the 
former condition is to be found the explanation of the want of reac- 
tion between such pairs of compounds as hydrogen chloride and 
ammonia when all moisture is absent. 

According to the present theory, therefore, the reactivity of all 
atoms and molecules is to be attributed to their electromagnetic 
fields. Chemical union between atoms, chemical reaction between 
molecules, are both due to these force fields, and primary valency 
would seem not to be the causa causans of such reactions, but to be 
a resultant effect. Valency in its stoichiometrical meaning is due 
to the interatomic rearrangement of the electrons when the poten- 
tial gradients within the addition complexes at first formed are 



8 E. C. C. BALY 

sufficiently steep and the electronic transference results in a smaller 
energy content of the product. The so-called residual affinity 
is the uncompensated residuum after the maximum possible con- 
densation of the force lines of the molecule has taken place. When 
this residuum is vanishingly small the molecule exhibits no evidences 
of chemical reactivity, but when, as is more usually the case, the 
residuum has a finite value the molecule does possess an observable 
and measurable reactivity. 

2. The opening up of the closed molecular force fields by the action 
of a solvent or of light. Theory of selective absorption. — It is evident 
from the foregoing that if the closed field of a molecule be opened 
or unlocked its reactivity will be enhanced. This unlocking may be 
brought about in one of two ways, namely, by the use of a substance 
possessing residual affinity or by the action of light. If a compound, 
the molecules of which possess closed fields, be dissolved in a solvent 
endowed with residual affinity, the free force lines of the solvent will 
interpenetrate the closed fields of the solute, with the result that 
these now will be opened and become capable of reacting with any 
other suitable substance dissolved in the same solvent. Clearly, 
however, the case is a perfectly general one. The tendency of 
molecules possessing residual affinity will always be to open up the 
closed fields of other molecules when the two molecular types are 
brought together, whether an actual solution is formed or not. 
When the two molecular types are brought together a certain pro- 
portion of the closed fields will be opened up and an equilibrium 
will be set up between the opened-up and non-opened-up molecules. 
Upon this equilibrium the reactivity of the system will depend. 

The second method of opening up the closed fields is by the 
influence of light. Due as they are in the first place to the rotation 
of the electrons of the constituent atoms, it follows that the force 
fields must be capable of absorbing those rays of light which have 
the same frequency as that of the electrons. The light in being 
absorbed does work upon the closed fields and opens them, and this 
at once gives a rational explanation of the selective absorption of the 
light. W T hen a solution of a compound selectively absorbs light 
the equilibrium previously existent between opened-up and non- 
opened-up molecules is shifted toward the opened-up or reactive 
side, a new photodynamic equilibrium being established. In 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE g 

passing, it may be noted that this affords an explanation of all the 
phenomena of photocatalysis. 

It may perhaps be pointed out that the absorption here referred 
to, and attributed to the selective absorption of light by the molec- 
ular force fields, differs from the fine-line absorption such as is 
shown by the halogen elements, chlorine, bromine, and iodine, and 
is no doubt due to the direct action of the electrons themselves. 
Each of those elements, in addition to their fine-line absorption, 
also exhibits a broad absorption band in the extreme ultra-violet, 
and it is this latter which is attributed to the molecular fields. The 
present theory does not deal with the absorption due to the electrons 
in their independent action but only with that which is due to the 
force fields arising from the electronic rotations. That there must 
be some connection between the two types of absorption seems to be 
obvious, but at the present time sufficient is not known of both 
phenomena as exhibited by the same compound to establish the 
relationship between the two. 

3. The opening up of a complex field must take place in stages, 
each stage being differentiated by its power of absorbing definite rays 
of light. — The mechanism of the opening up of a closed force field 
may now be dealt with in greater detail. The general statement 
has been made that a given closed field may be opened up by the 
influence of a solvent or of light, the action of the light being evi- 
denced by the selective absorption of definite rays. If the case be 
considered of a complex molecule, it is clear that the force field 
of that molecule must be complex. There must exist in such a 
complex field a network of potential gradients, and the influence 
of a solvent in opening up such a field will depend upon the nature 
of that solvent. It would be expected that the influence of a solvent 
on a complex field would be progressive and that it would attack 
various portions of the field in turn. It indeed follows that the 
opening up of a complex field must take place in definite stages, the 
number of such stages depending on the complexity of the field. 
The free vibration periods of the electrons will depend on the distri- 
bution of the force lines within the force field, and as the field is 
opened up different vibration periods will become active. Hence 
each stage in the opening up of a given force field will be character- 
ized by its power of absorbing definite light rays and may be 



io E. C. C. BALY 

differentiated in this way, since the light rays selectively absorbed by 
the various stages will be different. The number of possible stages 
will depend upon the complexity of the field and these stages in turn 
may be called into play by the use of suitable solvents. Very typi- 
cal examples of compounds that are opened in stages are the /3-naph- 
thalene derivatives which as a rule in alcoholic solution show three 
absorption-band groups. Three stages in the opening up of the 
force fields must therefore coexist in this solvent, each one char- 
acterized by its power of absorbing definite light rays. In 
concentrated sulphuric acid solution, on the other hand, the 
absorption spectra of these compounds are very different, since 
other stages are called into play, but usually one of these stages 
at least is common to the two solvents. 

Each stage marks a step in the opening up of a given force field 
and is a function of a given molecule with a definite primary struc- 
ture. It may be seen at once that this view entirely removes the 
necessity of postulating a change of primary structure for every 
variation of absorption evidenced by a given substance with change 
of solvent. Quite apart from the horrible complexity which is 
introduced into chemistry by the structure-absorption correlation 
theory, the view now put forward rests on a scientific basis, which 
is more than can be claimed for the older notion. Again, in one 
of his more recent papers Hantzsch 1 is constrained to confess that 
in at least one case there are not enough different structural 
formulae to go round, so numerous are the different absorption- 
curves obtained from one parent substance with different solvents. 

Mention was made above of the preparation by Hantzsch 2 

of several differently colored salts from one single colorless 

acid or base. He found, for example, that the lithium, sodium, 

potassium, rubidium, and caesium salts of dimethylvioluric acid 

CH 3 C 6 H 5 

= C<f > = XOH ^ d|phenylvio- 0=c /^ \ C = N0 H 
\v_r/ lunc acid \v_ r/ 

CH 3 C 6 H 5 

1 Bcriclilc, 43, 1662, 1910. 

2 Hantzsch and Robison, Berichte, 34, 45, 1910. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE n 

vary in color from yellow to blue as the electropositivity of the 
metal is increased in the salt. The two parent acids are colorless, but 
owing to their complexity of structure the force fields will be opened 
in several stages. Manifestly, since the closed field is acid in type, 
the most suitable substance to open it will be basic in type, and the 
more basic or electropositive this substance is the higher the stage 
to which the force field is opened and the longer the wave-length of 
light that will selectively be absorbed. The series of metals lithium, 
sodium, potassium, rubidium, and caesium increases in electroposi- 
tivity with increase in atomic weight, and it follows that the closed 
held of the parent acid will be opened to increasingly higher stages 
as the atomic weight of the metal in the salt is increased. The color 
of the salt will therefore change from yellow through red to blue, 
since the wave-length of the light selectively absorbed will increase 
as the higher stages are called into play by the increasing electro- 
positivity of the metal. All the stages in the opening up of a given 
force field are functions of one primary structure, and thus the 
present theory readily accounts for the many-hued salts of one 
colorless acid or base without postulating any change in that 
primary structure. Similar arguments may be shown to apply to 
all the results obtained by Hantzsch, but there is no need speci- 
fically to deal with these here. 

4. The stages in the opening up of a complex molecular force field 
proved by the existence of intermediate states in chemical reactions. — 
It follows from the preceding general statement of the theory that it 
is possible to put it to experimental test in a most rigid way. Cer- 
tain obvious deductions may be drawn which should be capable of 
clear experimental proof, and it may be said at once that the experi- 
mental results afford striking support to the theory. 

From the chemical point of view the theory established the fact 
that before any molecule with a closed force field can enter into 
any reaction it is necessary that its force field be opened up. Again. 
before a molecule can take part in a specific reaction it is probable 
that a certain particular stage in the opening of its force fields must 
be reached. Since such stage will be characterized by its absorptive 
power, it should be possible to follow the course of the reaction with 
the spectroscope. 



12 E. C. C. BALY 

Some years ago Miss Marsden (Mrs. Solomon) and I investi- 
gated the absorption spectra of certain aromatic aminoaldehydes 
and aminoketones. 1 In alcoholic solution each of these compounds 
exhibits a well-marked absorption band in the ultra-violet. The 
addition of a trace of an alcoholic solution of hydrogen chloride 
to any one of these solutions causes the development of a yellow 
or red color which disappears on the further addition of acid. 
This color is due to the appearance of a new absorption band at 
longer wave-lengths than those shown by the parent compounds. 
On the addition of the excess of acid the absorption changes to that 
of the hydrochloride of the base, which somewhat resembles the 
absorption of the free base itself. A typical set of absorption- 
curves is shown in Fig. i, and they represent the absorption of 

//CU— CH. 
/>-aminobenzaldehvde NH,-C< 7C-CHO . The full 

X CH=CH/ 

curve shows the absorption exerted by the aldehyde in alcoholic 
solution, the dotted curve shows the new absorption band developed 
in the presence of a trace of alcoholic hydrogen chloride, while the 
dot-and-dash curve expresses the absorption of the hydrochloride. 
The curves mark the limits of total absorption at the various con- 
centrations. 

It is clear that the conversion of the amino compounds into their 
hydrochlorides is not simply an addition reaction; that is to say, 
the reaction is not simply to be expressed by the equation 
H H H H 

H 2 N-c/ Sc-CH0 + HC1=C1H 3 X-C<f ^C-CHO. 

H H H 

There is no doubt that it is not the amino compound as it exists 
in alcoholic solution which forms the salt, but that the first quantity 
of acid added converts the base into an intermediate form and that 
it is this intermediate form which reacts with more acid to form the 
salt. These results both extend our knowledge of chemical reac- 
tion in that they undoubtedly establish the existence of a hitherto 
unrecognized intermediate stage, and they also afford strong sup- 

1 Chemical Society Transactions, 93, 2108, 1908. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 13 

port to the force-field theory, since it was exactly this phenomenon 
which was shown above to be foretold by the theory. 

The curves given in Fig. 1 make it clear that the entire amino 
base is not converted into the intermediate and reactive form 



32 



30 



£ 28 



g 26 



£ 24 



18 



14 



24 



Frequencies 

2& 3OOO S2 34 36 38 4OOO 4: 











\ 






\ 




















i 






\ 




















\ 






\ 




















\ 






1 

\ 




















\ 






1 




















A 






I 
\ 














\ 

\ 
1 




1 


\ 






\ 














\ 

\ 
\ 




1 

1 




1 






\ 












\ 


1 


1 






































A 




























\ 


























\ 


























\ 


























\ 

1 







Fig. i. — ^-Aminobenzaldehyde 

In alcohol 

In alcohol + T V eq. HC1 

— In alcohol + excess of HC1 

when the trace of acid is added. This is due to the fact that as 
the quantity of acid present is slowly increased some of the 
intermediate stage forms the salt, and at no concentration of 
acid is it possible to obtain the entire base in the reactive 



14 E. C. C. BALY 

form without any of the salt being formed. In order to 
obtain all the reacting molecules in the opened-up or reactive 
form, it is necessary to deal with some reaction the velocity of 
which is much slower. Such a reaction was found in the sulphona- 
tion of certain aromatic compounds. 1 This reaction in the case of 
/>-nitroanisole, for example, is chemically expressed by the equation 
H H H /S0 3 H 

p p Q Q/ 

2 N-c/ ^C-OCH 3 +H 2 S0 4 = 2 N-C<f ^>C-OCH 3 +H 2 , 

N:=c/ x c=(Y 

H H H H 

but according to the force-field theory the parent substance must 
pass through an intermediate stage in which its closed force field is 
opened to some stage higher than that in which it exists in alcoholic 
solution. If the stage characteristic of the alcoholic solution were 
sufficiently reactive to give the sulphonic acid, it is obvious that this 
acid would be formed when an equivalent amount of sulphuric acid is 
added to that solution. No reaction, however, takes place under 
those conditions, and in order to form the sulphonic acid it is neces- 
sary to dissolve the parent compound in concentrated sulphuric acid, 
when the sulphonation very slowly takes place. Hence it was to 
be expected that in solution in concentrated sulphuric acid the force 
fields would be found to be opened to a higher and more reactive 
stage. This expectation was fully realized, as may be seen from 
the absorption-curves shown in Fig. 2, where the full curve is that 
of the alcoholic solution, the dotted curve that of the strong sul- 
phuric acid solution, and the dot-and-dash curve that of the sul- 
phonic acid obtained by allowing the acid solution to stand for some 
hours in a warm place. It is perhaps worth mentioning that if 
the sulphuric acid solution, immediately after preparation, were 
poured upon ice the parent substance was recovered in a pure state. 
After the solution had stood a short time the reaction began to 
take place and its course could be followed throughout with a spec- 
troscope, for the absorption at first shown by the dotted curve 
in Fig. 2 slowly changed into that shown by the dot-and-dash 
curve. 

1 Baly and Rice, Chemical Society Transactions, 101, 1475, 1Q12. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 15 



Many compounds were examined in the same way and similar 
results were obtained in every case. There is thus no doubt that 

>6 28 3000 32 34 36 38 4000 42 



3§ 



36 



34 



32 



30 



28 



24 



16 



24 



* » 
\ 


\ 




















\ \ 


\ 




















1 \ 


\ 




















1 \ 

i \ 


1 


\ 






















\ 




















\ 


\ 






















\\ 






















\ 






















\ 

1 








f 
* 

f 
f 


> 












\ 

1 






/ 
/ 


• 


/ 


Y \ 






1 






I \ 


„«.-" 




/ 


f / 


\ 






1 




/ 

r 


\ 


\ 


/ 


/ 






\ \ 
\ 


\ 
\ 








\ 


I 


/ 

/ 

/ 








\ 


\ 


1 


1 

j 






\ 












\ 


\y 




















\ 



5000 



200 o 



Fig. 2. — />-Xitroanisole 
In alcohol 
In concentrated sulphuric acid 



— - In concentrated sulphuric acid after standing for some hours 

there is established without question the existence of an inter- 
mediate stage in a chemical reaction such as was deduced from the 
force-field theory. 



1 6 E. C. C. BALY 

5. Application of the theory to the explanation of the variation 
from Beer's law. — A second method of experimental verification 
of the theory can be found in the measurement of the absorptive 
power of a solution and its variation with concentration. As 
already pointed out, when a compound exists in solution there is an 
equilibrium set up between the opened-up and non-opened-up 
molecules of the solute. Such a solution exerts a definite selective 
absorptive power, a new photodynamic equilibrium being set up. 
As regards the equilibrium in solution, the position of this may de- 
pend on the concentration of the solution. Since any alteration 
in this equilibrium will undoubtedly entail a change in the absorp- 
tive power, we have an explanation of the variation that is so fre- 
quently observed from Beer's law. The actual variation to be 
demanded by the force-field theory is as follows. The ideal case 
may be considered of a liquid substance and a diactinic solvent, 
the substance and the solvent must be miscible in all proportions, 
and, further, on continued dilution of the solution the dark equilib- 
rium must progressively shift toward the reactive side until finally 
all the solute molecules are opened up. In such an ideal case the 
molecular absorptive power of the pure liquid will be relatively 
small since the fields will be more or less closed, so that the light 
cannot do much work on them. In the presence of a small quantity 
of the solvent the force fields of a few molecules will be opened 
up, and, since the light can now do more work on the system, the 
molecular absorptive power will be increased up to a maximum, 
i.e., when the light can do the maximum amount of work on the 
system. Further dilution will then cause a decrease in the absorp- 
tive power which, when all the force fields have been opened up, 
will fall to zero. 

It has not as yet been found possible entirely to realize these 
ideal conditions, which are very nearly realized with ethyl aceto- 
acetate, but two solvents, alcohol and water, are necessary. 1 In 
Tables I and II are given the absorptive powers of various molec- 
ular concentrations of ethyl acetoacetate in alcohol and in water, 
expressed in terms of the thicknesses of the layers which exert 
equal absorptive powers. In the first column is shown the 

1 Baly and Rice. Chemical Society Transactions, 103, 91, 1913. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 17 

"normality" of the solution, that is to say, the concentration 
expressed as the number of gram-molecules dissolved in one liter. 
The first observation, with normality 7 . 923, refers to the pure liquid 
ester itself. The second column gives the observed thicknesses 
which exhibit equal absorptive powers, while the third column shows 
the calculated thicknesses based on the weaker solutions. As may 

TABLE I 

Ethyl Acetoacetate axd Alcohol 



•v- ■ .. . Observed 
Normality Thickness 


Calculated 

Thickness 

a 


Difference 

Obs.-Calc. 

b 


b 
a 


7-293 

5° 

2.0 

1.0 

Q-5 

0.1 

. 05 


0.016 
0.020 

0.028 
0.037 
0.05 
015 

°-3 
3° 
6.0 


O.OO1893 
0.003 
0.0075 
0.015 
O.03 
Q-I5 
°-3 
3° 
6.0 
12.0 

150 
30.0 


0.015107 

0.017 

O.0205 

O.022 

O.02 

O 

O 

O 

O 

O 

O 

O 


7-4 

5 ■ 7 

2-7 

i-5 

0.67 






0.005 

0.0025 






0.00125 


12.0 
150 
30.0 





O.OOI 





. 0005 










TABLE II 
Ethyl Acetoacetate axd Water 



Normality 


Observed 
Thickness 


Calculated 

Thickness 

a 


Difference 

Obs. — Calc. 

b 


b 
a 


. 05 


6 
12 


6 
12 
3° 

I50 


O 

O 

- 5 

-30 


O 


O.025 


O 


O.OI 


25 
I20 

Selective ab- 
sorption 
ceased 


— O. 17 


0.002 


— O. 2 


O.OOI 





be seen in the case of alcohol as the solvent, the molecular absorp- 
tive power decreases as the concentration rises and is a minimum 
with the pure ester. In the case of water as the solvent, the absorp- 
tive power begins to decrease with dilution until finally the select- 
ive absorption vanishes. The reasons why one single solvent 
could not be used throughout were twofold. Although alcohol 



i8 



E. C. C. BALY 



and the ester are miscible in all proportions, the former is not 
sufficiently diactinic to allow the use of thicknesses greater than 
about 30 mm. On the other hand, although water is completely 
diactinic up to long lengths, it is not miscible in all proportions 
with the ester. 

The results of the observations, however, as far as they go, 
agree exactly with the deductions from the theory; namely, in 
passing from a pure substance through gradual decrease in concen- 
tration to dilute solution in a diactinic solvent, the absorptive power 
at first rises to a maximum and then falls to zero. As a more general 
rule the variation from Beer's law is not exactly of the same type 
as that shown by ethyl acetoacetate. In most cases the molecular 
absorptive power increases with dilution up to a maximum after 
which it remains constant. This type of variation is due to the 
fact that the equilibrium between opened-up and non-opened-up 
molecules shifts toward the reactive side with decrease in concen- 
tration until it becomes constant, further dilution having no effect. 
A typical example of this variation is shown by pyridine with 
water as the solvent (Table III). As can be seen, the molecular 

TABLE III 
Pyridine and Water 



XT ,.. Observed 
Normal'ty Thickness 


Calculated 
Thickness 

a 


Difference 

Obs.-Calc. 

b 


b 
a 


12.4 


O.OIO 
O.OII 

0.013 

0.014 

0.015 

0.019 
0.024 
0.067 
0.000 

40 

40.0 
400.0 


O . 00064 
O . OO08 
O.OOII4 
O.OO16 
0.002 
0.004 
O.O08 
O.04 
0.40 
4.0 
40.O 
400.O 


O . 00936 

0.0102 

0.01186 

0.0124 

0.130 

0.015 

0.016 

O.027 

O 

O 

O 

O 


14 7 




12 
IO 

7 
6 

3 
2 



7 


7-0 

5° 


4 

7 


2.0 


7 


I .O 





0.2 


67 







. 002 





0.0002 

















absorptive power starts from a minimum with the pure base 
(12.4 N) and increases until a concentration of 0.02 N is reached, 
when it becomes constant. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE iq 

6. Application of the theory to fluorescence and phosphorescence 
and the experimental proof. — The bearing of the force-field theory 
on fluorescence and phosphorescence may now be considered. It 
is perhaps not out of place to state the relation that these phenom- 
ena bear toward absorption. Speaking generally, no substance 
can exhibit luminescence unless it is undergoing chemical change 
or unless it has at some previous time absorbed energy. The first 
alternative embraces the type of phenomena known as chemi- 
luminescence and refers to those cases where the energy evolution 
accompanies a chemical change. Although the wave-length of 
such emitted energy in all probability is characteristic of the sub- 
stances concerned and therefore is to be explained by the present 
theory, this cannot be entered into here. The second alternative 
includes all those cases in which the emission is preceded by an 
absorption of energy. There are two distinct processes contribut- 
ing to the phenomenon, namely the absorption and the emission. 
There is no reason apparent why the velocity of these two should 
be connected, for the relation between the velocities must depend 
upon the active substance and the external conditions under which 
it exists. If the velocity of emission is equal to the velocity of 
absorption, then the phenomenon will be one of fluorescence, since 
the emission will not persist after the exciting cause has been 
removed. If the velocity of emission is slower than that of the 
absorption, the luminescence manifestly will persist after the excit- 
ing cause has been removed, and phosphorescence will be observed. 
Again, it is possible that owing to the molecular conditions of the 
active substance the velocity of emission will become vanishingly 
small. Under these circumstances the absorbed energy will remain 
stored up in the substance for an indefinite period, or until such time 
as it is released by special methods. Two such methods are 
known, one of which is friction and the other is the action of heat. 
Both are familiar enough and are known as triboluminescence and 
thermoluminescence respectively. By vigorous friction or by rise 
of temperature the molecular conditions can be so altered as to 
cause the velocity of emission to reach a measurable value, with the 
result that the substance begins to luminesce. The condition in 
which the substance can exist without any leak of its store of 



20 E. C. C. BALY 

absorbed energy is a metastable one and the substance returns to 
its normal condition with the escape of all the absorbing energy 
when rubbed or heated. 

Fluorescence, phosphorescence, triboluminescence, and ther- 
moluminescence may be looked upon as different manifestations of 
one phenomenon, namely the absorption of energy at one wave- 
length and the emission at another wave-length. For this reason 
they are all susceptible of the same explanation, and inasmuch as 
the force-field theory at once affords a solution of the problem of 
fluorescence, it may safely be assumed to do the same for the three 
sister phenomena. As a matter of experimental fact the measure- 
ment of the wave-lengths of the emission maxima of fluorescent 
organic compounds in solution is far more accurate than the 
measurement of the phosphorescent maxima of solid bodies and 
therefore it is more satisfactory to deal with fluorescence in the 
present condition. 

Doubts as to the validity of Stokes's law have from time to 
time been raised by some observers who have indeed categorically 
stated that under certain circumstances it is possible to obtain 
fluorescent emission of shorter wave-length than that of the exciting 
light. Such statements appear to arise from a misconception of 
Stokes's law and are likely to be misleading. If the absorption- 
curve of any substance in solution be examined, it will always be 
found to be very broad, and similarly the emission-curve of fluores- 
cence is also very broad. In very many cases the fluorescent and 
absorption-curves overlap. The simplest interpretation (which 
indeed is proved in the second section of this paper) of the breadth 
of the absorption bands is that all the different wave-lengths lying 
within the band are connected with one and the same mechanism 
of absorption. Since the absorption of these wave-lengths gives 
rise to the fluorescence, it is a fair assumption to make that any 
one wave-length lying within the absorption band will excite the 
fluorescence. As the fluorescent band may extend into the region 
of the absorption band, it will naturally follow that, if the fluores- 
cence is excited by light of a wave-length lying at the extreme red 
side of the absorption band, some of the fluorescent light will have 
a shorter wave-length than that of the exciting light. Such over- 






ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 21 

lapping cannot be taken as a contradiction of Stokes's law, which 
surely refers only to the optical centers of the absorption and fluores- 
cence bands. 

Numerous measurements have been made of the wave-lengths 
of the fluorescence maxima of organic compounds with the view 
of finding the relation between them and those of the absorption 
bands, but it must be confessed that no great success has attended 
these investigations. Again, various theories have from time to 
time been put forward attempting to correlate fluorescence with 
some type of reversible chemical change. All such theories are 
open to the most grave objections which, however, need not be 
entered into here. 

As has already been stated, the molecular force-field theory 
leads to the conclusion that there must exist a number of definite 
stages in the opening up of any one complex field, each one of which 
is characterized by its power of absorbing light of definite wave- 
length. Consequently each stage represents a free vibration- 
period of the molecular system which, however, is latent as an 
absorber of light unless a suitable solvent is present. The question 
now arises, What becomes of the light energy' which is absorbed ? 
Manifestly all of it must again be emitted and usually it is assumed 
to be emitted as heat. It is, however, only reasonable to assume 
that whatever be the vibration frequency of the emitted energy this 
frequency must be a characteristic vibration frequency of the 
absorbing system. When this vibration frequency lies in the infra- 
red, then of course the energy is emitted as invisible heat radiation. 
In certain cases, however, some of the energy is emitted in the 
ultra-violet or visible regions, when we have fluorescence. The 
vibration frequency of this fluorescent emission must also be char- 
acteristic of the molecular system, and, according to the force-field 
theory, must be characteristic of one of the stages in the opening 
up of the molecular force field. Fluorescence must therefore be 
due to the emission of light of a wave-length characteristic of a 
stage in the opening up of a closed field higher than that stage which 
is functioning as the absorber. We find on these lines a direct 
relation between absorption and emission in that they both arise 
from two stages in the opening up of one given molecular force field. 



22 E. C. C. BALY 

This explanation of fluorescence may very readily be put to 
experimental test, for, as already shown, it is possible by the use 
of suitable solvents to call into play many of the possible stages. 
It should be possible, therefore, by the use of one solvent to cause 
a substance to absorb light of the same wave-length as it emits when 
fluorescing in another solvent. For example, let the case be taken 
of a substance which in alcoholic solution absorbs light of wave- 
length X t and fluoresces with emission of light of wave-length X 2 . 
It should be possible by the use of another solvent to cause the sub- 
stance to absorb light of wave-length X 2 . This relation has been 
proved to exist in every case that has been examined. Many of the 
aminoaldehydes and aminoketones dealt with above show fluores- 
cence in alcoholic solution, and the wave-length of the light emitted 
is the same as that absorbed by these compounds when a trace of 
alcoholic hydrogen chloride is added to those solutions. 1 Similarly 
the light absorbed by the aromatic phenol ethers referred to above 
extends over the same range of wave-lengths as does the fluores- 
cence emission of their alcoholic solution. 2 Two instances may be 
quoted, one from each class of compound. 



Substance 



0-Aminobenzaldehyde 
Anisole 



Fluorescent Band Absorption Band 
in Solvent i in Solvent 2 



2020-2 2 20 2000-2300 
2220-3300 2220-3200 



These two examples are sufficient to show that the relation holds 
good and that the force-field theory gives a completely satisfactory 
explanation of fluorescence. 

The bearing of the deviation from Beer's law upon the phenom- 
ena of phosphorescence may be noted. Certain facts are now 
known about phosphorescence; 3 namely, that no pure substance 
will phosphoresce, that phosphorescence is essentially a property, 
of diluted matter, and that there is an optimum of phosphorescence 

1 Baly and Krulla, Chemical Society Transactions, 101, 1469, 191 2. 

2 Baly and Rice, ibid., 101, 1475, 1912. 

3 Lenard and Klatt, Ann. der Phys., 15, 225. 425, 633, 1904; Urbain and Brun- 
inghaus, Ann. chim. el phys., 18, 293, 1909. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 23 

with a definite concentration of the phosphorogen in the diluent. 
This is a natural result of such a variation from Beer's law as was 
described for ethyl acetoacetate in section 5. A pure non- 
phosphorescing solid exists with its force fields entirely closed, so 
that they do not selectively absorb the exciting radiation. On 
mixing the compound with a diluent the force field will be opened 
so that they can now absorb the exciting energy and hence phos- 
phorescence will ensue. Just as in the case of ethyl acetoacetate 
the absorptive power and hence the phosphorescent efficiency on 
increasing dilution reach a maximum and then fall off. The 
phenomena are therefore exactly those that the theory leads us 
to expect. 

In the present paper the application of the force-field theory 
to absorption and fluorescence only has been considered, very 
brief reference being made to^the chemical side. It may perhaps 
be pointed out that the theory can be applied to the phenomena 
of chemical reaction and reactivity with considerable success. 
Allotropy and isomerism on the one hand, catalysis and the 
mechanism of chemical reaction on the other, all seem readily to 
be explained by the theory, and an account of this will be found in 
other papers. Reference is made to this side of the general theory 
in order to emphasize the very intimate connection which is estab- 
lished between chemical properties and the phenomena of selective 
absorption of light and fluorescence. 

PART II. ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE IN 
RELATION TO THE ENERGY-QUANTUM THEORY 

i. The existence of constant differences between the central fre- 
quencies of absorption bands, which equal the frequency of an absorp- 
tion band in the infra-red. — In the preceding section reference was 
made to the mechanism by means of which the light energy, pre- 
viously absorbed by a substance, escapes. There is little doubt 
that in general the energy is emitted as infra-red radiation, but in 
certain cases some of the energy is emitted in the ultra-violet or 
visible regions when we have fluorescence or phosphorescence. 
Whatever may be the frequency of the emitted energy, there can 
be no doubt that this frequency must be a characteristic vibration 



24 E. C. C. BALY 

frequency of the absorbing system. Very little attention seems to 
have been paid to the destiny of the absorbed energy, the somewhat 
vague idea apparently being held that it escapes as black-body 
radiation. Such a notion does not seem to be tenable and would 
lack a scientific basis, for surely radiation cannot in any case occur 
except at those frequencies which are characteristic of the absorb- 
ing systems. Again it must also be accepted, unless a definite 
chemical change in state is induced by the absorbed energy — that 
is to say, unless new stable substances are formed with different 
energy contents — that the entire absorbed energy must be emitted 
again at one or more of the characteristic frequencies of the absorb- 
ing system. 

According to the energy-quantum theory, energy is absorbed 
and emitted in definite quanta, determined by the product hv, 
where h is the Planck constant and v is the oscillation frequency of 
the absorbed or emitted radiation. This is the old form of the 
theory, but recent work by Eucken and others entirely justifies 
the conclusion that both the emission and the absorption of energy 
take place in quanta. It follows, therefore, that for every quantum 
of energy absorbed at one frequency there must be emitted a whole 
number of quanta at a lower frequency. If v be the oscillation 
frequency of the absorbed energy, and v x the frequency of the 
emitted energy in the infra-red, then we have 
hv=xhv xl , and v=xv x , 

where x is some whole number. Clearly, therefore, the oscillation 
frequency of the absorbed energy must be a whole multiple of the 
oscillation frequency of the emitted energy. 

Now many substances exhibit several absorption-band groups, 
as already shown in the first part of this paper, each band corre- 
sponding to a stage in the opening up of the force field of the molec- 
ular system. The same relation must hold good for each of the 
absorption bands, and hence if v l} v 2 , v 3 , etc., be the oscillation fre- 
quencies of the centers of the absorption bands, we have 
v l = v x , xv 2 = yv x , v 3 =zv x , etc., 

where x, y, z, etc., are whole numbers. The oscillation frequencies 
of each absorption band shown by one substance must therefore 



ABSORPTION. FLUORESCENCE, AND PHOSPHORESCENCE 25 

be some multiple of the frequency of the infra-red band, and the 
simplest case will be when the absorption-band frequencies are 
consecutive multiples of that of the infra-red band. 

Again, it has already been shown that a fluorescence or phos- 
phorescence maximum arises from a characteristic vibration fre- 
quency of the molecular system. The oscillation frequencies of 
fluorescence and phosphorescence bands must therefore also be 
multiples of the frequency of an infra-red band. The final con- 
clusion may be drawn that there must exist a constant difference 
between the central frequencies of the absorption and fluorescent 
bands of any one substance and that this constant difference must 
equal a vibration frequency in the infra-red which is characteristic 
of that substance. Since the simplest method of determining the 
characteristic vibration frequencies is by mapping the absorption 
spectrum, so we may say that the constant difference between con- 
secutive absorption, fluorescent, and phosphorescent bands in the 
ultra-violet or visible regions must equal the frequency of an absorp- 
tion band in the infra-red. 

In actual practice the relationship may not be quite so simple 
because consecutive multiples of the infra-red frequency may not 
always appear, as one or more of these may be latent. This of 
course does not in any way militate against the soundness of the 
argument. A very large number of compounds have been investi- 
gated in these laboratories and it may be stated that in every case 
examined, where more than two characteristic vibration frequencies 
are exhibited whether by absorption or fluorescence, the constant 
frequency relation holds good. The most striking examples are 
the /3-napthalene derivatives, which show as a rule three absorp- 
tion bands and also fluorescent maxima. In these compounds 
the constant frequencies are extraordinarily accurate when the 
optical centers of the bands are measured. Unfortunately, how- 
ever, no measurements have been made of the infra-red absorption 
of these compounds and therefore the complete relation cannot be 
verified. 

There are, however, one or two compounds which exhibit several 
absorption bands and fluorescent maxima and for which the fre- 
quency of an infra-red band is known. Two may be selected from a 



26 



E. C. C. BALY 



series still under investigation, namely phenol and m-cresol. In 
dealing with the frequencies it is very much simpler to use the 
reciprocals of the wave-lengths in place of the true oscillation 

frequencies, and in the following pages the values of r- are given 

A 

to four significant figures. Phenol and w-cresol both show one 
absorption band and one fluorescence maximum in neutral alco- 
holic solution, and in alkaline solution they show two absorption 
bands and one fluorescent maximum. As none of the frequencies 
are the same there are five characteristic frequencies in each case. 

The values of r- for phenol are as follows: 

A 

Neutral solution Fluorescence 3200 

Absorption 3670 

Alkaline solution Fluorescence 2890 

Absorption 3370 

Absorption 4170 

The extreme difference between the fluorescence maximum and 
the second absorption band of the alkaline solution is 4170 — 2890 = 
1280 = 8X160. On this basis the maxima can be arranged as in 
Table IV, the constant frequency difference being taken as 160. 

TABLE IV 
Phenol 






Calc. 



Obs. 



Error 



2890. 

3050. 

3210. 

337°- 

353°- 

3690. 

3850 

4010. 

4170. 



2890 



3200 
3370 



3670 
4170 



Fluorescence in alkaline solution 

Fluorescence in neutral solution 
Absorption in alkaline solution 

Absorption in neutral solution 
Absorption in alkaline solution 



+ 10 



Four of the possible frequencies are latent in the solvents used, but 
will very probably be observed when other solvents are employed. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 27 



Now according to the theory there should be an absorption band 
in the infra-red with a frequency of 160. Coblentz 1 has measured 
the infra-red absorption of phenol and finds a very strong band at 
X = 6. 25 fx, the reciprocal of which is 160. 

The values of - obtained with w-cresol are as follows: 



Neutral solution Fluorescence 

Absorption 

Alkaline solution Fluorescence 

Absorption 
Absorption 



3100 
3610 
2920 
3440 
4120 



On the basis of a constant difference of 170 Table V may be given. 



TABLE V 

»z-Cresol 



Calc. 


Obs. 






1 


1 




Error 


A 


A 







2930. 
3100. 
3270. 
3440. 
3610. 

3780. 

395°- 
4120. 



2920 
3100 



3440 
3610 



4120 



Fluorescence in alkaline solution 
Fluorescence in neutral solution 

Absorption in alkaline solution 
Absorption in neutral solution 



Absorption in alkaline solution 



+ 10 



In the infra-red region there should be an absorption band with a 
wave-number of 170. Xot being able to find any published 
measurements of the infra-red absorption of w-cresol, I have investi- 
gated the region about 3 \i with a rock-salt prism and a Hilger 
thermopile. There is a strong band at 2 . 94 \x the frequency of 
which is 340, and this band is clearly 'the first multiple of the fre- 
quency of a band which must exist at 5 . 88 \i with the frequency 
of 170. There is no doubt from these results that the relation 
foretold by the theory is amply confirmed. 

In order to guard against misconception it may Be pointed out 
that when a substance fluoresces, the absorbed energy must be 
emitted both as fluorescent light and as infra-red radiation. If 



1 Publications oj the Carnegie Institution of Washington, No. 35, 1905. 



28 E. C C. BALY 

c„ p 2 , v x are the frequencies of absorption, fluorescence, and infra- 
red radiation respectively, then the relation must hold that 

hv 1 = xhv 2 -\-yhv x , 

where x and y are whole numbers. 

There is another direction in which the present conception can 
be put to experimental test. It has been shown by Sellmeyer that 
the refractivities of substances can be connected with an absorp- 
tion band in the ultra-violet, the relation in its simplest form being 

given by 

.A" 
f l - 1 = —r— r, » 



where N is a constant. v the oscillation frequency of the ultra- 
violet band, and v the oscillation frequency of the light for which 
a given value of the refractivity, \i — i, is found. The value of 
v Q is generally very large and lies beyond the working limit of a 
spectrograph in air and therefore the value has to be calculated 
from the refractivities for two different values of v. Recently 
Mr. and Mrs. Cuthbertson 1 have published the refractivities of 
several gases for which the wave-lengths of the infra-red absorption 
bands are known. It should be possible to express these refrac- 
tivities very accurately by a Sellmeyer formula in which v is 
replaced by xv x , v x being the oscillation frequency of an infra-red 
band and x some whole number. I have found this to be the case 
with every gas examined by Mr. and Mrs. Cuthbertson, and the 
accuracy is shown by the two following instances. In these cal- 
culations the true oscillation frequencies have been used. 

HYDROGEN CHLORIDE 

X (the mean of the two infra-red bands) = 3.474/x, 2 whence 
y. v = 8.636Xio 13 . The value of x was found to be 38 and the fol- 
lowing formula was used: 

4.6896X10 27 



IX-I 



10769X10 27 — V 2 ' 



where 10769 Xio 27 = (38f. r ) 2 . 



1 Phil. Trans., 213 A, 1, 1913. 

2 Eva von Bahr, Deutsch. phys. Gcscll. Verh., 15, 1150, 1913. 



ABSORPTION, FLUORESCENCE. AND PHOSPHORESCENCE 29 



TABLE VI 
Values of (/*— i)io 8 



6708 
6433 
579o 
577o 
5461 
5209 
5086 
4800 



Calc. 



44372 
44444 
44656 
44669 
44803 
4493° 
45001 

45i87 



Obs. 



44375 
44444 
44656 
44666 

44800 

4493° 
45007 
45187 



Differences 



-3 



+3 

+3 

o 

-6 



XITRIC OXIDE 



X (mean of the two infra-red bands) = 5 .33 /jl. 1 whence v x = 
o. 56285 X 10 14 . The value of x was found to be 62 and the follow- 
ing formula was used: 

3.5621X10 27 



fi — 1 = 



12233. 8Xio 27 -v 2 ' 
where i2233.8Xio 27 = (62^) 2 . 



TABLE VII 
Values of (m— i)io 8 



Calc. 



Obs. 



Differences 



6708 
6438 
5790 
5770 
546l 
5209 
5086 
4800 



29302 
29346 
29470 
29474 
29550 
29626 
29667 
29774 



29306 
29334 
29468 
29474 
29550 
29622 
29666 
29776 



-4 
+ 2 
+ 2 



+4 
+ 1 
— 2 



The agreement between the calculated and the observed values 
is exceedingly close and again supports the present theory very 
strongly. The agreement is certainly as good as Air. and Mrs. 
Cuthbertson obtained with Sellmeyer's formula, the constants of 
which they calculated from the observed refractivities by the 
method of least squares. The oscillation frequencies thus found 
for the ultra-violet absorption bands are consequently only theo- 



1 Warburg and Leithauser, Ann. dcr Pliys., 28, 313, 1909. 



30 E. C. C. BALY 

retical since they have not been observed and measured. The 
values given in Tables VI and VII have a materially important 
advantage in that they have been calculated from an absorption 
band that has directly been measured and is known, therefore, to 
be a characteristic function of the substance dealt with. 

Before passing on to a further extension of the theory, a ppssible 
deduction therefrom may be mentioned. There seems no doubt 
that absorption, fluorescence, and phosphorescence are directly 
connected with emission in the infra-red, and hence it would be 
expected that the converse would be true. In this may be found 
the explanation of the well-known fact that the phosphorescence of 
a substance after exposure to an exciting cause is at once destroyed 
on exposure to infra-red radiation. 

2. Application of the Bjerrum principle to absorption-band 
groups in the ultra-violet and visible regions. Experimental proof 
of its validity with absorption, fluorescent, and phosphorescent bands. — 
Throughout the preceding portion of this paper no attention has 
been paid to the breadth of the absorption and fluorescent bands. 
All the relationships have been based on the frequencies of the opti- 
cal centers of the bands, whether these latter be in the ultra-violet, 
visible, or infra-red regions of the spectrum. It is now proposed 
to discuss the breadth of the bands, and inasmuch as any single 
band is in reality composed of a group of fine absorption lines it is 
obvious that the relations described above cannot be considered 
to be complete unless the whole structure of any given band 
group can be explained by means of it. This explanation is to be 
found in a theory put forward by Bjerrum, 1 which when superposed 
on the theory advanced in this paper appears to give a complete 
solution of the whole problem. Bjerrum dealt with the absorp- 
tion bands in the short-wave infra-red region and pointed out that 
if v x be the frequency characteristic of the atoms in a given molecule, 
then, if v r be the frequency of rotation of the molecules, three ab- 
sorption bands will be shown close to v x . The frequencies of these 
bands will be v x -\-v r , v x , and v x — v r respectively, and since the 
central vibration is pure it will evidence itself only as a very narrow 
absorption line and will probably escape detection owing to the 

1 Nernst Festschrift, p. 90, 191 2. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 31 

comparatively large slit-width necessary in infra-red work. The 
result will be that the whole absorption band will appear to be 
double, each portion being broad, since v r represents the average 
rotational frequency of the molecules. 

Bjerrum further pointed out, however, that on the energy- 
quantum theory, the rotational frequencies must be discontinuous 
and that they must have well-defined values given by the formula 

nh 

271"/ 

where h is the Planck constant, / the moment of inertia, and n—i, 
2, 3, . . . . etc. As a result of this an absorption-band group in 
the short-wave region of the infra-red should consist of a series of 
maxima symmetrically distributed about a central line of frequency 
v x . Each pair of maxima will correspond to a definite rotational 
frequency of the molecules and hence to an absorption band in the 
long-wave region of the infra-red. Fraulein von Bahr, 1 has made 
very accurate measurements of the absorption band shown by 
water-vapor at X = 6.25 fx and found clear evidence of these pairs 
of maxima. From these she calculated the wave-lengths cor- 
responding to the rotational frequencies and showed an excellent 
agreement with the measurements of the absorption bands of water- 
vapor in the long-wave infra-red region by Rubens and von Warten- 
berg. Eucken 2 pointed out that a still closer agreement is obtained 
on the basis of there being two degrees of freedom possessed by the 
water molecule, that is to say, two values of / in Bjerrum's formula. 
The experimental evidence therefore most strongly supports 
Bjerrum's theory. 

There seems to be no valid reason why Bjerrum's conception 
should not be extended and applied to the absorption-band groups 
in the visible and ultra-violet regions. If v be a characteristic vibra- 
tion frequency, for example, in the ultra-violet, then we should 
find pairs of absorption lines in the band group with frequencies 
equal to v-\-v x , where v x stands for the frequencies of the centers 
of the short-wave infra-red bands. Some preliminary support 

1 Phil. Mag., 28, 71, 1914. 

2 Dcutsch. pliys. Gesell. Verh., 15, 1159, 1913- 



32 



E. C. C. BALY 



for this extension of Bjerrum's theory is gained from the fact that 
the ultra-violet absorption-band group of benzene consists of about 
200 fine absorption lines and these form nine well-marked sub- 
groups which obviously are arranged symmetrically around a 
central position. This also is the case with several other com- 
pounds. 

Again, it follows from the theory developed in this paper that 
the same structure should be found in the case of the fluorescent 
and phosphorescent bands of the same substance. I have cal- 
culated the values of the absorption lines of one or two compounds 
and find that they form in each case a series of pairs symmetrically 
distributed about a central line and that the frequency of each 
short-wave infra-red band has a corresponding line or pair of lines 
forming part of the structure of the ultra-violet absorption-band 
group. In short, the application of the Bjerrum conception is 
completely successful. The compounds may be considered in 
detail. 

BENZENE 

Hartley 1 stated that the ultra-violet absorption-band group 
of benzene can be divided into ten sub-groups, the values of r 

A 

being 3745, 3802, 3861, 3963, 4055. 4148, 4237, 4299, and 4388, 
respectively. These may be arranged around the one at - = 

A 

4055 as center, as shown in Table VIII. In the third column of 

TABLE VIII 



A in Angstroms 



Mean v% 



Infra-Red Bands 



Calc. 



Obs. 



2670 
2630 
2590 

2523 
2466 
241 1 
2360 

2335 
2326 
2279 



3745 
3802 
3861 
3936 
4055 
4148 

4237 
4282 
4299 
4388 



3io 
253 
194 

92 

o 

93 
182 

227 
244 
333 



249 



925 
92.5 



249 



3-23M 
4.08 

S-iS 

10.81 



10.81 
5-5° 
4.40 
4.08 
3.00 



3- 2 5V 



10.78 



10.78 
5-41 
4.40 



1 Phil. Trans., 208 A, 475, 1908. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 35 

the table are given the frequency differences between each line 
and the central line, and in the fourth column the means between 

the two values where such exist. The values of — or the wave- 
-- 
lengths of the infra-red bands are given in the fifth column, while 
in the last column are to be found the wave-lengths of the absorp- 
tion bands as measured by Coblentz. 1 Four of the calculated 
bands were observed by Coblentz and the agreement is exceedingly 
good. 

On the other hand, there are 16 absorption bands shown by 
benzene between 3 fx and 15 /z, which latter is the upper limit 
reached by Coblentz, and the question arises whether each of these 
gives rise to a corresponding pair of lines in the ultra-violet band 
group when compounded with the central vibration 4055. The 
complete list is given in Table IX, and, as can be seen, every 
infra-red band gives an absorption line or pair of lines in the ultra- 
violet. Certain of the calculated infra-red bands have not been 
observed by Coblentz and they are included in the table because 
the corresponding ultra-violet lines were given by Hartley as the 
heads of the sub-groups. Hence the presumption would be in 
favor of their being important lines. It will be seen in the sequel, 
however, that Hartley was apparently incorrect in his measure- 
ments of the heads of the sub-groups. 

From what has gone before it is clear that the frequency of the 
central line, 4055, must be a whole multiple of the frequency of one 
of the infra-red bands. This number is almost exactly 10X405, 
which corresponds to a wave-length of 2 . 47 ju, a value exceedingly 
close to that measured by Coblentz, namely 2.49 ju. Now the 
next smaller multiple of 405 is 9X405 = 3645, and this should form 
the central line of the fluorescence bands of benzene. The fluores- 
cence of an alcoholic solution of benzene has accurately been 

measured by Dickson, 2 who found six bands with frequencies ( r ) 

o f 3436, 3537, 3 6 3i, 3733' 3795< and 3848, respectively. In order 
that these may be compared with the absorption measurements 

1 Loc. cit. 

2 Zeit. wiss. Phot., 10, 166, 1912. 



34 



E. C. C. BALY 



(which were made with benzene vapor) they must be corrected for 
the effect of the solvent, which tends to shift the maxima toward 
the red. Hartley found that this correction is of the order of 15 



TABLE IX 
Benzene Absorption (Hartley) 



a in Angstroms 



Mean v x 



Infra-Red Bands 



Calc. 



Ob3. 



2687. 
2670. 
2630. 
2612 . 
2600. 
2591- 
2581. 
2567- 
2560. 

2552. 
2546. 

2538. 
2529. 
2526. 
2523- 
25I9- 
2516. 

25I4- 
2466. 
2420. 
2418. 
2416. 
241 1 . 
2409. 
2406. 
2398. 
2391. 
2386. 

2379- 
2372. 
2360. 

2354- 
2346. 

2334- 
2326. 
2279. 



3722 

3745 
3802 
3828 

3847 
3861 

3873 
3895 
3907 
3917 
3928 
3940 
3954 
3958 
3963 
397o 
3974 
3978 
4055 
4132 
4136 
4140 
4148 
4152 
4157 
4170 
4182 

4193 
4203 

4215 
4237 
4249 
4263 
4284 
4299 
4388 



333 
310 

253 
227 
208 
194 
182 
160 
148 
138 
127 

115 
101 

97 
92 

85 
81 

77 
o 

77 
81 

85 
93 
97 

102 

115 
127 
138 
148 
160 
182 
194 
208 
229 
244 
333 



333 



249 
228 
208 
194 
182 
160 
148 
138 
127 
115 
101 . 

97 
92. 

85 



92. 

97 
101 . 

US 
127 

138 
148 
160 
182 
194 
208 
228 
249 
333 



OO /x 

23 
08 

38 

80 



25 M 



4' 



units, and if 14 be added to the third of the foregoing frequencies 
we have 3645, which, as already shown, should be the central line 
of the fluorescence system. It may be assumed that 14 must be 
added to all Dickson's values, and this is done in the third column 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 35 

of Table X. In the fourth column are given the frequency differ- 
ences from the central line 3645, and in parentheses are given the 
mean values for the corresponding intervals in the absorption- 
band group as shown in Table IX. 

TABLE X 

Benzene Fluorescence (Dickson) 



\ in Angstroms 



2910 
2827 

2754 
2679 

2635 
2599 




195 

94 




(i94) 
(92.5) 


102 (101.5) 
164 (160) 
217 (208) 



When the substitution products of benzene are considered, 
some difficulty tends to arise owing to the fact that the molecule 
becomes unsymmetrical. There is no doubt that the regularity 
of the structure of the ultra-violet absorption-band group of benzene 
is due to the symmetry of the molecule; in toluene and its homo- 
logues much of this symmetry disappears and hence it cannot be 
expected that the absorption should be so symmetrical. While 
^-xylene shows considerable symmetry, as already pointed out by 
Miss Marsden and myself, 1 toluene, o-xylene, and wz-xylene evi- 
dence want of symmetry by the fact that there are fewer separate 
absorption lines on the ultra-violet side of the central line. 



TOLUENE 

The ultra-violet absorption-band group of toluene has been 
measured by Hartley, 2 Grebe, 3 and Cremer. 4 Grebe was the first 
to arrange the absorption lines in series with constant frequency 
differences, and although Hartley considered that such arrangement 
was unjustified, Cremer also arranged the lines in several such 
series. There would seem to be no doubt that Cremer's values 

1 Chemical Society Transactions, 87, 1347, 1905. 

2 Loc. cit. 

3 Zeit. U'iss. Phot., 3, 376, 1905. 4 Ibid., 10, 349, 1912. 



36 



E. C. C. BALY 



are the most accurate, and they are used in Table XI in which they 
are arranged around the line ^=4047 as center. The general 

A 

arrangement of the table is the same as that of Table IX. There 

TABLE XI 
Toluene Absorption (Cremer) 



A in Angstroms 



Mean v x 



Infra-Red Bands 



Calc. 



Obs. 



ABH 

AH 

A 

A 

ABH 

A 



AH 
A 

AB 



AB 
H 



H 

A 

BH 
B 
B 



2667 
2647 

2635 
2630 
2615 
2603 
2600 
2595 
2589 
2585 
2580 
2572 
2567 

2565 
2560 
2554 
2550 
2541 
2539 
2536 
2529 
2524 
2522 

2517 
2507 
2477 
2471 
2464 

2433 

2420 
2407 
2394 
2359 
2354 
2341 
2326 

2315 



3749 
3778 
3795 
3802 

3824 
3842 
3846 

3853 
3862 
3869 
3877 



3895 

3899 

3906 

3915 
3922 

3936 
3939 
3943 
3954 
3961 

3965 
3974 
3988 

4037 
4037 
4058 
4110 
4133 
4154 
41/7 
4235 
4248 
4272 

4299 
4320 



298 
269 

252 

245 
223 
205 
201 
194 

185 
178 
170 
159 
152 

148 

141 
132 
125 
in 
108 
104 

93 
86 

82 
73 
59 



63 
86 
107 
130 
188 
201 
225 
252 
273 



271 
252 



224 
201 
186' 



131 



107 
86 



61 

io-5 



io-5 

61 

86 

107.5 
131 
186 
201 
224 
252 
271 



3-36M 

369 

3-97 

4.08 

4.46 

4.88 

498 

15 

38 

62 



6.76 

7.09 
703 
8.00 
9.01 



9-35 
9.61 

10.75 
11 .60 
12. 20 
13.70 
16.39 
95 24 



95 24 
16.39 
11 .60 
9 30 
7 63 
5-38 
4.98 
4.46 
3-97 
369 



3-34M 

4.00 



5-io 
5-35 
5-5i 
5.80 
6.20 

6.45 
6.70 
6.86 

7 25 
7.70 
8.10 



9.27 

9-73 

10.60 
11. 15 
12.03 
13-78 



11. 15 
9.27 
7.70 
5-35 



4.00 



is again a good agreement between the observed and calculated 
values of the infra-red bands. The lettering of the lines has the 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 37 

following meaning: The lines marked A are those which Cremer 
found to be the strongest, those marked B are the ones which form 
the heads of Cremer's series, while those marked H are the lines 
which Hartley considered to be the strongest. 

It is of some interest to notice that the central line of toluene, 
4047, is very nearly the same as that of benzene, 4055. As 4047 = 
10X405 very nearly, so, as in the case of benzene, 9X405 = 3645 
should be the central line of the fluorescence bands. If Dickson's 
values for the fluorescence of toluene be taken, it is clear that the 
maximum of 3650 must be the center of the system. Dickson's 
measurements of the maxima can be arranged as in Table XII, 

TABLE XII 

Toluene Fluorescence (Dickson) 



A in Angstroms 



2886. 
2809. 
2740. 
2676. 
2646. 
2622. 



3465 
3561 
3650 

3737 


205 (205) 
89 (86) 

87 (86) 


3779 
3814 


129 (132) 
164 (159) 



the figures in parentheses again showing the corresponding values 

v 
of - found in the absorption-band group. The accuracy of 

measurement of the wave-lengths of fluorescent maxima is not very 
great, and if the correction for the effect of solvent be applied there 
appears to be an error of 9 units in the value found for the central 
line. This, however, is well within the limits of experimental 
error. 

/>-Xylene 

Although the vapor absorption spectrum of ^-xylene was investi- 
gated by Hartley, more accurate measurements have been published 
by Mies, 1 who showed that the fine lines can very readily be 
arranged in series. He observed in the spectrum a certain number 
of strong lines which he denoted by A, and also a number of slightly 
less strong lines which he denoted by B. The A and B lines form 

1 Zcit. wiss. Phot., 7, 357, 1909. 



38 



E. C. C. BALY 



two series with constant frequency differences. Then further he 
found other lines, the frequencies of which differ by definite amounts 
from the frequencies of the members of the A and B series. He 
thus established four series which he denoted by A, C, B, and D, 
the C and D series being connected with the A and B series respec- 
tively. In Table XIII are given the absorption lines of />-xylene 

TABLE XIII 

/(-Xylene Absorption (Mies) 



a in Angstroms 



Mean v. 



Infra-Red Bands 



Calc. 



Obs. 



2814 
2800 
A 2785 
C 2771 
B 2757 
D 2744 
A 2722 
2717 
C 2709 

B 2695 

2691 

2685 

D 2682 

2680 

A 2664 

2661 

2657 

C 2650 

2643 

B 2637 

B 2584 

B 2533 

2530 
D 2521 

251/ 

2512 

A 2508 

C 2494 

B 2483 

D 2471 
A 2460 

2447 
B 2434 

2425 
A 2412 
C 2400 
B 2389 



3554 
3671 

359i 
3609 
3627 
3644 
3673 
3680 
3691 

3710 

3716 
3724 
3728 
373i 
3753 
3758 
3764 
3773 
3785 
3792 
3869 
3948 
3953 
3967 
3973 
3980 

3987 
4009 

4028 

4048 
4066 
4087 
4109 
4124 
4146 
4167 
4186 



315 
298 
278 
260 
242 
225 
196 
189 
178 

159 

153 
145 
141 

138 
116 
in 

105 
96 

84 

77 

o 

79 



104 
in 
118 

140 

161 

178 
197 
218 

240 
255 
277 
298 

317 



316 
298 

277. 

258 

241 

222 

196. 



178 
160 



140.5 



1 1 



in 

104 
97 



78 

84 

97 
104 
in 
117 

140.5 

160 

178 

186. s 

222 

241 

258 

277-5 

298 

316 



25 M 
38 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 39 



arranged with reference to the line ^ = 3869 as center, and the 

letters refer to Mies's classification. Again every infra-red band 
is accounted for and the greater symmetry of the molecule is shown 
by the fact that out of the 14 infra-red bands n give rise to pairs 
of absorption lines. 

The frequency of the central line 3869= 15X258 almost exactly, 
and therefore 14X258 = 3612 should be the central line of the 
fluorescence. Only four fluorescence bands were observed by 
Dickson and the frequencies of these should arrange themselves 
around this as center. The four frequencies when corrected for 
solvent are 3504, 3584, 3665, and 3744, and these obviously may 
be arranged around 3624 as center as shown in Table XIV. Xow 

TABLE XIV 
^-Xylene Fluorescence (Dicksox) 



A in Angstroms 


1 
K 


J+» 


V X 


2865 

2801 

2739 

2681 


3492 
3572 
3653 
3732 


3504 
3584 
3665 

3744 


120 (117) 
40 (39) 
4i (39) 

120 (117) 



3624=14X258.8 and consequently the fundamental interval is 
very near that of the absorption-band system. The small number 
of the fluorescence bands makes it impossible to arrive at greater 
accuracy. 

The absorption lines and fluorescence maxima may also be 
arranged in the same way for o-xylene and w-xylene and they are 
shown in Tables XV. XVI, XVII, and XVIII. In these tables 
certain lines are marked A or F. Those marked A are the lines 
which Hartley considered to be the heads of the sub-groups, 
while those marked F give the same values of v x as appear in the., 
fluorescence spectrum. The wave-lengths are taken from Mies's 
paper. 1 

The effect of the want of symmetry of the molecule is very well 
shown in Table XV as also in m-xylene. The frequency of the 

1 Zeit. wiss. Phot., 8, 287, 1910. 



40 



E. C. C. BALY 



TABLE XV 
o-Xylene Absorption (Mies) 



a in Angstroms 



Mean 



Infra-Red Bands 



Calc. 



Obs. 



2777 
2770 
2730 
2699 
2691 
2683 
2668 
2666 

2659 

2654 
2650 
2647 
2633 

2628 

2624 
2620 
2607 
2572 
2558 
2509 
2500 
2497 
2474 



3601 
3610 
3663 

3705 
3716 

3727 
3748 
3751 
3761 

3768 
3774 
3778 
3798 

3805 
3811 
3817 
3836 



3909 
3986 
4000 
4005 

4042 



308 

299 
246 
204 

!93 
182 
161 
158 
148 

141 
135 
131 

1 1 1 

104 



92 

73 



77 

9i 

96 

141 



141 



97 
91. 

75 



75 

91-5 
97 
141 



25M 

33 
07 
90 

18 

49 
21 

33 
74 
09 
4i 
63 
01 

64 

3i 
9i 
33 
62 



'5 



1 3 



25 M 
38 



24 



60 



<>o 



central line 3909=13X300.7, and the next multiple is 12 X 
300. 7 = 3608, which may be taken as the center of the fluorescence 
bands. In Table XVI the frequencies of the fluorescence bands 



TABLE XVI 

o-Xylene Fluorescence (Dickson) 



a in Angstroms 



r+13 



3 J 35 
3038 
2986 
2896 
2798 

2713 
2680 
2636 
2603 



3190 
3292 
3349 
3453 
3574 
3686 

373i 
3794 

3842 



3203 

3305 
3362 
3466 
3587 
3699 
3744 
3807 
3855 



405 

303 (299) 

246 (141) 
142 (141) 

21 (21) 

91 (91 -5) 
141 (141) 
199 (204) 

247 (246) 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 41 

are increased by 13 units in order to correct for the effect of the 
solvent. The central line 3864 is almost exactly 13X297, and 
therefore 12X297 = 3564 should be the center of the fluorescence. 
Dickson found only three maxima of fluorescence and they all lie 

TABLE XVII 

w?-Xylexe Absorption (Mies) 



A in Angstroms 



Mean v x 



Infra-Red Bands 



Calc. 



Obs. 



2802 
2721 

F 2716 
2703 
2694 

F 2687 
2684 
2668 
2663 
2658 

2655 
2648 
2640 

F 2601 
2588 

F 2574 
2540 

2531 
2520 

F 2496 
2484 

F 2473 



3569 
3675 
3682 

3 6 99 
3712 
3722 
3726 
3748 

3755 
3762 

3767 
3776 
3788 
3645 
3864 



3937 
395i 
3968 
4006 
4026 
4044 



295 
189 
182 
165 
152 
142 
138 
116 
109 
102 

97 
88 
76 

19 

o 

21 

73 

87 

104 

142 

162 

180 



181 

163 -5 



142 



103 



87.5 
74-5 
20 



20 
74- 
87 
i°3 
142 
163. 
181 



3-39M 



29 
52 
12 
58 
04 
7-25 
8.62 
9.17 
9.70 
10.30 

H-43 
13-42 
50.00 



50.00 
I3-42 
n-43 
9.70 
7.04 
6. 12 
5-52 



3-38M 

5-25 



6. 20 

6.77 



8.70 

9.17 

9.68 

10. 20 

11.42 

13.20 



13.20 

11.32 

9.70 



6. 20 



on the ultra-violet side of 3564. If this be correct then, allowing 
14 units for the effect of the solvent, the bands may be arranged 
as in Table XVIII. It is, however, manifestly impossible to draw 
any definite conclusions from only three maxima. 



TABLE XVIII 

w-Xylene Fluorescence (Dickson) 



A in Angstroms 


1 
A 


A + - 


Vx 


2802 

2715 

2685 


3569 
3683 

3724 


3583 
3 6 97 
3738 - 


19 (20) 
133 (142) 

174 (181) 









42 E. C. C. BALY 

There can be little doubt from the foregoing results that the 
conception of combining the frequencies of the short-wave infra-red 
bands with those of the central lines of the absorption and fluores- 
cence bands is perfectly justified. The agreement between the 
calculated and observed values is remarkably good in every case. 

The general conception can be put to a very severe test in the 
following way. Dickson found in the fluorescence spectrum of 
naphthalene 14 well-defined maxima which are very regularly 
arranged. In fact their frequencies may be expressed by the 
formula 

- = 3326-47-i2X«, 

where k = o, 1, 2, . . . . 13. He found small differences between 
the observed values and those calculated from the formula, espe- 
cially in the case of the band with the smallest frequency. It 
would seem, therefore, that in making any calculations from the 
frequencies it would be preferable to use the values obtained from 
the formula. Now the absorption spectrum of naphthalene in the 
infra-red region has not been measured and the only fact known 
about it is that Coblentz found a band at 3 . 25 fx for a solution of 
the compound in carbon tetrachloride. It is not possible, con- 
sequently, to check the values of frequency differences against 
infra-red measurements. Since the fluorescent bands are very 
symmetrically arranged it is possible accurately to calculate the 
frequency differences from that of the central line. This central 
frequency must be a multiple of the fundamental frequency, and 
the next higher multiple should form the center of the absorption 
band. From this new frequency, by making use of the frequency 
differences found in the fluorescent spectrum, it should be possible 
to calculate the frequencies of the lines in the ultra-violet absorp- 
tion band. 

In Table XIX are given the frequencies of the fluorescent 
maxima of naphthalene as corrected by Dickson and arranged 
symmetrically with respect to the mean frequency 3020, together 
with the frequency differences. The calculated values of the infra- 
red bands are given so that when this region is investigated the 
observed values may be compared. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 43 



Now the central frequency 3020 = 302X10, and as the funda- 
mental frequency of naphthalene is 302, the central frequency of 
the absorption band should be 302X11=3322. In order to cal- 
culate the frequencies of the lines in the absorption-band group 
we thus use 3322 =±v x , the values of v x being those given in Table 
XIX. 

TABLE XIX 
Naphthalene Fluorescence (Dickson) 



2714 
2761 
2808 

2855 
2902 
2949 
2996 
3020 

3043 
3090 

3138 
3185 
3 2 3 2 
3279 
3326 




Infra-Red Bands 



3 


27 n 


3 


86 


4 


72 


6 


06 


8 


48 


14 


2 


42 


6 


42 


6 


14 


2 


8 


48 


6 


06 


4 


72 


3 


86 


3 


27 



The absorption of naphthalene vapor has been investigated by 
Purvis, who found that the band group shown by the alcoholic 
solution is not resolved into fine lines. It is necessary, therefore, 
to make use of the solution spectrum of naphthalene for the present 
comparison. This spectrum has been measured by several ob- 
servers, 1 and Mr. F. C. Guthrie in my laboratory has kindly 
repeated the observations, using the new Hilger ultra-violet spec- 
trophotometer, the accuracy of which far exceeds that of the old 
method of qualitative measurement. 

In Table XX the first column shows the values of v x obtained 
from the fluorescence bands and given in Table XIX. The second 
column contains the calculated frequencies of the absorption bands, 
while the corresponding wave-lengths appear in the third column. 
In the fourth column are given Mr. Guthrie's measurements. No 



1 Hartley, Chemical Society Transactions, 39, 153, 1881; 67, 685, li 
Tuck, ibid., 93, 1902, 1908; Purvis, ibid., 101, 1315, 191 2. 



Baly and 



44 



E. C. C. BALY 



correction for solvent is here needed since the fluorescence measure- 
ments were also made with a solution. The agreement between 
calculated and observed values is exceedingly good in view of the 
fact that there are no infra-red measurements against which the 
frequency differences (v x ) can be checked. Certain of the calcu- 

TABLE XX 

Xaphthalexe Absorption- 



Absorption Bands in A 



Calc. 



Obs. 



306 
259 

212 

165 
Il8 

71 

23 

O 

23 
71 

11S 

165 
212 

259 
306 



3016 

3° 6 3 
3110 

3157 
3204 

3251 
3299 
(3322) 
3345 
3393 
3440 
3487 
3536 
358i 
3628 



33ii 
3265 
3215 
3168 
3121 
3076 
3031 



3218 
3158 
3118 



3025 



2990 

2945 
2907 
2868 
2828 
2793 
2757 



296- 



2867 
2840 
2798 
2759 
2670 



lated absorption bands do not appear in the solution spectrum and 
the broad band at 2965 does not seem to divide. One more 
absorption band has been observed at 2670 beyond those that have 
their counterpart in the fluorescence spectrum. It may be asserted 
that the foregoing calculation confirms the theory here put forward 
in a striking fashion. 

Two interesting points may be noted, one of which is the agree- 
ment of the only observed infra-red band of naphthalene with the 
calculated value, and the other is the fundamental frequency of 302. 
This frequency is practically the same as that of o-xylene which is 
301. Naphthalene can be looked upon as containing ortho- 
substituted benzene rings and it would seem, therefore, as if 301 or 
302 might prove to be the fundamental frequency of ortho- 
disubstituted benzene compounds. 



ABSORPTION. FLUORESCENCE, AND PHOSPHORESCENCE 45 

There is no doubt that it should also be possible on the present 
theory to explain the phosphorescent spectra as observed by 
von Kowalski 1 and Goldstein 2 with certain organic compounds. 
Both these authors investigated the phosphorescence of the solid 
substances at very low temperatures, but we have no knowledge 
of the shifts of the bands under these conditions as compared with 
the vapor. It is impossible to calculate the frequencies from these 
authors' measurements in the way adopted above. 

The following substances may be taken, namely benzene and 
/>-xylene, both of which were investigated by von Kowalski 3 
and the latter also by Goldstein. The fundamental frequencies of 
these compounds are 405 and 258, respectively. The simplest 
method of calculation is to find whether the phosphorescence 
maxima can be arranged in each case with reference to a multiple 
of the fundamental frequency, due regard being paid to the fact 
that the maxima are certain to be moved toward the red. The 
accuracy reached by these authors is only about 25 angstroms and 
therefore the frequencies are expressed with only three figures. 
But in spite of this it is clear that the same relation holds good here 
also. 

Thus in benzene the frequencies of the phosphorescence maxima 

can be arranged symmetrically with respect to ^ = 242 as shown 

A 

in Table XXI, together with the values of v x (in parentheses) found 



TABLE XXI 
Bexzexe Phosphorescexce (vox Kowalski) 



I 

A 


" X 


1 

A 


Vx 


230 

233 

239 

242 

249 

252 

26o 


12 (12.7) 

9 .( 9-2) 
3 



7( 7-7) 
10 (10. 2) 
18 (18.4) 


263 

27O 

274 

28o 

284 


21 (20.8) 

28 

32 (31-8) 

38 

42 (4O.3) 


289 

295 


47 
53 



1 P/tys. Zeit., 12, 956, 191 1. 

2 Ibid., 12, 614, 1911; Dcutsch. pliys. Gcscll. Verh., 14, 33, 493, 1912. 

3 Loc. cit. 



46 



E. C. C. BALY 



in the absorption band. It may be pointed out that the frequency 
of 47 corresponds very nearly to the infra-red band at 2.18 ju 

We thus have for the fundamental frequency of benzene the 
following values: 

Phosphorescence 6X403.3 

Fluorescence 9X405 

Absorption 10X405 

In the case of ^-xylene the values given in Table XXII are 
obtained. It is possible that there is an error in von Kowalski's 



TABLE XXII 



Phosphorescence (von Kowalski) 


Cathodoluminescence (Goldstein) 


1 

A 


I'X 


Mean v x 


1 

A 


"x 


234 

239 

243 

249 

253 

256 

258 

265 


22 

17 

13 

7 

3 



2 

9 

14 

18 

26 


22 (22.2) 

17.5 (19 and 16) 
i3-5(i3-8) 
8 (7-8) 

2-5 


176 

ISO 

184 

l88 


30 (29.8) 
26 (26) 
22 (22. 2) 
18 (19) 


192 

I96 

200 

205 


14 (14) 
10 (10. 5) 


2-5 

8 ( 7-8) 
13-5 (i3-8) 
17.5 (16 and 19) 

? 


6( 5-9) 




27O 

274 

282 

Central line 256 


208 

212.. 


2 

6 (5.9) 


Central line 205.6 





measurement of the last maximum on his list. We thus have the 
following values for the fundamental frequency of /^-xylene: 

Cathodoluminescence 8X257 

Phosphorescence 10X 256 

Fluorescence 14X 258 

Absorption 15X258 

Very great accuracy from the values of the phosphorescent 
maxima is not to be expected, since the measurement of. these are 
far from accurate. There seems to be no doubt, however, that 
the same relations hold good with them as in the case of the ultra- 
violet band groups. 






ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 47 
z. Determination of the basis constants ( — - T ) from the known 

\27T if 

absorption in the short-wave infra-red region, and the calculation from 
these of the component lines in an ultra-violet absorption-band group. — 
Although the extension of Bjerrum's conception to the ultra- 
violet absorption-band groups is completely successful, it must 
clearly be understood that the whole problem is by no means solved. 
For example, only about 30 out of the 200 absorption lines compos- 
ing the ultra-violet absorption-band group of benzene have been 
accounted for. In the explanation of these 30 lines the short-wave 
infra-red bands only have been employed. It is true that prac- 
tically all the known infra-red bands have been pressed into service, 
but there still remain the long-wave infra-red bands, that is to 
say those bands due to the rotational frequencies of the mole- 
cules. Nothing is known at present about the rotational fre- 
quencies of any one of the compounds dealt with above. If it were 
possible by some means to arrive at these values, then by combining 
these with the frequency of the central line it should be possible 
to calculate the frequency of every absorption line in any one 
absorption-band group. 

The present position of the argument may be summed up as fol- 
lows: There exists a constant difference between the frequencies of 
the central lines of absorption-, fluorescence-, and phosphorescence- 
band groups of any one compound, and, further, this constant 
difference equals the frequency of a band in the short-wave infra- 
red region. Bjerrum has shown that the structure of any one 
band group in the short-wave infra-red is explained by the com- 
bination of the central frequency of that band with the rotational 
frequencies of the molecules, which frequencies are given by the 

expression v r — — — T . It has now been shown that it is possible 

27T"i 

to explain certain of the absorption lines in the ultra-violet and 
visible absorption-band groups and also the fluorescent- and 
phosphorescent-band groups by the combination of their central 
frequencies with the frequencies of the centers of the observed 
infra-red bands in the short-wave region. Is it now possible from 
a knowledge of the short-wave infra-red bands of any substance 



48 E. C. C. BALY 

alone to determine the value or values of — — for that substance, 

27T 2 / 

and from these values to calculate the entire structure of the 
absorption-band groups of that substance in whatever region they 
occur ? I may say that I have succeeded in doing this and further- 
more in calculating the absorption of certain compounds -from the 

values of — ~ T of their component radicles. 

27T7 

As already pointed out, Eucken showed that the infra-red 
absorption bands of water- vapor of longer wave-length than about 
10 ix can be expressed by the Bjerrum formula; that is to say, their 
frequencies form consecutive multiples of two basis constants, 

—rz. (he having assumed two degrees of freedom). If wave-length 

27T"i 

reciprocals are used, the values of these basis constants are 5 . 78 
and 2.5, respectively. Eucken, however, entirely failed to explain 
the very remarkable variations in the intensities of the infra-red 
bands of water. He extended his series from the far infra-red 
only to 10.5 (i and offered no explanation of the extraordinary 
intensity of the bands at 6.0 ju, 3.0 /x, 2.0 n, and 1.5/i. It is 
in this respect that Bjerrum's theory is incomplete, for the whole 
essence of the theory is that the frequencies of the centers of the 
infra-red bands are consecutive multiples of one or more funda- 
mental constants or bases. The theory in no way accounts for 
the fact that certain select multiples of the constants give rise to 
absorption bands which are far more intense than the neighboring 
multiples on each side. 

On the other hand, if two basis constants are functionally 
active, then there must exist a convergence frequency of the two 
which is the least common multiple of the two. Such a convergence 
frequency will necessarily be especially active, since it is keyed 
with both series, and I suggest, therefore, that this is the reason 
why an infra-red absorption band is especially pronounced in inten- 
sity — namely that the frequency of the band is either the least 
common multiple of the two basis constants or is a multiple of that 
least common multiple. If this principle be accepted, it seems 
entirely to solve the difficulty connected with the intensity of 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 49 

infra-red absorption bands and renders the calculation of the 
values of the basis constants relatively simple. This is adopted 
as the fundamental principle in all that follows. 

The most intense absorption bands of water-vapor in the short- 
wave infra-red region lie at 6 . 25, 6.0, 3 .0, 2 .0, and 1.5/1- and the 
wave-numbers of these are 160.0, 166.6, 333.3, 500.0, and 666.6, 
respectively. Eucken has pointed out that 2 . 5 is one of the basis 
constants of water, and the foregoing wave-numbers at once sug- 
gest that there is another basis constant of 6.6. The first recipro- 
cal, 160.0, is an even multiple of these two constants, for 160 = 
64X2.5 = 24X6.6, while the second reciprocal, 166.6, is the least 
common multiple of the two. The three remaining reciprocals 
are the least common multiple multiplied by 2, 3, and 4, respectively. 

It is probable that the intensities of the absorption bands due 

to the multiples of the basis constants acting alone must decrease 

ti h 
as the value of n increases in the formula — —. , and consequently in 

the short-wave infra-red region, where n is large, the absorption 
bands due to these multiples acting alone will be very faint indeed. 
For instance, in the case of water-vapor no small absorption bands 
have been detected between the great bands given above. When, 
however, that frequency is reached which is either an even multiple 
or the least common multiple of the basis constants, then a very 
strong absorption band is evidenced. It follows further from this 
that in the case of water, for instance, the only possible regions 
of still shorter wave-length at which absorption bands can evi- 
dence themselves will be at frequencies which are multiples of 
166.6. There will, obviously, be found a constant frequency 
difference of 166.6 between such absorption bands, and a physical 
explanation is again found for the relation previously dealt with 
between the frequencies of the bands in the ultra-violet and visible 
regions and an infra-red band. It is also now clear why only one 
band in the infra-red is concerned. 

From what has been proved before as regards the application 
of Bjerrum's theory to the structure of ultra-violet and visible 
absorption bands, it is clear that we are now in a position to cal- 
culate the region and the entire structure of any absorption band 



50 E. C. C. BALY 

of water-vapor. There are two basis constants, 2.5 and 6.6, and 
possibly a third, 5.78. In the first place, the central line of any 
absorption band must have a frequency which is some multiple 
of 166.6. In the second place, there will be symmetrically dis- 
tributed on each side of this central line pairs of absorption lines 
due to the combination of the central frequency with consecutive 
multiples of 2.5, 5.78, and 6.6. The central line with maximum 

absorption will therefore have a frequency ( ^ ) of 166 . 6x, and there 

will also occur pairs of absorption lines the frequencies of which 
will be given by i66.6x±«A' I , i66.6x*=nK 2 , and i66.6x= t ;?A' 3 , 
where x is some whole number, K l} K 2 , K 3 are 2.5, 5.78, 6.6, 
respectively, and n=i, 2, 3, etc. Again, it is to be expected that 
the absorption-band group will be divided into sub-groups and the 
frequencies of the heads of these sub-groups will be given by 
166.6a; =±=160, i66.6#= 1 =i66.67, 166. 6^=^333. 33, since 160, 166.67, 
and 333.33 are the frequencies of the most intense absorption 
bands in the short-wave infra-red region. 

Unfortunately nothing is as yet known about the ultra-violet 
absorption band of water except that it would appear from refrac- 
tivity measurements 1 to lie in the very extreme ultra-violet with 
a frequency of 10666.67 (64X166.6). Hence it is not possible to 
put the theory to the test of experiment in this case. 

Attention may here be drawn to the influence of temperature 
on the width of absorption bands, it being a well-known fact that 
they become narrower with fall of temperature. 2 At the boiling- 
point of hydrogen it has been shown that the bands appear only 
as fine lines. The effect of temperature in all probability is to 
change the molecular rotational energy, and as the temperature 

iih 
falls the effective values of n in the formula — — T become smaller 

27T 2 / 

in number, and indeed at very low temperatures only the lowest 
multiples of the basis constants will be active. Obviously the 
absorption bands will become narrower as the temperature falls, 

1 Baly, Phil. Mag., 27, 632, 1914. 

2 J. Becquerel, Comples rendus, 144, 420, 1907. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 51 

and at exceedingly low temperatures they may appear only as 
single lines, namely the central lines of the systems. 

Although an experimental test of the theory cannot be applied 
in the case of water-vapor, there would be no such difficulty in 
the case of benzene, the ultra-violet absorption-band group of 
which has been investigated very completely. If. therefore, it 
is possible to find the basis constants of benzene from its known 
infra-red absorption, the experimental verification can easily be 
found in this compound. Coblentz has measured 20 absorption 
bands of benzene between the limits 1 /jl and 13 n and they differ 
very much among themselves in intensity. Of these bands the 
most pronounced appear at 9. 78, 6. 75, 5 . 5, 3. 25, 2 .48, 2. 18, and 
1 . 68 [x. If the wave-numbers of all the infra-red bands of benzene 
are considered, it is at once apparent that they are very nearly 
multiples of 4, and it seemed at first sight that they could all be 
expressed with very fair accuracy as multiples of 4. It seems evi- 
dent then that 4 is one of the basis constants of benzene. This, 
however, gives no explanation of the very remarkable intensity 
differences between the bands, and. further, all the consecutive 
multiples of 4 do not evidence themselves as bands even between 
10 and 13 fi, where perhaps they might be expected to appear. 

Now the two most outstanding and characteristic bands of 
benzene are those at 6.75^ and 3.25/z; they are characteristic 
in the sense that they generally appear in the absorption spectra of 
the simple derivatives of benzene. The wave-numbers of these two 
bands are almost exactly 148 and 307.6 and on the least-common- 
multiple principle they are the least common multiples of 4 and 3.7, 
and 4 and 7.6, respectively. Consequently these three basis con- 
stants explain the two most characteristic bands of benzene. 

Again, these three constants also explain some of the other 
important bands the frequencies of which are whole multiples of 
two of the three constants. Thus 7.6X24 = 4X46 = 184, which 
is the wave-number of A =5. 43 ju, a value very close to Coblentz' 
measurement of 5.50//. Then also 7.6X60 = 4X115 = 460, the 
wave-number of \ = 2 . 174 ,u, a value exceedingly close to Coblentz' 
measurement of 2.18/x. Further, the wave-number of 6.75 /x is 
148, and 2X148 = 296, the wave-number of 3.37 fi. which is hidden 



52 E. C. C. BALY 

in the great band at 3.25 //, while 3X148 = 444, the wave-number 
of 2. 25 fx, which is hidden in the band at 2. 18 /x; but 4X148 = 592 
is the wave-number of 1.68 /z, the value actually measured by 
Coblentz. The three basis constants of 3.7, 4, and 7.6 therefore 
explain all the important absorption bands of benzene between 
1 11 and 13 ix except those at 2.48 and 9.78 fx. As regards the 
former, it is remarkable that the component absorption lines of 
the ultra-violet band group of benzene can be symmetrically 
arranged around the frequency of 4050 as center. This value is 
10X405 which is very near the wave-number of 2.48 ix. Again, 
no combination of the three foregoing basis constants gives a num- 
ber near this value, and since it appears to be a fundamental one 
for benzene it is in all probability due to the existence of a fourth 
basis constant of 10.125. The least common multiple of 4 and 
10.125 is 405, the wave-number of 2.49 //, a value exceedingly 
close to that measured by Coblentz, 2.48 /x. 

We are left with the band at 9. 78 fx, which, however, does not 
appear to be a specially characteristic band of benzene in spite of 
its intensity, since it does not evidence itself with any definiteness 
in benzene derivatives. This band and the remainder of less 
intensity are doubtless due to multiples of the four basis constants 
which happen to lie near together with the result that then - effect- 
iveness as absorbers is enhanced. Thus 10X10.125 gives a band 
at 9.88 ix, and 3.7X28 gives a band at 9.54 fx, and the mean 
of these is 9. 76 ix. Added to this, the other two bases give bands 
in the immediate neighborhood which tend still further to enhance 
the intensity. All the remaining bands can be accounted for in the 
same way by the fact that multiples of two of the constants happen 
to lie near together. It is interesting to note that when two such 
multiples are not very close a weak and broad absorption band is 
shown. 

The entire short-wave infra-red band system of benzene can 
thus be accounted for by the existence of four basis constants. 
Again, it is evident that no absorption band of any importance 
can be exhibited by benzene with a shorter wave-length than 1 lx 
except at a frequency which is some multiple of the least common 
multiple of two of the basis constants. If, therefore, the approxi- 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 53 

mate position of the ultra-violet absorption band of benzene be 
known, it should now be possible to calculate the wave-numbers 
of all the component absorption lines of that group. It happens 
to be peculiarly simple owing to the symmetry of the benzene mole- 
cule which results in a very obvious symmetry of the absorption- 
band group. The wave-number of the central line of the system 
is undoubtedly 10X405 = 4050, and the wave-numbers of the com- 
ponent lines can then be computed from 

4050 = 3. pi, 4050=4. on, 4050 = 7. 6m, 4050=10. 125W. 

The reciprocals of the wave-numbers thus obtained will give the 
wave-lengths, but these must be corrected for the refractive index 
of air before they can be compared with the observed values. In 
Table XXIII is given the complete list of absorption lines in the 
red side of the ultra-violet band group of benzene and in the ninth 
column are to be found their wave-lengths corrected for the refract- 
ive indices of air. In the last two columns are given the values 
observed by Hartley and by Grebe. The agreement between the 
calculated and observed values is very close and thoroughly justi- 
fies the theory here put forward. All the calculated wave-lengths 
have not as yet been observed, but this is not surprising as so many 
of them lie very close together. It would seem from Hartley's 
paper that there exist more lines than were actually distinguished 
by him. He recorded a great number of narrow absorption bands 
which were resolved on some of his negatives and not on others. 
The general conclusion may be drawn from the measurements of 
these bands that other lines exist beyond those specifically men- 
tioned by Hartley. The wave-lengths of the lines in the blue side 
of the band have also been calculated and the agreement between 
the observed and calculated values is equally good. There is there- 
fore no need for their reproduction. 

Reference has been made previously to the division of the 
benzene band into sub-groups, and the opinion was expressed that 
the heads of these sub-groups are due to the combination with the 
central frequency of the frequencies of the short-wave infra-red 
bands. As there seems to be some doubt about Hartley's measure- 
ments of these heads — that is to say, as regards which lines are 



54 



E. C. C. BALY 



TABLE XXIII 

Ultra-violet Absorption Band of Benzene 

K l = 3.7, £2=4.0, £3 = 7.6, £4=10.125 

Red Side of the Band 



»I 


1 

A 


n 2 


1 

A 


n s 


1 

A 


"4 


1 

A 


A Calc. 


AObs. 

Hartley 


AObs. 
Grebe 




4050.O 
4046 . 3 

4042.6 














2468.4 
2470.7 
2470.9 
2471.9 
2473- 1 
2473-4 
2474-7 
2475-2 
2475-8 
2477-5 
2477.8 
2478.2 

2479-7 

2480.7! 

2480.8/ 

2482.0 

2482.5 

2483 . 2 

2484-3 
2485.6 
2486.6 
2487.1 

2487-3 

2488 . 1 
2488.9 
2490 . 6 

2491 . 2 
2492.0 
2493 • 1 
2493-41 
2493-5/ 
2495-6 
2495 • 8 
2496.8 
2498 . o\ 
2498.1/ 

2499 • 5 
2500.0 
2500.4 
2501.6 
2502.7 
2503-0 
2505- 1 
2505.6 
2506.0 
2506.4 

25074 
2508.2 


2469 


2468.3 


















1 


4O46 . O 










2472 


2471 




















I 


4042.33 












2 


4O42.O 
















I 


4039-875 


2474 


2474.5 


3-- 


4038 . 9 
4035 • 2 












3 


4O38.O 










2476 
2477 


2476 


4-- 
















2 


4034.67 










4°3I-5 


4 


4034 . O 






2479 
2480 

2481 

2482 


2478.6 


5-- 










2480 


5 


403O.O 


















2 


4029.750 


2481. I 


6. . 


4027.8 


















3 


4027.OO 










4024 . I 
4020.4 


6 


4026.O 






2483 

2484 
2485 
2486 

2487 


2483 


7- 










2484 . 7 


7 


4022.0 












8. . 






















3 


4019.625 












4 


40I9-33 






4016. 7 
4OI3.O 


8 


4O18.O 






2489 
2490 
2491 
2492 
2493 
2494 

2495 
2496 
2497 

2498 

2499 


2488.3 


9 •■ 












9 


4OI4.O 












10. . 










2491 








5 


401 1 .67 












10 


40I0.0 














4 


4009 . 500 




11 . . 


4OO9 . 3 

4005 . 6 










2493-7 




11 


4006 . O 












12. . 










2496.3 








6 


4004 . OO 










4001 .9 


12 


4002 . O 








13 . . 






















5 


3999-375 


2499 ■ 1 




3998.2 


13 


3998.O 








14. . 










2501 
2502 


2501 








7 


3996-33 








I5-- 


3994-5 
3990. 8 












14 


3994 -o 










2503 
2505 




16. . 










2504.4 




15 


3990.0 


















6 


3989.250 


2506 


2506.3 










8 


3988.67 




17. . 


3987-I 










2407 
2509 






16 


3986.0 

























ABSORPTIOX. FLUORESCENCE, AND PHOSPHORESCENCE 55 
TABLE XXIII 



Wi 


1 

A 


Mi 


1 

A 


>h 


1 
A 


«4 


1 

A 


A Calc. 


AObs. 
Hartley 


AObs. 
Grebe 


l8 


3983 -4 














2509 7 


2510 






17 


3982.0 










2510 
25H 
2512 
2512 
2513 
2514 
2515 
2516 
2516 
2518 
2518 

2519 
2520 
2520 
2521 

2523 
2523 
2525 
2525 
2526 
2528 
2528 
2530 
2530 
2531 
2533 
2533 
2535 
2536 
2538 
2538 
2538 
2540 
2540 
2541 
2542 
2543 
2544 
2545 
2545 
2546 
2547 
2549 
2550 
2550 
2551 
2551 
2552 
2554 
2554 
2555 
2556 


6 
2 



4 

2 

4 
6 


7 
2 
8 
1 
7 
9 
4 
3 
8 

3 

8 

1 

4\ 

5 

7\ 

9/ 

7 

3 

5 

7 

1 



3 
6 

4 
6 

3 
8 
8 
8 
2 
5 
4 
6 


5 
4 
6 

4 
2 
8 

5 
8 


2510.4 




9 


3981 .00 






19. . 


3979-7 










2512 












7 


3979-125 






3976.0 


18 


3978.O 






2513 
25140 

2516 

2517 
2518 


















19 


3974 -o 










2515 . 5 




10 


3973-33 










3972.3 














20 


3970.0 










2517.8 








8 


3969 . OOO 




3968.6 










2519 

2521 
2522 






21 


3966.0 










2520. I 




II 


39 6 5-67 








23- • 


39 6 4-9 
3961.2 












2522 


22 


3962.0 










24. . 










2524 
2525 


352.4 5 










9 


3958.875 






3957-5 
3953-8 


23 


3958.o 


12 


3958.00 










2526.5 
2529 

2532 
2533 
2534 
2535 

2538 


2526.O 




24 


3954 










26 










2528 






13 


3950.33 






; f 2530 
\253I 
2532.1 




395° - 1 


25 


395°-o 












10 


3948.750 


28. . 


3946.4 
3942.7 
3939° 












26 


3946.o 










2534 


29.. 


14 


3942.67 






27 


3942.o 






2536.2 


3°- 


















11 


3938625 






3935-3 


28 


3938.o 






2539 
2540 




3i- 










2539.6 






15 


3935 00 










3931-6 


29 


3934-0 






2541 
2543 
2544 




32-- 










2542.4 


3° 


3930.0 










2544 








12 


3928.5OO 




33- • 


3927.9 


















16 


3927-33 












3924.2 

3920.5 


31 


3926.0 






2546 
2547 
2549 
2550 
2551 




34•■ 










2547.3 


32 


3922.0 












35- 
















17 


3919.67 
















13 


3918.375 






3916. 8 
39i3- 1 


33 


3918.0 










36.. 










2552 
2554 
2555 
2556 


2552. I 


34 


39140 












37. . 


















18 


3912.00 






2555 . 5 






35 


3910.0 























56 



E. C. C. BALY 
TABLE XXIII— Continued 



Hi 


1 

A 


tii 


1 

A 


n 3 


I 
A 


n, 


I 
A 


A Calc. 


A Obs. 
Hartley 


A Obs. 

Grebe 


38.. 


3909 -4 














2557-2 

2558.0 

2559-51 

2559-6/ 

2560.5 

2562. 1 

2564.4 

2564 -5 
2564.6 

2565-5 
2566.9 
2567.2 

2569-3 
2569.9 

2570.5 
2571.2 

257I.7 
2572.6 
2574-2 
2575-2 
2575-6 
2576.6 
2577-8 
2578.0 

25791 
2580.5 
2580.7 
2581.6 
2583-2 
2584.0 
2584 -7 
2585.9 
2586.5 
2588.5 
25S9.0 
2591.0 
2591.2 
2591-5 
2593-9 
2594-0 
2596. I 

2596.5\ 

2596.6/ 

2598.2 

2598.9 

2599-3 

2601 .3 

2601.4 

2602.0 

2604.0 

2604 . 7 

2605.1 


2557 

2559-5 

2561 

2562 












14 


3908.250 


2558 O 




3905-7 


36 


3906.O 








39- ■ 










2560 






19 


3904.33 








40. . 

41. . 


3902.0 
3898.3 


37 


3902.0 


























15 


3898.125 










38 


3898.0 






2565 
2566 

2567 
2569 






20 


3896.67 






2565 . 5 


42. . 


3894.6 
3890.9 












39 


3894.O 











2568 


43- • 












40 


389O.O 














21 


3889.OO 
















16 3888.000 


2571 
2572 




44. . 


3887.2 
38830 












4i 


3886.O 








2572.4 


45 •• 










42 


3882.O 














22 


3881.33 








46.. 


3S79.S 










2576.5 


2576. 7 


43 


3878.O 


















17 *877.87C 


2578 
2579 
2580.5 




47 ■ 


3876.1 














2579 




44 


3874-0 














23 


3873.67 








48.. 


3872.4 
3868.7 










2582 
2583 
2584 
2585 
2586 

2587 
2588.5 

2591 


2581 .9 


45 


387O.O 












49- 


















18 3867.750 


2585 




3865.0 
3861.3 


46 


3866.O 


24 


3866.OO 




50.. 




2587.0 


47 


3862.O 










=;i . 








2589 








25 


3858.33 








38576 
3853 -9 


48 


3858.0 






52.. 






19 38C7.62; 






49 


3854 -O 










2594 
2596 

2597 
2598 

2600 
2601 


25929 


53 •• 
















26 


3850.67 








54. . 


3850.2 














50 


3850.0 
















20 Z&A1 . ?OQ 


2597.8 


55 ■ • 


3846.5 














2599 




5i 


3846.O 














27 


3843.OO 






2601 .3 


56.. 


3842.8 
3839- 1 












52 


3842.O 










2602 
2604 




57 . . 










2603 .9 




53 


3838.0 


















21 


3837 • S7^ 


2605 


2605 

















ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 57 
TABLE XXIII— Continued 



111 


A 


1 

A 


tit 


1 

A 


n< 


I ACalc. 

A 


AObs. 

Hartley 


AObs. 
Grebe 


58 ! 


3335-4 
383I-7 
3828.O 1 






28 


3S25.33 






2606.5 
2607 . 5 
2609.O 
26lO. 2 
26ll .5 
26II.8 
26I2.0 
2612.9 
2613. I 

2615 .6 
2616.6 
2617.0 
2618.3 
2618.9 
2619. 1 

2621 . 1 
2621.8 
2622.3 
2623.8 

2624 . 2 
2626.0 
2626.6 
2627.5 
2629.3 
2629.4 
2631.9 

2632. 1 
2632.9 
2634.4 
2734-9 
2637.0 
2637.7 

2638. 2 
2639.6 
2640.0 
2640.4 
2642. 2 

2643 • s\ 

2643.6/ 

2644 . 8 

2646 . 1 

2647. 1 

2647.3 

2648.9 

2650.0 

2651.7 

2652.6 

2654.2! 

2654. 3f 

2654.5 

2655.2 

2657-4 


2606 
2608 

2610 
2611.5 






54 


3834-0 








59- ■ 










2609 . 3 


55 


3830.0 










60 


















29 


3827.67 
















22 


3827.25O 


2613 


2612 .4 




3824-3 
382O.6 


56 


3826.O 








61 














57 


3822.O 










2615 
2616 
2617 
2618 
2619 


2614.7 
2616 


62 
















30 


382O.OO 












58 


3818.O 














23 


38l7. 125 




63.. 


3816.9 
38l3- 2 












59 


3814.O 










2621 


2621 . I 


64.. 
















3 1 


3812.33 






2624 
2625 
2626 


2623 




3809.5 


60 


381O.O 






























24 


3807.OOO 


2625.4 


66 


3805.8 


61 


3806 . O 










32 


3804.67 






2628 
2629 




67. . 


3802. I 
37984 










2629 




62 


3802.O 












68 . 










2632 


2631 .6 




63 


3798.O 














33 


3797.OO 


25 


3796875 


2633 
2634 
2635 
2636 
2637 


2633 


69.. 


3794-7 
379IO 






2634.4 


64 


3794 












70. . 














65 


3790.0 














34 


378933 








71 . . 


3787.3 










2639 


2639 












26 


3786.750 






37S3-5 


66 


3786.0 






2641 
2642 

2644 

2645 

2646 . 5 




72. . 










2642 




67 


3782.0 














35 


3781.67 








73. . 


3779-9 














68 


3778.0 










2646. 2 


74- ■ 

75- ■ 

76.. 

77- ■ 






27 


3776.625 




3776.2 

3772.5 
376S.8 










2647-5 




69 


3774-0 


36 


3774.00 












2650 

2652 
2653 
2654 


2650.5 


70 


3770.0 






























28 


3766.5OO 










37 


3766.33 




3765- 1 


7i 


3766.0 
















2655 


2655. 2 


72 


3762.0 















































E. C. C. BALY 
TABLE XXIII— Continued 



til 


1 

A 


ni 


1 

A 


n 3 


1 

A 


n. 


1 

A 


A Calc. 


AObs. 
Hartley 


AObs. 
Grebe 


78.. 


3761.4 














2657.8 
2659.7 
2660. 2 
2660.4 
2661.3 
2663 . I 

2665. 1 
2665.6 
2665.9 
2668.3 
2668.5 
2668.7 
267O.6 
267O.9 

2671 .6 
2673.6 
2674.4 

2675.8 
2676. i\ 
2676. 2/ 

26773 
2678.9 

2650. 2 
2681.5! 
2681.6/ 

2683 . 1 
2684.2 
2685.9 
2686.9 
2687.1 
2688.8 
2689.6 

2690 . 4 

2691 . 7 

2692. 2 
2692.7 
2694.6 
2694.9 
2697.5] 
2697.6^ 

2697-7] 
2698. 2 
2700.3 
2700.4 
2703.0 
2703-4 

2703. 5 
2705- 1 
2705-7 
2706.3 
2 708 . 4 
2709. 2 
2709-5 


2659.5 


2658.2 






38 


3758.67 








3757-7 


73 


3758.0 








79.. 






















29 


3756375 


2662 
2664 
2665 




80 


3754-0 


74 


3754-0 






2663 




39 


375I-00 






81. . 


3750-3 
3746.6 














75 


3750.0 










2666 


2665.9 


82. . 




















30 


3746.250 


2668.5 

2669 

2670.5 

2671 

2672 








76 


3746.0 










40 


374? . ?? . 








83.. 


3742.9 
3739-2 














77 


3742.0 










2671.8 


84.. 










78 


3738.0 










2675 










31 


3736. 125 












4i 


373567 


2676 

2677.5 




85.. 


3735-5 
373 1 - 8 

3728.1 












79 


3734 










2676.9 


86. . 












80 


37300 










2680 

2681.5 

2683 
2684.5 




87.. 
















42 


3728.00 










3724-4 
3720.7 


81 


3726.0 


32 


3726.OOO 




88. . 






2684.I 




82 


3722.0 










89.. 


















43 


3720.33 






2687 
2689 
2690 
2691 






37170 


83 


3718.0 






2688.9 


90.. 
















33 


37I5.875 






37133 


84 


37UO 






91.. 








2692 








44 3712.67 










3709.6 
3705-9 


85 


3710.0 










2694 
2695 

2697 

2698 
2700 


2694 


92.. 










86 


3706.0 












93 • • 




















34 


3705.750 












45 


3705.OO 


2699 


94 .. 


3702. 2 
3698.5 










2700 


87 


3702.0 












95- ■ 










2703 




88 


3698.0 














46 


3697.33 


















35 


3695 625 


2706 


2705 


96.. 


3694.8 
3691. 1 












89 


2694.0 












97. . 










2708 
2709 
2709 -5 




90 


3690.0 














47 


3689.67 























ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 59 
TABLE XXIII— Continued 



ttl 


1 

A 


A 


«a 


1 

A 


«< 


1 

A 


A Calc. 


AObs. 

Hartley 


AObs. 
Grebe 


98.. 


3687.4 












2711 . I 
2712. I 
2712.5 
2713.9 

27rSI 

2716.6 
2718. I 

27I9-3 

2720.O 
2720.8 
2721 .O 
2722. I 
2724.O 

2724. s 
2726.5 

2727.0 

27275 
2729.9 

2730.3 
2732.2 
27330 
2733. I 

2735- 1 
2735-9 
2737-9 
27386 

2738.9 
2741.4 

2741.9 
2742.7 

2743-7 
2744.2 

2744-9 
2747.0 
2748.0 

2749-5 
2749.8 

2750.3 
2751.0 
2752.6 
2754-0 
2755-3 
2755-4 
27570 
2758.0 
2758.2 
2760. 1 






91 3686.O 




















36 


3685.500 


2713 
2714 

2715 




99 ■• 


3683.7 
3680.O 

3676.3 










92 3682.O 


48 


3682.OO 








100 




















2718 
2719 






























37 


3675-375 












49 


3674-35 








3672.6 
3668.9 


94 


36740 
























95 


3670.0 














103. . 


















50 


3666.67 






2726 






3665.2 
36615 










104. . 










38 


3665.25O 






97 


3662.0 






























5i 


3659.OO 






2732 






36578 


98 


3658.0 
































39 


3655-I25 


2735 
2736 
2738 






3654. I 


99 


3 6 540 










52 


365I-33 








108. . 


3650.4 
















a6co 










2739 
2741 




109. . 


3646.7 














101 


3646 • O 


















40 


3645.OOO 


2 743 












53 


3643.67 




no.. 


3643-0 
3639.3 










2744 
2 745 

2747 
2 748 






102 


•j6a2 












in. . 
















103 


3638.0 














54 


3636.OO 








112 . . 


3635.6 
























4i 


3634 875 








3631 -9 


104 


3634-0 










113.. 














105 


3630.0 










2754 






55 


3628.33 








114. . 


3628. 2 










2756 

2757 






106 


3626.0 


















42 


3624- 750 




115.. 


3624 -5 
3620.8 














107 


3622.0 














116.. 










2761.8! 

2761.9/ 


2761 










56 3620. 67 



























6o 



E. C. C. BALY 



the most intense in the sub-groups — it has seemed advisable to 
repeat these observations. Messrs. A. Williams and F. G. Tryhorn 
have very kindly measured for me the absorptive power of an alco- 
holic solution of benzene with the Hilger ultra-violet spectropho- 
tometer. When corrected for solvent the frequencies of the heads 
of the sub-groups agree with those calculated from the short-wave 
infra-red bands. The correction for solvent in this region is about 

i 



1 8 units in the values of 



A' 



The values are given in Table XXIV. 



TABLE XXIV 



Infra-Red Bands 



vx 



\ Calc. 



AOds. 



A Obs. 
Hartley 



3-25M 
4.40.. 
4.90. . 
5-43-- 
9.78.. 

Center . 

11.6... 

S-43-- 

4.40. . 

325.. 

2.18.. 



308 
227 
204 
184 
102 
o 

85 
184 

227 
308 
460 



3724 
3823 
3846 



3948 
4050 
4135 
4231 
4283 
4358 
45io 



3706 
3805 
3828 
3848 

3930 
4032 
4117 
4216 
4265 
4340 
4492 



2685 
2632 
2612 
2599 
2445 
2460 

2429 
2372 
2345 

2304 
2228 



2685 
2630 



2600 
2540 
2462 

2429 
2376 

2344 
2300 
2230 



2682 
2630 
2614 
2600 

2539 

2460 
2426. 
2376 



In the first two columns of the table are given the wave-lengths 
and wave-numbers of the infra-red bands, in the third column are 
given the wave-numbers of the corresponding lines in the ultra- 
violet group, while in the fourth column these values are corrected 
for solvent. The wave-lengths of these lines are to be found in 
the fifth column, and Williams and Tryhorn's measurements of the 
heads of the sub-groups in the sixth column. I also append 
Hartley's values for a benzene solution in the last column. The 
agreement between observed and calculated values leaves no doubt 
that the sub-groups are due to the principal short-wave infra-red 
bands and the combination of their frequencies with that of the 
central line. 

4. Calculation of the absorption lines of phenol from the basis 
constants of -water and benzene and of aniline from those of ammonia 
and benzene. — The infra-red absorption of a very large number of 
compounds has been investigated by Coblentz and one outstanding 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 61 

conclusion can be drawn from his work, namely that the character- 
istic infra-red bands of a substance are also to be found in the spec- 
tra of its simple derivatives. Thus the benzene bands at 3 . 25 and 
6.75 /x are also exhibited by a number of its derivatives. Again, 
the absorption bands of water are shown by salts with water 
of crystallization, and, moreover, at least one of these is shown 
by compounds containing the hydroxyl group. This at once sug- 
gests that in the spectrum of a compound there is some additive 
function of the spectra of its constituents. The existence of such 
an additive function can be tested in the case of phenol which is a 
derivative of benzene and water, for both of which we now know 
the values of the basis constants. 

Coblentz did not investigate the absorption of phenol over the 
entire region from 1 lx to 13 fx, but he found three very strong bands 
at 2.97, 6.25, and 6 . 75 ju. It is fairly obvious that the first of 
these is the water band at 3 . o ll and is therefore due to the basis 
constants of water, namely 2.5 and 6.6, while the band at 6.75 /x 
is due to the benzene basis constants 3 . 7 and 4.0. On the other 
hand, the wave-number of A = 6.25/x, namely 160, is a whole 
multiple of each of the three basis constants 4. 2.5, and 6.6, for 
160 = 4X40=2.5X64 = 6.6X24. Water shows two bands at 
6. 25 ix and 6.0 fx, and of these the wave-number of the first is the 
only one that is a multiple of a benzene basis constant as well as 
of those of water. Obviously, therefore, this band will be enor- 
mously enhanced in the case of phenol. It is thus clear that the 
three infra-red absorption bands of phenol, of which that at 6. 25 /x 
is the strongest, can be entirely accounted for by the basis constants 
of its component radicles benzene and water, for one is due to basis 
constants of benzene alone, one is due to the basis constants of 
water alone, while the third is due to those of water and benzene 
combined. 

From these facts the absorption-line system of the ultra-violet 
band group can be at once calculated, since it is evident that the 
central frequency of such a band group must be a multiple o: 160, 
the wave-number of the only infra-red phenol band that is due to 
the combined constants of benzene and water. It may be noted 
in passing that this is confirmed by the fact that phenol in solution 



62 E. C. C. BALY 

shows a constant difference of 160 between the wave-numbers of 
its absorption and fluorescent bands as already shown in the earlier 
part of this paper. Now Purvis and McCleland 1 have measured 
the wave-lengths of the component absorption lines of one of the 
ultra-violet absorption-band groups of phenol, and these all lie 
between the limits 2812 and 2500 angstroms. The only multiple 
of 160 which possibly can be the central wave-number of the system 
is 24X160 = 3840. I have therefore calculated the wave-numbers 
of the absorption lines from 

3840 = 2. $n, 3840 = 3. 7/7, and 3840='= 4.0;?, 

and the corresponding wave-lengths, corrected to their values in 
air, are given together with Purvis and McCleland's measurements 
in Table XXV. I have used two of the basis constants of benzene 
and one of those of water, because phenol is undoubtedly an 
aromatic compound; that is to say, its benzenoid properties are 
far more pronounced than those of a derivative of water. Atten- 
tion may be drawn to the manner in which the absorption lines 
group themselves and to the fact that Purvis and McCleland have 
measured in most cases those lines which mark the heads of those 
groups. Although the observed lines are very much fewer in num- 
ber than those calculated, yet all the former coincide with closely 
situated groups of lines, which groups, since they would not be 
resolved with the dispersion employed, would appear as single lines. 
The agreement between the observed and calculated values is very 
good and fully justifies the conclusion that the basis constants of 
benzene and water are acting independently. Some insistence may 
be laid on the fact that the entire absorption spectrum of phenol 
has thus been calculated from the infra-red spectra of benzene and 
water, no modification whatever being required in the fundamental 
constants of these two substances when combined in their com- 
pound phenol. The calculations for the beginning only of the red 
side of the band are given. The results obtained for the remainder 
of the red side and for the blue side are equally good. 

Many other examples of this principle of the combination of the 
basis constants might be given, but it is only in relatively few cases 

1 Chemical Society Transactions, 103, 1088, 1913. 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 63 

that the result can be tested on the ultra-violet absorption-band 
groups, since relatively few substances show these groups subdivided 
into fine lines. Indeed this very fact is in agreement with the 



TABLE XXV 

Ultra-Violet Absorption* Band of Phexol 

A" I = 2.5, K 2 = 3.7, K 3 = 4.o 

Red Side 



Hi 


1 

A 




'h 


1 

A 


A Calc. A Obs. 
Purvis 




384O.O 
3837-S 








2603 . 4 2603 














I 


3836 -3 






2605.9 

2606 . 1 
2606. 7 
2608 . 5 
2608.8 

2610. 2 
261O.9 
26H.6 
2SII.8 

26l3-5\ 

2613.6/ 

2614. 7 

2615.3 

2616.O 

2617.O 

2618.5 

2618.7 








1 


3836.O 




2 


3835-° 
3832.5 






2607 


3 


2 


3832.6 






2 


3832.0 




4 


383O.O 










3 


3828.9 






2611 






3 


3828.O 




5 


3827.5 








4 


3825.2 








6 


38250 






2613 








4 


3824O 




7 


3822.5 










5 


3821.5 








8 


382O.O 


5 


382O.O 






6 


3817.8 


2618 


9 


38170 












6 


3816.O 


2619.8 




10 


3SI5.0 










7 


3814. 1 






2621 .O 
2622. 2 
2622.5 
2623.6 
2623.9 
2625. 2 
27250 




11 


3812.5 














7 


3812.O 








8 


3810.4 


2623 


12 


381O.O 












8 


3808.O 


2625 


13 


3807 • 5 










9 


3806.7 








14 


3805.0 






2627.3 
2628.O 
2628.7 
2629.O 

2630. 7 
2631.3 
2632.5 
2633.6 
2633.9 

2634 -3 
2636.0 
2636.3 
2636.4 










9 


3804.O 


2628 






10 


3803 • 




15 


3802.5 
3800.0 








16 






10 


380O.O 


2630 
2631 




11 


3799-3 


17 


3797-5 












11 


3796.0 








12 


3795-6 


2634 
2635 


18 


3795-o 
3792.5 






19 
















12 


3792.O 








13 


379J-9 















64 E. C. C. BALY 

theory, since the more complicated is a molecular system, the 
greater the number of basis constants, and hence the greater the 
number of lines packed together within the limits of one absorption- 
band group. The closer these lines lie together the less likely are 
they to be resolved, and hence the condition is soon reached when 
no such resolution is possible. 

The principle of combination also holds good in the cases of 
aniline and toluene, for the ultra-violet band group of aniline can 
be accurately calculated from the basis constants of benzene and 
ammonia, and that of toluene from the constants of benzene and 
an aliphatic hydrocarbon. Coblentz investigated the infra-red 
spectra of a number of aliphatic hydrocarbons and found them all 
to be strikingly similar. As it is probable that normal hexane was 
examined in the state of greatest purity, this may be taken for the 
present purpose. It shows three very strong bands at X = 3-43, 
6.86, and 13.8 ju. The wave-numbers of these are very nearly 
multiples of 4 and the most probable values are 288, 144, and 72, 
respectively. Since these three bands are so intense in relation to 
all the others of these hydrocarbons, it may be concluded that there 
is a second basis constant of 7.2, of which the foregoing wave- 
numbers are multiples as well as of 4. These two basis constants 
explain all the intense infra-red absorption bands of the aliphatic 
hydrocarbons and it is very interesting that one of these, 4, is the 
same as in the case of benzene, which suggests that it is character- 
istic of a carbon chain. 

Further evidence can now be gained as to the principle of com- 
bination in the spectrum of a compound of the basis constants of 
its component radicles. Thus myricyl alcohol shows very strong 
bands at 2.97, 3.43, 6.86, and 13.88 ju. Of these no doubt the 
last three are due to the basis constants of the hydrocarbon chain, 
while the first is due to those of water. Again, triethylamine shows 
the hydrocarbon bands at 3 .43, and 6.86 /x, and also the ammonia 
bands at 6 . 1 and 9 . 3 m- 

The infra-red spectrum of aniline shows bands at 2.97, 3.25, 
and 6 . 1 n, and of these the first and third are clearly due to the 
basis constants of ammonia, and the second to those of benzene. 
The same is true in the case of toluene, for it shows strongly the 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 65 

benzene band at 6.75 /z and the hydrocarbon bands at 6.86 and 
13.88 fx. There is also a single deep band at 3.34 ju, and there is 
little doubt that this is due to the superposition of the benzene 
band at 3 . 25 fx and the hydrocarbon band at 3 .47 /x. These four 
compounds again support the principle of combination, and in the 
two last cases the matter can be tested on the ultra-violet absorp- 
tion system. 

Owing to the complexity of the infra-red spectrum of ammonia 
it becomes somewhat difficult directly to determine the funda- 
mental frequency of aniline, of which the central frequencies of the 
ultra-violet bands are multiples. On the other hand, aniline in 
solution shows two absorption-band groups, and at very small 
concentration 1 the frequencies of the centers of these bands are 
3496.7 and 4355, respectively. From these two measurements 
it is possible to calculate the most probable value of the funda- 
mental infra-red frequency, for we have ^^=3496.7 (1), yv x = 
4355 ( 2 )> an d (y—x)v x = 758.3 (3), where x and y are integers and 
y—x is small. It would seem obvious that the only possible values 
for x and y are 23 and 28, respectively, for the value of v x is then 
found to be 152.03, 151.97, and 151.65 from (1), (2), and (3), 
respectively. Xow Purvis 2 has measured the wave-lengths of the 
component lines of the less refrangible ultra-violet band group of 
aniline and has recorded a strong absorption line at i/X= 3496.1. 
This value may obviously be taken as a more accurate measurement 
of the central frequency than that obtained from the solution. 
The true value of v x or the fundamental infra-red frequency of 
aniline is therefore 3496.1/23=152.0. 

Xow the principal basis constant of benzene is 4, and 38X4 = 
152, and it would seem therefore that 3.8 must be one of the basis 
constants of ammonia. If this be so, then many of the infra- 
red absorption bands of ammonia must occur at frequencies which 
are multiples of 3 . 8. This is shown to be the case in Table XXVI, 
for eleven out of the sixteen ammonia bands between 3ju and 14/z 
are thus accounted for. 

1 The values for a very dilute solution are the same as for the vapor, a fact that 
will be dealt with in a further paper. 

2 Chemical Society Transactions, 97, 1546, iqio. 



66 



E. C. C. BALY 



The agreement shown in this table would certainly justify the 
conclusion that 3 . 8 is the principal basis constant of ammonia. 

TABLE XXVI 



Factors 



19X3 
22X3 

23X3 
25X3 
27X3 
28X3 

30X3 
40X3 
43X3 
45X3 
88X3 



8 72.2 

8 83.6 

8 87.4 

8 95 o 

8 102.6 

8 106.4 

8 I 114. o 

8 152.0 

8 ! 163.4 

8 [ 1 7 1 . o 

8 334-4 



a Calc. 



I3-8SM 
11 .96 
11.44 
10.53 

9-75 
9.40 

8-77 
6.58 
6.12 
5-85 
2-99 



AObs. 
Coblentz 



I3-7M 
II.98 

H-43 

IO.4 

9.9 

9-3 

8.9 

6.51 

6.1 

5-8 



It is now possible to calculate the wave-lengths of the com- 
ponent lines of the ultra-violet absorption-band group of aniline, 
and I have done this, using the central frequency 3496.1 and, as 
in the case of phenol, the two benzene constants 3.7 and 4.0, 
together with that now found for ammonia, namely 3.8. The 
following formulae were therefore used: 

3496 - 91 ± 3 • Vh 349 6 • 1 ± 3 • 8". and 3496 . 1 ±4 . on, 

and the results agree exceedingly well with those observed by Purvis 
and by Koch. 1 

I have also calculated the wave-lengths of the absorption-band 
group of toluene, using the four basis constants 3.7, 4.0, 7.2, and 
7.6, the central line being taken as the same as that of benzene. 
The latter is justified both by the fact that the absorption-band 
group of toluene is in exactly the same region as that of benzene, 
and also by the fact that so many absorption lines of toluene are 
the same as those of benzene. The agreement between the ob- 
served and calculated values is again exceedingly good and there is 
no need for the detailed reproduction of the calculations for aniline 
or toluene. 

These results seem entirely to confirm the view put forward 
in the latter pages of this paper, that it 's possible to calculate all 

1 Zeit. wiss. Phot., 9, 401, 1910. 






ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 67 

the absorption bands and their component lines from the infra-red 
absorption bands of the substance, and, further, that the absorption 
of compounds of two radicles throughout the whole spectrum from 
extreme ultra-violet to extreme infra-red is compounded from the 
infra-red absorption of the two radicles. 

The whole position may be summed up as follows: Every 
system of molecules possesses certain basis constants, which accord- 
ing to Bjerrum represent the molecular rotational frequencies and 

are derived from the expression — — T where / is the moment of 

inertia and h the Planck constant, there being at least two values 

of / for each type of molecule. Absorption bands exist in the long- 

nJi 
wave region of the infra-red with frequencies equal to — jy, where 

»=i, 2, 3, etc. As the values of n increase, the intensity of the 
resulting absorption bands decreases and the effective values of n 
depend on the temperature of the substance. Convergence 
frequencies of the two series of basis constants exist and these 
form centers of bands in the short-wave infra-red region. Xo 
strong absorption band can be exhibited by any compound at 
shorter wave-length than 3 /x, which is due to a single multiple of 
one basis constant. All absorption bands beyond 3 /jl must be due 
either to the convergence of two or more series of basis constants 
or to a multiple of such convergence frequency. There exists, 
therefore, a constant difference between the centers of such ab- 
sorption bands, and this difference must equal such convergence 
frequency. Every absorption band, whether in the ultra-violet, 
visible, or short-wave infra-red region, consists of a central line 
the frequency of which is a convergence frequency or a multiple 
of that convergence frequency. Symmetrically distributed on 
each side of the central line are pairs of absorption lines, each pair 
being due to the combination of the central frequency with a basis 
constant according to the expression C^=nK, where C is the fre- 
quency of the central line, K is a basis constant, and ;/ = i, 2, 3, 
etc. The ultra-violet or visible absorption-band group may be 
divided into sub-groups and in such case the heads of the sub- 
groups are due to the combination with the central frequency of 



68 E. C. C. BALY 

those frequencies which are sufficiently active to give bands in the 
short-wave infra-red region. The same also holds good for fluores- 
cence and phosphorescence spectra. Finally, in the case of a com- 
pound of two radicles the basis constants are the same as those of 
the two radicles. Every one of the foregoing deductions from the 
theory has clearly been proved to be true by experiment. 

Although the present theory has been developed in two direc- 
tions, it must be clearly understood that neither argument is 
complete without the other. In the first section of this paper the 
existence of molecular force fields is dealt with. These are opened 
by the effect of various solvents to different stages, each stage being 
characterized by its power of absorbing definite light vibrations. 
The theory therefore establishes the fact that a given molecular 
force field must possess certain definite free periods of vibration, 
and that these periods may be latent or called into play by the use 
of suitable solvents. These vibration periods may evidence them- 
selves as the centers of either absorption, fluorescence, or phos- 
phorescence bands. Although it is clear that the absorbed light 
must again be emitted at some frequency which is characteristic 
of the molecular system, the force-field theory does not carry 
us beyond the foregoing position and offers no explanation of the 
relation between the frequencies of ultra-violet and infra-red ab- 
sorption bands. 

On the other hand, the energy relations based on the energy- 
quantum theory show that there must exist a constant difference 
between the centers of successive absorption, fluorescent, and 
phosphorescent bands shown by a single substance and that this 
difference must equal the frequency of an infra-red band of that 
substance. They further show that all the free vibration periods 
possessed by a substance can be derived from two or more basis 
constants, but they do not explain why certain of these vibration 
periods in the ultra-violet and visible regions are active and why 
some of them are latent. 

It may fairly be claimed that a combination of the two branches 
gives a reasonably complete theory of absorption, fluorescence, and 
phosphorescence, a theory which seems amply to be confirmed by 
experiment. 



ABSORPTION. FLUORESCENCE, AND PHOSPHORESCENCE 69 

5. Summary and conclusions. — (1) The electromagnetic fields 
surrounding the atoms, used by Humphreys to explain the Zeeman 
and the pressure-shift effects, have been applied to molecules. 
The free and independent existence in a molecule of such atomic 
fields must be a metastable condition. There must ensue a con- 
densing together of the force lines to form a molecular field, with 
the escape of energy. 

(2) The chemical properties of a molecule must depend on the 
closed field of the molecule. If the field be entirely closed, the 
molecule will have no reactivity, and if after the maximum possible 
condensation has taken place there be left an uncompensated 
residuum, the molecule will possess residual affinity. 

(3) The closed molecular fields can be opened by the influence 
of other molecules possessing residual affinity, an equilibrium 
between opened-up and non-opened-up molecules being established. 
The chemical reactivity will depend on this equilibrium. 

(4) A second method of opening the closed fields is by the 
influence of light. The light shifts the equilibrium between the 
opened-up and non-opened-up molecules toward the reactive or 
opened-up side, a new photodynamic equilibrium being established. 
The light therefore does work on the system and is selectively 
absorbed. 

(5) The force field of a complex molecule is itself complex and 
consists of a network of potential gradients which are attacked and 
opened in turn by the use of suitable solvents. Stages must there- 
fore exist in the opening-up process. 

(6) Each stage will be characterized by its power of selectively 
absorbing definite light waves and can be recognized in this way. 
Each stage thus represents a vibration period of the molecular 
system. 

(7) The light energy absorbed must again be emitted at some 
frequency which is characteristic of the system. In most cases this 
frequency lies in the infra-red region, but in certain cases a portion 
of the energy is emitted in the visible or ultra-violet region when 
fluorescence or phosphorescence is manifested. Fluorescence and 
phosphorescence therefore mean the emission of energy with a 
frequency characteristic of the molecular system. 



70 E. C. C. BALY 

(8) Experimental proof is found in three sets of observations: 
first, by the existence of intermediate phases in chemical reactions, 
which phases represent higher stages in the opening up of the molec- 
ular force fields and are recognized by their power of absorbing 
light of longer wave-length; secondly, by the variation in absorp- 
tive power with progressive dilution of the solution; thirdly, by 
the fact that the fluorescence emission of certain organic compounds 
in one solvent has the same wave-length as the light absorbed by 
the same compounds in a second solvent. 

(9) The frequencies of the centers of all the absorption, fluores- 
cence, and phosphorescence bands shown by a substance are mul- 
tiples of the frequency of an absorption band in the short-wave 
region of the infra-red. This is proved by the existence of a con- 
stant difference between the centers of successive band groups, 
whether absorption, fluorescence, or phosphorescence, and by the 
fact that this constant difference equals the frequency of an absorp- 
tion band shown by the same substance in the short-wave infra-red 
region. Further proof is found in the fact that the refractivities 
of gases can be calculated from Sellmeyer's formula in which for 
the frequency of the theoretical absorption band there is substituted 
a multiple of a measured infra-red band. 

(10) The structure of absorption-, fluorescent-, and phos- 
phorescent-band groups is partly due to the combination of the 
central frequency with the frequencies of the short-wave infra-red 
absorption bands according to the formula C±v x , where C is the 
central frequency and v x the frequencies of the short-wave infra-red 
absorption bands. 

(11) The entire absorption, fluorescence, and phosphorescence, 

in whatever region they may lie, may be calculated from the 

molecular frequencies. According to Bjerrum these rotational 

nh 
frequencies are given by the expression — —., where h is the Planck 

constant, / is the moment of inertia, and n=i, 2, 3, etc. There 
are at least two basis constants ( — jy ) for every complex molecule. 

(12) The successive multiples of the basis constants give rise to 
absorption bands in the long- wave infra-red region. Convergence 



ABSORPTION, FLUORESCENCE, AND PHOSPHORESCENCE 71 

frequencies of two or more series of basis constants or multiples 
of such convergence frequencies give rise to absorption bands 
in the short-wave infra-red region. Multiples of these con- 
vergence frequencies give rise to the bands in the visible and ultra- 
violet regions. 

(13) By combination of these convergence frequencies or their 
multiples with the successive multiples of the basis constants accord- 
ing to the formula C=>=;?A\ where K is a basis constant, all the com- 
ponent lines of any band group may be calculated. This has been 
done for the ultra-violet absorption-band group of benzene and 
the values show exceedingly close agreement with those observed. 

(14) Where an absorption band shows subdivision into sub- 
groups, the heads of the sub-groups are due to the combination 
of the central frequency with those multiples of the basis constants 
which are sufficiently active to evidence themselves as absorption 
bands in the short-wave infra-red region. 

(15) The absorption bands in the infra-red and all the com- 
ponent lines of the ultra-violet absorption-band groups of a com- 
pound of two radicles can be calculated from the basis constants 
of the two radicles. This is proved by the calculation of the 
absorption lines of phenol from the basis constants of benzene and 
water, and the absorption lines of aniline from those of benzene and 
ammonia. 

The University 
Liverpool 



ON THIELE'S "PHASE" IN BAND SPECTRA 

By H. S. UHLER 

Several years ago, at the suggestion of Professor H. Kayser, the 
author undertook to test Thiele's hypotheses concerning emission 
band spectra by investigating their applicability to the third cyano- 
gen band and the various "tails" which have been associated with 
it by King, Jungbluth, and others. The first part of the work, 
which was primarily experimental, has been completed by R. A. 
Patterson in collaboration with the writer. The second part of the 
problem would be purely arithmetical and would consist in unravel- 
ing the various series pertaining to the X 3883 band by the aid of 
Thiele's methods and formulae. In the attempt to lay out a syste- 
matic plan for the computations, the difficulty of obtaining the 
numerical value of the phase c presented itself as apparently 
insuperable. That this difficulty has also appeared formidable to 
other investigators may be seen from the following quotations. 

A. S. King 1 writes: ". . . . and some of the constants used, 
notably n, the series-number of a selected line, are very hard to 
determine in the case of band spectra." Again: "Finding it 
impracticable to use Thiele's formulae, owing to the difficulty in 
determining the constants, I have tried to find some numerical 
relation " R. T. Birge 2 says: "It contains eight undeter- 
mined coefficients and so is very difficult to work with I 

have preferred to use simply Deslandres' Law " As far as 

the author has been able to find out, by a careful search through 
so much of the literature of the subject as is accessible to him, 
Thiele is the only investigator who has calculated the numerical 
values of c and of the remaining parameters involved in his formula. 
Since this state of affairs exists, as a good deal of importance is 
attached to the problem by Kayser and other writers, and since the 
author has succeeded in working out a method for evaluating c for 
any given band spectrum, he feels justified in publishing the results 

1 Astrophysical Journal, 14, 325, 326, 1901. 2 Ibid.. 39, 72, 1914. 

72 



T HI ELKS 'PHASE" IN BAXD SPECTRA 



73 



of his investigation, in spite of the fact that the processes involved 
are very elementary and now seem perfectly obvious. In this 
paper, therefore, it will be shown (a) precisely what Thiele's for- 
mulae and hypotheses mean from a purely mathematical point of 
view, (b) how to calculate the ''phase'' c for any band whose wave- 
lengths can be determined to a sufficiently high degree of accuracy, 
and (c) what conclusions may be drawn from the special cases to 
which the new method has been applied. 

Thiele has stated his hypotheses very clearly in the following 
words : 

The single established fact in the present theory of series, the only one 
which my investigations have more and more tended to confirm, is that the 
law which expresses the wave-length A of the lines of a series as a function of 
the series-number n of the lines must have the form 

\=f[(n+cY] (i) 

where c is a constant, which I shall call the phase of the series Taking 

this law as a fundamental hypothesis, I accept all of its consequences 

The most important consequence of our hypothesis, \=f[(n-\-c) 2 ], is that it 
is necessary to take into account not only the lines corresponding to positive 
values of ;z, but also those obtained when n<o. In other words a series 
must in general be composed of two groups of lines, each of which would 
ordinarily be called a series. I prefer to put it that the positive branch 
of each series must be accompanied by a negative branch of the same series, 
having the same head and the same tail and being represented alternately by 
a line in each interval of the other branch. These two branches may 
exactly coincide, in which case the phase of the series must be either c = oor 
c = \ (evidently c must be defined so as to include only fractions properly so 
called). 1 

That Thiele considers c to be rigorously and not approximately 
constant is emphasized in his second paper on this subject where 
he says: "That the phase must remain constant in each series is 
my fundamental hypothesis." 2 

Theoretically the phase c may be determined in three different 
ways for any given spectrum. One method consists in assuming 
a particular form of function in equation (i) and then evaluating 
the constants or parameters by repeated comparison of the calcu- 
lated wave-lengths with the experimental data. In general, this 

1 Astro physical Journal, 6, 66, 67, 1897. " 2 Ibid., 8, 5, 1898. 



74 H. S. UHLER 

process (which is the one used by Thiele in his analysis of the 
carbon band at X 5165) requires the determination of the values of 
all of the parameters simultaneously. This fact is advantageous or 
just the reverse according as one needs to know all of the constants 
or as one desires to study the behavior of some parameter alone, 
such as c. When the function is complicated, or involves a rela- 
tively large number of independent literal coefficients, the labor of 
computing their values becomes very great. This is the discour- 
aging feature of the equation used by Thiele, 1 namely: 



\=K 



I+ J»±£)+ .... +Sr P^)"- 

( n+c \ 2 \ 10 / \ 10 / 



Furthermore, the process of "trial and error'' would usually be 
extended over the entire length of the band under investigation 
and, when this is the case, it would yield mean values of the literal 
coefficients. Under these circumstances small but true variations 
in a hypothetical constant, such as c, might escape detection. 

A second method of calculating c would be to substitute a 
sufficient number of experimental wave-lengths in the chosen func- 
tion to make it possible, theoretically at least, to eliminate from 
the resulting equations of condition all of the parameters save the 
one required. If this scheme were feasible, it would afford an excel- 
lent means of testing some of Thiele's hypotheses. For example, 
comparison of the values obtained by calculating c from groups of 
selected wave-lengths at different places along one band series would 
show whether the phase is or is not a true constant, within the 
limits set by the probable errors of the experimental data. In 
general, however, it is not advantageous to make use of a process 
which requires the function to be exactly satisfied by the wave- 
lengths in a group. For, unless the number of data in a set were 
large, an anomalous line or a wave-length having a large error 
might alter the value of a small constant very appreciably. Both 
of the methods just outlined would give c if wave-lengths belonging 
exclusively to one and the same branch (positive or negative) of a 

1 Astrophysical Journal, 8, 10, 1898. 



THIELE'S "PHASE" IN BAND SPECTRA 75 

series were used in the computation. The value of c thus obtained 
would predict the wave-lengths of the conjugate branch (negative 
or positive respectively) and indicate the positions of the lines of 
one branch relative to those of the associated branch. 

Although the second method suggested for the determination of 
the phase seems very promising in many respects, nevertheless it 
is not practicable. This statement is made advisedly because a 
great deal of time was wasted by the writer in trying to derive a 
working formula for c before he happened to hit upon the third 
method, which will be explained in later paragraphs. If the num- 
ber of terms in equation (2) be restricted so that it may be written as 

a +a 2 {n+c) 2 



i+b 2 (n+ c y 



and if for X and n respectively the four wave-lengths M, N, P, Q, 
and the corresponding ordinals m, n, p, q, be substituted, elimina- 
tion of a , a 2 , and b 2 will lead to a quadratic in c which is readily 
reducible to the form given by Thiele, 1 namely: 

L+n+p+q+vY^im-n+p-qy-t V ' U ~ q) 



M-N P-Q m-p n-q 
M—P'X—Q'm—n'p—q 



This formula is unsatisfactory in practice because it is liable to give 
incorrect results, primarily as a consequence of the small number 
of wave-lengths involved. For example, when the latest wave- 
lengths of four good lines of the singlet series between the first and 
second heads of the third cyanogen band (M = 3880.999, N= 
3879.964, P = 3878. 303, <2 = 3876.843,;;*= 15, n= 18, p=22,q=2s) 
were chosen at random and substituted in the last equation, it was 
found that 4<;+8o= ±85.0345 or c = 1.2586, which is incorrect 
because c must be less than unity. [Of course, c can be changed to 
o. 26 by increasing m, n, p, and q each by 1 since the left member of 
the equation has to maintain a constant sum for m-\-n-\-p-\-q-\-4C, 
the right side involving differences only. The spectrograms show, 
however, that m=i5-] If, with m=i5, —0.002 and +0.002 be 
added to M and Q, respectively, it follows that 4^+80= =81 .6747 

1 Ibid., 6, 70. 1897. 



76 H. S. UHLER 

or £=0.4187, which illustrates how sensitive the quadratic may be 
to slight changes in the wave-lengths. If the wave-lengths satisfy 
an equation of the form 

\=a-\-fin-\-yn 2 

(which is approximately exact near the head of a band), it is easy 
to show that Thiele's quadratic leads to m-\-n-\- p-\-q-\-^c = =±= 

[m-\-n-\-p-\-q-\ ), so that the required root, c= — , is independent 

of the value of m. Far from the beginning of a series the quadratic 
in c becomes altogether useless. For illustration, from the series 
chosen for the last numerical example let the following data be taken, 
namely M= 3678. 098. #=3666.852, P= 3653. 455, (2 = 3642.477, 
m= 151, n— 156, p — 162, and q— 167. Then 4^+636= ='=271 .4942, 
that is, c= — 91. 1264 or —226.8736 and these roots are obviously 
meaningless. 

Theoretically the next approximation to c can be obtained from 
the equation 

x ^ a +a 2 (n+c) 2 +a A (n+cy 
~ i+b 2 (n+c) 2 +b A tn+cY ' 

Letting M, N, P, Q, R, S, denote wave-lengths and m, ;z, p, q, r, s, 
the corresponding series numbers, the equation for c becomes 

I M(m+cy, (n+c)*, P{p+c) 2 , {q+c) 2 , R, 1 | =0. 

Expanding the binomials and making use of the fact that a deter- 
minant having two (or more) identical columns vanishes, a complete 
sextic in c is obtained having 36 determinants, each of the sixth 
order, involved in its coefficients. If it were possible to transform 
this sextic so as to cause all of the wave-lengths to be present 
(preferably as binomial differences) in one term alone, as is the case 
with Thiele's quadratic, only one complicated coefficient would 
have to be evaluated in a given numerical case and the required 
root of the sextic might be obtained without too much labor by 
applying Horner's method of approximation. As a matter of fact 






THIELE'S "PHASE" IN BAND SPECTRA 77 

the coefficients of c 6 , c 5 , and c 4 may be reduced to 64A, 64A • 2w, and 

r A i 

16A (2w) 2 +2J»m+ r respectively, where 

A= I M, 1, />/>', j\ Rr, s I 
and 

A'= I M, 1, />/>*, g3 7 ^ s J . 

Division of all of the terms of the sextic by A still leaves an irre- 

A' 

ducible function of wave-lengths, namely — , in the coefficient of c A . 

As might be expected, the literal coefficients become more involved 
as the power of c decreases. 

In his study of the a, /3, 7I, el, ell, and f series of the carbon 
band at X 5165, Thiele found it necessary to taker =3 in formula (2). 
To determine c by the elimination of the seven remaining parame- 
ters, eight wave-lengths would be required and an equation of the 
twelfth degree in c would have to be solved. The coefficients of 
this equation would involve 576 determinants, each of the eighth 
order, after all zero determinants had been culled out. It is there- 
fore evident that the second general method proposed for finding 
the value of c is entirely out of the question. Furthermore, both 
of the methods suggested in the foregoing paragraphs are open to 
the objection that they require the assumption of some special type 
of function, such as formula (2), and hence may restrict the gener- 
ality of the hypotheses associated with 

\ = f[(n+cy}. 

The principle of the third method is perfectly general in so far 
as it depends solely upon Thiele's two fundamental hypotheses, 
namely: (a) only even powers of n-\-c are involved in the function 
for X, and (b) c is a constant for any one band series. More specifi- 
cally, if X=/[(/z+c) 2 ] be plotted in rectangular co-ordinates, the 
locus obtained will be symmetrical with respect to the straight line 
whose equation is n=—c (AV, Fig. 1). The two branches of an 
ideal Thiele band series (shaded off toward the shorter wave- 
lengths) would then have the general form of the curve BVF. The 
points of inflection correspond to the maximum first-differences of 



78 



H. S. IHLER 



wave-length approached in some bands and realized in the third 
cyanogen group. A straight line parallel to the axis of n, and at a 
suitable distance therefrom, will intersect the curve in two points, 
such as D and E. Hence, if n and n' denote (the algebraic values of) 
the abscissae of any two points on the curve which have the same 
value of X, it follows at once that c— — \{n-\-n'). [GH = c, HE=n, 
DH——n'.} In the case of any series whose wave-lengths have 
been accurately determined there is no inherent difficulty associated 
with the calculation of n and ri corresponding to a chosen numerical 
wave-length. It is only necessary to evaluate the coefficients of 



V 

M 




X 

\Q 

\l 

\r 


y "g 




H >F 

f\. 



A 

Fig. i 



n 



any simple, convenient interpolation formula which represents a 
curve PQ fitting the locus of actual wave-lengths sufficiently closely 
over a limited range of spectral lines, such as FL or BM. In other 
words, the value of c may be obtained by taking an adequate num- 
ber of terms of the power polynomial \=a -\-a 1 n-\-a 2 n 2j r .... 
-\-a k n k , determining the coefficients, a , a s , ■. . . . a% from the 
known wave-lengths, substituting for X an arbitrary wave-length 
(OH), and solving for n. Then, using the same value of X and 
repeating the process for the negative quadrant, the corresponding 
value of n is computed. Knowing n and n' , c follows immediately 



THIELE'S "PHASE" IN BAND SPECTRA 79 

from the relation c= — \{n-\-n'). If the numerical data were per- 
fect and Thiele's hypotheses correct, it would only be necessary to 
evaluate c for one value of X, that is, for one pair of corresponding 
intervals on the two branches of the curve. If the hypotheses are 
rigorous but the wave-lengths slightly in error, several pairs of 
segments along the curve can be used and the mean of the slightly 
differing values of c formed. If, on the other hand, the general 
function f[(n-\-c) 2 ] does not represent very closely a law of nature, 
the variations of c along the curve will bring this fact to light. 
Furthermore, the disadvantages arising from determining the 
coefficients of the interpolation formula by causing its curve to pass 
exactly through an equal number of experimental points may be 
avoided by making use of the method of least squares. By so 
doing, a comparatively small number of terms of the polynomial 
may be taken and the coefficients determined from a larger number 
of wave-lengths. In this way the influence of the unavoidable 
accidental errors of the experimental data will be minimized. In 
the present paper attention is focused primarily on the relative 
values of c at different places along a given series, and hence it is 
not necessary to know how many lines are comprised in the usually 
congested region of the head of a band or even if the band has a 
head of finite intensity. The difficulty of choosing between several 
values of c which are in a sense complementary is thus avoided. 
It is essential, of course, to number the lines of the same series con- 
sistently. Since, under these circumstances, relative ordinal num- 
bers alone are of significance and since n and n' have opposite signs, 
it is always possible to transform the co-ordinates involved in the 
interpolation formula so as to use small ordinals (1, 2, 3, . . . .) 
instead of the larger values (160, 161, 162, . . . .) pertaining to 
the lines of long series. 1 This fact reduces enormously the labor 
involved in the calculation and solution of the "normal" equations. 
The plan to be followed in the general case having been out- 
lined, attention will now be directed to the details of the applica- 
tion of the method to numerical problems. As stated in an earlier 
paragraph, the equation 

\ = a -\-a 1 n-\-a 2 )i 2 -\- .... -\-akii k 

1 c=—%[{n'+m) + (n — m)] . 



8o H. S. UHLER 

may be used to advantage as the interpolation formula. Before 
making any computations, however, it is necessary to find out how 
many terms of the polynomial will be sufficient. By actual trial 
the writer has found that the parabolic equation 

gives perfectly satisfactory results. As a matter of fact this tri- 
nomial has worked so well that it was not deemed worth while to 
test an equation containing n 3 . It is not surprising that the para- 
bolic formula is sufficient, in the case of band series, for two reasons. 
In the first place, the law of Deslandres holds very well near the 
head of a band and, for short intervals, it makes no appreciable 
difference whether wave-lengths or the reciprocals of wave-lengths 
("frequencies") be used. Secondly, far away from the head (E 
and D, Fig. i) the parabolic segments twine around the positive 
and negative branches of the ;/X curve in such a manner as to pro- 
duce, at worst, a differential error in the calculation of c. In other 
words, the numerical values of n and n' corresponding to the same 
value of \(OH) are both larger or both smaller, by approximately 
equal amounts, when obtained from the interpolation parabolas 
than they would be if derived from the (unknown) equation of the 
series. Therefore the first-order differences practically cancel out 
in the expression for c, namely — \{n-)-n'). Moreover, for one 
parabola alone even the first-order divergence becomes negligible 
near the middle of the interval of wave-lengths employed in com- 
puting the normal equations. 

As a concrete example, let the following wave-lengths, which 
Thiele has computed for the a series of the X 5165 carbon band, be 
taken. (The object in using ideal wave-lengths instead of experi- 
mental data is to illustrate the manner in which the least-squares 
parabolas thread the curve given by formula (2) when the idiosyn- 
crasies of the individual wave-lengths have been removed.) 

In the first and second columns of Table I are given the series 
numbers used in the present calculation and by Thiele respectively, 
while the third column contains the wave-lengths computed by 
Thiele from formula (2). Instead of using the equation 



TEIELES -PHASE" IX BAXD SPECTRA 8 1 

just as it is written, the arithmetical work can be very appreciably 
reduced by replacing a by a'+X', where X' denotes the wave- 
length of a line at, or near, the middle of the group. The equations 

TABLE I 



+ i 

2 

3 

4 
5 
6 

7 



"n" 


A ideal 


+36 
37 
38 


5003 

4994 
4985 


278 

688 
920 


39 
40 


4976 
4967 


976 
864 


4i 


4958 


085 


42 


4949 


146 



parab. 



+ O.OO44 

- .OO43 

— . OO49 
+ .OOO5 
+ .OO4I 
+ .OO47 
-O.OO45 



of condition will then have only differences of wave-lengths for their 
constant terms, thus: 

a'-\-n • Ci+h 2 • a 2 = A— A' . 

In the numerical example proposed X' = 4976 . 976 and the equations 
of condition become 

a'+iai+ ia 2 = -f-26 .302 
a'+2ai+ 4a, = + 17. 712 
a'+$a 1 + ga 2 = + S.944 
a'+4a I +i6a 2 = 0.000 
a'-f 5tfi+25(Z,= — 9. 112 
a'+6a I +36a 2 = — 18.391 
a'+7(/ I +490 2 = -27.S30 

Hence, the first normal equation is 

7a'+28fli+ 14002= — 2 .375. 

Much time and labor can be saved by solving a set of normal 
equations with literal coefficients and computing, once for all, the 
constants which do not involve the wave-lengths. Let the right- 
hand members of the three normal equations be symbolized by 
5. r, and U, respectively. (5'= — 2.375, T-— 262.158, U = 
— 2075.900, in the illustration.) The solutions may then be 
written as 



82 H. S. UHLER 

and 

c 2 = -(5 2 5+M i r+M 2 Z7). 

a' may be found most conveniently by substituting the values of 
a x and a 2 in the first normal equation. 

Since it is possible that other computers may desire to follow 
the method of calculating c suggested in this paper, the constants 
corresponding to 7, 8, 9, 10, 11, and k consecutive ordinal numbers 
have been collected in Table II. As implied above, the wave- 
lengths are to be numbered 1, 2, 3, Under these conditions 

In the concrete example 

,_ 243.147 _ 175.2215 ^ _ 1 ■ 784 



so that the point on the parabola corresponding to 11 = 4 has the 

ordinate X 4 = — ) — . The next step consists in calculating 

the coefficients of the parabolic equation pertaining to the lines 
whose series numbers are —37, —38, .... ,—43. Whenthishas 
been accomplished the value of X 4 is substituted for X and the 
resulting quadratic in n solved. In the case in question, the 
required root is n'= —4. 53173; consequently c= —^-(—4. 53173 + 
4) = 0.26586. The value of c used by Thiele in equation (2) was 
o. 266, hence the new method leads to a result which is too small by 
only 0.05 per cent. For practical purposes the agreement may be 
considered perfect. (The concordance might have been even better 
if Thiele's ideal wave-lengths had been recalculated.) 

It is now appropriate to present the results obtained by applying 
the processes just explained to two independent sets of experimental 
data, namely, (a) the a and 5 series of the X 5165 carbon band cal- 
culated by Thiele, and (b) the series starting from the first head of 
the cyanogen band at X3883. In the first case it will be shown 
that c is not constant, and in the second, that the two series emana- 
ting from the head are not the positive and negative branches of the 
same series. 



THIELE'S "PHASE" IN BAND SPECTRA 



83 



■48 


+ 

T 
+ 

1 


+ 

00 

+ 
J 

O 1 


+ 

O 1 
X3 w 

1 


7 

+ 

W M 

+ 


J 
Si 

+ 


"5 

j 

J 

CI M 1 

+ 





H 


CO CO O O O O 
•*(- t^ W ■ \C >- CO 
M VO IO T}- <N 

Tf <*3 "3" H — cc 

•* h q 
1 + 1 + + + 


O 


"1 »o O "~- 

O-O f^ VO PJ O 
O H 0_^ H_ CO O 

cc~ 10 O cc~ "I 

01 O 11 **3 

7 + 1 + + + 





0^0000 

f^ rf <*1 
oc r^ rf O ^o co 

01 -O 10 s - *o 

T + 1 • + + + 


00 


CO O *t O O CO 

vC w •* ro rf 
■* «0 0_ 0_ C5 Tt 

w" co" fo 10 »cT 

1 + 1 + + + 


- 


CO N cc 01 NO "1" 

VO ro O 10, O 
»— — u~i ro m *^" 
1— <~0 M tN O 

7 + 1 + + + 










£■ 




< 





8 4 



H. S. UHLER 



Since the wave-lengths at Thiele's disposal were not as accurate 
as the later values determined by Joseph Leinen, 1 use has been made 
of the more recent data in the computations. The second column 
of Table III contains the ordinal numbers assigned by Thiele to the 
spectral lines whose wave-lengths have been used by the author in 
computing the coefficients of the least-squares parabolas for seg- 
ments of the positive branches of the series. The corresponding 
ordinals of the negative branches are given in the third column. 
Each value of c recorded in the fourth column was calculated from 
the two parabolas based on the data associated with the numbers 
in the same row and in the preceding columns. 

TABLE III 



Series + Brand,. Ordinal , _ Branch . 0rd inal Nob. 


c 


Wave-Length Interval 


a . . . 
a . . . 
a. . . . 
a. . . 
a . . . 
a . . . 
a . . 
5. . . 
5. . 
5. 
5 


:'+ 3, • • 

+ 3,-- 

+ 9, •• 
+ 9, •• 

+ 20, . . 
+ 36, • • 
+ 36, • • 

+ 8, . . 
+ 23, • • 
+35, ■ ■ 
+ 52, . . 


. ., + 9 — 3, . 

. ., + 9 - 4, . 

• •, +16;- 9, • 
. ., +16 — 10, . 
. ., +26 — 20, . 

• -, +42 -36, . 

• -, +42 -37, • 
. ., +18 - 8, . 
■ -, +29-23, . 

• -, +4i -35, • 
. ., +60 -52, . 


. ., - 9 
. ., — 10 
. ., -16 

• -, -17 

. ., —22, —24, ..... —27 

• •, -42 

• •, -43 
. ., -18 

• ■, -29 
. .. -41 

• •, -57, -59, -60 


0. 2632 

• 2633 
. 2626 

• 2625 
.2666 
.2684 
.2686 
.2499 
.2417 

•2375 
0.2344 


J5164. 448-5153. 380 

r5i55-740-5i29-8oi 
5116.003-5075.507 

,5007.974-4944.885 

5156. 296-5119. 417 
5095 -397-5052-823 
5009.632-4951.622 
4843 . 180-4746 . 602 



In three cases two parabolic equations for the negative branch 
were calculated in order to find out how much alteration in the value 
of c would be produced by a slight shift in the position of the nega- 
tive interval with respect to a fixed region on the positive branch. 
As anticipated, the change in c is negligible, since it amounted to 
only 0.0002, or 0.075 P er cen t m the most unfavorable case. In 
the fifth and bottom rows of the table it will be noticed that lines 
— 23 and — 58, respectively, were omitted. This was done because 
the wave-lengths given by Leinen are displaced too far with respect 
to their neighbors to justify the inclusion of the data in the least- 
squares calculations. The numbers in the fourth column show 
conclusively that c is not strictly constant for the a and 8 series 
of the X 5165 carbon band. In the case of the a series the phase 



1 Zeit. uriss. Phot.. 3, 137, 1905. 



THIELE'S "PHASE" IN BAND SPECTRA 85 

increases from about o. 263 to o. 268 at least, while for the 5 series 
it decreases from o. 250 to o. 235, or less. The values of c used by 
Thiele were o. 266 and o. 2445 for the a and 8 series, respectively. 
As suggested in an earlier paragraph, it is probable that Thiele's 
method of computation would lead to a sort of integrated average 
value of the phase. This supposition is not inconsistent with the 
fact that the average of the extreme values 0.2625 an d 0.2685 
equals 0.2655, which happens to agree with 0.266 almost exactly. 
Likewise, for the 8 series |(o. 2499+0. 2375) = 0. 2437, which is only 
0.33 per cent less than 0.2445. I n this comparison the interval 
— 52 to —60 was omitted because the wave-lengths of these faint 
lines were not at Thiele's disposal. In any event, the writer desires 
to lay special emphasis on the fact that the variations of c, as shown 
by the numbers in the fourth column of Table III, are real and not 
fictitious. In other words, these variations arise neither from the 
irregularities and small anomalies of the wave-lengths nor from the 
use of only three terms in the interpolation formula. Of the various 
crucial tests which have been made in this connection the following 
one is alone sufficient to remove all suspicion. The average 
(0.2629) oi ~ the first four values of c given in Table III was taken 
as standard, because the lines near the head of the band fit the 
parabolic interpolation formula very closely; and then the correc- 
tion e, which would have to be applied simultaneously to each and 
every one of the seven lines +36 to +42 to change c from o. 2686 
to o. 2629, was calculated. In other words, e denotes the displace- 
ment of the entire group of seven lines of the positive branch rela- 
tive to the corresponding group (—37 to —43) of the negative 
branch, required to give c = 0.2629. It was found that e = 
+0. 104 A, which is altogether too large to be accounted for on any 
reasonable basis. On the one hand, the wave-lengths cannot be 
relatively displaced by o. 1 A because one of the primary objects of 
Leinen's work was to determine their values as accurately as pos- 
sible. He gives his experimental data to thousandths of an ang- 
strom unit and hence the relative errors should not exceed 0.01 A 
at most. Moreover, the errors would not all be of the same sign. 
On the other hand, the parabolic equation used in the present com- 
putations cannot be responsible for the large value of e because the 



86 H. S. UHLER 

arithmetical sum of all the fourteen residuals (X ca ic. — X bs.)> for both 
the positive and negative branches, amounts to 0.0927 A, which is 
less than 0.104 A. The just comparison, however, would be 
between 0.007 A (°°93"^ I 4) anc l 0.104 A. These two numbers 
are not even of the same order of magnitude. By applying the 
same test to the 5 series it was found that every one of the nine 
lines from +52 to +60 would have to be translated to shorter 
wave-lengths by 0.355 A in order to change c from 0.2344 to 
o. 2499. The arithmetical sum of the eighteen residuals (inclusive 
of the anomalous value +0.052 A pertaining to line —58) is 
0.2918 A, which is distinctly less than 0.355 A. The average 
residual is only 0.016 A instead of 0.355 A. 

Attention will now be turned to the series emanating from the 
first head of the cyanogen band at X 3883. In this case, it will not 
be necessary to make use of wave-lengths given by other observers 
because the author has personally taken more than thirty negatives 
of this band in the third order of Rowland's best grating, which has 
20,000 lines to the inch and a radius of curvature of about 21 feet. 
Moreover, some of the wave-lengths have been determined by the 
writer and all of the lines have been measured and studied very 
carefully by R. A. Patterson in this laboratory. 

Judged by appearances, only two series start from the head 
near X 3883. One series consists of doublets, which are very 
intense near the head, but which gradually decrease in strength 
until they fade out or get lost by superposition with lines of other 
series at the ordinal number 46. The other series (known as the 
Kayser and Runge series) starts out with single lines which are 
eventually resolved into close doublets. Under the experimental 
conditions, the lines of this series remain single beyond the more 
refrangible end of the doublet series first mentioned. The fact 
that the doublet series does not furnish data for the calculation 
of the phase beyond line 45 is very disappointing because the 
singlet series can be accurately measured to line 168. Moreover, 
it is rather unsatisfactory to be under the necessity of comparing 
resolved doublets with lines which are photographically single. 
The best that can be done is to calculate c from the axes of the single 
lines (positive branch) and the centers of each of the components 



THIELKS "PHASE" IN BAND SPECTRA 



87 



of the doublets taken as separate series (negative branches). Even 
under these unfavorable conditions it will be shown that the singlet 
and doublet series do not lead to constant values of c and hence 
do not constitute branches of single series according to Thiele's 
definition. 

In order to show how extremely well the least-squares parabolas 
fit the experimental data, the results obtained by subtracting the 
observed values of the wave-lengths from the calculated numbers 
are given in Table IV (in the columns headed A). The wave- 
lengths corresponding to the parenthetical residuals were not used 
in the computations because the spectrograms indicate that the 
lines are either anomalous or confused with lines of other series. 
The bottom row contains the figures obtained by substituting the 
residuals in the usual formula for the probable error of a single 
observation. The subscripts x and 2 refer to the less and more 
refrangible components of the resolved doublets, respectively. 

TABLE IV 



+15 
+16 

+17 

+ iS 

+19 

+ 20 
+ 21 

+ 22 

+23 

+24 

+25 



— 0.0024 
+0.0025 
+0.0011 

— o . 0006 
+0.0006 

(—0.0096) 
— 0.0010 

— o . 0006 

(+0.0045) 

— o . 0006 
+0.0010 



•151 

■i6, 
i7i 

•181 
191 

•2d 
■2I t 
■22 x 
■23i 
■24i 



±0.0010 e. 



+0.0016 

— 0.0018 
+0.0004 

— o . 0008 

— 0.0005 
+0.0004 

— 0.0002 
+0.0018 

— 0.0006 
+0.0005 

— 0.0008 



16, 

172 
■i8 2 

192 
•20 2 

2I 2 
22 2 
232 
242 



±0.0007 e. 



— o . 0006 
+0.0008 
+0.0006 

o . 0000 

— 0.0013 

— O.OOII 

+0.0025 

— o . 0004 
+0.001 1 

— o . 0030 
+0.0014 



'+37 
1+38 
+39 
+40 
+41 
+42 
+43 



o . 0000 
+0.0007 
— 0.0001 
— 0.0024 
+0 . 0008 
+0.0024 
— 0.001^ 



-37i 

-38x 
-39' 
— 4°i 
-4ii 
-42i 
-43i 
-44i 



— o . 0009 
+0.0003 
+0.0024 

— 0.0016 

— 0.0007 
+0.0001 

(-00553) 
+0.0003 



= O . OOO9 



The value of the phase obtained from the groups +15 , 

+ 19, +21, + 22, +24, +25, and — i5u — 2 5i is 0.1667. 

The intervals +37, . . . . , -f-43 and —37^ . . . . , —421. — 44i 
give (7=0.1515. In like manner the same groups of the positive 
branch combined with the sets —152, • • • • , — 252 and —372, 

—42,, —442 lead to c= 0.0950 and c — o. 1047, m the order 

named. Hence, on receding from the first head of the band, the 
phase decreases for the less refrangible components of the doublets, 



88 H. S. UHLER 

but increases for the components of shorter wave-length. The 
deviation from the mean is 4 . 8 and 4 . 9 per cent for the larger and 
smaller pairs of values of c respectively. In order to change the 
value of c from o. 1515 to o. 1667 all the lines of the group +37 to 
+43 would have to be displaced toward the shorter wave-length 
side by 0.025 A, the set —371, . . . . , — 42^ —441, being looked 
upon as fixed. Similarly, a translation toward the red of 0.016 A 
would have to be given to the entire group +37 to +43 in order to 
decrease the phase from 0.1047 to 0.0950, the set —372, • • • • , 
— 42 2 , —442 remaining stationary. If the lines of the branch which 
has been taken arbitrarily as positive (with no loss of generality, 
however) are really single, then the conclusion follows at once that 
the wave-length corrections are altogether too great to admit of 
the hypothesis that this series is related to the series of resolved 
doublets according to Thiele's method of combination. On the 
other hand, if the singlets are actually unresolved doublets, then 
two cases require consideration: (a) the less and more refrangible 
components of the discrete doublets are to be coupled with the less 
and more refrangible hypothetical components of the positive 
branch respectively; (b) the longer and shorter wave-length com- 
ponents of the resolved doublets correspond to the shorter and 
longer wave-length components of the unresolved series, in the 
order named. From general physical considerations case (a) seems 
to be the more reasonable. Moreover, Thiele himself combines 
the doublets of the X 5165 band according to this plan. Under 
these conditions each of the numerical corrections 0.025 A and 
0.016 A would have to be increased, thereby strengthening the 
evidence against the correlation of the positive and negative 
branches. On the other hand, it is only fair to examine the second 
possibility quantitatively. 

In the first place, in the region between the first and second 
heads of the band the lines of the Kayser and Runge series are 
comparable in width with the components of the resolved doublets. 
If then the observed singlets are truly doublets, their hypothetical 
components must be extremely close together so that no sensible 
error can arise from treating the lines in question as if they were 
rigorously single. In other words, it is perfectly safe to consider 



THIELE' S "PHASE" IN BAND SPECTRA 89 

the phase values o. 1667 and 0.0950 as correct and to investigate 
the possible duality of the broader single lines of the set +37 to 
+ 43- According to the present calculations each of these lines 
should consist of a pair about 0.041 A apart. The less refrangible 
component should lie on the longer wave-length side of the axis 
of the broad singlet and at a distance of 0.016 A from this axis. 
Similarly the more refrangible component should be situated on the 
shorter wave-length side of the center of the unresolved singlet and 
at a distance of 0.025 A from this center. Hence, the mean posi- 
tion of the hypothetical doublet would be displaced from the middle 
of the singlet by 0.0045 A (toward the more refrangible edge). 
This hypothesis is untenable for several reasons, namely: (a) expo- 
sures of different lengths do not indicate any asymmetry in the 
singlets, (b) when the Kayser and Runge series eventually becomes 
resolved into doublets the components have sensibly equal widths 
and intensities, and (c) the residuals of the lines in question (see 
Table IV) show that the members of a group of seven or more lines 
cannot all be displaced in the same direction by as much as o. 0045 A. 
The conclusion, therefore, that the singlet and doublet series start- 
ing from the first head of the X 3883 cyanogen band do not form 
the positive and negative branches of a complete Thiele series is 
thoroughly justified. 

In the cases of the a and 5 series of the X 5165 carbon band and 
the series from the chief head of the X 3883 band, the only way left 
to make the phase constant is to assume either that c = o or that 
c—o.^. These values of the phase mean that the lines of the series 
are made to coincide either with themselves or with the adjacent 
lines of the same series. Such a special arrangement is, of course, 
always possible. If it had been found that c was strictly constant 
and had a value different from o or o . 5 for a large number of bands, 
then self-conjugate series might occur in a relatively small number 
of cases as a consequence of special conditions in the radiating sys- 
tems. Since, however, it has just been shown that c is not constant 
for the series examined, and since doubt is thereby thrown on the 
constancy of the phase for the remaining series computed by Thiele, 
the values o and o . 5 for c lose their significance as special cases 
and assume the aspect of artificiality. Conformable to strict logic 



go H. S. UHLER 

Thiele's hypotheses can be disproved in only two ways: by theoreti- 
cal considerations based on the laws of radiation or by an examina- 
tion of all bands capable of existence. From this point of view 
nothing can be done at the present time. On the other hand, in 
the opinion of the writer, the evidence adduced in the foregoing 
paragraphs throws enough doubt on certain of Thiele's hypotheses 
to require new evidence in their favor before they can be considered 
tenable. 

In conclusion, a few additional comments will be appended 
which confessedly bear the imprint of personal opinion. Thiele's 
computations gave apparently constant values of the phase for two 
reasons, namely: (a) the method employed led to mean values of 
c, and (b) the agreement between the calculated and the experi- 
mental wave-lengths appeared satisfactory because the data at 
his disposal did not attain to the degree of accuracy which charac- 
terizes the more modern work. Moreover, a small error in c would 
constitute a still smaller percentage error in n-\-c, especially for the 
higher values of the ordinal n, and consequently formula (2) could 
reproduce the wave-lengths fairly well. No importance attaches 
to the fact that Thiele predicted the wave-lengths of faint lines 
which were found later by Leinen, because this could have been 
accomplished (with much less labor) just as well by extrapolation 
with a power series, involving only five terms, 1 for the positive and 
negative branches taken separately as natural series. The con- 
stancy of c, within the limits given above, is nothing more than the 
analytical expression of the well-known fact, pointed out by 
Deslandres, that series starting from the same head of a band run 
approximately parallel courses. Formula (2) owes its flexibility to 
the fact that it is the most general rational, algebraic function of 
even degree in n-\-c. Doubtless Thiele chose this form because, in 
general, the curve possesses a point of inflection and is asymptotic 
to the ''tail" wave-length 

'r 

Nevertheless, with eight parameters (7=3) formula (2) does not 
predict the wave-lengths of the "tails" of the series successfully. 

1 See H. Kayser and C. Runge, Abhandlungen der kaiserlichen Akadcmic der 
Wissensckaften, Berlin, 1889, Anhang, p. 31. 



THIELE'S "PHASE" IN BAND SPECTRA 



91 



In the third column of Table V may be found the wave-lengths 
which the writer has computed from Thiele's own coefficients by 

TABLE V 



Series 



"A " 



"Tail" 



7l. 
el. 
ell 

r.. 



5165. 1733 
5165. 5911 
5163.7023 
5166. 2211 
5164.9003 
5130.5489 




putting ;z=*> in formula (2). Aside from the relatively trivial 
fact that these wave-lengths are not mutually consistent, the pre- 
dicted limits fall in a region of the spectrum where no tails have 
ever been found. In this connection, it is but fair to give the 
following quotation from Thiele's second paper: 1 

Upon the whole it must be evident that these systems of constants are by 
no means to be considered as definitive and reliable for speculations regarding 
the true properties of the law of spectral series. The main interest of my 
computations is not to be found in these constants, but in the tables of 
computed wave-lengths founded upon them. 

SUMMARY 

i. The two older methods for calculating the "phase" c of a 
band series are shown to be too complicated for practical purposes. 

2. A new and relatively simple method for evaluating c at 
different places along a band series is developed. 

3. Details of the practical application of the third method are 
given. 

4. The phase is shown to be variable, within specified limits, for 
the a and <5 series of the X 5165 carbon band, investigated arith- 
metically by Thiele. 

5. The two obvious series starting from the first head of the 
X 3883 cyanogen band are shown to be unrelated according to 
Thiele's scheme of combination. 

6. Various lines of evidence are presented to indicate that some 
of Thiele's hypotheses are invalid. 

Sloane Physical Laboratory 

Yale University 

May 1915 

1 Astro physical Journal, 8, 12, 1898. 



EFFECTIVE WAVE-LEXGTHS OF 184 STARS IN THE 
CLUSTER X.G.C. 1647 1 

By EJXAR HERTZSPRUXG 
I. THE OBSERVATIONS AXD THEIR REDUCTION 

The following pages contain the details of my determination of 
effective wave-lengths in the cluster N.G.C. 1647 (4 h 40 m ,+ io°) 
briefly described in Yearbook, No. 12, p. 222, 1913, of the Carnegie 
Institution of Washington and referred to by Seares in his paper 
"The Color of the Faint Stars" in this Journal (39, 361, 1914). 
The instrument employed was the 150-cm (60-inch) Mount Wilson 
reflector diaphragmed down to 100 cm (40 inches) aperture in order 
to increase the diameter of the useful field. 

Over the end of the tube of the reflector was placed a grating 2 
consisting of overspun rubber cords 3 mm thick separated by free 
spaces of the same width. This grating forms short spectra on 
both sides of the central star image as shown in Fig. 1, which is 
enlarged 3 . 3 times from the original plate. The focal length of the 
reflector being 7606 mm (299.5 inches), the distance between the 
centers of the two spectra of first order is about 1 mm (0.04 inch). 
When the diameter of the wires of the grating is equal to the spaces 
separating them, all the spectra of uneven order are at their maxi- 
mum intensity and all those of even order disappear. In this case 
the spectra of first order are t 2 times or 2 . 486 mag. fainter than 
the star image without grating. As the spectra with the disper- 
sion here used are somewhat elongated, especially for the whiter 
stars, it will be safer to say that the limiting magnitude down to 
which, for a certain exposure time, effective wave-lengths can be 
determined is about 3 mag. less than that for which, under the 
same conditions without grating, measures of position can be made. 3 

1 Contributions from the Mount Wilson Solar Observatory, Xo. ioo. 

2 Made by Toepfer of Potsdam. 

3 As the spectrum of a red star is sensibly shorter than that of a white one, the loss 
in light from elongation of the spectra is somewhat smaller for the red than for the 
white stars. It will therefore be possible to measure the effective wave-lengths of the 
former down to a magnitude a little fainter than in the case of the latter. It is easy 
to avoid an undesirable selection caused by this phenomenon by measuring only 
to a certain intensity of the central image. 

92 



EFFECTIVE WAYE-LEXGTHS OF STARS IN CLUSTER 



93 



Fig. i shows the appearance of two stars of extremely different 
color. The objects are B.D. + 9°4367, which is a white star, and 
B.D. +q°4369, which has a spectrum of the fourth type. The 
plate received five exposures of 360, 114, 36, 12, and 4 seconds, 
respectively, so that one step in the exposure time corresponds to 
0.5 in its logarithm or to about 1 mag. in intensity. The faintest 
images are not visible in the figure. A line is drawn between the 
images of longest exposure for the two stars. The distance is 
12.58 mm on the original plate, or 341 ".1 according to the A.G. 
Catalogue. Visually the two stars are of equal brightness — mag- 




+9°4367 



+9°4369 



Fig. 1. — Central images and first-order spectra 



nitudes 8.5 and 8.7, according to the B.D. and magnitudes 8.6 
and 8 . 4. respectively, according to A.G. Leipzig. Photographically 
the difference is about 2 mag. in accordance with the difference 
in color. 

It is seen at a glance, that the distance between the centers of 
the two spectra of first order is greater for the red (+o°4369) than 
for the white (+o°4367) star, owing to the difference in spectral 
distribution of energy. This distance between the two spectra 
determines the effective wave-length and may be taken as an 
equivalent of color. The mean error of one such distance for well- 
exposed images is about ="=6^, corresponding to =*= 26 A in the effective 



94 EJNAR HERTZSPRUXC, 

wave-length. 1 The effective wave-lengths of the two stars shown 
in Fig. i are found to be 4280 A for the white star B.D. + 9°4367, 
and 4590 A for the red star +9°4369, the difference being 310 A. 

The difference in effective wave-lengths for stars of spectra 
A and K is about 200 A, while the corresponding difference in color- 
index, w pg — ;»vi S , is 1 mag. The mean error ±26 A in one effective 
wave-length therefore corresponds to a mean error of ±0. 13 mag. 
in the color-index. 

The effective wave-length varies not only with the color of the 
star but also sensibly with the strength of the spectrum image. 
To be considered as a color equivalent, therefore, a correction is 
needed to reduce the measured distance between the two spectra, 
or the effective wave-length, to a normal intensity of image. This 
correction will vary with the instrument (reflectors or refractors 
of different achromatization and focal length), the spectral sensi- 
tiveness of the plate, and the color of the star. Its accurate 
determination requires an undesirable increase of work. I there- 
fore preferred to take several photographs of the same region with 
different exposures, and on each plate to measure only those spectra 
which are approximately of normal strength. 2 Actually the 
longest exposure given to the plates used in this investigation was 
30 minutes, which with 9.5 and 3 minutes, and 57, 18, and 6 seconds, 
forms a geometrical progression, the logarithm of whose constant 
ratio is o. 5. 

The intensity of images just well exposed was taken as the 
normal. One effective wave-length from an image of normal 
intensity was given weight 6; and effective wave-lengths from 

3 This accuracy, as is to be expected, is of the same order of magnitude as that 
attained in the photographic measurement of double stars. With the Copenhagen 
refractor a = 20 cm, 7=480 cm, I found for one exposure, on the average, a mean error 
of =4.2 m for the distance between the two components of a double star. With 
the 50-cm Potsdam refractor a = $o cm, 7=1250 cm, I found the corresponding 
mean error to be =*= 4 . 5 /*• 

2 From all this it appears that the zero-point of the effective wave-lengths is to 
a certain extent arbitrary. It would be practicable to define the color-indices and the 
effective wave-lengths in such a way that the indices o mag. and + 1 mag. correspond 
to effective wave-lengths of 4200 and 4400 A, respectively. To this end 34 A would 
have to be subtracted from all the effective wave-lengths given in this and in the 
following note. 



EFFECTIVE WAVE-LENGTHS OF STARS IN CLUSTER 



95 



images i and 2 mag. weaker or stronger than the normal intensity 
received weights 4 and 1, respectively, after the correction for 
deviation from normal intensity had been applied. Xo accurate 
knowledge of the correction to normal intensity is needed, there- 
fore, unless the stars are very bright or very faint. Only for the 
very faintest stars, which do not reach normal brightness even on 
the longest-exposed plates, is the correction of any importance. 

As an average, I found the effective wave-length to increase 
19 A for each magnitude of increase in the intensity of the image 
measured. This rate has been adopted for all stars of all colors. 1 

A chart of the stars in the cluster N.G.C. 1647, used in this 
investigation, is given in Plate I. The central star, Xo. 100, is 
A.G. Berlin 1290, 4 h 40 m 9 s 69, +i8°56 / i9 , 'i (1900). The diameter 
of the inner circle is 40' and that of the outer i°; the central por- 
tion being, of course, in much better field than the outer zone, the 
results derived for the central stars are therefore the most reliable. 

TABLE I 
List of Plates 



Plate Xo. 



Date 



Sid. Time 
Middle of Exp. 



Exp. Time ' Kind of Plate 



249. 
250. 
251- 
252. 
3I3- 
314- 
323- 
324- 
325- 
326. 

327- 
328. 



191 

Oct. 



13 



16 
17 



l 2 y 

57 
20 

33 
14 
53 
15 
40 

4 

-'7 

4 11 

4 26 



3° m 
3° 

9-5 

9-5 
3° 
3° 

9-5 
3° 

9-5 
30 



Lumiere 2 
Seed 27 • 
Seed 27 
Lumiere 2 
Lumiere 2 
Seed 27 
Lumiere 2 
Seed 27 
Seed 27 
Lumiere S 
Seed 27 
Lumiere S 



*3 m ,3 m , 57 s , S7 3 . 18 s , 18', 6», 6'. 

The plates used are listed in Table I. 2 As will be seen, there 
are two complete sets, one taken on Seed ''27," the other on 

1 For further details of the method of effective wave-lengths see Potsdam Publ., 
X0.63, Part 1, 1911. A list of the earlier literature is found in Astron. Nachr., 182,301, 
1909. 

2 They were measured at the Astronomical Laboratory at Groningen on my 
return from Mount Wilson to Potsdam. 



96 EJNAR HERTZSPRUNG 

Lumiere "2" plates. The two sets have been treated separately. 
As an average, the effective wave-lengths reduced to the normal 
strength of image proved to be 29 . 5 =±= 1 . 5 A (mean error of median 
value) greater for the Seed "27" than for the Lumiere "2" plates. 
Furthermore, there is a slight indication that this difference between 
the two sets increases about 2 . 9 A for each magnitude of decrease 
in brightness. The smallness of this magnitude equation is 
satisfactory. 

To reduce the effective wave-lengths to the same system, the 
Seed '"27" plates were first corrected for the constant difference of 
29.5 A between the ''2" and "27" plates. Secondly, the results 
from each kind of plate were corrected by half of the magnitude 
equation, or IX2.9 A per magnitude. Admitting that this mag- 
nitude equation arises only from errors of reduction in the two 
different sets of plates, the final effective wave-lengths are on the 
Lumiere "2" system. 

In this system I found from other plates an effective wave- 
length of 4234 A to correspond to a typical A star, the color-index 
of which I u= m pg — w v i s , Harvard, is zero according to the Gottingen 
Aktinomctrie, B, 191 2. It was furthermore found that a difference 
in the color-index 7h of 1 mag. corresponds to a difference in effective 
wave-length of 200 A. Hence we have the following formula 
for the relation between color-index, 7 H . expressed in magnitudes 
and the effective wave-length X eff expressed in A: 

200 7h = Kb — 4234 • 

In Table II the reduced effective wave-lengths and their relative 
weights, as indicated above, are given for each set of plates sepa- 
rately. The weighted means contained in Table IV are the final 
values. 1 

It will be remembered that the weight 6 was assigned to an 
effective wave-length derived from a single image of normal 



1 Star Xo. 218, which is 2' inside the border of the field, has accidentally been 
omitted from this investigation. This mistake is of no importance for the general 
conclusians. The star is included in the catalogue for the sake of completeness. Xc 
219 was first called 218. For all other stars my original notation was kept in spit 
of there being a few objects which proved to be too faint for measurement of effect- 
ive wave-lengths. 



ra' 
Co. 
it* 






EFFECTIVE WAVE-LENGTHS OF STARS IN CLUSTER 97 

TABLE II 
Mean Results from Lumiere "2" and Seed "27" Plates 



LUMIERE 2 



'ell 



Rel.Wt. 



Seed 27 



ViT 



Rel.Wt. 



Star Xo. 



Lumiere 2 



A eff Rel.Wt. 



Seed 27 



A eff Rel.Wt 



4337 
334 



3" 
251 
257 
287 



592 
273 
297 

337 

'386' 
249 
324 
377 

277 

334 

33° 
302 



43° 
315 
338 



33i 

241 

354 

272 
300 

259 
359 
328 

258 
329 
315 



17 
23 
28 

3i 



3° 
20 

3i 

3 
32 
16 

9 
33 

17 

9 
33 



3 
15 
15 



14 

27 

20 
26 
31 

32 



3° 

3 

23 



4358 
372 
321 
512 
421 
328 
269 
267 
302 
3i9 

57o 
252 
298 
33i 
348 
348 
258 

315 
368 
270 

378 
321 
339 
342 
2 74 
443 
401 

435 
497 
368 
326 
330 

559 

407 

358 
335 
235 
37o 
347 
271 
308 
397 
254 
363 
327 
261 

3i3 
308 



19 



3° 
3 



29 

28 
29 

7 

24 
29 
3° 
3i 

1 
12 
28 

19 
16 

32 

o 

25 
o 

21 
29 



25 

27 
I 

4 

7 

23 

29 

3 

26 

30 
3° 

1 

30 
28 
30 

3 1 

8 

3° 



Si- 

52. 
53- 
54- 
55- 
56. 
57- 
58. 
59- 
60. 
61. 
62. 
63- 
64. 
65. 
66. 
67. 
68. 
69. 
70. 
7i- 
72. 
73- 
74- 
75- 
76. 

77- 
78. 

79- 
80. 
81. 
82. 

83. 

84. 

85- 
86. 
87. 



90. 
91. 
92. 
93- 
94- 
95- 
96. 

97- 
98. 

99- 
100. 



428 



331 

317 
389 

333 
324 
213 

589 
250 



254 

333 
339 
529 
3i8 



265 
284 

3°9 



297 
249 



291 

352 

360 

267 

258 
43° 



251 
3°4 
284 

241 
323 

282 



14 
24 
3° 



28 



3 
3i 



29 



34 



3 

15 



32 
32 



32 

27 
11 

30 
9 



37 

28 



30 
26 



29 
13 



30 



43i 
507 
384 
345 
336 
412 
372 
337 
347 
215 
428 

547 

235 

401 

512 

251 

372 

314 

332 

521 

3 22 

424 

489 

257 

277* 

347 

353 

359 

562 

298 

251 
482 

352 
290 
358 
366 
348 
361 
287 
252 
404 
322 

330 
252 
308 

347 
249 
320 

417 
266 



14 

7 



29 
29 

4 



29 

o 

9 

3° 

1 

7 

29 

o 

32 



25 
o 

2 
30 

3° 
o 

22 

2 

2 

31 

30 

24 

2 

31 

17 

3 

19 

2 

32 
28 
19 
4 
7 
29 
28 

9 
29 
24 

o 

29 



9 8 



EJNAR HERTZSPRUXG 
TABLE II— Continued 



LlMIERE 2 



Star No. 



IOI. 

I02. 

I03 • 
IO4. 
IOS. 

I06. 
IO7. 
I08. 
IOg. 
IIO. 

Ill . 

112 . 

"3- 

114. 

"5- 

116. 
117. 
118. 
119. 
120. 

121 . 

122 . 
123. 
124. 
125. 
126. 
127. 
128. 
129. 
130. 

131- 

132. 

*33- 
134- 
*35- 
136. 

137- 
138. 
1 39- 
140. 
141. 
142. 
143- 
144 
MS- 
146. 

147. 
148. 
149- 
150. 
151- 
152. 



Vf. 



Rel.Wt 



288 
323 

331 
263 

406 
287 
33* 
352 
387 

332 
293 



3" 

37i 
359 
266 



498 



280 
242 



355 
344 
266 

295 
439 



320 
283 
315 

298 
346 
491 



16 
21 
29 

3 
32 
10 

4 
21 

15 
28 

10 
25 

31 
10 

3° 



16 



3° 
31 



2 
11 
3° 
29 

5 



32 
29 

3 
6 

23 
32 



Seed 27 



Ytt 



Rel.Wt. 



3U 
368 
379 
330 
515 
268 

375 
463 
306 

343 
385 
39i 
388 
327 
292 
408 

393 
306 

484 
388 

327 

270 

353 
333 
512 
395 
338 
367 
5io 
429 
326 
282 



301 

297 
312 

483 
340 
313 
543 
398 
258 
482 



7 
10 

3 
24 
27 
30 

1 
12 
32 
19 
18 

27 
o 

24 

30 

o 

19 

27 

o 

31 
17 
31 

6 



4 
3° 



3° 
32 
30 



3° 

1 

32 



Star Xo. 



153- 
154- 
155- 
156. 

157. 
158. 
159- 
160. 
161. 
162 . 
163. 
164. 
165. 
166. 
167. 
168. 
169. 
170. 
171. 
172 . 
173- 
174. 
175- 
176. 
177. 
178. 
179. 
180. 
181. 
182. 
183. 



245 
22s 


29 



185 
186 


347 
327 
256 


10 
19 
30 


187 
188 
189 


299 
462 


3i 

12 


190 
191 



192. 

193- 
194. 

195- 
196. 
197. 
198. 
199. 
200. 

201 . 

202 . 
203. 
204. 



LUMIERE 2 



Seed 27 



A eff Rel.Wt. A eff Rel.Wt 



524 
391 
516 



278 
338 
3°7 
311 
334 



357 
433 
316 
287 
35i 
323 
254 



305 
421 



243 



325 
308 

3°7 
326 
360 

314 

228 

365 
3ii 

34i 
325 

301 
461 

399 
551 
382 



34 
32 
3i 
33 



30 

o 
6 

25 



5 
26 

1 
19 

5 

16 

17 

3 
3i 

15 

8 

32 



17 
2 



EFFECTIVE WAVE-LENGTHS OF STARS IN CLUSTER 99 
TABLE II— Continued 



Star No. 



205. 
206. 
207. 
208. 
209. 
210. 
211 . 
212. 



LUMIERE 2 



A eff Rel.Wt. 



336 

558 
306 



15 
25 

22 



Seed 27 



A eg Rel.Wt. 



405 
374 



343 
57o 
325 



24 
3i 
28 



Star No. 



213. 
214. 

215- 

216. 
217. 
218. 
219. 



LUMIERE 2 



Seed 27 



A eff Rel.Wt. A eff Rel.Wt 



299 



306 
315 



339 



306 
382 
323 
331 



334 



28 
28 



intensity, the mean error of such a result being about ±26 A. 
From the differences between the values derived from the Seed "27" 
and the Lumiere "2" sets the mean error corresponding to weight 
6 is found to be ±20 A. The agreement is satisfactory. There is 
some indication of a systematic error common to all effective wave- 
lengths derived from the same plate. So far as the material goes, 
this plate error seems to be of the order of =*= 10 A. 



II. DISCUSSION OF RESULTS 

Fig. 2 is a graphical representation of the results. The appear- 
ance of this diagram is very striking, the most curious fact being 
the lack of faint white stars. For a further discussion it must be 
remembered that the effective wave-lengths of the fainter stars, 
say below magnitude 13, are much less accurate than for the 
brighter ones. The ordinates of the dotted line in Fig. 2 indicate 
approximately the value of the mean error of the effective wave- 
lengths for different magnitudes. The faint stars consequently 
seem more scattered over the different colors than they really are. 
Everything taken into consideration, we may say: 

The fainter the stars in the region examined, the greater the 
minimum effective wave-length. This minimum value, which 
increases with decreasing brightness, is rather sharply defined, 
and scarcely any stars are to be found w r ith effective wave-lengths 
less than this limit. 

The only faint star which is a pronounced exception to this rule 
is Xo. 190 of magnitude 12.40, showing an effective wave-length 



IOO 



EJNAR HERTZSPRVXG 



of only 4216 A; the next following of similar magnitude has 
an effective wave-length of 4316 A (No. 189), which is 100 A 
greater. The star No. 190 is found to be white on 6 plates, so that 
there can be no doubt about the reality of its exceptional color. 

The question arises whether this relation between apparent 
magnitude and distribution of colors is to be explained by selective 
extinction of light in space or whether it may be accounted for in 
other ways. It must be considered that the region in question 
includes stars belonging physically to the cluster and also other 



s .:■■ 



•/.. 



•«»• 



v 



Fig. 2. — Effective wave4engths and photographic magnitudes in N.G.C. 1647. 
Dotted curve indicates mean error of effective wave-length. 



stars belonging to the system of the Milky Way. The galactic 
latitude is — 15 . All the physical members of the cluster may 
be considered as at the same distance, and hence for these" stars 
we should expect the relation between color and apparent bright- 
ness to be about the same as that found for other clusters like the 
Hyades between color and absolute brightness. For the other stars, 
belonging to the general system of the Milky Way, we may, from 
all we know, adopt a distribution in space which, in its first approx- 
imation, is defined by a rather sharp outer limit beyond which 



EFFECTIVE WAVE-LENGTHS OF STARS IN CLUSTER ioi 



practically no stars occur. That is to say, stars of a certain 
apparent brightness cannot have an absolute brightness greater 
than that corresponding to the limiting distance. The maximum 
absolute brightness must therefore decrease with the apparent 
brightness. 

Now for stars of known absolute brightness and color we lind 
that the smaller the absolute brightness, the yellower is the mini- 
mum effective wave-length, and that only extraordinary stars 
occur which are whiter than the limit thus defined. 1 Dividing the 
stars of N.G.C. 1647 into groups of 29 or 30, I find the following 
relation between apparent magnitude and the median value of the 
effective wave-length : 



Pg. magnitude. . 
Eff. wave-length 
O-C 



10.02 


11 45 


12.40 


13.06 


13-74 


14.20 


4260 


4300 


4327 


4347 


4364 


4389 


+ 4 





— 2 


— 2 


-6 


+ 5 



1445 
4396A 

+4A 



This relation as shown by the differences 0— C js well repre- 
sented by the linear formula : 

A eff -4340 = 30 . 5 (ra-12 .76). 

The increase in median effective wave-length for each magnitude 
decrease in apparent photographic magnitude is 30.5 A. It is 
remarkable that this rate, all uncertainties taken into consideration, 
is practically the same as that, namely 26 A per magnitude, found 
for stars of known absolute brightness and color within the same 
interval of effective wave-lengths (4260-4396 A). 2 This is what 
we should expect for stars physically belonging to the cluster. 
But for the other faint stars we may also expect something similar, 
for it is a consequence of our ideas of the distribution of stars in 
space that the median distance of the fainter stars here in question 
will not vary much with the apparent magnitude. 3 

1 See the following article. 

2 See the following article. The fact that photographic magnitudes have been 
used here, and visual magnitudes in the following article, has been taken into con- 
sideration. 

3 The order of magnitude of this median distance of the fainter stars, say of mag- 
nitude 14, may be estimated in the following way. For stars of the photographic 
magnitude 14 we find the median effective wave-length to be 4378 A. It is obvious 



102 



EJNAR HERTZSPRUNG 



We may therefore say that the results found in this note are 
in fair agreement with what we know about the distribution of stars 
in space and the relation between absolute brightness and color. 
They do not afford any evidence of selective extinction of light 
in space. 



III. DETERMINATION OF THE PHOTOGRAPHIC MAGNITUDES 

The photographic magnitudes used in this note have been 
determined in the following way: During the measurement of the 
effective wave-lengths, the diameters of the central stars were esti- 
mated. Assuming that a difference of o . 5 in the logarithm of the 
exposure time corresponds to a difference of one magnitude, the 
estimates were converted into provisional magnitudes. These 
were used in the manner described above to reduce all the effective 
wave-lengths measured to the same intensity of image. For the 
more accurate determination of magnitudes in the central portion 
of the cluster, the following Schleussner plates were taken on 
January 14, 1913, by the "Halbgitter" method, with the 80-cm 
Potsdam refractor: 





Plate No. 




371 


372 


373 


374 


Halbgitter 


None 

2XlO m 

3 h 23 m 


None 

30 m 

3 h 52 m 


North 
30 m 

4 h 59 m 


South 


Exposure time 


30 m 
5 h. 2 m 


Sidereal time . 





The plates were measured with the Hartmann micro- 
photometer. The zero point of the magnitudes was fixed by 

that the "giant" yellow stars will form only a small minority among the yellow stars 
here considered. Now for "dwarf" stars of known absolute brightness and color the 
effective wave-length 4378 A corresponds to an absolute photographic brightness 
(referred to distance corresponding to 7r = i") of about +0.5 mag. Assuming the 
same absolute brightness for the stars of magnitude 14 here considered, we find their 
median parallax to be o".oo2 and their median distance 1600 light-years. This is 
a plausible value. The parallax of N.G.C. 1647 itself may be estimated in the same 
way, supposing most of the tenth-magnitude A stars to belong physically to the cluster. 
Taking the absolute magnitude of these A stars to be —4, we find the parallax 
to be o''ooi6. I imagine that the determination of effective wave-lengths of faint 
stars will be a valuable help in sounding the Milky Way in different directions. A 
considerable number of the plates I took at Mount Wilson are meant to serve this 
purpose. 



EFFECTIVE WAVE-LENGTHS OF STARS IN CLUSTER 103 



TABLE III 
Photographic Magnitudes 



Schleussner 
"Halb- 
gitter" 



mag. 
I3-04 



1.4-47 
12.39 



12.80 
11.32 



14.17 



13-43 
12.62 
12.36 

14-47 
14.18 
14.01 



10. 16 
14. 10 
12.25 
10.48 
11.66 

14-31 
10.18 
12.09 



10.46 
13.80 



Lumiere £ 

Estimates 



12.04 



12 .04 

9.81 

IO.31 



13-46 



12.76 

IO.67 

9.68 

II .40 



13-41 

IO. 22 



12.95 
IO-95 



12.67 
II. 13 
13-86 



13-41 
12 .50 
12 .58 



13-77 
I2.4O 
IO.O3 



12 .22 
IO. J.O 



IO.I3 
12.13 
12.13 
IO.3I 
13.86 

n-95 
13.69 



Seed 27 
Estimates 



mag. 
4-45 
2-95 

4.40 
1.86 

4. 20 

4-45 
2.42 

9-94 
0.28 

1-31 

3 -70 
4-51 
2.64 
0.50 
9.82 
1 .42 
4-35 
3-44 
0.28 

2-53 
3-15 
0.91 

4 5i 
2.42 

4-51 
2-75 
1 . 21 
4.20 
4. 20 
4.07 
4. 20 

3-44 
2.42 
2.20 

4-35 

4.07 

3-78 

3i 

94 



2.31 

0-39 
1 .62 

4-3° 
0.17 
1.97 
1.86 
0.28 
3 -70 
1.58 
3-35 



Star No. 



52- 
53- 
54- 
55- 
56. 
57- 
58. 
59- 
60. 
61. 
62. 
63- 
64. 
65- 
66. 
67. 
68. 
69. 
70. 

7i- 
72. 

73- 
74- 
75- 
76. 

77- 
78. 

79- 
80. 
81. 
82. 
83- 
84. 
85- 
86. 
87. 



90. 
91. 

92- 
93- 
94- 
95- 
96. 

97- 
98. 
99. 

100. 

101 . 

102. 



Schleussner 
"Halb- 

gitter" 



14-32 



II.82 
10.07 
14.OI 
12.89 
12.76 
IO.04 
14-51 
13-55 
IO.06 



I3-90 
8.83 
14.38 
II .00 
12.81 
I3-48 
12-43 
14-57 



10.41 
10.09 

1449 
12.82 

1425 



14 



65 
11.50 

9 37 

12.64 

1423 
11. 31 

13.10 
14.07 
12.93 



10.79 
9 -5 6 



14-15 
i3-7o 
8.91 
11 .90 
13.70 

9-13 
12.69 
14.40 

9-77 
13.88 

13-79 



Lumiere 2 
Estimates 



mag. 
13-77 



12.40 

H-95 
9.92 



12.76 
12.67 
10.03 



13.60 



13-77 
8.71 



10.95 
12. 76 
13.60 
12.50 



10.40 
10. 22 



12 . 76 



11.50 

9.27 

12.67 



11. 31 

12.86 



12.76 



10.95 
9-55 
13-04 
13 -77 
13-77 
8.85 

"•95 

13-77 

9.27 

12.67 



9.81 
13-77 
13-77 



Seed 27 
Estimates 



mag. 
3 -70 
4-30 
2.42 
1 .92 

9-94 
4.07 
2.85 
2.85 
9-94 
4-45 
3.62 
o. 11 
4-3° 
3-79 
8.68 

4-45 
1. 01 
2.85 

3-53 
2.42 

4.48 
4.00 

039 
o. 17 

4-50 
2-75 
4.26 

4-35 
1 .62 
9.41 
2.64 

4 35 
1 .42 

305 
4. 20 
2-95 
430 
0.90 

9-55 
2.85 
4.00 
3-79 
8-95 
2.09 
3-70 
9.26 
2.64 
4-50 
9.69 
13.70 
13.62 



io4 



EJNAR HERTZSPRUNG 
TABLE III— Continued 



Star No. 



103 • 
104. 

I05 • 
106. 
107. 
108. 
109. 
no. 
Ill . 

112. 

"3- 

114. 

"5- 

116. 
117. 

118. 
119. 
120. 
121. 
122. 
123. 
124. 
125. 
126. 
127. 
128. 

I2Q. 
I30. 

131- 
132. 

134- 

135- 
136. 

137- 
138. 
139- 
140. 
141. 
142. 

143- 
144. 

145- 
146. 

147- 
148. 

149- 
IS°- 
151. 

152. 
153- 
154- 



Schleussner 
"Halb- 
gitter" 



mag. 
14.27 
12.64 



IO.02 
I4-36 
13-43 
11 . 12 



"•95 
1432 
12.54 
n .76 

14-5° 
13.02 
11.80 

I4-5 6 
10.83 
13.00 
10. 19 

13-74 
14.40 



13-78 
13-95 
1430 
14-34 
14.49 
14-03 
11 .61 

9-65 
14.67 

13-65 
12.90 
10. 20 
11.80 
13-54 



15-3 
15-3 
"•95 
11 .00 
11.48 



13-37 
13.28 



10.49 
14.86 
13-55 



Lumiere 2 
Estimates 



mag. 



12.59 

8.85 

IO.13 



13.60 
II. 13 
12.76 
12.67 
12 .04 



I2.5O 
II.76 



12. 76 

11.86 



10.95 
12.77 
10. 22 



(6.6) 
13-78 



11 .67 
9 55 



13.60 
12.68 
10.31 
"•59 
i3-4i 



"•95 
11. 13 
11.50 



13.60 

13-23 
9.81 



10.67 



i3-4i 
i3-4i 



Seed 27 
Estimates 



mag. 
4.20 

2-53 
9.02 
0.05 
4. 26 
3-44 
1 . 21 



2.85 
2.85 
2. 19 
4.41 

2-53 
1.86 

4.41 

2-95 
2. 19 

4-44 
0.81 

3-05 

0.28 

3-78 

4.41 

(6) 

3 -7o 



3 -7o 
4. 20 
4-45 
4-5° 
4.00 
1 .62 
9-55 
4-44 
3-54 
2-95 
0.18 

i-75 
3-44 
4-55 



1 75 
1 .00 
1 .62 
425 
3-54 
3-54 
9.82 

4-35 
0.60 
4-50 
3-44 
3-25 



Star No. 



55- 

56. 

57- 

58. 

59- 

60. 

61. 

62. 

63- 

64 

65- 

66. 

67. 

68. 

69. 

70 

7i- 

72. 

73- 

74- 

75- 

76. 

77- 

78. 

79- 

So 
81. 
82. 
83- 
84. 
85- 
86 

87- 



90. 

91. 

92. 

93- 

94 

95- 

96. 

97- 

98. 

99- 
200. 
201 . 
202. 
203. 
204. 
205. 
206. 



Schleussner 
"Halb- 
gitter" 



mag. 
I3-64 
14.44 
14-77 
14.24 
14.24 
14.40 



IO.52 
II .22 

11.66 
II . 29 



14.42 
13.22 

13-83 



10.83 

13-73 
13.27 
8.92 
13 93 
I4-3I 



13 .61 
13-84 



I4-56 
I3-4I 
11. 81 

I3-50 
12.22 
13-48 
14. 16 
12.38 
12.37 



13. 2i 



Lumiere 2 
Estimates 



mag. 
I3-78 



13-78 
IO.67 
11.22 
II.50 
II .40 

12.68 



12.95 
13-78 
13.69 

10.95 

13-78 

13 23 

9.00 



13.69 
13.69. 



9.81 



13-32 
11.86 
13.60 
12. 22 
13-32 



1 2 
12. 



13.60 
11.67 



12.50 
13-04 



12.13 



13.69 
12 .40 
13.69 



EFFECTIVE WAVE-LENGTHS OF STARS IN CLUSTER 105 
TABLE III— Continued 



Star No. 



207. 
208. 
209. 
2IO. 
211 . 
212. 
213. 



Schleussner Lumifere 5 
gkter" I Estimates 



mag. 
13.86 



12.50 
IO.40 
12.04 



Seed 27 
Estimates 



mag. 
13 -86 



Star No. 



214. 
215- 

216. 
217. 
218. 
219. 



Schleussner 
"Halb- 
gitter" 



Lumiere 2 
Estimates 



mag. 
13 -78 



12.13 
12.04 



12.77 



Seed 27 
Estimates 



mag. 
13 -70 
14.48 
12.09 
12.09 



13-35 



means of plate No. 371, which contained, besides the two ex- 
posures of N.G.C. 1647, one °f the same duration (io m ) on the 
central part of the Pleiades. 

The extinction constant of the Halbgitter used was not deter- 
mined directly from photometric measures, but, as described in 
Astron. Nachr., 199, 247, from the ratio 0—C/C—S 1} where O is 
the magnitude of the stellar image without halbgitter, C of the 
central image behind the halbgitter, and St of the spectra of 
first order. The constant was thus found to be 2 . 14 mag. The 
results are contained in Table III together with the estimates from 
the diameters of the stars on the Lumiere "2" and the Seed " 27" 
plates, both reduced to the halbgitter scale. To these three 
series were assigned the relative weights 4, 1, and 1, respectively. 
The weighted means are contained in the catalogue, Table IV. The 
magnitudes of the stars outside the inner field of 40' diameter are, 
of course, very uncertain owing to the neglect of the correction 
for distance from center of field. 



IV. COMPARISON OF EFFECTIVE WAVE-LENGTHS WITH SPECTRA 

It will be of special interest to compare the effective wave- 
lengths found here with the spectra of the same stars. With a 
mirror of 90 cm (35 inches) focal length, in connection with an 
objective prism 16X16 cm square, Professor Eberhard has kindly 
made a few exposures on the cluster, using Seed "30" plates. The 
best plate was taken on March 1, 1913, from 6 h o m to 7 h 32 m sidereal 
time, Potsdam. In order to reach stars as faint as possible, the 
dispersion was very small, the distance between H/3 and He being 



io6 



EJNAR HERTZSPRLWG 



TABLE IV 

Catalogue 



Star No. 



a (1900)* 



S (1900) 



Dist. from 

Center of 

Field 



Ph. Mag. 



Effective 
Wave- 
Length 



I 
2 

3 
4 
5 
6 

7 
8 

9 

ic 
1 1 
12 
13 
14 
15 
16 

17 
18 

19 
20 

21 
22 
23 
24 
25 
26 

27 
28 

29 

.SO 

31 
32 

33 
34 
35 
36 
37 
38 
39 
40 

4i 
42 
43 

44 
45 
46 

47 
48 



4 h 38 r 



'14? 

20. 

24- 

28 

28. 

3i 

33- 

39 

40 

40. 

40. 

42 

43 

44- 

46 



5° 

50. 

5i 

Si- 

54 

56 



+ 



39 



8. 
10. 
1 1 . 
12. 
13 
14 
15 
16 

17 
19 

JO 

20 
23 
24 
24 
26 
26 
27 



8° 53^5 
9 2.2 

9 7-3 
9 6.5 
8 48.0 
8 58.6 

8 38.6 

9 40 
8 47-4 
8 52.2 
8 38.8 

8 39-4 
8 52.6 
8 40.3 

8 49.6 

9 6.3 

8 52.1 

9 2.3 
9 6-4 
9 6.4 



8 38.5 

8 51-7 

9 6.0 
8 35o 
8 52.0 

8 52.5 
8 36.2 
8 48.4 
17-5 
8 35-4 

8 5i-4 

9 11 . 1 

8 39 4 

9 5° 
8 54-8 

8 51.8 

9 20.4 
8 57-i 
8 43-3 
8 54-5 
8 50.1 

8 56.9 
8 56.2 

8 56.3 

8 57-1 

9 23.4 
9 1.7 



27 
26 

27 
26 

25 
23 
29 

23 
23 
21 

27 
27 
21 
26 
21 
22 
20 
20 
21 
21 

19 
26 

18 
20 
27 
16 
16 
25 
17 
26 

25 
15 
20 
22 
16 
13 
14 
27 
12 
18 
12 
13 



10 
29 



4-45 
2 .91 

4.40 
i-95 
4. 20 

4-45 
2. 23 
9.88 
0.29 

1 .40 
t3-7° 
[4 5i 
•70 
to. 58 

9-75 

■ 41 

'4-35 

t3-43 

10.25 

12.52 

13-04 

93 

14-48 

•40 

14-51 

•77 

•27 

[4 03 

[4.18 

.07 

. 20 

•43 

•57 

[2.37 

14-45 

14. 16 

[3 93 
12.3s 
to. 10 

4.12 
2. 25 

0.45 
1.63 

4-31 
0.17 
2.08 
1.99 
0.41 



435i 
4372 
4327 
4512 
442i 
4320 
4261 
4262 
4294 
4319 



4577 
4263 
4298 
4334 
4348 
4357 
4253 
4319 
4371 
4274 
4378 
4326 
4339 
4346 
4289 

4443 
4401 

4435 
4497 
4380 
4322 
4333 
4559 
4407 
4358 
4333 
4238 
4370 
4350 
4271 
4304 
4397 
4257 
4361 
4327 
4260 



* The period after the seconds of right ascension indicates an additional o?s- 
t The weight 6 corresponds to a mean error of ±20 A, and, consequently, weight 1 to 
= 28 A, 12 to ±14 A, 24 to ±10 A, 38 to =*=8 A, 48 to ±7 A, 67 to ±6 A. 



= 50 A, 3 to 



EFFECTIVE WAVE-LENGTHS OF STARS IN CLUSTER 107 
TABLE TV— Continued 



Star Xo. 



a (igoo) 



S (1900) 



Dist. from 
Center of 

Field 



Ph. Mag. 



Effective 
Wave- 
Length 



Rel. Wt. 



40 



4 D 39 m 29 s 
3i 
32. 
33 
33- 
34 
35- 
31 
31 
39 
40 
4i 
42 
42 
42 
43 
43 
43 
43 
46 
48 
48 
48. 
50 



53 
56 

57 

57- 

57- 

58 

59- 

o 

o 

1 

3 

3- 

3- 

4 

4 

4 



+ 



7 
7 
8. 

9 
9- 

10 



8 49 

8 46 

9 8 

8 44 

9 8 

8 54 

9 3 
9 5 

8 45 

9 5 
8 55 
831 
8 56 
8 55 
8 47 
8 53 
8 54 

8 59 

9 3 
9 5 
8 42 

8 47 

8 46 

9 5 
8 42 

8 56 

9 U 

8 48 
8 46 

8 29 

9 6 
8 55 
8 59 
8 59 
8 55 
8 59 
8 54 
8 39 
8 56 
8 51 



8° 4 6U 
8 27.7 
8 40 

8 35 

9 11 
8 28 

8 54 

9 10 

8 53 

9 8 
8 54 
8 50 



14 
3° 

18 
22 

17 
29 

8 
16 

8 
14 

7 

9 

10 
10 
12 
14 
14 
14 

6 

9 



10 

5 

25 

4 

4 

10 



9 
10 
10 

14 

2 

19 

8 

10 

27 



4 
3 

1 

3 
2 

17 



13 



79 

76 
48 
73 
32 
41 
86 
02 
02 
86 
76 
02 
50 
57 
07 
3° 
86 

79 
39 
99 
81 

5i 

44 
55 

00 

4i 
12 
49 

80 

25 
59 

52 
36 
64 
25 
33 
05 
10 

9i 
30 

83 
56 
94 

or, 

73 
9i 
94 
7i 
17 
68 
4- 
76 
83 



4317 
431 1 
4431 
4507 
4384 
4340 
4327 
4400 
4372 
4336 
4339 
4214 
4428 

4559 
4243 
4401 
4512 
4253 
4372 
4324 
4334 
4523 
4320 
4424 

4489 
4261 
4281 
4347 
4337 
4359 
4562 
4297 
4250 
4484 
4352 
4290 
4356 
4366 
4352 
4361 
4276 

4255 
4411 
4322 
433° 
4251 
4306 

434i 
4245 
4321 
44i7 
4274 
4312 



53 
16 



36 
53 
59 

4 
33 
34 
57 

o 
12 
61 

1 

7 
58 

o 
66 
33 
13 
40 

o 

2 
62 
62 

o 
34 



63 
57 
35 



61 
26 

3 
20 

2 
69 
56 
26 

4 

7 
59 
54 
10 
58 
37 

o 

59 
7 



ioS 



EJNAR HERTZSPRUNG 
TABLE IV— Continued 



Star No. 



a (iooo) 



8 (iooo) 



Dist. from 

Center of 

Field 



Ph. Mag. 



Effective 
Wave- 
Length 



Rel. Wt. 



102 . 

103 

104. 

I05 • 
106. 
107. 
108. 
109. 
no. 
Ill . 

112. 
113 

114. 
"5- 

116. 

117. 
118. 
119. 
120. 
121. 
122. 
123. 
124. 
125. 
126. 
127. 
128. 
129. 
i3°- 
I3i- 
132. 

133- 
134- 
135- 
136. 

137- 
138. 
139- 
140. 
141. 
142. 

143 
144. 

145- 
146. 

147- 
148. 
149. 
i5°- 
151- 
152. 
153- 
154- 



4 n 40 m i4 3 
14- 
15 
15 
15 



16 
16. 



19 

20 
20 
20. 



22. 

24- 

25 

26 

26 

26. 

27. 

27. 

27. 

28 

29 

29. 

30 

3i 

34 

34 

34 

35 

38 

40 

40 

40. 

4i. 

42. 

42. 

43 

43 

43- 

44 

44- 

44- 

46 

48 

5i 

52 



+ 



8°58: 7 
9 7 
8 52 
8 37 
8 51 
8 54 
8 47 
8 54 
8 28 

8 53 
8 S3 

8 44 

9 7 
8 47 

8 51 

9 1 
9 1 
9 12 

8 53 

9 o 
9 6 
8 42 
8 46 
8 33 
8 44 

8 47 

9 10 
8 41 

8 44 

9 1 
9 8 
9 1 
9 4 

8 57 

9 3 



8 30 
8 58 
8 46 
8 47 
8 54 
8 56 
8 34 
8 48 

8 48 

9 18 
8 29 
8 55 

8 47 

9 2 
8 37 



3 
n 

4 
19 

5 
2 

9 

2 

27 
3 
3 

12 

1 1 

9 
6 
6 
6 

16 
4 
5 

10 

15 
10 

23 
12 

9- 
15 
15 
13 

7 
13 

7 
10 

6 

9 



27 

8 

13 



23 



-'4 
28 

9 
13 

1 1 



3 -76 
4.26 
2.61 
8.94 
0.04 
4 34 
3 46 
1. 14 
2.81 
2.76 

2 .00 
4-34 
2-53 
1.78 
4.48 
2.97 
1.87 
4-54 
0.85 
2.97 
o. 21 

3 75 

4.40 

6. 

3-77 

3-9° 

4.28 

436 

4-49 
02 
62 
62 
62 
62 

87 
o. 20 
1.76 
3-5° 
4-55 
5-3 
5-3 
1 .92 
1 .02 

151 
425 

3-44 
3-31 
9.82 

4-35 
o.54 
4-79 
3-51 
3-33 



4366 
4379 
433° 
4513 
4266 

4375 
4452 
4297 
4339 
4378 
4389 
4388 

4329 
4292 
4408 

439i 
4308 
4484 
4379 
4339 
4268 

4353 
4333 
4506 

4395 
4338 
4367 
45io 
4429 
4326 
4281 

4243 
4225 

4349 
4333 
4261 
4297 
4455 



43io 
4290 

4313 
4483 
4329 
4325 
4520 
4398 
4272 
4482 
4507 
4377 



10 

3 
40 
48 
59 

1 

15 
64 
29 



o 
39 

58 

o 

29 

52 

o 

62 

27 
61 

6 



7 
3 
o 
o 
4 
60 
60 



30 
60 
60 
17 



55 

64 

59 

1 

12 

17 

53 

1 

64 

o 

16 

18 



EFFECTIVE WAVE-LENGTHS OF STARS IN CLUSTER iog 
TABLE IV— Continued 



a (1900) 



4 n 40 n 



53 

53 

53- 

54 

54 

54- 

55 

55- 

56- 

56. 

57 

58 

58 

58. 

59 

41 1 

2. 

3 

3- 

4 

4 

4- 

5 

5 

6 

7 

9 

10 



14. 
16 

17 
22 
22 
23 
23 

23- 

25 
27. 
28 
3i- 

3i- 
35- 
38. 
43- 



49- 



& (IQOO) 



+ 



i 9 ° 6: 


18 55. 


18 46. 


18 52. 


19 5- 


19 0. 


19 16. 


19 24. 


18 45- 


19 9. 


19 6. 


18 47- 


19 16. 


18 S3- 


18 51. 


18 57- 


18 36. 


18 56. 


18 45- 


18 50. 


18 53- 


18 53- 


18 52. 


18 35. 


18 58. 


19 8. 


18 31. 


18 43- 


18 56. 


18 57- 


18 41. 


19 5 


19 5- 


18 44. 


18 39- 


18 57- 


18 32. 


18 45- 


18 35- 


18 33- 


19 19. 


18 44 


18 53- 


19 6 


18 36 


19 5 


18 37 


19 2 


19 16 


19 10 


18 59 


19 


18 40 



Dist. from 

Center of 

Field 



14 
IO 

14 
II 

14 
II 

23 
3° 



14 
23 
12 

13 
12 

24 



14 
13 
13 

14 
25 
13 
18 
29 
19 
14 
14 
21 

17 
17 
19 
23 
16 

29 
20 

27 
29 
29 



28 



3° 

27 
23 
24 
29 



Ph. Mag. 



63 
40 
69 
23 
23 
42 
45 
89 
56 
20 
61 

3i 
69 

43 
16 

83 
70 
86 

75 
29 

99 
94 
3i 
6S 
61 

87 
88 

55 
44 
83 
55 
23 
46 
21 
46 
40 
07 
42 
7i 

JO 

55 
24 
20 
21 
50 
16 
30 
70 
4i 
74 
5- 
15 
86 



Effective 
Wave- 
Length 



Rel. Wt. 



4486 
4463 



4338 
4392 
4321 
4432 
4370 
.4275 
4334 
4297 
4304 
436i 
4360 
4342 
4363 
4340 
4287 
4376 
4329 
4251 



4449 
43i6 
442 2 

4355 
4238 
4392 
43i6 
4305 
4304 
4328 
4353 
4581 
43i6 
4216 

4339 
4360 
4308 
4368 
4342 
4340 
4395 
4290 

4352 
4465 
4464 

4413 
4549 
4397 

4405 
4374 



3 
3 
o 
o 

4 
66 

65 
62 
62 

34 

o 

24 
6 

7 
62 

6 

16 
54 



10 
11 

4 

52 
o 

13 
56 

9 
45 
16 

o 
37 
42 

4 

9 
61 

3 
39 
18 

3 
64 



9 

42 

9 

4 
6 



no 



EJNAR HERTZSPRUNG 
TABLE TV— Continued 



Star No. a (1900) 


& (1900) 


Dist. from 

Center of 

Field 


Ph. Mag. 


Effective 
Wave- Rel. Wt. 

Length 1 


208 

209 

210 


4 h 4i m 49! 
49- 
5i 
Si- 
56. 
58 
42 1. 

3 
3- 
4 
9 
10 


+ 19° 

18 44 

19 3 
19 8 
19 12 
18 54 
18 51 
18 51 
18 47 
18 55 
18 58 
18 50 


5 
4 
7 
3 
2 

3 
4 
8 

1 
9 
5 
7 


24' 
26 

25 
27 
3° 
26 

27 
27 
28 
27 
28 
29 


14-45 
14-55 
12.57 


4408 


O 


AZAO 


39 
56 
50 

4 
7 


49 
50 


211 


11.45 45^5 
12.01 4317 
14.15 4388 
13-74 4306 
14.48 4382 
12. 11 4316 
12.07 4324 
(11. 9) (azzo) 


212 


213 

214 

215 

216 

217 

218 


219 


13.06 


4336 


22 



only o. 75 mm (0.03 inch). The classification of the spectra could 
therefore be made only roughly. The results I obtained are given 
in Table V, arranged according to effective wave-length. The 
median value of the effective wave-lengths of 23 A-type stars is 
4266 A, which agrees well enough with the value given above for 
stars of zero color-index, viz., 4234 A. 



TABLE V 

Effective Wave-Lengths and Spectra 



Star Xo. 



60 

39 
181 

63 

133 

97 

81 

94 
175 
19 
66 
90 
45 



Sp. 



A? 

A 

F? 

F? 

A 

A 

A 

A? 

F? 

A 

A 

A 

A 

A 

A 1 



Y.Y 



4214 
4238 
4238 
4243 
4243 
4245 
4250 
4251 
4251 
4253 
4253 
4255 
4257 
4260 
4261 



Star Xo. 



137 
9 

14 
106 
122 

42 

151 
22 

100 

163 
89 
75 

172 

27 
84 



Sp. 



A 

A? 

A 

A 

A 

A 

A 

A 

A 

A? 

A? 

A? 

A 

A 

A? 



Ytt 



4261 
4262 
4263 
4266 
4268 
4271 
4272 
4274 
4274 
4275 
4276 
4281 
4287 
4289 
4290 



Star Xo. 



109 
165 

15 
193 
143 

68 

55 
164 

56 
125 
i°5 
149 
211 



Sp. 



A 

A 

A 

F? 

A? 

A? 

A 

A? 

F? 
G,K 
G, K 
G, K 
G, K 
G, K, M 



\-ff 



4290 
4297 
4297 
4298 
4308 
4310 
4324 
4327 
4334 
4400 
4506 

4513 
4520 

4565 



Potsdam 
January 25, 191 5 



EFFECTIVE WAVE-LENGTHS OF ABSOLUTELY 
FAINT STARS 1 

By EJNAR HERTZSPRUXG 

It is a well-known fact, of which the stars a and /5 Orionis may 
be taken as extreme examples, that absolutely bright stars may 
have all colors between red and white; but the fainter the absolute 
brightness, the more limited is the range of color within which 
the stars are distributed. This limitation is practically one-sided 
in the sense that only rarely are faint white stars to be found. The 
less the absolute brightness, the yellower is the color, with only a 
very few stars which are relatively white. 

In order to test this relation between absolute brightness and 
color down to absolute magnitudes as faint as possible, I took with 
the i . 5-meter (6o-inch) Mount Wilson reflector in the manner de- 
scribed in the preceding article 2 on N.G.C. 1647 a number of 
effective wave-length plates of faint stars having large well-known 
parallaxes. All exposures were made on Lumiere "2" plates. 3 
Care was taken to reduce the effective wave-lengths to the same 
zero-point as those for N.G.C. 1647. The values given here can 
therefore be directly compared with the former. The effective 
wave-lengths have been reduced to the same zenith distance. 4 

The results are given in Table I. This table contains among 
others the absolutely darkest stars so far known, which unlike the 
companion to Procyon are not too near a bright star for proper 
examination. The absolute parallaxes are those in Groningen 

1 Contributions from the Mount Wilson Solar Observatory, Xo. 101. 

2 Ml. Wilson Contr., Xo. ioo; Astrophysical Journal, 42, 02, 1015. 

3 The measures were made at Potsdam, a Toepfer machine with measurable 
movement of plate being used. 

4 Owing to selective extinction of light in our atmosphere, the effective wave- 
length of a star increases with its zenith distance. At sea-lavel this increase amounts 
to 35 A in passing from the zenith to a zenith distance of 6o°. The greatest differ- 
ence in corrections occurring here was 20 A for t Ceti as compared with stars near 
the zenith. 



112 



EJNAR HERTZSPRUNG 



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H4 EJNAR HERTZSPRUNG 

Publications, No. 24, due regard having been given to additional 
measures. 

Judging from the common proper motion and radial velocity, 
the brighter stars belonging physically to the system of the 
Hyades are, as is well known, 1 divided into two distinct groups, 
one consisting of a few yellow stars and the other of white stars, 
which form the majority. The mean effective wave-lengths for 
two yellow and for eight white physical members of the Hyades 
have been entered in the table. 

Concerning our sun, I have been able to determine the effective 
wave-length of its light only as reflected by five of the satellites 
of Saturn and by the planetoid (8) Flora. 2 The weighted mean 
(5 to 1 according to the number of objects), 4375 A, has been 
entered in the diagram (o) on the assumption that the quality of 
the sun's light is not seriously altered by the reflections in question. 3 
Finally, for a few bright stars of well-known parallax, I have trans- 
formed the color-indices, /, given by E. S. King, 4 into effective 
wave-lengths by the formula 

A eff=4 2 34+2IO /. 

These results are to be found in brackets in Table I. 

All the results are shown graphically in Fig. 1. The full 
line represents the radiation of a black body of the size of our 
sun. The points represent the stars, and the sign , the reflected 
sunlight, for which the effective wave-lengths have been determined. 
The circles show the color-indices by King, transformed into effective 
wave-lengths. 

The appearance of this diagram is interesting. When we neg- 
lect the absolutely bright yellow stars, which are represented in 
the figure by the mean of only two bright yellow Hyades, we may 
state the following: 

1 Cf. Potsdam PubL, No. 63, p. 26, 191 1. 

2 October 16, 1912, 23^3 sidereal time. Three underexposed plates of (433) Eros 
were obtained on September n, 191 2, between 20^5 and 21^4 sidereal time. The 
uncertain effective wave-length derived is 4506 A. 

3 It may be recalled that the satellite I of Jupiter (Io) shows a markedly greater 
effective wave-length than satellites II, III, and IV {Potsdam PubL, No. 63, p. 40). 

4 Harvard Annals, 59, 177, 191 2. 



EFFECTIVE WAVE-LENGTHS OF FAINT STARS 



On the supposition that stellar surfaces radiate approximately 
as a black body, the relation between absolute brightness and color 
from absolute magnitude — 7 to + 3 deviates from the same relation 
for a black body (full line) in the same way, and approximately 
to the same extent, as we should expect from the known increase 
in density 1 and decrease in mass 2 with decreasing absolute bright- 
ness. But below absolute brightness + 3 mag., between +3 and 

4700 



4600 



4500 



4400 



4300 



4200 









/ * 1 ■! ■ 


• 


/• 

/ • 




/ 

-° ./ 


/ • 

> 


7 

/ 




/ 


• 



4100 



-8 -6 
Fig. 1. — 



-4 -2 



+ 2 +4 +6 +8 +10 



Abscissa: Absolute magnitude (sun =—0.33) 
Ordinate: Effective wave-length 



+ 8 mag., the deviation from the radiation of a black body is too 
great to be explained by facts already known. 

With the single exception of the white faint companion to 
o 2 Eridani 3 we may say that the stars between absolute magnitudes 

1 Shapley, Astrophysical Journal, 38, 158, 1913. The average density of a star 
of the first spectral type may be taken to be about o . 1 of that of our sun. 

2 The statistics of spectroscopic binaries have been specially investigated by 
H. Ludendorff, Astron. Nachr., 189, 145, ion. 

For 15 stars with known mass and parallax I find a decrease of 0.06 ±0.01 
(mean error) in the logarithm of the mass for each magnitude of decrease in absolute 
brightness. 

3 This exception is, in fact, very strange. It is the weli-known double star 2 518, 
which has a proper motion of 4*1 yearly in common with o 2 Eridani. The com- 
bined magnitude of the two components is 9.48 mag. and the difference about 1.7 



n6 EJNAR HERTZSPRUNG 

+3 and +8 are approximately all of the same color. 1 Proceeding 
from the absolutely brightest stars to the fainter ones, evidently 
a new unknown element comes into action at about absolute bright- 
ness +3, which stops the further increase in effective wave-length 
with decreasing absolute magnitude. 2 

If the difference of 5 mag. in the absolute brightness between 
+3 and +8 mags., within which the color remains constant, were 
due only to differences in the size of the stars, the ratio of mass to 
density would be 1000 times greater at absolute magnitude +3 
than at +8. We cannot imagine such a difference as due to change 
in density alone. 

Concerning the mass, we are able to eliminate the effect of its 
variation on the size of a star when the object is one of the com- 
ponents of a double star the apparent orbit of which, together with 
the ratio of the masses of the two components, is known. Call 
the masses of the two components, in terms of the sun, M t and M 2 \ 
their apparent magnitudes, w x and m 2 ; the apparent major axis 

mag. From the apparent orbit and the parallax, which are both approximately 
known, we find the sum of the masses to be Mt-\-M 2 = o. 76©. This is no exceptional 
value. 

At the Solar Union, 1913, Professor H. N. Russell told me that this star had been 
found at Harvard to have a spectrum of Class A. This agrees with Adams, who found 
the spectrum to be A {Publ. Astron. Soc. Pacific, 26, 198, 1914), and with my effective 
wave-length. 

The exceptionally white color of the faint companion to o 2 Eridani recalls the 
white 12.4 mag. star Xo. 190 of the cluster N.G.C. 1647 (compare the preceding 
article). Perhaps there is also physical analogy between these two stars. 

In this connection it may be noted that Adams has found the 7 . 3 mag. star Lai. 
28607 ( I 5 h 37™7) — 1°°37'; 1900), the proper motion of which is i''i7 yearly, to have an 
A spectrum and a radial velocity of —170 km. The absolute brightness of this 
star, when estimated from these data in the way described in Astron. Nachr., 185, 
92, 1910, is found to be — 1 . 3 =t 2 . 45 mag. (mean error) . The absolute brightness may 
therefore very well be the normal value for an A star, namely, about —4 mag. The 
measured parallax, -f-o''o3, is very uncertain. 

1 From different sides it has been suggested to me that this phenomenon might 
be due to the rapid falling-off of the sensibility of the plate at the end of longer wave- 
lengths of spectrum. In objection to this I wish to mention that the linear relation 
between color-index and effective wave-length still holds for fourth-type stars with a 
color-index of about +2 mag. and an effective wave-length of about 4600 A. 

2 The earlier inferior results, Potsdam Publ., No. 63, p. 40, 191 1, showed only the 
general increase of effective wave-length with decreasing absolute brightness. 






EFFECTIVE WAVE-LENGTHS OF FAINT STARS 117 

of the orbit in seconds of arc, a; and the period in years, P. The 
absolute magnitude (for a parallax 7r=i") of a star having the 
same surface brightness and density as, for instance, the first com- 
ponent, and the same mass as the sun, will then be: 

»I, n = i", M=Q=m 1 +- log 



K:)- 



The number of double stars of known mass ratio being small, I have 
adopted for other double stars equality of masses. Especially 
when the two components are nearly equal in brightness and color 
is this assumption plausible. 

We may still increase the number of objects reasonably well 
suited to this investigation by including double stars when only 
the first trace of orbital motion has been observed. For such double 
stars we are able to calculate a minimum value 1 of a 3 /P 2 . Mr. C. 
Luplau-Janssen has kindly examined statistically all double stars 
with known orbits and found that the true value of a 3 /P 2 is on the 
average (1.65) 3 times greater than the minimum value derived 
from a single element of the apparent orbit. 2 

By these more or less tentative methods the values given in 
Table II and shown in Fig. 2 were found. It will be admitted that 
the effect of differences in mass on the size of the stars has been 
eliminated to a great extent; nevertheless, Fig. 2 has the same 
general appearance as Fig. 1. We may therefore conclude that 
differences in mass are as little capable as differences in density 
of explaining the constancy of color between the absolute mag- 
nitudes + 3 and +8. 

It is an obvious suggestion for the explanation of the fact 
found above that the absolute magnitude + 3, corresponding to 
the temperature 3400 Abs. of a black body of the size of the sun, 
represents the stage of a cooling star at which the formation of 
relatively dark solid matter on its surface begins, the remaining 

1 Astron. Xachr., 190, 113, 1911. 

2 The proportion between the true value of a.P— % and its minimum value does 
not vary much for different double stars. The mean deviation from the logarithm of 
the mean (log 1.65 = 0.22] is about =0.085, corresponding to =0.43 mag. 



u8 



EJNAR HERTZSPRUNG 



fluid part giving practically all the radiation. At any rate, these 
absolutely dark stars deserve further attention. They should, for 
one thing, be examined for variability in light. 

It must be kept in mind that the longer effective wave-lengths 
especially depend only upon the distribution of energy within a 

TABLE II 



Star 



Vis. 
Mag. 
Harv. 



Minimum 

Hypo- 
thetical it 



Hypo- 
thetical w 

M,+M, = Q 



M,/Mi 



Hypo- 
thetical 
Abs. Mag. 



efi 



f Orionis A . . . 
7 Leonis A . . . . 
f Urs. Maj. A . 
/3 Aurigae A . . . 
a Urs. Maj. A. 
a- Gemin. A. . . 
a Can. Maj. A. 

5 Gemin. A. . . 
* Urs. Maj. A. 
a Can. Min. A. 
f Herculis A . . 
y Yirginis A . . . 

6 Persei A . . . . 
Sun 

V Cassiop. A.. . 

2 443 A 

2 443 B 

2. 1280 A 

2 1280 B 

61 Cygni A. . 

V Cassiop. B . . 
61 Cygni B. . 

02 547 A ... . 
OS 547 B ... . 

2 132 1 A 

2 1321B 

Groom. 34 A. 

Persei B 

o a Eridani B . . . 
2 2398 A 

Kriiger 60 A . 
2 2398 B 

Groom. 34 B. 

Kriiger 60 B . 



2™05 

2.61 
2.40 
2.82 

i-95 

1.99 

-1.58 
3-53 
3.12 
0.48 
305 
3-65 
423 

-26.9 
367 
8-35 
8.89 
8.65 
8.65 
5-57 
7-41 
6.28 

9-31 
9-31 
8.0 
8.0 

97 
86 
69 
33 
59 



10. 10 
10.99 
n-59 



o':oo8 
.024 
.027 



. 040 5 



038 
.061 5 



.067 



.024 
.024 
.048 
.048 
.199 



.199 
•059 
■059 
. 120 
.120 
.123 
.067 



.123 

134 
,123 
123 
134 



0.040 



.117 
568 



•352 
.128 
.119 



0.163 



0-39 



°-33 
043 



7<> 



0.76 



-7 m 8 5 
-4.90 
-4.86 
-466 
-4 43 
-3-I7 
~3°5 
-2-99 
-2-35 
-1.99 
— 1 .67 
-1.47 
-1.05 

-°-33 

—0.23 

+0.84 
+ 1.38 
+ 2.64 
+ 2.64 
+ 2.65 
+3-31 
+3-30 
+3 ■ 75 
+3-75 
+3 .98 
+3 -98 
+4.00 
+4-58 
+5-25 
+5-36 
+5.81 
+6.13 
+ 7.02 
+7.81 



A 

Ui54] 
[4442] 
[4240] 
U219] 
[44741 
U257] 
[4272] 

U314] 
U297] 
[43o8] 

[4337] 
[4282] 

4299 
(4375) 
4325 
4393 
4527 
4543 
4533 
4532 
45 J 2 
4556 
4494 
4534 
4523 
4523 
4529 
4504 
4179 
4520 
4531 
4530 
4574 
4544 



narrow part of the spectrum. It would be of special interest to have 
the results found here confirmed by measuring the color-indices. 

As all my plates were taken between July 18 and October 17, 
191 2, inclusive, a number of faint stars with well-known parallaxes 
could not be included in this note. 



EFFECTIVE WAVE-LENGTHS OF FAINT STARS 



no 



I am greatly indebted to the director of the Mount Wilson 
Solar Observatory, Professor George E. Hale, who not only immedi- 
ately granted my request to use the 60-inch reflector for the deter- 
mination of effective wave-lengths, but also offered his assistance 
in realizing my plans. I owe the main part of the necessary funds 









• />.•••*• 






/ • 




/ 
° V 




° " °7 
/ 

/ 

/ 




/ 


• 



4700 



4600 



4500 



4400 



4300 



4200 



4100 



— 10 —8 —6 



+ 2 +4 +6 +8 +10 



Fig. 2. — Abscissa: Hypothetical absolute magnitude (mass=©) 
Ordinate: Effective wave-length 

and five months' leave from Potsdam to the Prussian government 
and the Academy of Science of Berlin. I wish also to express here 
my best thanks for the kind and disinterested help given to me by 
all of the Mount Wilson Observatory staff, not the least to Mr. Hoge, 
the indefatigable night assistant. 

Potsdam Astro-physical Observatory 
January 25, 19 15 



COLOR-INDICES IN THE CLUSTER N.G.C. 1647 1 

By FREDERICK H. SEARES 
I. INTRODUCTION 

For the determination of the color of the stars two methods are 
available. The first, with the aid of a coarse objective grating, 
measures directly the mean effective wave-length of the light 
which impresses itself upon the photographic plate, 2 while the 
second compares the relative intensities of the radiation in two 
more or less widely separated regions of the spectrum. The 
latter method is most conveniently applied by choosing for the 
comparison the spectral regions whose intensities are expressed 
by the photographic and the visual, or photo-visual, magnitudes. 
The measure of the color is then 

Color-index = C = Pg — Pv, 

in which Pg and Pv are the photographic and photo-visual magni- 
tudes of the star in question. 

With suitable instrumental equipment the measurement of the 
effective wave-length is an expeditious and convenient method of 
procedure; but since precise magnitudes are required for the 
investigation of many questions, the determination of star colors 
is readily made incidental to the measurement of brightness, so 
that the second method also has its advantages. 

The mutual control afforded by two processes so different 
in their observational details is invaluable, especially as both are 
liable to more or less troublesome systematic errors. The effective 
wave-length, for example, depends upon the intensity of the small 
spectral image from which it is derived, and the results must 
accordingly be reduced to a normal intensity. Hertzsprung avoids 
the greater part of the difficulty by making a number of exposures 
on the same plate with gradually increasing exposure time, and 

1 Contributions from the Mount Wilson Solar Observatory, Xo. 102. 

2 Hertzsprung, Potsdam Publ., 22, No. 63, 1911. The earlier literature is listed 
in Astron. Nachr., 182, 301, 1909. 

120 



COLOR-INDICES IN THE CLUSTER X.G.C. 1647 121 

then selecting for measurement only those images which, as nearly 
as possible, are of a certain standard intensity. The color-index, 
on the other hand, shown by the equation defining it, is seriously 
influenced by relative errors in either the slope or the zero-point 
of the magnitude-scales. 

As the precise determination of a scale of magnitudes is not an 
easy matter, the color-index is peculiarly liable to error, and the 
difficulty increases rapidly with decreasing brightness of the stars. 
To be useful, color results must be homogeneous; they must be 
directly comparable, whatever the relative brightness of the stars 
to which they refer. It is not sufficient, therefore, that the magni- 
tudes should be relatively accurate for a limited range; in both 
scales and for all degrees of brightness, they must be correct rela- 
tively to the zero-point defined by the stars of the sixth magnitude. 
If either scale is in error, the equation 

C = Pg-Pv 

will give an incorrect result unless the other happens also to be in 
error by the same amount. The demand is therefore exacting, 
especially when it becomes a question of the color of the fainter 
stars, for with these the cumulative error in the scales has its 
greatest effect. 

In fact, the difficulties hitherto experienced in establishing 
satisfactory scales of magnitude have been so considerable that it is 
advantageous to utilize in another direction the possibilities of the 
two methods of color determination by employing them to test the 
reliability of the scales. Given a series of carefully determined 
effective wave-lengths, we can, by means of stars of known color- 
index, turn the entire series into color-indices. A comparison with 
the corresponding results obtained directly from the magnitudes 
will then show at once the relative errors of the scales, although 
not their absolute values. Any systematic error in the effective 
wave-length is of course also involved; but this is small, and prob- 
ably but little dependent upon the brightness of the objects 
observed, while the uncertainty affecting the color-indices derived 
from the magnitudes of faint stars is relatively large. It is not to 
be understood that the errors inherent in the colors derived from 



122 FREDERICK H. SEA RES 

magnitudes are necessarily large, for when once we have been 
assured that reliable magnitudes are available, it is probable that 
the two methods will give results comparable in precision. The 
difficulty is that we have no such assurance — in fact, no inde- 
pendent control which is capable of specifying what the uncer- 
tainties affecting the magnitude-scales may be. 

II. OBSERVATIONS 

It is the purpose of this note to test in the manner indicated the 
photographic and photo-visual scales established at Mount Wilson 
for stars near the North Pole. Effective wave-lengths for these 
objects are not available, but Hertzsprung has derived such 
results for nearly 200 stars in another region, N.G.C. 1647, which 
are immediately applicable to the problem. 1 To effect a com- 
parison it is only necessary to transfer the polar scales to the region 
of the cluster by photographs of multiple exposure. 

To this end comparisons were made between the Pole and the 
cluster, using the same kinds of plates as in the investigation of the 
polar magnitudes — -Seed "27" for photographic, and Cramer 
"Inst. Iso." with a yellow filter for photo-visual magnitudes. Five 
separate transfers of each scale were made, and to minimize atmos- 
pheric irregularities no two of the same kind were undertaken on 
the same night. 2 In all cases the exposures were symmetrically 
arranged, usually in the order: cluster, Pole, Pole, cluster; the 
exposure times were short, 2 m for Seed "27," and 5 m for "Iso. " 
plates. 

The photographs were measured and corrected for distance 
error in the usual way. The magnitudes of the stars in the cluster 
were read from curves derived from the scale-readings and the 
magnitudes of the Mount Wilson Polar Standards. 3 After correction 
for extinction the results were combined into the mean values which 
appear in the second and third columns of Table II. Owing to 
temperature fluctuations of unusual magnitude, the largest images 

1 ML Wilson Contr., Xo. 100; Astrophysical Journal, 42, 92, 1915. 
2 1 am indebted to Mr. P. J. Van Rhyse for one of the pairs of polar comparison 
plates here used. 

3 Mt. Wilson Contr., Xo. 97; Astrophysical Journal, 41, 206, 1915. 



COLOR-INDICES IN THE CLUSTER N.G.C. 164J 123 

on some of the plates were unsuitable for measurement. As these 
have been excluded, the objects listed begin at about magnitude 
1 1. 5; the faintest shown is 15.45. The plates were centered on 
star Xo. 100 of Hertzsprung's list and, within the limits of the useful 




Mount Wilson 
color-index 



Hertzsprung's 
effective 
wave-lengths 
transformed 
into color- 
index 



L Hz 



n m 12 13 14 15 

Fig. 1. — Color-indices and photographic magnitudes 

field which is 2$ in diameter, there are nearly fifty stars available 
for comparison with his effective wave-lengths. 

As there is but little information bearing upon the precision with 
which polar comparisons can be effected, Table I may be of interest. 



124 



FREDERICK H. SEA RES 



It shows the divergence of the results of individual polar comparison 
plates from the mean scales for the cluster. The unit is o.oi mag. 
and the quantities in parentheses indicate the number of stars 
used in deriving each mean residual. The zero-point residuals 
relative to the mean zero-point established by all plates of the 
same kind are shown in the second line at the bottom of each 



TABLE I 
Scale Divergence for Magnitudes in N.G.C. 1647 



Mean Mag. 


Photographic Plates 


1392 


1405 


1417 1428 


VRi 


12. 1 

12.7 

13-3 

13 -7 

14 -3 

14.6 

14-9 


+ 11 (8) 
+ 3(5) 
+ 7(7) 
+ 2 (9) 

- 1 (6) 

- 4(8) 

- 7(8) 


-6(5) 
+4(6) 
-9 17) 
+ 5(9) 
+4(6) 
-1(8) 

-2(8) 


+ 12 (8) 
+ 15 (.5) 
+ 2 (7) 

- 4(9) 

- 5(6) 
0(8) 

-10(8) 


-12(8) 

- 8(6) 

- 3(7) 
+ i(9) 
+ 6(6) 
+ 2 (8) 
+ 3(8) 


- 8(7) 
-11 (6) 
+ 2(7) 

- 4(9) 

- 3 (6) 
+ 4(7) 
+ 16 (8) 


A.D 

Z.P 

No 


9 5 
-6.2 

5i 


93 "5 100 
+0.1 +14-3 —11. 1 
49 5i 52 


14.2 
+ 2.8 
50 




Photo-visual Plates 




1393 M06 


1418 1429 


VR2 


12. 1 

12.7 

13 3 

13 -7 

14.3 


- 3(8) 
- 10 (6) 
+ 12 (5) 
+ 9(3) 


-2(8) 

-5 (6) 

-4(7) 

+ 5 (7) 

+ 5 (5) 

0(2) 


+ 4(8) 
+ 4(6) 

- 6(7) 

- 5 (9) 
+ 3 (5) 


+ 7(8) 
+ 12 (6) 
+10(7) 

- 7 (9) 
-1W6) 


- 6(7) 

- 1 (6) 

- 8(7) 
+ 5(9) 

+ 7 (6) 


14. 6 




+ 16 (3) - 9 (6) 


+ 4 (6) 








A.D.. . 


10.5 7-3 
— 11. —1.5 

22 ?^ 


8.2 11. 3 

+9-4 + 7-2 
38 


1 1 . 


Z.P 

No 


- 3-6 
41 















section of the table. The average deviation of a single magnitude 
and the total number of stars also appear at the bottom of each 
section. The probable error of a single determination of the zero- 
point is =!=o.o6 mag., and of the mean from five plates =*= 0.025 mag. 
The probable value of the constant error in the color-indices arising 
from the transfer of the scales is therefore ±0.035 mag. 



COLOR-INDICES IN THE CLUSTER X.G.C. 1647 125 

Table II contains the detailed results for individual stars. 
The numbers in the first column are those of Hertzsprung; the 
co-ordinates may be found by consulting his list. 1 The derivation 
of the Mount Wilson photographic and photo-visual magnitudes 
in the second and third columns has already been described. The 
number of values upon which each is based appears in the fifth 
column. In the fourth and sixth columns, respectively, are the 
Mount Wilson color-index and its weight. Then follow Hertz- 
sprung's effective wave-length and its weight, the color-index 
obtained from X e , the difference between the two color-indices and 
its weight, and finally, as a check upon the scales, a comparison of 
the Mount Wilson photographic magnitudes with those of Hertz- 
sprung. 

III. TRANSFORMATION OF EFFECTIVE WAVE-LENGTHS INTO 
COLOR-INDICES 

The data for the comparison of the effective wave-lengths with 
the color-indices were very kindly supplied in manuscript by Pro- 
fessor Hertzsprung some months before his paper was received for 
publication, and in consequence some of my results differ slightly 
from his. Allowance, however, is easily made for these differences. 

The data bearing on the relation between \ e and C here used 
are as follows: From 15 white stars, mean C (Harvard) = +0. 21 
mag., distance between first-order spectra is 

D = i .o78o ± o.oo26 mm. 
From n red stars, mean C (Harvard) = +1.2 2 mag., 

D—i. 1338=1=0.0030 mm. 
AC=+i.oi mag. is equivalent to 

A/) = 0.05 58=*= 0.0040 mm or AA = 222= t 16 A. 

From these and other data Hertzsprung adopts an increase of 
200 A in \ e as the equivalent of a change of 1 mag. in the Harvard 
color-index. We have, however, the following relations between 
the Harvard and Mount Wilson color-indices: 

+0.21 Harvard = +0. 21 MW 
+ 1.22 Harvard = + 1 . 45 MW. 

1 Ml. Wilson Contr., Xo. 100; Astrophysical Journal, 42, 97, 1915. 



126 



FREDERICK H. SEA RES 



TABLE II 
Magnitudes, Effective Wave-Lengths, and Color-Indices 





Mount Wilson 


Hertzsprung 


Cyi 


Wt. 


Pg w 


No 


















Junius 


OF 


minus 




Pg 


Pv 


r 


n 


Wt. c 


K 


Wt. A 


C Hz 


C Hz 


DlFF. 


PWz 


43- 


1 1 . 69 


II .62 


+0.07 


3,4 


17 


4304 


61 


+O.27 


— O. 20 


13 


+ 6 


44 


• 14-53 


13.80 


+o.73 


4, 2 


12 


397 


1 


+O.85 


— O. 12 


I 


+ 22 


46 


. . 12.21 


n-57 


+0.64 


4,5 


22 


361 


50 


+O.63 


+ O.OI 


15 


+ 13 


55 


.. 12.08 


11 .64 


+0.44 


4,5 


22 


327 


53 


+O.42 


+ 0.02 


16 


4-22 


57 


•• 14-27 


13-58 


+0.69 


5,4 


22 


372 


4 


+O.69 


O.OO 


3 


+ 25 


59 


. . 1 2 . 90 


12.59 


+O.31 


5,5 


25 


339 


34 


+O.48 


— O. 17 


14 


+ 14 


61 


•• 1478 


13-75 


+ 103 


5,i 


8 


428 





+ I.04 


— O.OI 





+ 28 


62 


• • 13-74 


12.33 


+ 1.41 


5,5 


25 


559 


12 


+ I.84 


-0.43 


8 


+ 17 


67 


. . 14-67 


13.90 


+o.77 


5,2 


14 


372 





+O.69 


4-0.08 





+ 28 


69 


■• I3-50 


12.58 


+0.92 


5,5 


25 


334 


33 


+0.45 


+0.47 


14 


+ 69 


7i 


. . 13.04 


12.31 


+0.73 


5,5 


25 


320 


40 


+O.38 


+0.35 


15 


+ 60 


72 


■• I4-96 


14. 11 


+0.85 


5,2 


14 


424 





+ 1 .01 


— 0. 16 





+ 41 


76 


. . 14-91 


1381 


+ 1 . 10 


5,i 


8 


347 





+ O.54 


+0.56 





+ 42 


77 


. . 12.92 


12.48 


+O.44 


5,5 


25 


337 


34 


+O.48 


—0.04 


14 


+ 12 


78 


• ■ 14-53 


13.80 


+o.73 


5,2 


14 


359 


2 


+O.61 


+0. 12 


2 


+ 28 


79 


.. 14-70 


13.16 


+ I-54 


5,4 


22 


562 


2 


+ 1.86 


-0.32 


2 


+ 11 


80 


. . 12.01 


n-53 


+0.48 


5,5 


25 


297 


63 


+0.23 


+0.25 


18 


+49 


83 


.- 14-51 


13.61 


+0.90 


5,i 


8 


352 


2 


+0.57 


+033 


2 


+ 26 


85 


.. 13-49 


12.87 


+0.62 


5,4 


22 


356 


26 


+0.60 


+0.02 


12 


+44 


87 


.. i3-°3 


12.58 


+0.45 


5,5 


25 


352 


29 


+0.57 


— 0. 12 


13 


+ 12 


92 


.. I4-36 


I3-56 


+0.80 


5,4 


22 


322 


4 


+039 


+0.41 


3 


+3° 


93 


. • I3-92 


13-54 


+0.38 


5,4 


22 


330 


7 


+0.44 


— 0.06 


5 


+ 19 


95 


. . 1 2 . 34 


11.80 


+0.54 


5,5 


25 


306 


54 


+0.29 


+0.25 


17 


+40 


96 


.. 13-84 


13-59 


+0.25 


5,4 


22 


34i 


10 


+0.51 


— 0. 26 


7 


+ 13 


98 


.. 12.86 


12.60 


+0. 26 


5- 5 


25 


321 


37 


+0.39 


-0.13 


15 


+ 18 


IOI 


.. 1403 


i3- 6 4 


+0-39 


5,4 


22 


312 


7 


+0-33 


+0.06 


5 


+ 20 


102 


. . 13.96 


13-33 


+0.63 


5,4 


22 


366 


10 


+0.66 


-0.03 


7 


+ 20 


i°3 


.. 14-49 


13-75 


+0.74 


I, J 


5 


379 


3 


+0.74 


0.00 


2 


+ 23 


104 


.. 12.55 


12.40 


+0.15 


5, 5 


25 


330 


40 


+0.44 


— 0. 29 


15 


- 6 


107 


•• 14 54 


14.06 


+0.48 


5,3 


19 


375 


1 


+0.72 


— 0. 24 


1 


+ 20 


108 


.. 13.70 


12.97 


+0.73 


5,4 


22 


452 


i5 


+ 1.19 


— 0.46 


9 


+ 24 


114 


.. 12.77 


12. 24 


+0-53 


1, 1 


5 


329 


39 


+0.43 


+0. 10 


4 


+ 24 


115 


. . 1 2 . 24 


n.83 


+0.41 


5,5 


25 


392 


58 


+0.82 


— 0.41 


17 


+46 


116 


.. 1492 


1382 


+ 1. 10 


5,i 


8 


408 





+0.91 


+0.19 





+44 


117 


.. 13.29 


12.51 


+0.78 


5,5 


25 


39i 


29 


+0.81 


-0.03 


13 


+32 


118 


1 2 . 40 


11 .92 


+0.48 


5,5 


25 


308 


52 


-i-0.30 +0.18 


T-7 


+ 53 


121 


.. 13-26 


12-75 


+0.51 


5,5 


25 


339 


27 


+0.49 


+0.02 


13 


+ 29 


124 


.. 14-72 


I3-78 


+0.94 


5,i 


8 


333 





+0.45 


4-0.49 





+32 


127 


•• 14 32 


13.82 


+0.50 


5-2 


14 


338 


7 


+0.48 


+0.02 


4 


+42 


131 


.. 14.08 


13-55 


+053 


5,4 


22 


326 


4 


+0.41 


+0. 12 


3 


+ 6 


134 


-- 14-73 


13.82 


+0.91 


5, 1 


8 


225 





—0. 22 


+ 113 





+ 11 


135 


.. 13-88 


13-42 


+0.46 


5,3 


19 


349 


12 


+o.55 


— 0.09 


7 


+ 26 


136 


•• 13-19 


12. 71 


+0.48 


5,4 


22 


333 


30 


+0.45 


+0.03 


13 


+32 


138 


.. 12.17 


11. 81 


+0.36 


5,5 


25 


297 


60 


+0.24 


+ 0. 12 


18 


+41 


139 


.. 13.61 


12.52 


+ 109 


5,5 


25 


455 


17 


4-i . 20 


— O. II 


10 


+ 11 


141 
i43 


• J 5-45 
.. 12.58 


14-45 
12.14 


+ 1 .00 

+0.44 


5, 1 
3,5 


8 












( + 15) 


19 


310 


55 


+0.31 


+ O.13 


14 


+66 


US 


. . . 11 .92 


11. 51 


+0.41 


5,5 


25 


3^3 


59 


+0.34 


+ 0.07 


18 


+41 


147 


... 13.86 


13-23 


+0.63 


5,3 


19 


329 


12 


+0.43 


+0. 20 


7 


+42 


148 


... 13.61 


13.12 


+0.49 


5,4 


22 


4325 


17 


+0.41 


+0.08 


10 


+3° 



COLOR-INDICES IN THE CLUSTER N.G.C. 1647 127 

TABLE II— Continued 



No. 


Mount Wilson 


Hertzsprung 


C w 

minus 
c Hz 


Wt. 

OF 
DlFF. 


P<w 


Pg 


i>» 


c w 


n 


Wt. c 


A e 


Wt. A t'Hz 


^Hz 


153- • 
156.. 

158.. 
160. . 
168.. 

169. . 

170. . 


i 11 
14 
14 
14 
14 
13 
13 


62 
66 
52 
63 
49 
32 
93 


12 
13 
13 
13 
13 
12 

13 


3° 
68 

72 
66 
78 
95 
33 


+ 132 
+0.98 
+0.80 

+0 97 
+0.71 
+0.37 
+0.60 


5,5 
5,i 
5,i 

5,2 

i, 1 

1,1 
1, 1 


25 
8 
8 

14 
5 
5 
5 


4507 
463 
338 
321 
360 
342 

4363 


16 ' + 1-53 
I +1-25 
3 +0.48 
! +o.39 
1+0.62 

24 +0.50 
6 +0.64 


— 0. 21 

— 0. 27 
+0.32 
+O.58 
+O.09 
-0.13 

— 0.04 


IO 
I 

2 
O 
O 

4 
3 


+ 11 
+ 26 
+ 29 
+ 21 
+ 6 
+ 16 
+ 10 



Hence AC(MW) = + i ■ 23 mag. corresponds to AX =200 A and, 
finally, for 

AC (MW) = + 1 . 00 mag. , AA = 163 A. 

The next step was the determination of X , the value of X e 
which corresponds to C = o. As the exact value of the grating con- 
stant was not available, X was obtained by combining the fore- 
going data as follows: 

A ° = * ° ,o >< 222 A-o. 21X163 A = 4255 A. 

There is here a computational uncertainty of ±10 A owing to the 
fact that the factor 222 A is given only to the nearest angstrom, but 
probably this is within the uncertainty arising from other sources. 

A rough control is afforded by Professor Hertzsprung's classifi- 
cation of the spectra of the brighter stars photographed by Eber- 
hard, which was also kindly placed at my disposal. From the 
26 A stars in this list the value X = 4262 was found on the assump- 
tion that the maximum frequency of occurrence is for stars of the 
type Ao. From the same data Hertzsprung finds for the median 
X f = 4266. The close agreement of these tw r o values with that 
found above must not be accepted as an indication of a correspond- 
ing precision in the result, for presumably the value X = 4234 
adopted by Hertzsprung on the basis of all the material at his 
disposal is more reliable. 

The difficulty in any comparison with spectra lies in the fact 
that the frequency distribution of the various types which applies 
to the stars in general does not necessarily hold for clusters. In 



128 



FREDERICK H. SEA RES 



fact, for this particular cluster it appears that the maximum fre- 
quency is for stars approximately of type Fo, although there 
is a secondary, but much less conspicuous, maximum for the A stars. 
Then, too, there is a further difficulty with such a comparison in 
that we are not certain that the color-index of an Ao star belonging 
to the cluster is really zero. 

In the absence of more definite information the value X = 426o 
was adopted for the reduction, and the linear relation used for 
the transformation of the effective wave-lengths into color-indices 
was accordingly 

i 63Chz = A e — 4260. 

Had the value X = 4234 subsequently adopted by Hertzsprung 
been employed, the values of Cr z would have been systematically 
larger by o. 16 mag. than those given in Table II. 1 



IV. COMPARISON OF RESULTS 



A comparison of the color results found by the two methods is 
shown by the differences C\\ — Cm in Table II. Although there 
are several large values among them, the corresponding weights 
usually are low. For a final comparison reference may be made 



TABLE ill 
Mean Results for Groups of Stars 



MW Pg. Mag. 


MW 
CI. 


Rel. Wt. 


minus 
C Hz 


Rel. Wt. 


No 
Stars 


Pg. Mag. 
MW 


Mean Range 


min us 
Hz 


12 
12 
13 
13 
14 
14 


I 

7 

3 

7 

3 

6 


11 
12 

1 ? 
13 
14 
14 
14 


69-I2 
40-I2 
03-I3 
50-I3 
O3-I4 
49-14 
72-T C 


34 
92 
49 
96 

49 

70 


+0.43 
+0-35 
+0-59 
+0.78 
+0.60 
+O.91 
+0.98 


186 
149 
149 

253 

112 

119 

62 


+ 0.02 

— O.04 
+O.04 

— O.06 
+0. IO 
+ 0.02 


132 
93 
83 
97 
20 
11 


8 

7 

7 

12 

7 
9 
7 


+O.32 
+0. 26 
+O.32 
+ O.24 
+ 0. 22 
+ O.23 
+ O.3O 












Means. . 


T 1 7 


+0 66 


O.OO 






+ 0. 27 





















to Table III which gives mean results for groups of stars. Here the 
agreement is very good, both in the progressive increase of the 



'In a recent letter Professor Hertzsprung writes that ^ = 4234 corresponds to a 
color-index whose value is zero with a mean error oi the order of 0.05 mag. 



COLOR-INDICES IN THE CLUSTER X.G.C. 164J 129 

color-index and in the absolute values; but it should not be over- 
looked that the latter are subject to a small constant error because 
of the uncertainty in the value of X . 

The adopted system of weights requires a word of comment 
inasmuch as the two series Wt.c and Wt. A which appear in Table II 
originated quite independently of each other and are not necessarily 
directly comparable. An examination of the mean errors corre- 
sponding to unit weight showed, however, that they are very 
nearly on the same system; in calculating the weights of the 
differences C\y — Ch z it was therefore assumed that Wt.c and \Vt. A 
are strictly homogeneous. 

Of the 57 stars in Table II the value of Wt. A is zero for 9 of the 
fainter objects; for one there is no value of X f , so that the results 
in Table III are based on 47 stars. Had the value X = 4234 been 
used, the mean difference C\y — Ch z for all the stars would have 
been —0.16 mag. instead of zero as shown in Table III. These 
results, 0.00 and — o. 16 mag., respectively, indicate the uncertainty 
affecting the comparison, and, at the same time, the probable limits 
of the relative errors in the Mount Wilson photographic and photo- 
visual scales between the twelfth and the fifteenth magnitudes. 

The only other scales extending into this region which have 
been connected with the international zero-point defined by the 
stars of the sixth magnitude are those of H.C., No. 170. From the 
known relations which these bear to the Mount Wilson scales it is 
possible to compare at once the results from the effective wave- 
lengths with those which would have been obtained had the Harvard 
magnitudes been used for the calculation of the color-indices. 

For the region of the scale with which we are concerned we have 

MWP£-HH = +o.28 mag. 
MWPw-H Vis = 0.00 

in which HH represents what has been called the Harvard homo- 
geneous scale, 1 namely, the photographic scale of H.C.. Xo. 170, 

1 .1//. Wilson Contr., Xo. 97; Astrophysical Journal, 41, 206, 1915. For the 
region in question MW Pg — H.C, Xo. 170= +0.40 mag. The color correction to 
H.C., Xo. 170, which reduces the results to a uniform system is +0.04 mag. Apply- 
ing this and the zero-point correction of +0.0S mag. we have the foregoing value 
lor MWPg-HH. 



130 FREDERICK H. SEARES 

reduced to a uniform color system and corrected by +0.08 mag. 
to refer it to the international zero-point; the second relation is 
approximate and, strictly speaking, holds only for the twelfth 
magnitude. We therefore find 

Cw— Ch=+o.28. 

But from the preceding discussion 

Cw— Chz = o.oo or —0.16 

according to the value adopted for X . 

These two equations cannot, however, be combined as they 
stand, for the values of Cn z in the second relation refer to the 
Mount Wilson color system which differs from that of Harvard. 
The necessary modification is that corresponding to the substitution 
of 200 for 163 in the equation on p. 127. Since the mean color- 
index for the 47 stars is o. 66 mag., the values of Ch z on the Harvard 
system will be 0.11 mag. less, on the average, than those found 
above. We therefore find 

C H -C Hz =-o.i7 or -0.33 mag. 

which represents the mean difference in the color-indices derived 
from the effective wave-lengths and from the photographic and 
visual magnitudes of H.C., No. 170. 

In addition to the color results, Table III also shows a com- 
parison of the Mount Wilson photographic magnitudes with those 
found by Hertzsprung. The scale for the latter was established 
with the aid of a grating used in connection with the Potsdam 
80-cm refractor ("Halbgitter" method). The agreement is good, 
although there is a constant difference of +0. 27 mag.; but this is 
of no significance, as Hertzsprung has determined the zero-point 
of his magnitudes by a comparison with Pleiades stars instead of 
with the Pole. 

V. PROBABLE ERRORS 

It is of interest, finally, to compare the two methods of determin- 
ing the color of the stars from the standpoint of precision. The 
average deviation of a single magnitude as found above is ±0.10 
mag. The corresponding probable error for a color-index based 



COLOR-INDICES IN THE CLUSTER N.G.C. 1647 131 

upon one photographic and one photo- visual magnitude is therefore 
±0.12 mag., while that for the mean of five such determinations 
is ±0.054 mag. This indicates sufficiently the precision with 
which relative values of the color have been determined. In 
estimating the uncertainty of the absolute values of the color- 
indices, allowance must also be made for the zero-point errors. In 
this case their effect upon the color-index is of the order of ±0.04 
mag. 

Hertzsprung gives as the mean error of a single effective wave- 
length 26 A, which corresponds to a probable error of about =*=o. 11 
mag. For absolute determinations a zero-point error has also to 
be considered. This includes, first, the uncertainty in the adopted 
value of X which is used for the reduction of all the plates, and, 
second, a systematic plate error which seems to be of the order of 
10 A. 1 The data relating to the error in \ are not available; but 
since this is an instrumental constant whose value is determined 
once for all, its error can be made negligible by an appropriate 
investigation. In the matter of precision, therefore, there seems 
to be little choice between the two methods. 

SUMMARY 

Star colors may be determined by measuring the mean effective 
wave-length of the light of individual stars or by deriving their 
color-indices. Since the latter depend directly upon the photo- 
graphic and the visual, or photo-visual, magnitudes, a comparison of 
color results found by the two methods affords a control upon the 
relative errors of the magnitude-scales; the fainter the stars the 
more important is the control. 

Such a comparison has been made for 47 stars in X.G.C. 1647. 
The effective wave-lengths used were those by Hertzsprung. The 
color-indices were found by transferring the Mount Wilson photo- 
graphic and photo- visual scales for stars near the Pole to the region 
of the cluster. The mean of the differences between the color- 
indices calculated from the effective wave-lengths and those derived 
from the magnitudes is 

C\y — Ch z = o.oo or —0.16 mag. 

1 .1//. Wilson Contr., Xo. 100; Astrophysical Journal, 42, 92, 1915. 



132 FREDERICK H. SEARES 

according as 4260 A or 4234 A is adopted as the effective wave- 
length of a star whose color-index is zero. 

The comparison includes stars between photographic magni- 
tudes 1 1. 5 and 15. Within this interval the two series of color- 
indices show the same increase in the mean color with increasing 
magnitude. The relative errors of the magnitude-scales seem to 
be within the uncertainty affecting the reductions of the effective 
wave-lengths. 

Mount Wilson Solar Observatory 
March 4, 1915 



(V> 



THE 

ASTROPHYSICAL JOURNAL 

AN INTERNATIONAL REVIEW OF SPECTROSCOPY 
AND ASTRONOMICAL PHYSICS 



VOLUME XLII 



SEPTEMBER 191 5 number * 



THE ECLIPSING VARIABLE STAR 5 ORIONIS 

By JOEL STEBBIXS 

Among the stars which from time to time have been suspected 
of variability is 8 Orionis, the faintest of the three in the belt of 
Orion. This object has been in and out of the variable star cata- 
logues, and observers have been unable to agree whether or not 
there are any changes in brightness. As far as is known to the 
writer, the star has never been exhaustively studied with a photom- 
eter, and we have only the results from estimates with the unaided 
eye. When the selenium photometer was first being tested, among 
the most favorable objects were seen to be 8, e, and £" Orionis, as 
these are of the same spectral type, of about the same brightness, 
and near enough together so that the correction for atmospheric 
absorption is small. Numerous attempts were made, but the 
measures for a considerable period were tests of the constancy of the 
instrument rather than observations of the stars. At last, in the 
early part of 1910, serious measures were undertaken, but the 
results were not accordant. It was assumed that any short-period 
light-variation of 8 Orionis would be synchronous with its spectro- 
scopic period, 5 . 7325 days. On this assumption the observed mag- 
nitudes were arranged according to phase, and it looked as though 
the comparison stars were not constant, that the suspected variable 
was irregular, or, what seemed more probable, that there was some 

*33 



134 JOEL STEBBINS 

undetermined source of instrumental error present. The observ- 
ing season of 1909-1910 passed without the chance to clear up the 
trouble, but the following winter the observations were taken up in 
earnest. Another discordant measure making 8 Orionis unusually 
faint was found to come just at the eclipse time as predicted from 
the spectroscopic elements, and the previous observations were 
therefore re-examined. On checking up the reductions, it was 
found that a mistake of two days had been made in transcribing 
the date of one of the observations, and with this correction it was 
seen that all of the evidence pointed to the fact that 5 Orionis is 
an eclipsing variable with the times of two minima in accordance 
with the spectroscopic orbit. 1 Further observations established 
this discovery beyond the possibility of a doubt, and it was deter- 
mined to derive the best possible light-curve. 

It is probable that the early eye-estimates of the variability of 
this star cannot be brought into agreement with the new light-curve. 
As the total range turns out to be only 0.15 mag., and the two stars 
near by are about half a magnitude brighter, the variation would 
be practically impossible to determine. So far as my own eye is 
concerned, I am sure that the light-changes are entirely imper- 
ceptible, for I have looked at the star time after time when I 
knew it was near a minimum, but I could see no change whatever 
from normal brightness. 

The spectroscopic orbit of 5 Orionis was worked out in some 
detail by Hartmann, 2 but he did not make a least-squares solution 
for the elements. In view of some discrepancies between the 
photometric and spectroscopic results, the present work, which was 
completed in 191 2, has been held until a new orbit should be avail- 
able. Professor R. H. Curtiss took up spectrographic observations 
at Ann Arbor and has kindly sent me his unpublished results. In 
the meantime, another orbit has been worked out by Jordan 3 at 
Allegheny, who also has made a least-squares reduction of Hart- 
mann's observations. We have therefore three sets of elements, 
all independent. For the purposes of this paper, any one of the 
orbits may be selected, but as all of the reductions were made when 
only Hartmann's first elements were available, these computed 

1 Astrophysical Journal, 34, in, 1911. 2 Ibid., 19, 268, 1904. 

3 Publications of the Allegheny Observatory, 3, 125, 1914. 



THE ECLIPSING VARIABLE STAR 8 ORION IS 



135 



phases for the observed and normal magnitudes have been retained. 
In the further discussion of dimensions of the system, the results 
of Curtiss have been used. 

TABLE I 
Spectroscopic Elements and Times of Minima 





Hartmann 


Hartmann 
(Jordan) 


Jordan 


Curtiss 


p 


5 d 7325 
5793-35 
0.103 

339°3 
100.8 km 
+ 23. 1 km 
9068. 190 
3 d 2i8 


5 d 7325 
5793-756 
0.096 

4°9 
100. 12 km 
+ 22.85 km 
9068. 196 
3 d 2i5 


5 d 7325 
8981.295 

0.085 


20.4 

99.98 km 

+ 15. 20 km 

9068 . 248 

3 d i57 


5 d 73 2 44§ 


T.,. 


J.D. 241 


9806.383 
0983 






359°33 


K. . 
7- • • 
Min. 
Min. 


I., J.D. 241 

II-Min. I 


100.96 km 
-f- 20. 15 km 
9068.162 
3 d 224 



The journal of observations is given in Table II. In the first 
series of 1910, the measures were taken of 6, e, and f Ononis, and 5 
is therefore referred to the other two. but after that only e was used 
for a comparison star, and the entire series is practically homo- 
geneous. The phase was reduced to the sun, though this was 



Diff. 

of ma 




Days 



1234 
Fig. 1. — The light-curve of 5 Orionis 



Periastron 



probably unnecessary. The difference of magnitude is in the sense: 
5 minus e. A " set'' of measures usually consisted of two exposures 
on the comparison star, then six on the variable, and finally two 
on the comparison star. Under ordinary conditions, it was possible 
to observe at the rate of five sets per hour. The residuals, rounded 
off to hundredths of a magnitude, were obtained graphically from 
the irregular curve shown in Fig. 1. 



136 



JOEL STEBBINS 



TABLE II 
Observations of 5 Orionis 



Date 



G.M.T. 



Phase 



Difference of 


Sets 


Magnitude 


mag. 




0.576 


2 


0-52S 


2 


O.485 


2 


0-549 


2 


0.552 


2 


0-545 


2 


0.5I7 


2 


0509 


2 


O.528 


5 


0587 


5 


0.544 


5 


0.549 


5 


0.665 


5 


0.637 


5 


0.582 


4 


0.559 


5 


0525 


5 


O.SII 


5 


0-533 


5 


0.541 


5 


0-557 


5 


0.518 


5 


o.543 


5 


535 


5 


0-553 


5 


0571 


4 


0.605 


5 


0.623 


5 


0.627 


5 


0.603 


5 


0-575 


6 


0525 


5 


0.562 


5 


0.608 


5 


0-593 


5 


0.600 


5 


0.625 


4 


0-537 


5 


0.511 


3 


0.511 


5 


0.478 


5 


0-543 


5 


0.520 


5 


0558 


5 


0.511 


5 


0.560 


5 


0.585 


5 


0.601 


5 


0-579 


5 


0-553 


2 


0.500 


5 



Residual 
Obs.— Curve 



1910 January 9 

18 

27 
February 1 

3 
4 
6 

12 
October 10 

n 

13 
November 7 
n 
11 
17 
19 
21 
21 
28 
29 
29 
December 7 

7 
7 
7 
7 
10 
10 
10 
10 
10 
1 1 
13 
13 
13 
13 
13 
14 
14 
20 
20 
26 
26 

191 1 January 3 

4 
4 
8 
8 
8 
22 
29 



i7 n o7 E 

16 34 

17 01 
17 01 
i5 25 
16 43 

15 05 

16 02 
21 42 
21 41 
21 34 
20 33 

20 48 

21 55 
19 01 

19 15 

20 51 

22 08 
20 55 

8 56 

9 30 



7 49 

8 47 

9 45 

42 

1 42 

5 18 

6 26 



8 24 

9 42 

7 59 

6 35 

8 31 

9 30 

20 30 

21 26 

7 02 

8 02 

7 53 

8 51 

7 02 

8 00 

8 49 

9 07 
o 05 

6 21 

7 21 

8 20 
7 36 



3 d 338 
0.850 
4-136 
3-402 

5-335 
0658 



366 

365 
362 
658 
669 

7i5 
130 
140 
207 
260 
477 



0.685 
2.883 
2.924 
2.964 
3 003 

3 045 

0.045 
0.093 

0.134 



o. 1 



o 



0. 229 

I 157 

3 099 
3.180 
3.220 
3.262 
3-301 
4. 118 

4- 159 
4.419 
4.460 
4-653 
4-693 

1 . 262 



2. 2 



/J 



2-315 
0.426 
0.468 



013 
289 



mag. 

— O.02 

— .02 

- .04 

- .04 



•04 
■03 



+ .01 

+ -03 

+ -Ol 

~ 03 

+ .01 
O 

— .OI 

- .02 

o 
.02 
.02 

c 
.02 

o 



+ 



+ .03 



-03 

• 05 



• 04 

• 03 



THE ECLIPSING VARIABLE STAR b ORION IS 
TABLE II — Continued 



137 



Date 



191 1 February 1. 

9 

22. 

23 

24 

March 4 

4 

24 

September 29 . 

October 1 1 

12 

14 
15 
15 
17 
17 
18 
18 
18 
22 
22 
23 
?3 
24 
24 
28 
28 
28 
November 1 
1 
1 
1 
1 
14 
14 
14 

!5 

15 
17 
17 
18 
18 
18 
18 
18 
18 
24 
24 
25 
25 

25 

25 



G.M.T. 



Phase 



29 
38 
37 
12 

44 
42 
22 

21 37 
21 02 
21 58 



iu 



3 C 
42 
48 
45 
57 
35 
35 
07 
05 
03 
37 
45 
35 
34 
45 
44 
35 
35 
33 
16 

20 14 

21 12 

22 06 
22 54 
18 22 

21 33 

22 33 
18 36 

35 



10 



19 



19 



37 
56 
53 
53 
52 
59 
01 
02 
55 
54 



i d 453 
3.809 

5-3o8 

o-573 
1-556 

3.762 
3.802 
0.816 
0.948 
1.458 
2-497 
4.404 
4-4SO 
5-448 
5 498 
1.709 



2. 729 
2.770 
1.020 
1 .067 
2.018 
2.059 
2.984 
3025 
1.203 

1.245 
1.285 

5 190 
3-230 
5- 270 

5.308 
34i 



0.956 
1 .089 
1. 131 

1 .966 
2.007 

4025 
4.071 

4-939 
4.980 

5 OI 9 
5.061 
5. 102 

5-149 
5-334 

5-376 
0.472 
0.512 
0556 



Difference of 
Magnitude 



mag. 
0-543 
0-557 
0.570 
o-556 
0.510 
0.572 
o.574 
(0.589) 
0523 
0.528 
0530 



0.590 
0.601 
o.554 
0.55S 
0.542 
0-53I 
0.524 
0.501 
0.522 
0.542 

0-539 
0.568 
0.586 
0530 
0.499 

o.5 J 3 

0.526 

0.530 
0-543 
o.574 
0.560 

0519 
0530 
0.546 
0-533 
o.574 
0.528 
o-535 
0-557 
0556 
o.574 
0.561 

0549 
0.564 

o.534 
o.544 
0.506 

0.541 
o.543 
0.532 



Sets 



Residual 
Obs.— Curve 



mag. 

+ O.OI 

O 

4- .02 

+ .01 

- 03 

o 

+ .01 
(+ .05) 



+ 



• 04 
.04 



— 


04 


— 


.02 


— 


.01 


— 


.01 


+ 


.02 


+ 


.02 



— 03 

— .01 

— .02 

— .02 

— .01 

+ 02 

+ .01 

— .02 

— .01 



03 



+ .01 



.01 
.02 
.02 
.01 

.06 



138 



JOEL STEBBINS 
TABLE II— Continued 



Date 



G.M.T. 



Phase 



Difference of 
Magnitude 



Sets 



Residual 
Obs.— Curve 



1911 November 25. 
26. 
29. 
29. 
29. 
29. 
29. 
3° ■ 
3°- 
3°- 



December 



191 2 January 



3- 
4- 
5- 
5- 
5- 
5- 
5- 
10. 



13- 

19. 
iQ- 
23- 
23- 
23- 
23- 
23- 



27- 

27. 



12. 

12 . 
12. 



2i h 49 n 
18 54 

17 35 

18 46 

19 44 

20 42 

21 28 

17 26 

18 27 

19 32 

19 13 

20 15 

20 27 

17 15 

17 01 

18 07 

19 06 

20 11 

21 10 

16 51 

17 47 
16 48 

19 37 
16 13 



18 11 

19 00 

19 52 

20 46 

15 43 

16 37 

18 25 

19 28 

15 47 

16 58 

15 39 

16 55 

14 50 

15 38 

16 26 

19 29 

20 05 



16 


18 


17 


28 


18 


40 


14 


51 


15 


57 


15 


15 


1', 


22 


17 


18 


18 


49 



634 
512 

458 

507 

547 
587 
619 

45i 
494 
539 
794 
837 
845 
712 
702 
748 
789 
834 
875 
9 6 3 
002 
961 
345 
47i 
5i7 

5*0 

553 
587 
623 
660 
7i8 
755 
830 

874 
989 
038 

983 

036 
216 
249 
283 
410 
435 
233 
277 
326 
376 
217 
263 
499 
546 
585 
648 



mag. 
0-536 
O.540 
O.468 
O.463 
O.510 

0-473 
O.522 

0-5I7 
0.545 
O.615 
O.508 
O.518 
0.547 
0.570 



0.549 
O.560 
O.546 
O.528 

0.574 
O.564 

0-554 

0.494 
0.542 
0-555 



0.562 
0.585 
0.585 
0.610 
0.528 
0.536 
o-535 
o-495 
0.52O 

0-534 
o.557 
0.568 
0.605 
0.627 

0-595 
0.564 
0.560 
0.566 
o.575 
0.591 
0.538. 
0.538 
0.548 
0.528 
o.547 
0-543 
0-532 



mag. 

— O.OI 

O 

— .02 

- 03 

o 

- .04 



— 


• 03 


— 


.01 


+ 


•03 


— 


• 03 


— 


.02 


+ 


.01 


+ 


.02 


— 


•03 


+ 


.01 


+ 


■ 03 


+ 


.02 


— 


.01 


+ 


• 03 


+ 


.02 







— 


■03 







+ 


.01 


— 


.01 


— 


.02 


— 


.01 


— 


.02 


— 


.02 


— 


.02 


— 


.02 


— 


.01 


— 


■ 04 


— 


.02 


— 


.01 



+ .03 



.02 
.02 
.02 



+ 
+ 
+ -03 

— .01 
+0.02 

+ .02 

o 

+ 02 
+ 01 



THE ECLIPSING VARIABLE STAR 5 ORION IS 
TABLE 11— Continued 



139 



191 2 January 15 



Februarv 



March 



G.M.T. 



15 
IS 
15 
18 
18 

19 
19 

JO 

20 
20 

22 

7 

7 

7 

8 

8 

8 

9 

9 

9 

27 

-9 

29 

5 

5 

9 

9 

16 

16 

i7 



Phase 



Difference of 
Magnitude 



Sets 



Residual 
Obs.— Curve 



T ,h 9 -m 
14 25 


-d 

0- 


15 23 

16 24 

17 38 

18 43 


5 ■ 
5- 
5 • 

5 • 


19 5° 
16 29 


5- 
2. 


17 54 


2 . 


14 41 


3- 


15 4i 

16 35 

15 58 

16 56 


3- 
3- 
4- 

4- 


1 7 53 


4- 


17 44 


1 . 


14 °3 
14 46 

16 24 


5 • 
5- 

5 • 


14 37 

i5 38 


0. 
0. 


16 34 


0. 


15 22 


1 . 


16 26 


1 . 


17 20 


1 . 


13 22 


2. 


14 09 

15 26 


4- 

4 


14 29 


3- 


IS 21 


3- 


14 31 


2. 


15 29 
13 28 


2. 
3- 


14 35 


3- 


13 34 


4 



465 
505 

547 
599 
644 
690 
819 
878 
744 
785 
823 

797 

838 

877 
139 
5i8 
548 
616 
810 
852 
891 
841 
886 

923 
558 
59i 
644 
872 
909 
141 
181 

364 
409 

367 



■591 

■578 
.605 
.632 
•590 
• 5 2 ° 
■57° 
■565 
•559 
■ 555 
.506 

•53 2 
•536 
■533 
•542 
•567 
.606 

■553 
■577 
■598 
513 
■547 
•519 
.516 

■547 
.548 
■546 
■532 
.560 
■522 
■577 
.630 

•497 



mag. 
+ 0.02 
+ -03 



+ 02 
- .04 



■03 
.02 



.02 
o 



.02 
.02 



.04 

.06 

.02 
.02 
.OI 
.02 
•03 



+ -OI 



+ 



.02 

OI 
.04 



A discussion of the observations shows no large difference 
between seasons, so the normal magnitudes were formed in the 
usual manner by combining observations near the same phase, and 
the resulting normals are considered to be all of about the same 
weight. The observations within a single normal were weighted 
according to the number of sets, and ordinarily a normal com- 
prises 19 or 20 sets taken on at least two nights. In Table III the 
phase and difference of magnitude are in the same sense as before, 
while the ''rectified" magnitude refers to the deviation from a 
curve which will be explained later. 



140 



JOEL STEBBINS 



The results in Table III are shown in Fig. i, and it is evident at 
once that this is an eclipsing system with two minima, the predicted 
times being shown from the last three columns of Table I. The time 
of periastron is from the mean of the three orbits. As there seems 
to be variation due to other causes, we may first consider what 
would influence the measures other than a variation of 5 Orionis. 

TABLE III 
Normal Magnitudes of 5 Orionis 



Phase 



0?09Q 

0. 216 

0413 
0.512 
O.613 
O.782 
O.925 

1. 108 
I . 217 

I-367 
I.489 
1.668 

1 -9°5 
2.056 
2.213 
2.321 
2.452 

2-579 
2.752 
2.872 
2.969 
3052 
3-247 



Difference 
of Magni- 
tude 



mag. 
O.611 
.600 
584 
542 
543 
534 
543 
533 
528 
5i8 
54i 
543 
527 
554 
540 
564 
532 
533 
529 
54i 
55o 
57i 
603 



Rectified 

Magnitude 



mag. 
+ O.060 

+ 050 
+ -037 

- 003 
+ .OOI 

- 005 
+ 007 

— OOI 

— ■ 005 



.008 
.009 
.01 1 

-015 
.002 
.021 
.012 
.Oil 

.014 
.000 

.Oil 

• 033 



+0.070 



Sets 


be 


19 


2 


19 


2 


19 


2 


20 


2 


22 


3 


20 


3 


23 


5 


19 


3 


20 


3 I 


16 


3 


20 


3 1 


20 


3 


19 


2 


20 


3 


18 


3 


20 


3 


16 


3 


18 


3 


20 


2 


17 


4 


20 


2 


16 


4 


21 


2 



Phase 



380 

733 
790 

851 
968 
063 
187 
270 
412 

493 
620 

733 
836 

939 
025 
167 
3°5 

358 
469 
508 

547 
614 
684 



Difference 
of Magni- 
tude 



mag. 
59° 
549 
566 

529 
548 
533 
520 
521 
505 
480 

524 
534 
528 
551 
565 
543 
554 
549 
548 
57i 
58i 
604 
631 



Rectified 
Magnitude 


Sets 


mag. 




+ 


.060 


16 


+ 


.027 


19 


+ 


•045 


20 


+ 


.008 


19 


+ 


.028 


19 


+ 


.013 


21 




.000 


17 




.OOO 


16 


— 


.018 


21 


— 


•045 


20 


— 


.004 


20 


+ 


.003 


20 


— 


.007 


20 


+ 


• OI 3 


20 


+ 


.025 


20 


— 


.002 


21 


+ 


.006 


19 




.000 


16 


— 


.002 


23 


+ 


.020 


18 


+ 


.030 


19 


+ 


•052 


22 


+ 


.079 


17 



All of the measures have been retained except those of March 24, 
191 1, which was the last night of that season, twenty days later 
than the next preceding. For some reason the 5 sets are dis- 
cordant, and are 0.05 mag. different from others at the same phase. 
This is the only case where observations were rejected after they 
were once recorded as satisfactory. Nevertheless, an inspection of 
Table II will show various nights when the results are systematically 
in error by several hundredths of a magnitude. I have been unable 
to find any instrumental or observing conditions which would 
account for these discrepancies. 



THE ECLIPSING VARIABLE STAR 5 ORION IS 141 

We may ascribe any unexplained difficulty to a variability of the 
light of the single comparison star, e Orionis. This is a spectro- 
scopic binary of unknown period, though Professor Curtiss writes 
that he suspects it to be short, and nearly commensurable with 
some fraction of a day, like one-third or one-fourth. In order to 
test the results in Table II for possible variation of the comparison 
star, the normals in Fig. 1 were connected with straight lines in 
order to avoid any prejudice, and each separate observation was 
compared with the irregular zigzag curve found in this way. My 
assistant, Mr. J. D. Bond, made numerous attempts to find some 
period of light-variation of e Orionis from these residuals of 
Table II. but without success. Any variation must be very small, 
as the following distribution of the residuals will show. 

Residual Xumber Residual Number 

mag. mag. 

- O.06 I +0.02 23 

- • 05 I + . 03 13 

- • 04 7 + - 04 5 

- • 03 Q + . OS O 

- .02 32 +O.06 I 



- .OI 36 

• OO 43 

+ O.OI IQ 



190 



The distribution is nearly enough according to the law of error so 
that no variation of e Orionis seems probable. The average 
residual is ±0.016 mag., which is small enough to call the star 
constant by ordinary standards. 

Returning again to the discussion of the curve in Fig. 1, it is 
evident that there is an increase of light near periastron, due pre- 
sumably to the greater interaction of the two components at the 
decreased distance. It is not impossible, however, that this 
brightening up is due to the fainter component being a variable. 
The view that some kind of light-variation may be caused by a 
resisting medium is strengthened in the present case by the sta- 
tionary H and K lines in the spectrum. Also it is impossible to 
satisfy the observed points by drawing minima symmetrical about 
the predicted times of eclipses. There is indication that the times 
of least light are in accordance with the spectroscopic data, but in 



142 JOEL STEBBINS 

both the primary and secondary minima, the decrease of light 
is more rapid than the increase, which could be attributed to the 
fact of each component being brighter on the front side in its 
orbital motion. The total effect is so small in comparison with the 
errors of observation, that no estimate can be made of the variation 
of the intensity on each apparent disk, and likewise there is no 
chance of determining the possible darkening at the limb of each 
star. The secondary minimum is apparently much longer in 
duration than the primary, which can be explained by assigning 
to the main body a larger diameter for occultation or absorption 
than it has for emission; in other words, it has an extensive absorb- 
ing atmosphere. We see that we are dealing with a complicated 
system, and any complete theory will have to wait for spectro- 
scopic and photometric data far more accurate than anything now 
attainable. 

We may represent the variation between minima by the first 
few terms of a Fourier series 

M = a -\-ai cos 4>-\-b x sin <f>-\-a, cos 2<f>-\-b 2 sin 2<£ , 

where M is the observed difference of magnitude at the phase <f>, 
and the as and 6's are constants to be determined. Although 
this is only an empirical relation, the terms in will take care of 
any simple continuous variation throughout the whole period, 
while the terms in 2 4> will approximate the ellipsoidal shape of the 
components. As only observations outside of the eclipses may be 
used, the limits of phase excluded were: o d oo to o d 55, 2 d 9o to 3 d 8o, 
and 5 d 47 to $ d 73- The observation equations were formed, and 
then the least-squares solution gave, after combining terms, 

lf = o M 5368+o M oo76 sin (<£+43?o)+o M oio5 sin (2<£+ii2?8). 

This equation is shown graphically by the dotted curve of Fig. 1, 
and the deviations from this curve give the ''rectified" normals 
in Table III. It is seen that the effect at periastron is not closely 
represented by the curve, and it is probable that the effects of the 
various causes of light-change between minima are so intermingled 
that it is quite impossible to separate them. The representation of 
the observations by means of the series is perhaps not as good as 



THE ECLIPSING VARIABLE STAR 8 ORION IS 143 

could be accomplished by drawing a freehand curve, but there is 
the advantage that any personal bias is eliminated. There is a 
suspicion that there is an additional minimum on each branch 
between the eclipses, making a total of four minima, and hence 
four maxima, for the light-curve; but the reality of these secondary 
fluctuations must remain in doubt for the present. 

The rectified normals indicate the approximate variation due to 
eclipses, which we now consider. Let the surface brightness and 
the radius of the first component, and the light of the system 
between minima, each be taken as unity. Further let 

k= radius of second component. 

X— surface brightness of second component. 

— = fraction of first disk obscured at primary minimum. 

Li = light of system at primary minimum. 
L 2 = light of system at secondary minimum. 

Then it easily follows that 

1— ii 

Assuming that the primary minimum is a decrease of 0.08 mag., 
and the secondary 0.07 mag., then .^ = 0. 929 and £., = 0.938, and 
from (1) we have A = o.88. Referring to the light-curve, we see 
that an additional observed point might bring the secondary 
minimum down another hundredth of a magnitude, and then A = 
1 .00. It is evident that the surface intensities are about the same, 
which with only one spectrum visible must mean that the second 
component is smaller than the primary. 

It is quite hopeless to derive the radius of the companion from 
the form of the light-curve at minima, but we can find certain 
limits between which it must lie. The least possible value of k 
would be when the companion is wholly projected against the 
larger body at minimum, or 

«»>— !=(i-L x )(i+k 2 A). 

7T 

Hence it follows that 

1 — Li _i — Li 
i-A+AL," L 2 ' 



144 



JOEL STEBBIXS 



and substituting the values of L z and L 2 we have k>o.28. The 
upper limit of k as derived from the curve alone is of no value, but 
we have a consideration from the spectroscopic results which is 
more exacting. Spectrographic observers seem to agree that if 
the difference of light of two components of a binary exceeds about 
one stellar magnitude, the fainter spectrum will be blotted out. 
Stretching this limit a little, I assume that the companion gives 
not more than one-third of the light of the primary, and therefore 



k-'A< 0.333, 



k-'<o.o379, 



K<0.62. 



For subsequent computations we adopt then 

A = o.88, 

O. 28<K<0.62 . 

While the range of k is large, the uncertainty is no greater than 
in many of the well-known eclipsing systems where only one mini- 
mum has been observed. 

The other elements of the system are fixed by the approximate 
time of duration of the eclipses, which is adopted to be 0.9 day, 
an avowedly rough value, since the two minima seem to differ in 
length. From well-known simple formulae, it is an easy matter 

TABLE IV 



Radius of companion, k 

Surface brightness of companion, X 

Inclination of orbit, i 

Semi-major axis of orbit, a 

Semi-major axis of orbit in km 

[ Radius of first component . . . . 
Radius of second component. . 
Mass of first component, m s - ■ 
Mass of second component, m 2 
Density of first component . . . 
Density of second component . 

Mean density of system 



Assumption 

tHi= 2)>1 2 



O.28 
O.88 
7 2?2 
2.38 

,320,000 km 
15.1© 

4. 2© 

12. 6© 
6. 3© 
0.0036© 
0.084 © 
0.0054© 



0.62 

0.88 

62?6 

2.64 

8,920,000 km 

14.6© 

9.0© 

15-5© 
7. 8© 
0.0050© 
o.on 
0.0061 



to compute the results for each limit of k, and then to combine 
with the spectroscopic data. The quantities in the second column 
are considered the more probable. The assumption that the 
masses are in the ratio of 2 to 1 is quite arbitrary, but it agrees with 
the general rule among spectroscopic binaries, that the component 



THE ECLIPSING VARIABLE STAR 5 ORION IS 145 

with the stronger spectrum is always the more massive. If we con- 
sider the mass of the first body to be very small compared with the 
second, we get the least possible value for the radius of each com- 
ponent, and on any assumption this comes out 50 for the larger 
and 1 .40 for the smaller body. The mean density of the system, 
0.0060 , may be taken as well determined, and is quite independent 
of the spectroscopic results. This is a somewhat lower density 
than is ordinarily found in a star 1 of Class B, but 5 Orionis may be 
typical of the many eclipsing stars of small range which await dis- 
covery. 

When an eclipsing variable has been observed with the spectro- 
graph there are three quantities for which a knowledge of any two 
determines the third, namely, the surface brightness of one of the 
components compared with the sun, the ratio of the masses of the 
bodies, and the absolute parallax of the system. In the present 
case none of these quantities are known, but it may be of interest 
to compute what value of the parallax comes from reasonable 
assumptions for the others. Russell 2 estimates the surface bright- 
ness of stars of Class B to be 28 times that of the sun, which, com- 
bined with the assumed mass-ratio of 2 to 1, and the larger value 
of k, gives for the parallax 

ir=o".oo? ) 2. 

Considering the three stars of the belt of Orion to be at the same 
general distance, and substituting their mean magnitude, 2.1. and 
proper motion, n = o". 0042, in Kapteyn's formula, 3 I find 

7T=o''oOIQ, 

which agrees well enough with the other value. The only inference 
that I draw from these figures is that 5 Orionis, like other stars of 
Class B, has a great luminosity, and its parallax is so small that 
direct measures are probably hopeless at present. 

There is one point in connection with spectroscopic binaries 
which the eclipses of 8 Orionis seem to settle once for all. It has 
been argued that some of these systems are not double, but that 

1 Shapley, Astrophysical Journal, 38, 173, 1913. 

2 Astrophysical Journal, 40, 417, 1914. 

3 Groningcn Publications, No. 11, 1902. 



146 JOEL STEBBINS 

we are dealing with only single rotating bodies. In fact, Julius 1 
selected 8 Orionis as an illustration of his idea that the variations of 
the lines of the spectrum are due to anomalous dispersion. Such 
considerations would have much more weight in the case of vari- 
ables of the 8 Cephei type, but in 8 Orionis the eclipses seem to 
answer all argument against the existence of two bodies. Not only 
does the velocity-curve satisfy a Keplerian ellipse, but the times of 
the two minima are in agreement with the eccentric orbit, and 
though there are some outstanding anomalies, the main facts of the 
double system are established without possibility of doubt. 

SUMMARY 

i. The star 8 Orionis has been found to be an eclipsing variable 
with two minima in agreement with the spectroscopic orbit. The 
approximate light-elements are: 

Min. I = J.D. 2419068. 2o+5 d 7325 -E 
Min. II-Min. 1 = 3*20 

2. The light between minima is also variable, there being an 
increase near periastron, but ellipticity of figure and other causes 
may also contribute to this effect. The total light-range is about 
0.15 mag., of which 0.08 mag. is due to the eclipses. 

3. The minima are not symmetrical about the times of greatest 
eclipse, and suggest that the surface brightness of each apparent 
disk is not uniform, but that each body is brighter on the front side 
in its motion in the orbit. 

4. The elements of the system can be determined only within 
certain limits (see Table IV). but as definite results we have that 
the mean density of the system is 0.006 that of the sun, the larger 
component being at least 5 times and the smaller at least 1 . 4 times 
the solar radius. 

I beg to acknowledge my indebtedness to Messrs. P. F. Whisler 
and H. F. Zoller for assistance in taking the observations, and to 
Mr. J. D. Bond for checking many of the reductions. 

1 Astrophysical Journal, 21, 286, 1905. 



THE ECLIPSING VARIABLE STAR 8 ORIONIS 147 

Some years ago, I received a series of grants from the Rumford 
Fund of the American Academy of Arts and Sciences, amounting in 
all to $750.00, and the present paper is the final report on the work 
accomplished with the selenium photometer by the aid of these 
grants. I take this opportunity of returning my sincere thanks to 
the Rumford Committee for its timely support, and especially for 
the encouragement which it gave me to continue the experiments 
with the selenium photometer long enough to secure some kind of 
control over this peculiar instrument. 

University of Illinois Observatory 
May 28, 1915 



A STUDY OF THE LIGHT-CURVE OF XX CYGNP 

By HARLOW SHAPLEY and MARTHA BETZ SHAPLEY 

XX Cygni, discovered in 1904 by Madame Ceraski, 2 is the 
shortest-period variable star known. It is classed as a Cepheid by 
Kron, 3 and the light- variation seems to have all the general charac- 
istics peculiar to that class of variables; but unlike other Cepheids 
for which we have the necessary data, it is said to have a greater 
range visually than photographically. 4 That such an abnormality 
of color should be attributed to a variable already exceptional on 
account of its unusual period, suggests that the peculiarity may not 
be due to observational uncertainties. Its explanation would be 
that at maximum the star is redder than at minimum, the greatest 
intensity of the spectrum shifting toward the red with increasing 
light, instead of toward the violet as with all other Cepheids. 5 This 
would indicate that, if there is a change of spectral type with change 
of light, the redder spectrum occurs at maximum and not at mini- 
mum, as has been observed for RS Bootis, 6 and as is presumably 
true for all other Cepheids whose photographic ranges are known 
to exceed the visual. To determine whether the visual range of 
XX Cygni is really greater than the photographic, and to investi- 
gate other peculiarities of the star, 7 a study of its light-curve has 
been undertaken at Mount Wilson, the results of which are con- 
tained in the present communication. 

1 Contributions from the Mount Wilson Solar Observatory, Xo. 104. 

2 Astronomische Nachrichten, 165, 61, 1904. 

3 Publikationen dcs Astro physikalischen Obscrvatoriums zu Potsdam, 22, Part III, 
52, 1912. 

4 Parkhurst and Jordan find a photographic range of 0.63 mag. Kron's mean 
visual range is o. 76. But cf. Kron, op. cit., p. 56. 

5 Campbell, Stellar Motions, p. 309, 1913. 

6 Publications of the Astronomical Society of the Pacific, 26, 256, 1914. 

" Such as irregularities in time and shape of maxima, or other features that might 
throw light on the cause of Cepheid variation; Mt. Wilson Conir., Xo. 92; Astro- 
physical Journal, 40, 448, 1914. 

148 



A STUDY OF THE LIGHT-CURVE OF XX CYGNI 149 

Because of the favorable field and the abundance of close and 
suitable comparison stars, XX Cygni is well adapted for accurate 
eye-estimates, as well as for photometric and photographic observa- 
tion ; and since its discovery the light-variations have been followed 
regularly. In 191 2 E. Kron 1 published a monograph on the star, 
containing 2705 observations by eight different observers, 2 together 
with a critical discussion of the data. The period derived is 
3 h i4 m i2 s 3547, with the addition of a quadratic secular term. Al- 
though Kron concludes that the existence of this term is clearly 
demonstrated, the Mount Wilson observations show that, quanti- 
tatively at least, it is not sufficient. 

On the nights of August 21 and 23, and September 18, 1914, and 
March 17, 191 5, series of observations were made with the 60-inch 
reflector. On each of the first two nights the star was followed 
throughout an entire period. In all the observations Seed ''27" 
and Cramer "Instantaneous Isochromatic'' plates (used with a 
yellow color-filter) were alternated, thus giving in quick succession 
photographic and photo- visual magnitudes. The importance of this 
procedure lies in securing complete photographic and photo-visual 
determinations of the same epoch of maximum with the same instru- 
ment. As we shall find later, neither the shape of the curve nor 
the range is constant for successive periods. Therefore it is impor- 
tant that every photographic-photo-visual comparison should relate 
to the same interval of variation. 

The plates obtained were as follows: August 21 and 23, 13 of 
each kind on each night; September 18, 5 Seed 27 and 4 isochro- 
matic; March 17,8 Seed 27 and 7 isochromatic, but owing to haze 
five of the latter were not sufficiently exposed to insure reliable 
measurement. In addition there are nine polar comparison plates, 
one of which was rejected because the cycle of comparisons with the 

1 Op. cit. 

2 Blazko, Astronomische Nackrichten, 172, 58, 1906; Schwab, ibid., 170, 370, 1906; 
Parkhurst and Jordan, Aslrophysical Journal, 23, 84, 1906; Graff, Astronomische Nach- 
richten, 171, 55, 1906; Luizet, Bulletin Astronomique, 25, 251, 1908; Nijland, Astrono- 
mische Nachrichten, 188, 149, 191 1; Kron, op. cit., p. 35; Hartwig, Vierteljahrsschrift 
der Astronomischen Gescllschaft, 41, 309, 1906. The observations by Guthnick, as well 
as those by most of the observers named, are not published outside of Kron's mono- 
graph. 



150 HARLOW SHAPLEY AND MARTHA BETZ SHAPLEY 



Pole is not closed and the altitude of the variable was so great that 
the extinction correction is large and uncertain. With the ex- 
ception of the polar comparisons, each Seed 27 plate received four 
one-minute exposures, 1 while each isochromatic received three two- 
minute exposures. 

The method of measurement and reduction closely follows that 
described by Seares in ML Wilson Contr., Xo. So. 2 Of each separate 
image of the variable and the comparison stars two independent 
measures were made, and all of the measures on each plate, cor- 
rected for distance from the center and for irregularities of the 
measuring scale, yielded a single mean value of the brightness of 
the variable. 

Diaphragms were used to determine the scale of the comparison 
stars referred to an arbitrary zero-point; the magnitudes so ob- 
tained were reduced to the international zero by comparison with 
the Mount Wilson Polar Standards. Corrections for differential 
extinction between the variable and the Pole were made with the 
aid of the Potsdam tables, 3 interpolating for the altitude of Mount 
Wilson, and doubling the tabulated visual values to obtain the 
photographic corrections. 

TABLE I 
Polar Comparison Plates 



Plate 


Date 


G.M.T. 


No. 

Exp. on 

Yar. 


No. 
Exp. on 

Pole 


Length 

of Each 

Exp. 


Extinction 
Correction 




No. Kind 


to Int. Zero 


1792.. 


Iso. 


1914 


Aug. 


22 


23 h gm 


2 


2 


2 m 


— 0.00 mag. 


10.83 ma g- 


1828.. 


Iso. 






23 


23 16 


2 


1 


2 


— 0.02 


10.74 


2325- • 


Iso. 


I0I5 


Mar. 


1 5 


23 43 


2 


2 


3 


+003 


io.75 


2327. . 


Iso. 






16 


28 


2 


3 


2 


+0.06 


10.86 


1791. . 


S. 27 


1914 


Aug. 


22 


22 52 


2 


2 


I 


+0.02 


10. 19 


1829. . 


S. 27 






23 


2 3 25 


2 


2 


I 


— 0.04 


10.08 


1890*. 


S. 27 




Sept. 


18 


is 23 


9 


1 


I 


+0. 22 




2324. . 


S. 27 


J 9i5 


Mar. 


15 


23 5i 


2 


2 


I 


+0.07 


10.07 


2326. . 


S. 27 






16 


° 25 


2 


3 


I 


+0. 11 


10.13 



* Rejected as a polar comparison. 

Table I gives a list of the polar comparisons. The last column, 
giving the value of the reduction constant derived from each plate, 

1 Plate 1892 has five exposures; 1890 has two. 

2 Astrophysical Journal, 39, 307, 1914. 

3 M tiller, Photometric der Gcstirnc, p. 515, 1SQ7. 



.4 STUDY OF THE LIGHT-CURVE OF XX CYGNI 



I5i 



shows the satisfactory accordance of the results and indicates that 
that part of the probable error in the color-index which depends on 
the uncertainty of the zero-points is considerably less than a tenth 
of a magnitude. 

Table II gives the adopted magnitudes of the five comparison 
stars as determined from seven diaphragm-plates of each kind. 

TABLE II 
Magnitudes of Comparison Stars 



Star 


Photographic 
Magnitude 


Av. Dev. 


Photo-visual 
Magnitude 


Av. Dev. 


I 

2 

3 

4 


II . 10 
12.56 
13-35 


±0.09 
±0. IO 

±0.04 


IO.76 
H-33 


±0.06 
±0.09 


11.77 
12.23 


± 0.02 








±o . 07 











On the Seed 27 plates, Nos. 1, 2, and 3 (see Fig. 3 and Table VI) 
were used; on the isochromatic plates, Nos. 4 and 5 were substi- 
tuted for Xo. 3 which was too faint photo-visually to be suitable. 
The photographic magnitudes of Nos. 4 and 5 and the photo- 
visual magnitude of No. 3, which are missing from this table, were 
later determined, but less accurately, by a direct comparison with 
the Polar Standards (see Table VI). 

In Table III we have the photographic and photo-visual material 
upon which the light-curves are based. The first column contains 
the number of the plate, the second the Greenwich heliocentric 
mean time of the middle of the exposure, the third the phase com- 
puted from Kron's elements II, 1 and the fourth the magnitude of 
the variable. Diaphragms were used in making the plates marked 
with an asterisk, the order of apertures being 60-32-60 for the iso- 
chromatic and 60-32-32-60 for the Seed 27 plates (with the excep- 
tion of Plate 1892 on which the order was 60-40-32-40-60). 

The data bearing on the accuracy of the light-elements are col- 
lected in Table IV. The times of maximum predicted from Kron's 
adopted elements (Kron II; see op. cit., p. 47) 2 are given in the 

1 Op. cit., p. 47. 

-Max. = J.D. 2416563. 41065, G.H.M.T. +o d 134865225 -o d i578Xio~ 10 E 2 . 



152 HARLOW SHAPLEY AND MARTHA BETZ SHAPLEY 

fourth column. They do not agree within allowable errors with the 
observed times, the greatest difference being 1 7 minutes. Using the 

TABLE III 
.Mount Wilson Observations of XX Cygni 





Photographic 








Photo-visual 




Plate 


G.H.M T. 


Phase 


Mag 


Plate 


G.H.M.T. 


Phase 


Mai;. 




1914 Aug. 21 








1914 Aug. 21 






1752. 


20 h 9™ 2 


+ 2 h 34 m 9 


12.47 


1753- ■ 


20 hj-m 2 


+ 2 h 4 2 m 9 


12.21 


1754- 


27.2 


52 


9 


12.48 


1755- ■ 


34-5 


3 °-2 


II .92 


1756* 


423 


3 8 





11 .90 


1757*- 


49-7 


O 1.2 


II.47 


1758. 


57-2 


8 


7 


H-54 


1759- • 


21 4.4 


15 9 


"■54 


1760. 


21 11. 9 


23 


4 


11.68 


1761 . . 


20.0 


315 


11.70 


1762* 


33 • 1 


44 


6 


12.00 


1763*. 


40.7 


52.2 


11.98 


1764. 


48.3 


59 


8 


12.33 


1765.. 


55-7 


I 7.2 


1203 


1766. 


22 3.4 


1 14 


9 


12.23 


1767.. 


22 10.8 


22.3 


12. 11 


1768. 


18.4 


29 


9 


12 . 29 


1769. 


26.5 


38.0 


12.06 


1770. 


34-8 


46 


3 


12.52 


1771 


42.3 


53-8 


12.15 


1772. 


49-8 


2 1 


3 


12.45 


1773- ■ 


57-9 


2 9-4 


12.15 


1774* 


23 5.3 


16 


8 


12.52 


1 7 7 5 * 


23 13- 1 


24.6 


12.17 


1776. 


21 . 2 
Aug. 23 


32 


7 


12.48 


1777 


28.6 
Aug. 23 


40. 1 


12 11 


1794- 


15 37-7 


44 


5 


11 75 


1795- ■ 


15 466 


53-4 


11.99 


1796. 


55 


1 1 


s 


12.08 


1797.. 


16 2.2 


1 9.0 


11.98 


1798* 


16 9.9 


16 


7 


12.25 


1799*. 


18.7 


25 -5 


11 93 


1800. 


27.6 


34 


4 


1237 


1801. . 


35-4 


42. 2 


12.05 


1802. 


46.5 


53 


3 


12.50 


1803.. 


54 3 


2 1.1 


12.18 


1804. 


17 i-5 


2 8 


3 


12.41 


1805 . . 


17 8.6 


15-4 


12.17 


1806. 


15-8 


22 


6 


12.46 


1807.. 


23.0 


29.8 


1213 


1808. 


30 -4 


37 


2 


12.50 


1809. . 


37-3 


44.1 


12.05 


1810. 


45 1 


5i 


9 


12 .40 


1811.. 


524 


59-2 


11.67 


1812* 


59-5 


3 6 


3 


12.08 


1813*. 


18 8.0 


0.6 


11 .40 


1814. 


18 19.7 


12 


3 


11.82 


1815.. 


26.9 


19 5 


11-32 


1816. 


34-1 


26 


7 


11.74 


1817.. 


41 .0 


33 6 


11 .40 


1818. 


48.4 


41 





11. 81 


1819. . 


55-6 


48.2 


11 .62 


1829. 


23 27.2 
Sept. 18 


2 5 


6 


12.56 


1828.. 


23 18.2 
Sept. 18 


1 56.6 


12.25 


1890. 


15 26.7 


3 6 


3 


12.31 


1891*. 


15 34-0 


3 13-6 


11.48 


1892* 


44 5 


9 


9 


11. 61 


1893 


54- 1 


19 5 


"•59 


1894. 


16 1.7 


27 


1 


11.76 


1895- ■ 


16 9-3 


34-7 


1183 


1896. 


17.8 


43 


2 


12.16 


1897*. 


26.9 


52-3 


11.86 


1898* 


35 9 
1915 Mar. 17 


1 1 


3 


12 . 29 




1915 Mar. 17 






2338a 


22 38.9 


2 46 


9 


12.64 


2339a. 


I 22 47 .0 


2 55o 


11.86: 


b 


55-° 


3 3 





12.04 


b. 


23 i4 


3 9 4 


11 . 76 


2340a 


23 9-4 


3 


2 


11 79 


2341a. 


15-9 


9.7 


H-35 


b 


. 22.0 


15 


8 


11.65 


b. 


28.5 


22.3 


11.56: 


2342a 


34-9 


28 


7 


11.70 


2343«- 


41-3 


35- 1 


1154: 


b 


47-7 


41 


5 


12.00 


b. 


53-8 


47.6 


11 .67: 


2344a 


24 O.I 


53 


9 


12.18 










b 


.6.5 


1 10.3 


12. 20 











f The plates marked a and b each have two complete sets of exposures. 



.4 STUDY OF THE LIGHT-CURVE OF XX CYGXI 



153 



elements Kron designates as lid, which involve a least-squares 
correction to Blazko's values of the initial epoch and period but do 
not contain a secular term, the residuals are somewhat reduced. 
Although the observational data here given are not sufficient to 
justify a correction to Kron's elements, as far as they go, they argue 
against the existence of the secular term. 

TABLE IV 



Date 



Epoch 



Julian Day 



Predicted 
Hel. Max. 



Observed 
Hel. Max. 



Obs - 
Kron 1 1 



Obs. — Kron 
I la 



1914 



Aug. 21 
Aug. 23 
Sept. 18 
1915 Mar. 17 



28202 
28216 



29745 



2420366 
2420368 
2420394 

2420574 



20 h 48™5 
18 7.4 
15 34-6 
23 6.2 



18 24 
15 49: 

23 2I 



+ 8 
+ 17 

+ 14: 
+ 15 



+ 3 
+ 11 
+ 8: 
+ 8 



Two of the light-curves tabulated in Table III are shown in 
Figs. 1 and 2. In each case we have two simultaneous records, one 
based on blue light, the other on light of longer wave-lengths; but 
both are determinations of the same maximum, so that the differ- 
ences in shape, range, time of maximum, etc., which exceed the 
errors of observation, must be interpreted as differences of color. 
In shape there appears to be no great difference between the photo- 
graphic and photo- visual curves on the same night, although there 
is a marked difference between the curves of August 21 and those 
of August 23. This, however, will be discussed later. 

Within the errors of observation, the time of maximum is 
practically the same photographically and photo-visually. There 
is some indication, nevertheless, that the photographic maximum 
may come slightly later, as would be expected if there is an appre- 
ciable absorption of light in space. 1 It is in the amplitude, however, 
that we find the most marked difference, especially on August 21. 
On that date the photo-visual range is o . 72 mag. as against a photo- 
graphic range of 0.97 mag. This difference in color is normal for 
Cepheids. The second night, on the other hand, gives a photo- 
visual range of o . 10 mag. greater than the photographic. The mean 
photographic range for the two nights is 0.86 mag., the mean 

1 Kron finds the difference vanishingly small but, if anything, in the opposite 
sense; op. cit., p. 56. 



154 HARLOW SHAPLEY AND MARTHA BETZ SHAPLEY 



3 n o n 



ii. 6 



12.4 




Fig. 1. — Photo-visual (above) and photographic light-curves of XX Cygni for 
August 21, 1914. 



3" o" 



11. 6 




12.4 



Fig. 2. — Photo-visual (above) and photographic light-curves of XX Cygni for 
August 23, 1914. 



.4 STUDY OF THE LIGHT -CURVE OF XX CYGNI 



155 



photo-visual is 0.78 mag.; the mean visual range found by Kron 
from all observers is 0.76 mag. On March 17 the photographic 
range is o. 99 mag., but minimum light depends on only one normal 
point. Thus it appears from the data now available that the photo- 
visual range is not greater than the photographic, and is apparently 
somewhat smaller. 

The color and magnitude at minimum (as shown in Table V) 
are sensibly constant, suggesting that the irregularities occur at 
maximum and that the minimum is the normal condition of the 

TABLE V 
Color Data for XX Cygxi 





August 21, iyi4 


August 23, igi4 




Photog. 1 Photo-vis. r-„i„_ t„j„ 
Mag Mag. Color-Index 


Photog. 1 Photo-vis. r . T , 
Mag. Mag. Lolor-lnciex 


Minimum 

Maximum 


12.50 12.17 +°-33 mag. 
11.53 "-4S +0.08 


12.49 12.17 +0.32 mag. 
11.74 H.32 +O.42 


Range 


0.97 0.72 0.25 


0.75 0.S5 O.IO 



star. This is verified by the measures on the polar comparison 
Plates 1828 and 1829 which show a color-index at minimum of 
+0.31. The color-index at maximum, however, varies more than 
0.3 mag. 

In addition to the values tabulated above, others can be 
determined, but with less weight, from the two incomplete series 
of observations; for September 18 we find +0.15, and for March 
17, +0.30. The mean for four maxima is +0. 24, showing that in 
the mean and three times out of four the star is bluer at maximum 
than at minimum, and corroborating from other data the conclusion 
expressed above that the photographic range exceeds the photo- 
visual. The value of the color-index indicates an average spectrum 
more nearly of type F than of type A as classified at Harvard. 1 

In connection with the study of XX Cygni it was thought of in- 
terest to investigate the color of the surrounding stars. Fig. 3 shows 
all those within a distance of 11 minutes of arc from the variable, 

1 Harvard Annals, 56, 194, 191 2. 



156 HARLOW SHAPLEY AND MARTHA BETZ SHAPLEY 

brighter than magnitude 13.7 photo-visually — the limit of visibility 
on our plates. Table VI contains in the first column the adopted 
designation of the stars, in the second Kron's designation for such 
of them as he has named, and in the third Kron's visual magnitude 
(on an extension of the Potsdam scale). In the last three columns 




Fig. 3. — Field of XX Cygni, 2o h i™3, +58°4o' (1900), giving all stars brighter 
than magnitude 13 . 7 photo-visually, within n' of the variable. 



are the mean Mount Wilson photographic and photo-visual mag- 
nitudes, and the color-index derived from them. These magnitudes 
were determined from the eight polar comparison plates (Table I), 
which were taken in four pairs, each consisting of one isochromatic 
and one Seed 27 plate. Since in each case the plates compared 
were taken in quick succession, the color-indices are free from errors 



A STUDY OF THE LIGHT-CURVE OF XX CYGNI 



157 



due to possible light-variations in the stars themselves. On com- 
paring Kron's visual results with the Mount Wilson photo-visual 
magnitudes, we find that the two scales are parallel throughout this 
range of 2.3 magnitudes, and, correcting for the systematic differ- 
ence in zero-point of 0.12 mag., the average difference for the 12 
stars is ±0.05 mag. 

TABLE VI 

COLOR-IXDICES OF STARS NEAR XX CYGNI 



Star 



Kron 



Mount Wilson 



Designation ■■ Visual Mag. | Photog. Mag. 



Photo-vis. 
Mag. 



Color-Index 



10.56 
1 1 . 21 



II.94 

10.80 



IO. 20 
II .64 



9.72 



10 -33 



11.84 
11 54 



12.03 



2.56 
3 35 
2-35 
2.38 

1 . 21 



•14 
■70 
.36: 

2 1 

■76 
36 
■70 
.19 

■3i 
.76 

.46 



3-i* 



o. 76 
i-33 
3i5 

1 77 
2 . 23 
0.83 
0.27 
2.94 

039 
1 .80 

2 11 
983 
3.62 

1-37 
0.40 

2-99 
1.86 

1.76 

3- 2 9 
2.19 
2.58 



+0.34 mag 

+ 1.23 

+0. 20 

+0.58 

+0.15 

+0.38 

+0.94 

— o. 14 

+1.13 

+034 

— 0.07 

+0.53: 

+0.60 

+039 

+o.q6 
+0.71 

+ 1-33 
+Q-55 
+0.47 
+0.27 
+0.60 



The color-indices of these stars near XX Cygni were compared 
with those of North Polar stars within the same limits of photo- 
visual magnitude. 1 The results, given in Table VII, show that the 
average color-index of all the stars considered is less in the field of 
XX Cygni than near the Pole. Perhaps because the former is in 
the Milky Way we should expect to find these stars bluer. 

It was noted above that the light-curves of XX Cygni appeared 
to have an entirely different shape on August 21 and 23, 1914. Such 
a difference from night to night is found in a much more striking 
degree on investigating the observations published by Kron. The 

' .1//. Wilson Contr., Xo. 97; AstrophysiccU Journal, 41, 206, 1915. 



158 HARLOW SHAPLEY AND MARTHA BETZ SHAPLEY 

variations from the mean curve are certainly much larger than the 
errors of observation. Three pairs of curves are reproduced in 
Figs. 4, 5, and 6 to illustrate the extent of this irregularity of form. 
The first pair is taken from Guthnick's photometric measures, the 
second from Schwab's visual estimates, and the third from Kron's 
observations with the Potsdam photometer. These diagrams give 
examples of extreme types of maxima; all intermediate stages 
between them are found among the curves examined. Of the two 
Mount Wilson curves illustrated, that of August 21 is of the inter- 
mediate type, slightly narrower than the mean, while August 23 
shows a broad round-topped curve nearing the extreme of that type. 
In the light of these wide variations in the form of the curves, the 
observed differences in range and color on different nights are much 
more plausible. 

TABLE VII 

Comparison of the Color of Stars in the Field of XX Cygni with the 
Color of Stars at the North Pole 





North Pole 


Field of XX Cygni 


Limits of Mag. 


No. Stars 


Average 
Color-Index 


No. Stars 


Average 
Color- Index 


10. to 11 .0 

11. " 12.0 

12.0 " 13 .0 


7 

3 

14 

29 


+0.57 mag. 

+0.45 
+1.01 
+0.98 


6 
6 
6 
3 


+0.71 mag. 

+0.74 
+0.25 
+0.42 


13.0 " 14.0 




10.0 " 14.0 


53 


+0.90 


21 


+o.55 



An attempt was made to see if the change from one type of curve 
to another occurred at regular intervals, but from the observations 
published by Kron no periodicity could be established. It was 
noted, however, that there are no instances in which consecutive 
maxima showed a great difference in type (on account of the three- 
hour period of the star, it was on some nights observed throughout 
two or more successive periods). From one night to the next, on 
the other hand, there is often considerable change, and in the 
instances where observations are available for many successive 
nights, there is a rough indication of a periodicity of possibly a 
week. As all of these curves are reasonably smooth, only a part of 



.1 STUDY OF THE LIGHT-CURVE OF XX CYGNI 



J 59 



the difference can be attributed to errors of observation. All that 
can be said at present, however, is that the variation in the shape 
of the curve definitely exists, and that the change from one type 
to another appears to be gradual. The successive maxima of XX 
Cygni. then, are obviously not exact repetitions of the same phe- 
nomenon. Whether the minima, as well as the maxima, vary in 
shape, it is impossible definitely to say. for they have not been 
sufficiently observed; but the runs of residuals during those minima 
that have been observed indicate the existence of different types. 



n. 4 























*l~ 


M--K 

\ \ 
















13 k 


. \ 

\ * 








/ 

/ 

/ 










V-* 






1 

* 

1 

1 


/ 














/ 

















ii. 8 



Fig. 4. — Guthnick's visual light-curves of XX Cygni for September 22, and 
October 5 (broken line), 1908, showing two extreme types of maximum. 



To give still more evidence (if that is needed) for the reality of 
the different types of light-curve. Table VIII has been prepared to 
show that the many large residuals from the mean curves do not 
represent accidental errors. The deviations in each case are from 
the mean curve for that observer. If the variations from a mean 
are distributed according to the Gaussian law of error, there should 
be in the long run as many changes as persistences of sign. A 
glance at the table shows that here this is plainly not the case. 
These persistences of sign apparently verify from the measures of 



160 HARLOW SHAPLEY AND MARTHA BETZ SHAPLEY 



ii. 6 





3 h 




I 


h 










X--_ 

■ X 














J f 

/ / 

/ / 

// 


\ 


\ 

N 
\ 

\ 
\ 

\ 










/! 
h 




X 


\ 
\ 










©/ 
/ / 
/ / 

/ ; 
/ / 








\ 

\ 
\ 
\ 
\ 

X 








Ii 








•> 


\ 





Fig. 5. — Schwab's visual light-curves of XX Cygni for January 9 (broken line) 
and March 13, 1905. 



























\ / 


V* 


\ 








11. 6 




> 
/ 
/ 

/ 

/ 








\ 

V— - 


K 






^ 1 

1 Q 
1 1 

1 / 

1 d 


















i 1 















Fig. 6. — Kron's visual light-curves of XX Cygni for September 21 (broken line) 
and December 3, 1909. 



A STUDY OF THE LIGHT-CURVE OF XX CYGNI 



161 



each observer the existence of entirely different types of light- 
curve. They cannot be due to any appreciable extent to ordinary 
night error or to inconstancy of the light of comparison stars, as 
individual examination of each curve shows. 

TABLE vill 
Systematic Runs of Residuals from Mean Curves 



Observer 


Xo. Persistences 
of Sign 


Xo. Changes 
of Sign 


Ratio 


Blazko 


431 

33° 

42 

64 

157 

239 

105 

338 

13 


142 

123 

16 

37 
SO 
84 
69 
127 
9 


3° 

2.7 
2.6 

i-7 
3-i 

2.8 

i-5 

2-7 
1 .4 


Schwab 

Parkhurst and Jordan . 

Graff 

Luizet 

Guthnick 

Xijland 

Kron 






Total 


1719 


657 


2.6 



The conclusion must be that, whatever the cause, there is a 
short-period though possibly irregular change in the actual shape of 
the curve, and also probably a short-period oscillation in the time 
of maximum, though the mean period remains sensibly constant. 



SUMMARY 

i. To test the supposition that its visual range exceeds the 
photographic, and to investigate the general question of regularity 
in Cepheid variation, a study has been made at Mount Wilson of 
the light-curve of XX Cygni, the variable with the shortest known 
period. More than 300 exposures were made for this purpose with 
the 60-inch reflector. 

2. It is found that, in agreement with all results for other 
Cepheids, the visual range does not exceed the photographic, though 
from the data now at hand we cannot say definitely that the photo- 
graphic range is greatly in excess (Table V). 

3. The stars in the field of XX Cygni within eleven minutes of 
arc of the variable yield an average color-index considerably less 
than that of North Polar stars of the same magnitudes. 



162 HARLOW SHAPLEY AND MARTHA BETZ SHAPLEY 

4. Though a short-period oscillation in the time of maximum is 
suspected, the mean period of XX Cygni is sensibly constant. The 
secular term in Kron's elements is perhaps unnecessary; at least 
the light-elements which contain no secular term predict times of 
maximum in better accordance with the Mount Wilson observations 
in 1914 and 1915. 

5. An examination of observations made by many observers and 
published by Kron shows definitely the existence of several types of 
maximum (Figs. 4, 5, and 6). The Mount Wilson observations 
confirm this (Figs. 1 and 2). 

6. The maxima of XX Cygni, therefore, are not exact repetitions 
of the same phenomenon, but rather disturbances in the star's 
brightness occurring at regular intervals but varying in character. 

Mount Wilson Solar Observatory 
April 2, 19 1 5 



THE ELECTRIC SPARK 

By W. O. SAWTELLE 

PART I. THE CONTROL OF THE SPARK DISCHARGE IX AN 
OSCILLATORY CIRCUIT 

The work on the control of the spark discharge is preliminary 
to a spectroscopic study of the electric spark. The plan is to 
reflect the image of the spark from a rotating mirror upon the slit 
of a spectroscope and to analyze the spectrum as it changes with 
the time during the oscillations. But since a single discharge does 
not give light enough for the purpose, it is necessary to superpose a 
succession of spark images upon the slit of the spectroscope with 
such accuracy that any particular phase of the oscillation may be 
brought upon the slit. Oscillations of a period of the order of a 
millionth of a second are used and the preliminary investigation is 
directed to the matter of the control or the "triggering'' of the 
spark discharge. This problem of control of the spark has been 
attacked by several investigators, but the conditions imposed have 
been severe and success in a limited sense only has resulted. 

Feddersen. 1 in his work on the electric spark, made contact in 
the oscillatory circuit by means of an arm attached to the axis of 
the rotating mirror, and with this device tried to make the dis- 
charges pass when the mirror was in the position to reflect the 
image of the spark upon a ground-glass plate properly placed to 
receive it. Later investigators, in their attempts to control the 
spark discharge, have employed other methods which depended 
upon some mechanical arrangement of commutators involving 
rotating arms, 2 revolving knife-edges, 3 or clockwork. 4 Although, by 
these agencies, the spark images fell upon the photographic plate, 
it was impossible to control the time variation between discharges 
anv closer than a few thousandths of a second. This slight control. 



y. Ami., 116, 132, 1862. 

2 Trowbridge and Sabine, Phil. Mag., 30, 323, 1890. 

3 Trowbridge, Proc. Am. Acad., 27, 115. 1891. 

4 Batelli and Magri, Phil. Mag. (6), 5, 1, 1903. 

163 



1 64 W. 0. SAW TELLE 

however, served the purposes required of it, such as a determination 
of the period of the spark discharge or the verification of Thomson's 
formula. 

For spectroscopic work, however, it is another matter, and such 
a degree of accuracy must be realized, if the rotating-mirror method 
is to be used, to permit of a time variation between successive spark 
discharges, not greater than the period of the oscillation whose 
spectrum is under investigation. This difficulty led Schuster 
and Hemsalech, 1 in their work on the spectrum of the electric 
spark, to abandon the rotating-mirror method because of the 
difficulties which it was impossible to eliminate at the time, although 
repeated efforts were made by Schuster to do so. To quote from 
his paper: "They [the attempts] failed because the method requires 
that the spark should pass when the mirror is in the same position, 
and no satisfactory device could be found to secure this object, 
without at the same time complicating the spark circuit, which it 
is necessary to confine as much as possible to the electrostatic 
capacity and spark-gap." 

CONTROL OF THE SPARK DISCHARGE 

The control of the spark discharge is obtained by means of a 
beam of ultra-violet light reflected from a rotating mirror, upon the 
negative terminal of a spark-gap in series with the principal gap, 
the radiations from which are to be spectroscopically studied. 
Ionization is thus effected, which added to that produced by the 
electric field is sufficient to cause the spark to pass, provided that 
the potential of the charging device is sufficiently high; that is to 
say, when the potential is building up between the terminals' of the 
gap, the. ultra-violet light, ionizing the air in the gap, "triggers" 
the discharge at the desired instant. 

No complication of the discharge circuit results in introducing 
such a "triggering" device, since the second gap in series with the 
first or principal gap is equivalent to an increase of length of the 
spark in the oscillatory circuit. The method possesses none of the 
disadvantages of the arrangements to which reference has been 
made, for it allows of no uncertainty of approach of the optical 

1 Schuster and Hemsalech, Phil. Trans.. 193 A, 189, 1899. 



THE ELECTRIC SPARK 165 

trigger lever, introduces no complications in the spark circuit, pre- 
vents the jumping of different distances with different charging, 
eliminates the uncertainty of rubbing contacts, and permits of any 
length of lever arm. Since the beam of light is reflected from the 
rotating mirror, a double velocity may be acquired without the 
danger and the mechanical uncertainty which accompanies all forms 
of rotating arms or knife-edges. 

DESCRIPTION* OF APPARATUS 

Rotating system. — The rotating system comprised two concave 
mirrors attached to the same shaft, driven by an electric motor 
and rotated about a horizontal axis. These mirrors were both of 
the same dimensions, radius of curvature 122 cm and diameter 
6.2 cm, of glass with front surface silvered. They were mounted 
in a frame made of composition casting 31X14 cm and 2 cm thick; 
one end of the frame was supported by a bearing and the other was 
rigidly attached to the shaft of a no-volt, one-half horse-power 
induction motor which made 35 revolutions per second. The 
whole arrangement was secured to a heavy cast-iron base 
(Plate II, a). 

Oscillatory circuit. — Two spark-gaps between pointed metallic 
terminals in air. in series with an inductance of 3.3X10 -5 henries 
(afterward increased to 8. 2Xio~ 5 henries) and a capacity of 0.012 
microfarads, constituted the oscillatory circuit. The leads were 
made of heavy copper tubing, and precautions were taken to 
eliminate leakage. It was found that good results could be expected 
only when the whole circuit was carefully paraffined. The con- 
denser was built up of thin aluminium plates (15X20 cm) between 
sheets of especially selected window glass, all immersed in cold 
pressed castor oil. The current was supplied to the circuit by a 
large storage battery 1 which could yield potentials up to 40,000 
volts, but it was found that a potential of 20.000 volts was sufficient 
for the work. It is not necessary to confine one's self to a battery 
only, for with proper precautions a static machine may be used as 
a source of current. 

"For a detailed description of this battery see: Memoirs Am. Acad., 13, Xo. 5, 
p. 185; John Trowbridge, High Electromotive Force. 



i66 



W. 0. SAWTELLE 



Source of ultra-violet light. — The ultra-violet light was furnished 
by an iron-magnesium arc in air. The terminals were water-cooled 
and the distance between them was about 0.5 mm. This arc, 
which required only a few amperes at 500 volts, gave a very steady, 
well-defined spot of light, rich in ultra-violet. Investigation has 
shown, however, that a carbon arc with proper arrangement of slit 
may be substituted if a 500-volt circuit is not available, and good 
results obtained. 




Fig. 1 

Arrangement of the apparatus. — The two spark-gaps may best 
be designated as the "working'' spark-gap (A) and the "trigger" 
spark-gap (D), which with the inductance (L) and the capacity (K) 
formed the oscillatory circuit. Early in the work the current was 
supplied to this circuit by a static machine with inclosed plates (G). 
This machine was later discarded because of faulty mechanical 
construction, and the storage battery substituted. The mirrors 
corresponding to the spark-gaps may be designated as the "work- 
ing'' mirror (B) and the "trigger" mirror (E). 

The working spark at the focus of the working mirror was 
inclosed in a light-tight box and formed part of an optical system 
with the working mirror (B) and the photographic plate (C). 
Similarly the trigger spark, at the focus of the trigger mirror, 
formed part of an optical system with the trigger mirror (D) and 
the iron-magnesium arc (F). A schematic drawing of the arrange- 
ment is shown in Fig. 1. The spark-gaps were so protected that 



THE ELECTRIC SPARK 



167 



both sides of the photographic plate might be uncovered and the 
oscillations seen through the emulsion. The final arrangement 
without partitions, mirror box, and motor is shown in Fig. 2. 

The two spark-gaps were so adjusted with reference to the mir- 
rors, arc, and photographic plate that when the ultra-violet light. 





Fig. 2 



after reflection from the trigger mirror, fell on the tip of the initially 
negative terminal of the trigger spark-gap, the reflected light from 
the working spark must strike a certain predetermined spot on the 
photographic plate. Since the two mirrors were mounted in the 
same rigid frame, their relative positions are not changed upon 
rotation, and variations in rotational speed can produce no appreci- 
able effect upon the triggering action of the ultra-violet light. 
Moving the plate by hand after a spark had been recorded brought 
an unexposed portion into position, and upon continuing this 
process until all of the emulsion had been utilized, a series of several 



1 68 W. 0. SAWTELLE 

spark images was obtained. Any deviation of the pilot sparks from 
the horizontal gives a direct measure of the difference in time 
between successive spark discharges. Since the working mirror has 
a radius of curvature of 1220 mm and was rotated 35 times per 
second, the linear distance traveled by the spark image in one 
second was about 500,000 mm. A millimeter's distance, therefore, 
on the photographic plate, measured in the direction in which the 
spark image was resolved, corresponds to about 2X10 -6 seconds. 

Different metals were used as electrodes in the working spark- 
gap ; the period of the circuit was altered by varying the inductance, 
but in every instance the photographs obtained indicate a remark- 
able control of the spark discharge (Plate III). That this control 
may be realized, several important factors must be considered: the 
source of potential must be constant; leaks in the oscillatory circuit 
must be avoided; the terminals of the trigger spark-gap should be 
of copper, conical in shape, and turned to a point; the ultra-violet 
light should emanate from a point source and must be carefully 
focused upon the very tip end of the initially negative terminal of 
the trigger spark-gap; the optical surface of the trigger mirror 
must be figured with great care. It is not necessary to pay any 
special attention to the terminals of the trigger gap after they have 
once been carefully adjusted. 

The reproduced photograph, with a line thread stretched 
across the printing frame to serve as a horizontal co-ordinate, shows 
that if there exists a variation in the time interval between the spark 
discharges in the oscillatory circuit, as they are controlled by the 
ultra-violet light, it lies beyond the limits of my apparatus to 
show it. 

It may then be stated, since a variation of a tenth of a millimeter 
could be detected on the negative, that this new effect of the ultra- 
violet in its action on the control of the spark discharge permits of a 
time variation between successive discharges of less than 2X10" 7 
seconds. 

The terminals of the arc light were separated by a distance of 
less than half a millimeter and the image of the arc as it fell upon 
the terminal of the trigger spark-gap, after reflection from the trigger 
mirror, was sharp and well defined. Consequently the terminal 



THE ELECTRIC SPARK 169 

remains illuminated for an extremely short time, less than one- 
millionth of a second. This time interval is sufficiently long, 
however, to produce ionization and to regulate the electric field 
with a precision heretofore unsuspected. 

PART II. THE SPECTRUM OF THE LIGHT FROM THE 
OSCILLATORY SPARK 

It has been demonstrated that the ultra-violet control of the 
oscillatory spark discharge is sufficiently sensitive to cause the 
resolved images of the spark to fall within at least a tenth of a milli- 
meter of the same position in space. With a slight modification 
of my apparatus it becomes possible to subject the light from the 
oscillatory spark to a spectroscopic study and at the same time to 
place a time co-ordinate upon the spectrogram. Quantitative 
measurements on the mechanism of the spark then become a matter 
of comparative ease, for a study of the spectrograms shows con- 
clusively the time of appearance and decay of any particular 
radiation as well as its oscillatory or non-oscillatory character. 

It is only necessary to mount the spectrograph with the slit 
vertical and in the focal plane of the rotating mirror; that is, to 
replace the photographic plate as used in the preliminary work. 
Other investigators have first formed the spectrum and then allowed 
it to fall upon a film attached to the periphery of a wheel which 
could be rapidly rotated, 1 or upon a rotating mirror so placed that 
if the mirror chanced to be in the proper position when the spark 
discharge took place, the image would be projected upon the lens of a 
camera. By means of this latter device C. C. Schenck 2 was enabled 
to observe on a ground-glass plate what I have succeeded in photo- 
graphing. 

A prism spectrograph, of ordinary form, designed especially for 
the photography of spectra from very weak sources of light, was 
mounted in such a way that the instrument as a whole could be 
rotated about the geometric axis of the rotating mirrors, while a 
horizontal adjustment permitted the slit, which was vertical, to be 
placed on either terminal of the spark-gap, or in any intermediate 

1 Schuster and Hemsalech, Phil. Trans., 193 A, 189, 1899. 
- Astro physical Journal, 14, 116, 1901. 



170 W. 0. SAWTELLE 

position between the terminals. In this manner any portion of the 
oscillatory spark may be studied at will, while the slit, because of 
the arrangement, remains in the focal plane of the working mirror. 
Since the dispersion of the prism is small and the cone of light 
large, there is very little depth of focus with a noticeable curvature 
of the field. 

Proceeding as in the preliminary work on the triggering effect, 
it was found that the superposition of about one hundred spark 
images gave a good spectrogram, but there is of course no limit to the 
number of images that may be made to superpose upon the slit, all 
falling within a tenth of a millimeter of each other. 

The first metal investigated was cadmium, and with the slit 
upon the initially negative terminal of a spark-gap 8 mm in length, 
then in the middle of the gap, and finally on the initially positive 
terminal, the following results were obtained. On the initially 
negative terminal the lines of wave-length X5379 and X5338, which 
appear as one line because of the small dispersion, are seen to 
oscillate. They are followed in an extremely short time by the 
lines X4800 and X4878 and then in about 3X10 -6 seconds the line 
X5059 appears. These three lines are continuous with respect to 
the time and they persist after the oscillations die out. 

With the slit placed in the middle of the gap a spectrogram of 
different character was obtained. The oscillations no longer exist 
and the line X 5059 radiates strongly, while the lines XX 4800 and 
4676 appear brighter than they did in the region near the terminals 
(Plate II, b, 1, 2, and 3; the horizontal lines appearing midway and 
near the bottom of the photographs are due to fine wires placed for 
reference across the slit). 

These three lines XX 4800, 4676, and 5059, continuous with 
respect to the time, persisting after the oscillations die out, brighter 
in the middle of the gap than near the terminals, and appearing 
in a measurable time after the passage of the initial discharge, are 
due to glowing metallic vapor. They are the cause, in the case of 
cadmium, of the luminosity which persists long after the oscillations 
cease. Schenck pointed out that this luminosity is probably due to 
metallic vapor, but by the methods which he employed he was 
unable to indicate this fact photographically. 



THE ELECTRIC SPARK 171 

This investigation was begun at the Jefferson Physical Labora- 
tory of Harvard University, and I wish to express my thanks to 
Director Theodore Lyman for generously placing at my disposal 
the facilities of the laboratory. President Sharpless has made it 
possible for me to continue the work at Haverford. To the Ameri- 
can Academy of Arts and Sciences I am deeply indebted for a 
liberal grant from the Rumford Fund. The problem of the spark 
discharge is still under investigation, and these papers are but a 
preliminary report. 

. Haverford College 
June 19 1 5 



THE RADIAL VELOCITIES OF FIVE HUNDRED STARS 1 

By WALTER S. ADAMS 

The program of radial velocity work for the Cassegrain spectro- 
graph during the past few years has consisted for the most part of 
observations on the following classes of stars: 

i. A- and B-type stars, mainly between magnitudes 5 and 6.5, 
a knowledge of whose motions is of particular interest as aiding in 
the determination of the elements of the two principal star-streams. 

2. A, F, G, K, and M stars of magnitudes 5 . 5 to 6 . 5 which have 
very small astronomical proper motions. These may in general be' 
considered as very distant stars of high luminosity, and are of 
interest as regards both their radial velocities and certain character- 
istics of their spectra. 

3. Stars with measured parallaxes, most of which have very 
large proper motions. The magnitudes of these stars are chiefly 
between 5 . 5 and 8.5.-' 

In addition to these lists a number of brighter stars have been 
observed, for which determinations of radial velocity have been 
published from other observatories. 

It seems desirable to make the results so far obtained available 
for the use of astronomers who are engaged in the discussion of 
stellar motions, and accordingly values are given in this communi- 
cation for five hundred stars for which, with a few exceptions, three 
or more observations have been secured. Many other stars have 
been observed once or twice, and results for these will be published 
as soon as additional material, has been obtained. 

Several different optical combinations have been employed in 
the spectrograph during the course of these observations. The 
principal consideration which governs the dispersion to be used is, 
of course, the character of the spectrum of the star, but this has 
been modified in many cases by other factors. For example, the 

1 Contributions from the Mount Wilson Solar Observatory, No. 105. 

2 The radial velocities of 100 of these stars were published in Ml. Wilson Conlr., 
No. 79; Astrophysical Journal, 39, 341, 1914. 



RADIAL VELOCITIES OF FIVE HUNDRED STARS 173 

spectra of the small proper-motion stars have in almost all cases 
been photographed with low dispersion, although most of them are 
of the solar type, and so are well adapted for the use of high dis- 
persion. It seemed desirable in their case to sacrifice accuracy to 
some extent in order to secure statistical material more rapidly, 
and to make it possible to institute direct comparisons between 
their spectra and those of the fainter stars of large proper motion 
and measured parallax. The different combinations used in the 
spectrograph may be summarized as follows. The linear scale 
denotes the number of Angstrom units per millimeter. The 18-cm 
camera has been used in the case of only three of the published 
results. 

TABLE I 



No. Prisms Camera 



Linear Scale at Hy 



Stars Observed 



2 38 and 46 cm 

102 
46 



21 and 18 A \ 
16 

92 



A, B, and brighter parallax stars 

Small p.m. and parallax stars 
Parallax stars fainter than 8 . s 



Table II contains values for the individual stars. In view of 
the importance of the Preliminary General Catalogue of Boss for 
determinations of proper motion it has seemed preferable to desig- 
nate the stars which occur in his catalogue by their numbers rather 
than to give a heterogeneous collection of names and catalogue 
numbers. The stars with measured parallaxes have the designa- 
tions given in Groningen Publication, No. 24. Additional stars are 
indicated by the Lalande number so far as possible, the B.D. num- 
ber being used only in a very few cases. The magnitudes are those 
of Harvard, with the exception of such as are given in parentheses, 
which are from miscellaneous sources. 

The spectral classification has been made from the Mount Wilson 
negatives, and most of the determinations, particularly for the A 
and B stars, are due to Air. Kohlschiitter. Especial attention 
should be called to the M stars which are marked ''peculiar." The 
peculiarity in nearly all cases consists in the combination of hydro- 
gen lines of an intensity corresponding to that in G- and K-type 
stars with the bands of the Al stars. Some of these stars, classified 



174 WALTER S. ADAMS 

according to the intensity of their hydrogen lines, have been dis- 
cussed by Adams and Kohlschutter in a previous communication. 1 
The total proper motion /j. is in most cases derived from the 
values given by Boss. For the parallax stars it is taken from 
Groningen Publication, No. 24. The angle X is the angle between 
the star and the sun's apex. The co-ordinates used for the apex- 
are those adopted by Kapteyn. 

a =i7 h 59 m > s =+3°- 8 > 

and the values both for /j. and X are taken from a list calculated 
under his direction for all of the stars given in Boss's catalogue. 

The first of the two columns in Table II denoted by v contains 
the means of the observed radial velocities; the second the corre- 
sponding values published by other observatories. The following 
abbreviations are used: A, Allegheny Observatory; L, Lick 
Observatory; Y, Yerkes Observatory. 

The final column of the table contains the values of v corrected 
for the solar motion. The values are given by the equation 

v' = v-\-V cos A 

in which the value 20 km has been assumed for V, the sun's motion 
in space. 

1 .1//. Wilson Coulr.. Xo. 89; Astrophysicql Journal, 40, 385, 1914. 



RADIAL VELOCITIES OF FIVE HUNDRED STARS 175 

TABLE II 



Star 



6 1900 



Mag. 



Spec. 



Boss 5 

18 
41 
43 
56 
81 
90 
118 
124 

125 
Pi. o h i30 
Boss 131 

54 Piscium 
Boss 138 

Lai. 1 198 
Bos 



Groom. 
Boss 



165 
169 

145 
183 
198 
209 
210 



Groom. 211 
Boss 223 



Lai. 
Boss 



Lai. 
Boss 



Lai. 
Boss 



224 
1799 
252 
261 
263 
267 



295 
2450 
3°5 
349 
355 
3022 

375 
379 

107 Piscium. 

Boss 410 

414 
420 
43° 

432 
434 
457 
466 

472 

478 

Lai. 3922 

Boss 488 

493 



1 16 
1 17 
1 30 
1 3i 
1 33 
1 36 
1 36 

1 37 
1 44 

1 45 
1 47 
1 50 



1 57 



+6 3 °38' 

+ 10 35 
+ 60 59 
+38 8 
+ 7 38 

+ 17 20 

- 4 31 
+ 53 37 
+ 14 41 
+34 51 
-25 19 
+48 48 
+ 20 43 
+38 55 
+ 1 IS 
-f 6 12 

- 22 16 
+69 54 
+ 5o 58 
+ 26 40 
+ 28 27 
+ 13 9 
+ 5 57 
+44 55 
+40 48 
+31 16 
+ 4 3i 
+ 5 7 
+ 19 7 
+63 40 
+ 1 55 
+ 15 36 
+ 35 
+ 18 10 

- o 58 
+ 72 32 
+57 28 
+ 27 36 
+ 29 32 
+ 34 44 
+ 19 47 
+ 21 47 

+ 10 33 
+40 14 
+36 47 
+36 46 
+ 23 5 
+63 54 
+32 48 
+ 17 46 
+ 57 57 

- 1 5 
+ 57 10 
+ 25 28 



G2 
A 2 
Ko 
Mbp 
K 5 
B 7 
B3 
Go 

G 5 

Ki 
Ki 
G6 
K 4 
G6 
Ai 
Ko 
F 5 
ai 

Kop 
G 4 

Map 
G 4 
A6 
B 9 
K6 
A4 
F3 
B 9 
Ki 
B2p 
A 2 
Go 
Ko 
G 5 
G 7 
G 7 
G 4 
B 9 
G8 
G 9 
F2 
Ki 
Ki 
Ko 
G8 
B8 
A 1 
K2 
A 4 
Go 
B8 
K 4 



.009 

• 034 

.002 

•052 

■015 

.117 

.011 

.021 

.028 

.019 

■36 

.019 

•59 
.007 

■63 

.016 

.036 

■44 

.128 

.006 



63° 
86 

65 
74 



70 

89 

79 

109 

73 
87 
78 

100 
96 

no 
65 
73 
86 



0.022 


95 


0.023 


99 


0.105 


78 


0.024 


80 


0.039 


85 


0.48 


100 


0.326 


IOI 


0.004 


94 


0.038 


69 


0.004 


103 


0.028 


96 


0.056 


104 


°-57 


96 


0.017 


107 


0.008 


67 


0.004 


76 


0.50 


94 


0.013 


93 


oo53 


90 


0.72 


99 


0.018 


99 


0.074 


106 


0.009 


88- 


0.005 


9 1 


0. 180 


91 


O.OII 


100 


O.CII 


74 


0.023 


94 


0.024 


104 


0.009 


78 


0.51 


117 


0.013 


79 


O.OII 


IOI 



- 6.8 

+ 13-5 

- 4.1 
+ 0.1 
+ 16.4 
+ 6.8 
+ 5-2 
4- 2.8 
-18.3 

- 0.7 
+ 15-5 

- 9-3 
-33-9 

- 8.6 
+ 6.9 
+ 14.8 
+ 19. 1 
-28.0 
+ 1.8 

- 8.8 
0.0 

+ 15.7 
-14-5 
-71. 1 

+ 3-3 
+ 9-7 
+ 20. 2 
+ 6.6 

- 8.5 

- 6.2 

- 2.1 
-16. 1 
+ 4-6 

o 
+ 14-9 

- 6-7 

- 7-6 
+ 57-Q 

+ 5-7 
+ 0.2 
-34-2 

+ 3-3 
+ 10.6 

- 6.4 

+ 7-Q 
+ 59-Q 
+ 14. 1 

- 20. 7 

+ i.S 
+ 10.4 
-36.8 
-40.7 
-36.8 
-18.3 



+ 6.2L 



+ i8:L 



+ 2.3 
+ 14-9 
+ 4-4 
+ 5-6 
+ 16.7 
+ 8.2 
+ 2.4 
+ 9-6 
-18.0 

+ 3-i 

+ 9° 

- 3-5 
-32.9 

- 4-4 
+ 3-4 
+ 12.7 
+ 12.3 

- 19.6 
+ 7-6 

- 7 4 
+ 1.4 
+ 14.0 
-17.6 
-66.9 
+ 6.8 
-j-11. 4 
+ 16.7 

- 3-8 

- 9.9 
+ 1.0 

- 6.6 
-18.2 

- 0.2 

- 2 
+ 91 
+ 1.1 
+ 2.8 
+ 55 6 

+ 4-7 

+ 0.2 

-37-3 

+ 0.2 

+ 5i 

- 5-7 
+ 6.7 
+58.7 
+ 10.7 
-15-2 
+ 0.1 
+ 5-6 
-32.6 
-49-8 
-33-0 



176 



WALTER S. ADAMS 
TABLE II— Continued 



Star 



& 1900 



Mag. 



Spec. 



W.B. 

Boss 



W.B. 
Boss 



B.D. 

Boss 



Boss 498 
508 
521 
526 
529 
536 
539 
55i 
572 
58i 
616 
619 
648 
654 
660 
666 
674N 
674 S 
677 

2 h 927 

707 
719 
724 

3 b ™3 

742 
757 
767 
768 
790 

79i 
800 
801 
802 
817 
832 
W.B. 3 h 6i7 
Boss 838 
845 



23 535 



933 
956 
960 

977 
989 

997 

1014 
1024 
1039 
1064 
1069 
1084 



2 h 6™6 

2 10. o 

2 12.6 

2 13.2 

2 14. 2 

2 16.6 

2 16.8 

2 21 . 1 

2 26.3 

2 29.5 

2 37-1 

2 37.6 

2 46.0 

2 47-4 

2 50.2 
251.6 

2 53-5 

2 53-5 

2 53-7 

2 55 



.6 

6-3 
8.1 
9-4 
"■5 
14-7 
16. 1 
16. 2 
22. 2 
22.4 
24.9 
24.9 

25- 1 
29.4 

34-5 
35-3 
35-8 
38.0 
38.8 
41.4 
48.6 
48.8 

58.4 
4.8 

5-5 
9 .6 

11. 4 
13 -5 
16.5 
18.7 
21.3 
27.0 
28.8 
32.1 



+66 c 
+32 
+ 19 
+ 28 
+46 
+40 

- o 

- 12 
+ 1 
+36 
+ 10 
+43 
+ 14 
+37 
+ 17 

- 4 
+ 20 
+ 20 

- 3 
+ 5 

- 6 
+ 26 
+ 56 
+ 8 
+49 
+42 
+48 
+ 27 
+49 
+ 55 
-13 
+ 11 
+47 
+ 47 
+ 59 

- 3 
+47 
+ 36 

- 10 

+ 23 
+62 

+47 
+ 23 
-16 

- 7 
+80 
+ 20 
+ 20 
+ 20 

- 3 
+ 22 

+64 

+ 5 
+ o 



3 
54 
26 
11 
5i 
57 

4 
44 
49 
52 
19 
52 
40 
56 
56 

7 
561 
56/ 
11 
36 
29 
53 
46 

37 
5i 
58 
5i 
15 



F 4 
Ao 
B 9 
A 2 

B 7 
Fo 

Map 
B8 
K 4 
Ko 

Ajp 
F 9 
B5 
F2 
Mc 
B 9 
A3 
A3 
A 2 
G8 

Map 
Ao 
A 2 
Ko 

B 3 
A 1 

B 4 
G8 

B 5 
B 9 p 

A 1 
B8p 

B 9 
B 7P 

G8 

F 5 

B 5 

A 2 

A3 
F 3 
B 9 

B 5 

F8p 

B5 

G6 

G 7 
A3 
B9 
G 9 
Ao 

B 5 
A 2 
A 2 
B 5 



0.003 
0035 
0.015 
0.012 
0.005 
0.128 
0.006 
0.027 
0.013 

O.OIO 

0.040 
0.004 

0.045 

o. 10 
0.018 

0.054 

0.017 
0.017 
0.070 

0.68 

0.002 
0.019 
0.004 
0.62 

0.045 
0.058 
0035 

0.020 
0.044 

0033 

0.017 
0.021 
0.040 
0.044 
0.002 

0.78 

0.046 

0055 

0.020 



0.005 
0.039 

0.022 

0.013 

O.OIO 

0.020 
0.066 
0.063 

O.OII 

0.072 
0.019 
0.029 
0.028 
0.018 



73 

96 

106 

100 

88 

92 

119 

127 

120 

96 

"7 

92 

115 

98 

113 

128 

112 

112 

128 

123 

132 

109 

85 

* 2 3 

9i 

97 

92 

no 

93 

88 

140 

124 

94 

94 

84 

137 

96 

i°5 
142 
116 

83 

96 

118 

151 
144 

67 
I2 3 
122 
123 
144 
121 

83 
138 
142 



— 12.6 

- 3-2 



35- 

23- 



+ 

+ o 

+ 46 

+ I 



- 4 
+ 66 

+ 17 
+ 12 



o 
14.9 



14-7 

19.8 

2.9 

0.7 

9.9 

+ II3-7 

0.7 

21.8 

16. 2 

i°-5 

4 

9.9 
18.3 
13-3 



+ 



+ 



8.6 
15.8 
+ 138 

- 8.5 

- 0.3 
+ 10.5 

- 15-7 

- 7-2 
+ 22.6 



-4- 2.0L 



+ 6.0L 



+ 5:L 



+ 16. 8L 



RADIAL VELOCITIES OF FIVE HUNDRED STARS 
TABLE U— Continued 



177 



Star 



a 1 900 



& 1900 Mag. 



Spec. 



Boss 



B.D. 35 
Boss 



W.B. 4 h : 
Boss 



Groom. 
Boss 
Pi. ; 
Boss 
Lai. 1 
Boss 



088 
089 

o93 
097 

103 
128 
136 
146 
163 
'930 
165 
176 
182 

183 
189 

195 
221 

234 

268 
281 
295 
3°9 
310 
318 
332 
334 
348 
354 
990 
380 
'146 

394 
.797 
424 
441 
444 
453 
479 
513 
514 
523 
560 
568 
'572 
[ 573 
[ 575 

1578 
1599 
[608 
[627 
[632 
[643 



5 7 



- 2-40' 



+ 15 3" 

+ 48 6 
+ 12 o 
+43 10 
+ 63 20 
+ 15 44 
+42 25 
+ 10 o 
+36 1 
+ U 53 
+ 53 o 
+ 39 15 
+39 3° 

- 5 52 
+ 58 5° 
+ 19 44 
+ !5 55 
+ 5 2 
+33 5i 

- 21 20 

- o 15 
+62 59 
+30 7 
+ 15 47 
+ 3 13 
+ 74 59 
+ 54 22 
+ 23 58 
+ 5i 23 
+65 39 
+ 53 26 
+61 26 
+37 15 
+ 17 4i 
+ 9 5° 
+ 27 56 
+ 55 4i 
+45 56 
+ 5 26 
+ 4 10 

- 4 11 
+ 61 33 
+ 16 10 
+ 12 35 
+ 24 o 
+ 59 3 

+ 23 46 

- 2 54 
+ 58 28 
+58 14 

+46 45 

+ 78 5 



A S 
A 2 
Ao 
B 9 
Ao 
Ma 
Ko 
A 1 
B 9 
B3 
B 9 
K 3 
Fi 

K 5 
K 9 
B3P 
G 3 
K6 
Ki 
A 4 
Ao 

B 3 

Kip 
B 9 
B8 
B3 
K 5 
K2 

B3 

Ko 

K 3 
Ko 

G 5 
K2 

Fo 
G 4 
G8 
A 2 
Mbp 
G 4 
G3 
B6p 
Map 
B 9 
B 9 
G 4 
A 1 

B6 
Ma 
K 3 
G 7 

K 3 

K6 



0*067 
0.074 
0.052 

0.027 
0.067 

o. Ill 
0.017 
0.013 
0145 

0.025 
0.012 



146° 
129 
99 
133 
104 

85 
130 
i°5 
136 
in 

131 

95 



0.015 

0.005 

0.019 

0.031 

0.009 

0.019 

0.007 

0.032 

0.56 

0.024 

°-55 
0.002 
o. 72 

O.OIO 

0.014 
0.009 
0.014 

O.OII 

0.007 
O.OI2 
0.007 
0.005 

0.021 
0.017 
0.029 
0.022 

0.014 
o. 276 

O.OII 

033 

0.007 
0.019 



013 

OIO 


109 

10S 


25 

007 


151 

89 


018 


127 


004 


131 


017 


142 


016 


114 


020 


166 



86 
118 
132 
145 

74 

95 
125 

98 

83 
96 

88 
112 
131 
139 
121 

93 
i°3 
144 
144 

153 

87 
T-33 
136 

125 
90 



125 

152 
9i 
9i 

i°3 
7i 



+ 18 

+ 23 
+ 22 
+ 18 
+ 5 
-35 
+ i3 

— 2 

+ 17 

— n 

+ 9 

— 1 

+ 5 
-23 
+ 20. 

-13 

+ 6 

— 7 

— 7 

— 6 
+ 29 

+ 22 

— 1 

+ 13 
+ 13 
+ 21 

— 2 
+ 1 
+ 23 

-43 
-18 

+ 1 

— 3 
-3° 
+ 6 
+43 
+ 8 
-15 
+ o 
+ 20 
+32 
+ 16 

+ 13 
+ 29 



— 20. 

— 2. 

+ 11. 
+48 

— 4 
+35 
-46 

-13 



1 +3i:L 



2 +31 oL 



8.0 
.6 
.6 
.6 
•5 
•4 
. 2 
8 
.6 

■7 
. 1 

•4 
.6 

■ 7 
. 1 
.6 
9 
•4 
■7- 
. 1 

•9 
■5 
.6 



-13.6L 
+ 1.3L 



-3L, 



+ 1.6 
+ 10.4 
+ 19-7 
+ 4-5 
+ 0.8 
-33-8 
+ 0.6 

- 7-6 
+ 2.9 
-18 

- 4 

- 3 5 

- 0.8 



-6Y 



■9 



- 29.6 
+ 2.6 

- 12.9 

- 6.0 

- 20. 1 
-22.8 
-14. 1 
+ 9-8 
+ 5-4 
-16.6 
+ 4-2 
+ 0.2 

+ 5-2 

+ 3° 

- 0.3 
+ 11. 7 
-46.6 

- 16.2 

- 0.4 

- 2.4 
-37-9 

- 6.5 
+ 28.6 

- 2.2 
-16.6 

- 3-6 
+ 4-2 
+ 16.5 

- i-7 
+ H-9 
+ 15-9 

- 1.8 

-31-9 

- 2.2 

+ 0.1 
+30.6 

- 4-9 
+35-4 
-51-3 

- 7-4 



i 7 8 



WALTER S. ADAMS 
TABLE II— Continued 



Star 



& i goo 



Mag. 



Spec. 



Boss 1672. 

23 Hev. Cam. 

Boss 1 704 
1739- 
i75i- 
1756. 

97 Monoc. . . . 

Boss 1788. 



Lai. 
Boss 



13427- 
1846. 



Lai. 
Boss 



1873- 

14146. 

1894. 

1897. 

1916. 

1926. 

1930- 

1935- 

1956. 

2020. 
28 Hev. Cam. 
Boss 2054. 

2144. 

2148. 

2150. 

2159. 

2178. 

2203. 

2220. 

2236. 

2245- 
2246. 

2293. 

16904. 

2335- 
2338. 
2357- 
2378. 
2400. 
2407. 
2410. 

2413- 

2449. 

2455 

2461 . 
81 7r Cancri. . 
Boss 2465 . 

2490. 

2492. 

2584. 

2598. 
Lai. 19022. 
Boss 2612. 



Lai. 
Boss 



6 h 29 ir 
6 29. 



35° 
42.3 

44.1 
44-8 



6 
6 
6 
6 
6 
6 
6 
7 
7 
7 10. 2 

7 "-3 
13 -5 
14 
16 



45 

50 

54 

5 

9 



8 4 
8 7 
8 14 
8 17 
8 20 



5 

18.3 
19.4 

20. 1 

23 - 1 

3 6 -4 
39-8 
42.6 

0.4 

2.5 

2.9 

9 
4 
3 
9 
6 



8 21.5 
8 31-9 
8 33-1 
8 38.8 
8 39.2 
8 42.2 
8 46.5 
8 5i-7 
8 530 
8 53-5 
8 54 - 1 
3-6 
4.6 



11. 8 
321 
35-5 
37-i 
38.3 



53 
5 

25 
6 



+56°56' 
+ 79 40 
+ 28 17 
-14 19 
+ 16 19 

+ 13 32 

— o 25 
+ 10 5 
+48 32 
+5i 36 
+ 28 4 
+ o I 

— 12 

+ 60 

+45 
+81 
+ 27 50 
+ 11 52 

— 16 o 
+ 28 19 
+ 14 27 
+ 80 31 
+ 23 23 
+ 22 55 
+42 43 
+68 46 

-15 57 
+60 41 
+ 60 57 
+42 20 
+45 59 
+ 12 59 

— 3 
+ 53 
+ 56 

— 6 

+3i 

+ 28 

+ 15 
+ 12 15 
+ 18 31 
+42 11 
+ 22 27 
+ 22 24 
+ 73 22 
+ 15 24 
+43 38 



40 

4 

2 

52 
4 
32 
38 
42 



- 5 56 

- 8 20 

+40 41 
+ 79 36 
+43 i° 
+ 14 29 



5-8 
5-6 
6.5 
5-3 
5-8 
5-9 
5-8 
6.0 
8.2 
5-7 
5-9 
6.5 
7-3 
6-3 



5-7 
5-3 
5-i 
5-0 
5-8 

6-5 
6.2 
6.2 
6.4 
5-5 
5-5 
6.4 
6-5 
6.2 

6.3 
5-8 

5-5 
6.0 
8.1 
4.6 
6.1 
5-2 
6.3 
5-i 
4-i 
6.6 

4-i 
5-2 
6.1 

6.0 
6.4 
5-4 
5-5 
5-5 
5-2 
6.2 
8.2 
5-6 



Ao 
A 2 
Gi 
B8 
B 9P 
G 9 
AS 
B8 
Ki 
Map 
K 3 
G 4 
F 9 
A-7 
■U 
G5 
Fo 
A 2 

B 5 P 
A 2 
Mbp 
G6 
Fi 
Map 
K2 
G 3 
B 3 
A2 
G8 
Kip 
Gi 
Map 
A6 
K 3 
G3 
Go 

G3 
B 9 
Mbp 

A3 
A3 

Mbp 

F5 
G6 

G S 
A3 
G 5 

Aop 

K 5 
B 9 
Ai 
A 5 
K 5 
Map 



.013 

.64 

.017 

.012 

.023 

.013 

. 20 

.027 



>-7 



0.019 
0.020 
O.019 
0.56 

O.OII 

0.036 

0.004 

0.020 

0.028 

0.034 

0.067 

0.015 

0.49 

0.020 

0.024 

0.07 

0.006 

0.014 

0.017 

0.008 

O.OII 

0.021 
o. 116 
0.070 
0.04 

0.44 

0.007 
0.020 
0.046 
0.022 
0.062 

0.054 
0.089 

0.504 

0.008 

O.OIO 
O. IOO 

0.58 

0.052 

0.004 
0.040 
0.020 
0.029 

0.80 

0.014 



92" 
69 

121 
l6l 
132 

J 34 

148 

137 

IOO 

96 

119 
145 

156 



11S 

133 
156 
118 
130 

68 
121 
119 
101 

78 
148 

85 

84 

IOI 

126 

124 

137 
90 

87 

136 

107 
132 

108 

118 

121 
115 

97 
in 
in 



116 

94 

129 

130 

93 

65 

9i 

in 



+ 0.4 
+ 12.0 

- 3-8 
+ 17-3 
+ 12.8 
+ 26.8 

- 17.2 
+33 o 
-22.3 

-49-3 
+ 22. 2 

- 9.6 
+ 57-0 
+ 6.2 
+ 24.6 

- 1-5 

- 5° 
+ 6.3 

- 7-6 
+42.8 
-156 

- 7-8 

- 4 9 
+ 26.7 

+38.4 

- 9-5 

+32.7 

- 16. 2 

- 5-4 
+ 27.1 
-34-3 

- 70 

+ 25-5 
+ 26 

+36 
+30 



+ 2 8:A 



+ 

+ 11. 8 

- 0.8 

- 8.3 
+ 21.7 
+ 239 

- 6.7 

- 6.6 

+ 1-9 
+45-9 
+ 26.6 

- 7-3 
+ 11 .0 



-i 5 L,A 
+ 27. 3L 

+ 16A 



+ 



6-5 
•9 



RADIAL VELOCITIES OF FIVE HUNDRED STARS 
TABLE II — Continued 



179 



Star 



5 igoo 


Mag. 


Spec. 


M 


A 


+S7°3S' 


5-4 


Mbp 


o:'o25 


8o° 


+ 14 14 


8 


4 


A2p 


0.83 


no 


+ 2 55 


5 


9 


A 2 


0. 204 


116 


- 7 38 


s 


I 


A 1 


0.076 


122 


+41 9 


6 


5 


Ko 


0.017 


88 


+ 3 39 


7 


7 


Go 


0.47 


III 


+65 36 


5 


8 


A3 


0.090 


72 


+69 15 


5 


9 


A 2 


0.06s 


70 


+84 46 


S 


7 


A2 


0.130 


62 


+34 25 


5 


9 


A 1 


0.027 


91 


+42 7 


5 


9 


Ai 


0. 102 


86 


+39 26 


5 


9 


A 1 


O.OII 


88 


+81 1 


6 


6 


G6 


0.016 


63 


+35 3° 


5 


6 


A 1 


0.040 


88 


+ 57 36 


5 


2 


A8 


0.074 


75 


+36 51 


6 


2 


A6 


0.050 


87 


— 11 42 


5 


7 


Fi 


0.67 


"5 


+32 3° 


4 


8 


Go 


0.008 


90 


+ 28 30 


6 


1 


Ay 


0.021 


89 


+ 25 17 


4 


3 


A3 


0.077 


9i 


+34 2 


5 


9 


G8 


0.15 


86 


+ 6 43 


6 





Mcp 


0.023 


IOI 


+36 38 


6 


2 


Ma 


0.09s 


83 


+44 2 


8 


9 


Ma 


4.46 


78 


+ 23 38 


4 


9 


Map 


0.018 


88 


+ 2 34 


5 


4 


K8 


0159 


99 


+38 44 


4 


8 


Ao 


0. 102 


80 


+ 3 33 


6 


5 


G8 


0.76 


96 


+ 3 33 


7 


6 


K8 


0. 76 


96 


+ 17 21 


5 


s 


B3 


O.OII 


88 


- 9 15 


5 





B Q 


0.061 


100 


+44 " 


5 


6 


A3 


0.154 


74 


+ 8 41 


5 


5 


Mb 


0.013 


9i 


+48 14 


7 


9 


Go 


0.67 


70 


+ 7 5 


4 


2 


Map 


0.188 


90 


+ 57 9 


5 


9 


G Q 


O.OI2 


66 


- 9 53 


6 


4 


G6 


0.47 


96 


+43 3t> 


4 


9 


AS 


0.323 


69 


+ 22 1 


5 


9 


A5 


0.044 


79 


+ 82 16 


6 


3 


K 4 


0.019 


59 


+ 4 37 


(7 


2) 


A8 


0.006 


86 


- 2 32 


7 


3 


G 4 


0.74 


90 


+ 11 24 


7 


5 


G3 


0.59 


82 


+ 10 49 


5 


8 


A8 


0.096 


82 


+4i 13 


5 


7 


K3 


0.051 


68 


+ 23 35 


6 


1 


A? 


0.038 


75 


— 21 40 


5 


4 


B8 


0.092 


98 


-13 1 


5 


5 


K.2 


0.002 


93 


+ 57 20 


6 





Map 


0.028 


62 


+ 56 16 


5 


8 


Ma 


0.031 


62 


+ 25 7 


5 


4 


A2 


0.020 


7i 


- 5 17 


5 


9 


Ao 


0.040 


84 


+ 2 24 


6 





Mb 


0.090 


81 


+ 10 47 


4 


8 


B8 


0.135 


76 



Boss 
Lai. 
Boss 



Lai. 

Boss 



2614 
19229 
2647 
2650 
2701 
19896 
2726 
2737 
2 745 
2756 

2 773 
2787 
2795 
2808 
2813 
2819 
2822 
2829 



2909 
2910 

2915 

2921 

21258 

2976 

2983 

.2987 

83 Leonis Br 

83 Leonis Ft 

Boss 3045 

3055 
3063 
3067 
Groom. 1822 
Boss 3089 
3125 
3137 
3143 
3150 
3i77 
3178 
i2 h 69 



Lai. 
Boss 



W.B. 
Lai. 

Boss 



3183 
3193 
3206 

3215 
3217 
3234 
3248 
3266 
3290 
3294 
3309 



9 n 39' 



o 13 

o 15 
o 17 

O 21 

o 24 
o 25 
o 27 
o 28 
o 30 
o 31 
o 33 
o 44 
o 50 
o 50 
o 5° 
o 54 



1 13 
1 21 
1 21 
1 29 
1 3i 
1 33 
1 33 
1 40 
1 40 
1 50 
1 55 
1 57 

1 59 

2 6 
2 6 

2 7 
2 8 
2 8 
2 n 
2 14 
2 15 



+ 9 
-23 

+ 95 
+ 15 
+ 13 
-24 

— 1 

+ 3 
+ 10 



12.7 
• 5-2 
■ 8.2 

1 1 ■ 5 



+ 2. 

- 9- 
-24. 

- 9- 

- 7- 
+ 2. 
+ 6. 
-23- 

— 12. 

— 22 

+ 65" 
+ 15- 
-57- 

+ 5- 

— 2. 

+ 2. 
+ 17. 



+ 5-6 
+ 1-4 
+ 23-9 
+ 51-2 

+ 131 

0.0 

+ 8.2 

+ 43 

— 26.0 

- 6.0 

+ H-3 
-30.0 

+ 34 
-14.4 
+ 1.2 

— 20.9 

+ 12.5 

— 16. 7 
+ 176 

- 0.5 

- 3 6 
-15.0 
+ 3-5 



6.3L 



+ 16.0L ! 



+S1.2L 



+ 


12 


9 


+ 


3° 

17 






+ 


4 


8 


+ 


14 


1 


— 


3i 


9 


+ 


4 


4 


+ 


10 


7 


+ 


19 


4 


— 


n 





+ 


6 


6 


+ 


8 


9 


— 


2 


4 


+ 


3 


3 


— 


4 





— 


23 


2 


— 


17 


4 


— 


7 


6 


+ 


2 


7 


+ 


S 


8 


— 


22 





— 


16 


1 


— 


20 


3 


+69 




+ 


i.S 


9 


— 


5o 


6 


+ 


9 


2 


— 


4 


S 


+ 





1 


+ 


18 


5 


— 


n 


S 


+ 


11 


1 


+ 





9 


+30 


7 


+ Si 


2 


+ 


21 


2 


— 


2 


1 


+ 


i.S 


4 


+ 


8 


1 


— 


IS 


7 


— 


4 


6 


+ 


11 


3 


— 


27 


2 


+ 


6 


2 


— 


6 


9 


+ 


6 


4 


— 


23 


7 


+ 


rr 


5 


— 


7 


3 


+ 


27 





+ 


6 





— 


1 


5 


— 


11 


9 


+ 


8 


3 



i8o 



WALTER S. ADAMS 
TABLE II — Continued 



Star 



Boss 



Lai. 

Boss 



33 ID - 
333 ] 
3332- 
3334- 
333 6 - 
3337- 
3338. 
3339- 
3348. 
336o. 
3367- 
3382. 
3406. 
3408. 
3442. 
3462 
3478. 
25012. 

3499- 
35o6. 
3534- 
3542. 
358o. 
3585. 
3589. 
3629. 

3653- 
3654- 
3663- 
26196. 
3684. 
37°3- 
3706. 

3734- 
3743- 
3756. 

Lai. 27298. 

A.Oe. 14320. 

Boss 3867- 
3875- 
3883. 
3885. 
3893- 
3918. 
3942. 
3955- 
3985- 
4007 . 
4022. 
4026. 

39 Serpentis . 

Boss 4070 . 
4096. 
4i°3- 



Lai. 
Boss 



i2 h 36"? 


12 42. 


• 12 43- 


■ 12 43- 


■ 12 43- 


• 12 43. 


. 12 44. 


■ 12 44- 


• 12 47. 
. 12 48. 


• 12 5°- 

12 56. 


■ 13 4- 


• 13 4- 


• 13 "■ 


■ 13 1 7- 


. 13 20. 

• l 3 26. 

• 13 26. 


• 13 29. 

• 13 36. 


13 39- 
■ 13 46. 


■ 13 47- 

■ 13 48. 


■ 14 3- 


14 9. 


14 9. 


14 11. 


. 14 14. 


• 14 15- 


14 21 . 


14 22. 


. . 14 31. 


• • 14 35 


■ ■ 14 37 


■ ■ 14 52 


• 15 4 


• 15 7 
■■ 15 8 


■ 15 10 


■ • 15 10 


•• 15 13 
■• 15 18 


■ ■ 15 25 


•• 15 29 


• i5 35 


• ■ 15 40 


• ■ 15 45 


• • 15 45 
■ . 15 48 


• ■ 15 55 

. . | 16 2 


..16 3 



& 1900 


Mag. 


Spec. 


+ 7°2i' 


54 


Ao 


+ 4 7 


6.7 


Ma 


+63 20 


5-8 


A 4 


+ 14 & 


6.4 


Ao 


+ 67 20 


5-6 


G5 


+ 14 40 


5-7 


Ao 


+49 1 


6.1 


As 


+ 28 6 


5-7 


Ao 


+ 17 37 


6.5 


G Q 


+ 12 S 8 


6.2 


A3 


+ 3 56 


3-7 


Mbp 


+ 56 54 


4-9 


\2p 


+ 10 33 


6.0 


<^7 


- 9 48 


6.2 


K6 


+ 81 


6.3 


Gs 


+ 5 4i 


5-8 


A 1 


+ 24 23 


5-8 


A 1 


- 1 49 


7-5 


G6 


- 5 44 


4-9 


K 5 


4- 4 10 


50 


A2p 


- 8 12 


6.2 


Ma 


-15 4i 


5-7 


F8 


+ 33 16 


6.6 


A 2 


4-12 40 


5-9 


A 1 


+65 13 


4-8 


Map 


- 9 52 


6.5 


G8 


-17 44 


5-5 


B 9 


+ 52 15 


4-4 


A S 


+ 19 23 


5 9 


A 7 


- 4 41 


7.6 


Ki 


+39 15 


6.0 


Ao 


+38 5i 


6-3 


Ki 


- 5 4o 


6.1 


A 1 


-11 53 


6.0 


F.S 


+ 54 27 


5-5 


A 1 


-24 34 


5-6 


Bq 


+ 54 4 


7-9 


Ko 


-15 54 


9.2 


Go 


+ 19 21 


6.0 


Mbp 


-17 24 


6.3 


B8 


+ 29 32 


5-2 


A 2 


+ 45 


5-7 


A 2 


+67 44 


5-2 


*3 


— 40 


6.0 


A3 


-16 16 


5-9 


Ko 


- 8 51 


5-i 


B 7 p 


+47 8 


5-8 


A8 


+ 5 46 


5-5 


A 2 


+ 55 4i 


5 9 


F2 


+ 4 47 


3-8 


A6 


+ 13 3i 


6.2 


F8 


-88 


5-4 


Ao 


— 26 4 


.5.6 


Map 


+ 8 48 


5-9 


Mbp 



A* 



:'o78 

• 013 

.022 

.068 
.008 

• 051 



0.055 
0.095 
0.023 

0.067 

0.479 

o. 101 

0.020 
0.023 
0.008 
0.080 
0.014 
0.94 

O. 112 

O.O52 

O.Ol8 

O.OO9 

OO33 

O.O38 

O.OO4 

O.O16 

O.O44 

O.067 

OO55 

O.68 

O.O3O 

O.OI9 

O.O98 

0.97 
0.027 
O.O26 
I.08 

3-76 

O.OO4 
O.O29 
O.O78 

o. 109 

0.459 
O.O77 
O.OI9 
O.O29 

o. 162 

0.033 

O.OIO 

0.136 

0.56 

0.034 

O. 122 
O.O24 



78° 
78 
58 

73 
58 
74 
60 
68 
71 
73 
77 
57 
70 
81 
56 
70 
61 
72 

75 
68 

74 
78 
53 
60 

5i 
70 
74 
46 

52 
64 
46 

45 
63 
66 

43 
74 
40 
63 
40 
63 
36 
50 
44 
50 
60 
54 
32 
41 
34 
40 
34 
49 
63 
34 



+ 



+ 



8.7 

18.0 

o. 2 

9.0 

70 

2.4 

14 

0.4 

3-8 

17-4 

3-i 

0.1 

6.8 

10.0 

11. 4 

1.6 

53-9 

19. 1 

8.4 

32-7 

o. 2 

123 
17. 1 
10.4 
19.6 
15-7 
15-9 
6.3 

- 130 

- 12.6 
+ 25.8 

- 156 

- 70.5 
+ 4-2 

- 4-2 

- 144 
+ 290 

-34-2 

- 25.9 

- 18.8 

- 5-5 
-45-4 

- 2.7 

- 1.2 

- 4-3 

- 2.3 

- 7-3 

- 1.9 

- 10.6 
+ 38.7 

- 19-4 

- 21.2 

- 21.6 



+ 



+ 



+■ 



17. 6L 



19. 2L 
6:L 



9.9L 
i9:L 



10. oL 



RADIAL VELOCITIES OF FIVE HUNDRED STARS 181 

TABLE II — Continued 




4686 
4702 
4707 
4719 
4724 
4740 
4748 



182 



WALTER S. ADAMS 
TABLE II — Continued 



Star 



& IQOO 



Mag. 



Spec. 



^ 



Boss 



Lai. 
Boss 



475° 
4758 
4703 



4772 
4780 

4783 
4805 
4816 
4842 
4866 
4873 



4899 
4910 
4912 
4914 
4917 
4919 
4942 
4967 
4974 
4976 
4978 
5024 
5044 
5063 
5073 
5088 
5096 
5122 
5125 
5134 
5142 
B.D. 3 6°388 3 
Boss 5 J 77 
5188 

S213 
5218 
5220 
S224 
20452 
5240 
5258 
5267 
5284 
5296 
530i 
5307 
53i6 
53i7 
5319 
5325 
5366 



A. <)<_•. 
Boss 



8 h 4i™2 
S 42.0 
8 43 ■ 1 
8 43-8 
8 46.0 
8 48.0 
8 49.0 
8 51-7 

8 53- 8 
S 57-7 

9 2.5 
9 3-7 
9 10.8 



22. 1 
24.0 

24-5 
24.8 
36.2 
4° -5 
45-9 
47-9 
49.2 
512 
54 -7 
55-5 
57-8 
59-2 
20 3.5 
20 7.6 
20 10.8 
20 14.8 
20 15.9 
20 16.6 
20 17.8 
20 17.7 
20 21.6 



20 25.5 
20 27.2 
20 31.5 
20 33-5 
20 34.1 
20 34-4 
20 36.0 
20 36.6 
20 37.0 
20 39.1 
20 46.9 



— 10 14 
+ 26 3S 
+60 57 
+ 10 39 
+32 42 

— 21 29 

-15 44 

+41 28 

-12 59 

+ 50 23 

+ 24 6 

+35 57 

+ 14 55 

+ 21 3 

+49 54 

+ 37 57 

+ 11 25 

+ 22 51 
+ 09 

+ 26 4 

+ 19 42 

+ 1 45 

+ 24 28 

+ 24 34 

+42 35 

— 20 o 
+38 27 
+ 18 25 

- 8 30 
+36 44 
+ 30 43 
+ 17 15 
+ 24 39 

- o 59 

+36 16 
+ 26 31 

+36 3° 

+34 40 

+ 55 5 

+39 5 

+ 24 8 

— 21 40 
-18 32 
+36 7 
+36 36 

- 2 54 
+31 10 
+ 20 51 
+ 15 29 
+45 19 
+ 14 14 

+3i 57 
+49 59 

- 5 53 



1) 



F 5 
Ko 

G 5 
K 5 
B3 
G 3 
B 7 
G5 
BSp 

B 3 

A 4 

B6 

Ki 

A 2 

G6 

G8 

A3 

B3 

Ki 

BSp 

K8 

B8 

K 5 

G6 
Ao 
G 9 
G2 

B2 P 

B 7 

F 5 

B8 

Map 

A3P 
K2 

Map 
G 9 
B 9 
l-'o 
A 2 
Ao 
BSp 
Gop 
BSp 
A 1 

F 7 

K: 

A3 
A 1 

B 3 

B6 
K2 
G 7 
B 3 

Aop 



0.005 
0.029 
0.010 

0.45 

0.014 
0.012 

0.023 

0.007 

0.025 
0.025 
0.056 

0.009 
0.020 
0.044 
0.014 
0.010 

O.OII 

0.014 
0.009 

0.015 
0.057 
0.037 

o. 170 

0.012 
0.032 

0.165 

0.016 
0.007 
0.029 
0.008 

0.031 
0.015 

0.099 
o. 119 



.020 

■ 094 

.017 

.021 

.022 

.018 

. 21 

.Ol6 

.014 

OI3 
Oil 

.069 

.058 

■ 025 

.010 

.012 

.018 

.006 

Oil 



42 

10 

31 

23 

10 

53 



46 
22 
15 
14 
23 
19 
24 
17 
26 
18 
36 
18 
22 

35 
20 

20 

23 
56 
"-3 
28 
48 
24 
25 
30 
27 
43 
26 
28 
28 
29 
34 
29 
3i 
62 
61 
3i 
3i 
50 
33 
36 
39 
34 
39 
33 
36 
54 



f 



+ 



9.8 

- 17.2 

- 24. 2 

- 17.4 

- 16. 1 

- 3-8 

- 6.3 

- 8.2 

- 12.5 

- 19-3 
-23.0 

- 305 

- 22.4 

23 -9 
6.5 
-30.7 

- 16. 2 

0.0 
-28.0 

- 12.2 

- 35-1 
4- 16.8 

- 86.6 

- 26.4 

- 38.8 
+ 16.5 
+ 10.6 

- 10.9 

- 13-4 

- 24. 2 

- 0.2 

- 16.9 

- 33-8 
4- 0.8 

- 320 

- 22. 2 

- 13-4 

- 4.0 

- 2.8 
0.0 

- 9.1 
-179 

- 18.4 

- 18.0 

- 22.7 
10.9 



+ 



19. 2 

2.0 

IS- 1 

3ii 

28.0 

2.6 

4-2 



-16.6L 



-30. 3L 



2L 



-85. oL 



+ 23L 



-15L 



RADIAL VELOCITIES OF FIVE HUNDRED STARS 
TABLE II — Continued 



l8 3 



Star 



S igoo 



Mag. 



Spec. 



Boss 
Lai. 
Fed. 
Boss 



W.B 

Boss 

B.D. 
Boss 



Lai. 
Boss 



5373 
29208 
3638 
5389 
5397 
5417 
5420 

20 h i454 
5422 
5432 

38°4362 
5456 
548i 
5486 
30218 
5498 
55i2 
5522 
5542 
5546 
555° 
5555 
5558 
5583 



5590 
5599 
5614 
5650 
5055 
5057 
B.D. 6i°2233 



Boss 

Groom. 
Boss 



Lai. 
Boss 



5664 
5669 
3689 
5749 
5757 
5709 
5805 
5858 
5868 

5904 
5920 

5923 
45028 

594° 
5962 

5907 
5909 
5972 
5973 



bo it, 



20 n 47 : 
20 so 



20 52 
20 53 
20 58 
20 59 
20 59 

20 59 

21 2 

21 5 

21 9 

21 16 

21 16 

21 18 

21 19 

21 21 

21 25 

21 30 

21 30 

21 32 

21 33 

21 34 

21 39 

21 39 

21 39 

21 41 

21 44 

21 53 

21 56 

21 56 

2i 57 



21 58 



22 15 

22 18 
22 25 
22 37 
22 39 
22 49 
22 S3 
22 54 
22 56 

22 58 

23 4 
23 5 
23 5 
23 5 
23 6 

23 10 

23 

23 



18 



+ 26°4 3 ' 

+40 19 
+ 74 23 
+47 2 
+ 21 56 
— 20 15 
+3S 16 



36 
6 



26 
5 



f 
+ 

+ 3° 47 

+38 19 

-21 4 

+ 58 12 

+ 70 35 

+ 13 3° 

+ 23 5i 

+36 14 

+ 23 12 

- 4 
+ 38 

- o 50 
+ 18 52 
+ 19 49 
+ 40 42 

- 9 33 
+ 16 53 
+ 22 29 
+ 60 14 
+63 
+ o 
+ 7 
+61 59 
+ 52 24 
+44 10 
+ 52 39 

- 5 53 
+ 5 i7 

- 7 42 
+ 57 54 
+ 28 47 
+38 56 

- 16 21 
+ 8 50 

-13 3° 

- 4 23 

+ 27 32 
+ 88 

+ 9 17 
+ 58 47 
+43 o 
+ 8 n 

- 9 38 
+ 27 42 
+ 59 35 



9 

7 

47 



(6 



6) 



5) 



G8 
BSp 
G 4 
B8 
K 5 
A 2 
G 7 
F3 
K6 

F5 

Ko 
G8 
F8 
K2 
B6p 
A6 

B3 

Ma 

G 5 
G8 

Ao 
A 1 
A3 
K3 
G 4 
G 7 
Go 
K 4 
Map 
Ki 
K2 
B6 

B9 
A 1 
G8 
G 5 
B 7 
G 4 
B8 
A3 
K 4 
A 2 

F 5 
K2 
K2 
Map 

Mbp 
B 9 
A3 
F2 
B 9 p 
GS 
Ko 
G 9 



o. 103 
0.025 
o. 70 
0.006 

0.005 

0.060 
O.OI2 

0.56 

0.019 

O.OIO 






007 





014 





020 



o. 124 

O.OII 

0.017 
0.021 
o. 148 
0.026 

O. IOO 

o. 117 
0.026 

O.OIO 

0.029 
0.016 
0.006 
O.OI2 
0.006 
0.022 
0.013 

0.004 

0.039 

0.61 

0.020 

0.019 

0.000 

0.028 

0.039 

0.016 
0.052 

0.420 
0.014 

0.50 
0.234 

0.004 
0.024 
0.015 
0275 

0.017 



37" 

36 

49 

37 
40 

67 

37 



39 
39 
69 

43 
5i 
49 
45 
42 
46 
61 
44 
60 

49 
49 
45 
67 



47 
49 
64 
60 

49 
48 
48 
49 
7i 
65 
73 
52 
59 
57 
84 
7i 
84 
79 
64 
74 
74 
57 
60 



+ 3-3 - 0.2L +19. 



-3° 
-15 

-27 
+ 23 

- 9- 
-IS- 

- 6. 

- 8. 

- 6. 

- 21 . 
+ I5- 

- 9- 
-18. 
+ 1. 
-19. 

- o. 

-63. 
+ 16. 
-38. 
-13- 

- 25 ■ 

- 6. 



-19 
-19 

+ 7 



•22.8 



0.367 


85 


0.015 


67 


0.003 


59 



+ o. 

-35 

+ 6. 
-15 
-13 

-25. 
+ 7 
-26. 

+ 13. 
-26. 

+ 13. 
-50. 
+ 10. 

+ 13. 

+ 11. 
— 11 

-43 

+ 5 
-28 

+ 3 
— 11 



+ 26L 



175L 
; 6 5 '5L 



22. iL 



+ 8.7L 
+ 22L " 



+ 8.4L 



-17 
+ o 

- 12 
+3i 
+ 13 
+ 3 

+ 9 

+ 7 

+ o 

- 6. 

+ 25. 

+ 4. 

- 4- 

+ 16. 

+ 9- 
-Si- 

+ 26. 



+ 1. 
-13- 

+ 2. 

— 5 

- 6 
+ 16 

— 1 

- 8. 
+ 14. 

+13- 



4 — 26.9L 



-13 
+ 17 
-15 
+ 15 

— 20 

+ 15 
-46 
+ 19 
+ 18 
+ 17 

— o 

-33 
+ 10 
-26 
+ n 

— o 



1 84 



WALTER S. ADAMS 
TABLE II— Continued 



Star 



a i goo 



& IOOO 



Mag. 



Spec. 



A.Oe. 25685 
B.D. 62°2244 
Boss 6063 
6089 
6105 
6106 
6111 
6113 
6123 
6i33 
6i35 
6145 
6166 
6176 
6180 



23 h 26' 

23 28 
23 29 

23 38 

23 42 
23 42 

23 44 
23 44 
23 40 
23 48 
23 49 
23 52 
23 56 
23 57 
23 59 



+ 58°37' 

+62 36 

+ 39 4i 

+ 9 47 

+ 56 54 

+ 58 6 

+61 40 

+ o 31 

+ 2 22 

+ 1 32 

+ 56 57 

+42 6 

+60 40 

+ 65 33 

+61 44 



Ki 
G 4 
Aop 
Map 
Ko 
G 9 
A3P 
A3 
Ki 
A 1 
Fgp 
F2p 
A6 
Ko 
Ao 



ifo8 

0.44 

0.042 

0.007 

0.021 

0.087 

O.OIO 

0.027 
0.020 

0.013 

0.007 
0.012 
0.007 
0.018 
0.008 



60 

60 

66 
81 
62 
62 
61 
86 
86 
87 
63 
69 

63 
62 

63 



-24 

+ 8 
+ 13 
-35 

- 5 

— 22 

-55 
+ 9 
+ o 

+ 9 
-42 

- 7 

— 22 
-16 



-20.3L 



—42. iL 



-14.7 
+ 18.0 
+ 21.3 
-32.1 
+ 4° 
-13-4 

- 46.0 
+ 10.7 
+ 2.3 
+ 10.7 
-33-5 

- °-5 
-13-3 

- 7-5 

- 98 



ACCURACY OF THE OBSERVATIONS 

The great variety of spectral types among the stars of Table II 
involves a wide range in the accuracy of the determinations of radial 
velocity. Many of the A- and B-type stars have vague and very 
ill-defined lines, and for such stars the accuracy necessarily is low. 
In some cases as many as seven or eight determinations have been 
made to guard against the inclusion of possible spectroscopic 
binaries, and the range among the individual plates occasionally 
amounts to more than 10 km. On the other hand, the results for 
spectra having well-defined lines are usually in excellent agreement. 
The accompanying short table (III) shows the average of the 
probable errors of v for ten stars of each type selected at random 
from Table II. 

TABLE III 



Type 


Quality for 
Measurement 


Average No. Linear Scale of 
Plates Plates 


Probable Error 


A and B 


Poor 
Good 
Good 
Good 
Good 


5 
3 
3 
3 
3 


per mm 
16 A 
16 
36 
36 
36 




A and B 


0.73 
O.98 

O.97 
± I .09 


F 


G and K 


M 



For the sake of uniformity it has seemed preferable to retain 
the fractional part cf the kilometer for v wherever three observations 



RADIAL VELOCITIES OF FIVE HUNDRED STARS 185 

are available, although it can have little significance in the case of 
individual stars photographed with such relatively low dispersion. 
The fact that the linear scale of the spectra of the A and B stars 
is over twice that of the F, G, K, and M stars aids in counteracting 
the effect of the poorer quality of their lines, and so tends to make 
the accuracy of the determinations for all of the stars in Table II 
more nearly the same. 

COMPARISON WITH RESULTS OF OTHER OBSERVERS 

There are fifty stars in the list for which determinations of 
radial velocity have been published by other observers, a very large 
proportion being from the Lick Observatory photographs. The 
Lick spectrograms were in most cases taken with a dispersion of 
three prisms, and have a linear scale about three times that em- 
ployed for most of the F, G, K, and M stars of Table II. A com- 
parison by spectral types with the Lick Observatory results gives 
the values shown in Table IV. 





TABLE IV 




Type 


No. Stars 


Lick — Mount Wilson 


B and A 

F and G 


21 
12 


+o.q km 
+ 1.6 


K and M 


+0.4 



The star W.B. 4 h n8o. has been omitted from this comparison, 
as it seems probable that the large difference between the two 
results may be due to the fact that the star has a variable velocity. 
The same remark may apply to one or two other stars in the list, 
particularly Boss 5904 and 5044. The exclusion of these stars 
would reduce the difference for the B and A stars from +0.9 to 
+0.4 km, and for the F and G stars from +1.6 to +1.1 km. 

A large number of observations on the two stars a Bootis and 
a Tauri have been made during the period covered by the results 
shown in Table II. The values for these stars are given in Table V. 

The evidence seems to indicate a small systematic difference in 
the direction of larger negative or smaller positive values for the 
Mount Wilson results, but it is probably no larger than may be 



i86 



WALTER S. ADAMS 



accounted for by the wave-lengths of the lines employed. A slight 
difference might arise from the fact that the iron arc has been used 
for comparison purposes at Mount Wilson, and that Rowland's 
wave-lengths have been utilized both for comparison lines and for 
such stellar lines as appear in the sun. The adopted values of the 



TABU. V 



Star 


No. Plates 


Mount Wilson 


Lick 


Yerk.es 


a Bootis 


31 
16 


- 4.3 km 
+ 54-0 


- 3 • 9 km 

+ 55-1 


-4-5 km 







laboratory wave-lengths used for the helium lines of type B and 
the magnesium line X 4481 of type A may also differ to some extent. 
In view of the fact that the Mount Wilson results are based mainly 
on comparatively low-dispersion photographs, the agreement with 
the Lick Observatory values must be considered as quite satis- 
factory. 

SOME INDIVIDUAL STARS 

Among the stars with exceptionally high velocities the following 
are of especial interest: 

v' '/ 

A.Oe. 14320 +299 km Lai. 21258 4-69 km 

A.Oe. 20452 — 170 Boss 2647 4-87 . o 

W.B. i 7 h 5i 4 -131 

The first of these stars has a proper motion of 3 ''76 and a parallax, 
as determined by Russell, of +0*035. Its motion in space as 
based on these values and its radial velocity would amount to 
577 km, directed toward the vertex a=i8o°, 5=— 70 . At a dis- 
tance of 5' there is a second star which shares in the proper motion. 
The spectrum of this star is Go. 

The star Lalande 21258 has a proper motion of 4*46 and a 
parallax of o''2o. Its absolute brightness is extremely small, its 
magnitude being 10.4 (sun =5. 5). In proper motion, absolute 
magnitude, and spectrum it resembles very strongly Lalande 21 185, 
but the radial velocities of the two stars, though both large, are of 
opposite sign. 



RADIAL VELOCITIES OF FIVE HUM) RED STARS 



187 



Boss 2647 is one of the very few stars of type A with a high 
radial velocity. 

A star of exceptional interest because of the character of its 
spectrum is Lalande 19229. The spectral type is A2. but the line 
X 4481, usually so prominent in stars of this type, is either absent 
or very faint. Two stars with a very similar spectrum had been 
found previously in the list of those having large proper motions. 
The data for the three stars are given in Table VI. 

TABLE VI 



Star 


Mag. y. 


77 


Spectrum 


Lai. 5761 

Lai. 19229 

Lai. 28607 


8.0 O ."90 
8.4 O.83 
7-3 I.I7 


+0:039 
— . 046 
+0.029 


A3P 

.A2p 
A2p 



The hydrogen lines in these stars are exceptionally narrow and 
well defined. Although the measured parallaxes are small, it seems 
probable that these stars are of comparatively low luminosity, and 
the suggestion may be made that the normal A-type spectrum is 
modified in this way in the case of stars of small absolute brightness. 
If such is the case, these spectral peculiarities should serve as a 
valuable criterion for the discovery of stars of this character. On 
physical grounds the absence of the spark line of magnesium at 
X4481, which is associated in the laboratory with high vapor- 
density and probably high temperature, and the narrowness and 
sharpness of the hydrogen lines, which would indicate a hydrogen 
atmosphere of low density, would be in harmony with this 
hypothesis. 

Attention was called in the publication already referred to on 
the radial velocities of 100 stars with measured parallaxes 1 to the 
marked preponderance of the negative sign among the highest 
velocities. There seems to be no such noticeable effect in the case 
of the velocities given in Table II. The number of positive and 
negative velocities is essentially equal if r / = 5o km is set as a limit. 
Between 45 and 50 km, however, there are six negative velocities 
and only one with the positive sign. 

1 .1//. Wilson Contr., Xo. 79; AstrophysiccU Journal, 39, 341, 1914. 



1 88 WALTER S. ADAMS 

RADIAL VELOCITY AND PROPER MOTION 

It is well known that, in general, the proper motions of the stars 
of type B are extremely small, those of type A considerably larger, 
and those of types F, G, and K larger still. The M-type stars have 
proper motions averaging about the same as the A stars. An 
observing list of stars of different types selected on the basis of 
apparent magnitude alone would, therefore, contain material which 
would not be homogeneous as regards the distances of the stars. 
Since large proper motions when treated statistically indicate not 
only small distance, but also high velocity, as is shown clearly by 
the values for stars of large proper motion, 1 the tendency would be 
in such an observing list to compare rapidly moving stars of one 
type with slowly moving stars of another type. 

Most of the F, G, K, and M stars and some of the A stars which 
appear in Table II have been selected for observation because of 
their small proper motions. A knowledge of their radial velocities 
enables us to institute a comparison between the average velocities 
of groups of stars having these spectra with those of types B and A 
of the same average proper motion. In Table IV are collected the 
radial velocities of all of the stars in Table II, for which the proper 
motion is less than 0^030 annually. One K-type star and one M 
star with velocities exceeding 50 km have been omitted. This 
makes it possible to compare directly with a similar table published 
by Professor Campbell based on his velocities of stars of all types. 2 
For the present purpose Campbell's first table based on 1034 stars 
is used, no constant correction A' having been applied to these 
results. The proper motions for Campbell's stars have been taken 
from Boss's catalogue for the individual stars published in Lick 
Observatory Bulletins, Nos. 195, 211, and 229. Not all of these stars 
are used in Campbell's table, and, accordingly, the average proper 
motions derived are not strictly correct. In view of the large 
number of stars used, however, it does not seem probable that the 
values can be materially in error. 

1 The average value of the radial velocity (corrected for the sun's motion) of 135 
stars of large proper motion, /j. = o"8i, as determined at Mount Wilson is 24.3 km. 
Stars with velocities exceeding 100 km are omitted. 

2 Lick Observatory Bulletin, No. 196. 



RADIAL VELOCITIES OF FIVE HUNDRED STARS 



189 



The peculiar feature of this comparison is the relatively close 
agreement of the A and B stars and the large difference for the 
other stars. The question at once arises whether this may not 
be associated with the great increase in proper motion for Campbell's 
stars between type A and type F. In a recent publication by 
Kapteyn and Adams, 1 Professor Kapteyn has made a computation 
of the relationship between radial velocity and proper motion for 
the K stars, using as a basis Campbell's published values of radial 

TABLE VII 





Campbell Mount Wilson 


Spectral Types 


Xo. Stars Xo. Stars Proper 
for v' for P.M. Motion 


km No. Stars g«g£ ! km 


and B 141 

A ; 133 

F ! 159 

G and K 529 

M 72 


224 0*031 i 8.99 61 o"oi6 8.23 
206 0.094* 9-94 55 0.019 10.04 
192 ; 0.234 | 13.90 20 o.oii 10.14 
549 0.202 15.15 119 0.014 1103! 
78 0.074 16. 55 27 0.015 12.56 



*The omission of 5 stars would reduce this value to 0*079. 

fThe separate values of the G and K stars are G: 63, o?oi3, 10.60; K: 56, 0T014, n .53. 

velocity and some of the Mount Wilson observations. The stars 
were selected in such a way as to eliminate so far as possible the 
effect of stream motion, and the components of the linear velocities 
were computed by aid of the mean parallaxes for stars of known 
proper motion and magnitude given in Groningen Publication, No. 8. 
If we assume that the results of this computation for the K stars 
may be applied to stars of other types, we have Table VIII connect- 
ing proper motion and radial velocity. 

"table VIII 



o "ooo to o "02 5 1 2 . 1 km 



0.026 
0.040 
0.060 
o . 080 



0.039 12.5 

0.059 12.9 

0079 13.3 

0.099 13-7 



o"ioo to o'ng 14.3 km. 

o. 120 " o. 149 14.8 

0.150 " 0.199 15-9 

o. 200 " o. 299 17-7 

-0.300 24.5 



1 Communications to the National Academy of Sciences, Xo. 1; Proceedings of the 
National Academy of Sciences, i, 14. 1915. 



190 



WALTER S. ADAMS 



The use of these values gives the following corrections to the 
radial velocities for the proper motions of the Campbell stars in 
Table VII in order to reduce to the average proper motion 0^031 
of the O and B stars: 

A, —1.3; F, — 4.9; G and K, — 4. 1; M, — 1.0 km. 

Table IX shows the values with these corrections applied, and 
also with the reductions applied to correct for stream motion which 
have been calculated by Eddington. 1 

TABLE IX 



Type 


v' 
km 


Campbell 
»' Corrected for 
Stream Motion 


P r r °I? er ! km 
Motion 


Mount Wilson 
v' Corrected for 
Stream Motion 


Proper 
Motion 


Oand B.. . 

A 

F 

G 

K 

M 


9.0 

8.6 
9.0 

\ 

1 1 .0 

15.6 


9.0 km 
6.8 

7-8 

9.6 
13-6 


. 03 1 8.2 
10.0 

10. 1 

a 10.6 

11. 5 

" 12.6 


8.2 km 

7-7 

8.8 

9.2 
10. 
10.9 


o"oi6 
O.O19 
O.OII 
0.013 
0.014 
0.015 



In his definitive solutions of the solar motion for the several 
spectral types 2 Campbell has given the average radial velocity for 
each type with a constant correction K applied to the velocity of 
each star. This constant has a value ranging from about zero for 
the F and G stars to over 4 km for the B stars. If we treat these 
values in the same way as those of Table VII we obtain Table X. 

TABLE X 



Type 


v' 


»' Corrected for 
Stream Motion 


Proper Motion 


and B 

A 

F 

G 

K 

M 


6.5 km 

96 

9-5 
9-1 

13.2 
16. 1 


6. 5 km 

7-4 

8-3 

7-9 
"S 
14.0 


0:031 

(i 
a 
u 
a 



The value of the constant K as used by Campbell is the average 
velocity v' taken according to sign for the stars of the several spec- 
tral types,- and is, of course, dependent upon the value of the solar 

1 Stellar Movements, p. 157. 2 Lick Observatory Bulletin, Xo. 196. 



RADIAL VELOCITIES OF FIVE HUNDRED STARS 



191 



motion V as derived for each type. Since the same value of V has 
been used for all of the Mount Wilson stars, no direct comparison 
is possible. It is, however, of interest to note how the value V= 
20 km satisfies the stars of the several types. The average velocity 
v' taken according to sign for the stars of Table VII is as follows: 

B, +1.26; 4,-0.24; F, — c.86; G, +0.05; A', — 1 .18; M, +0.31 km. 

A change in the value of V from 20 to 19 km would reduce the 
residual for the B stars from +1.26 to +1.06 km. These quan- 
tities must be regarded as very moderate in size. The number of 
stars used is not very large, however, and hence the values might 
be changed materially by the inclusion of additional velocities. 
Thus if all of the M stars both of large and of small proper motion 
in Table II are included, together with one or two stars for which 
only a single observation is available, we obtain the following result : 



No. Stars 


fi 


»' 


»' According to 
Sign 


43 


o:'05S 


14-54 km 


— O.97 km 


A similar computation for the B stars gives: 


No. Stars M 


v' 


v' According to 
Sign 


113 0?02S 


8.89 km 


+ 1 .62 km 



The value +1.62 km would be reduced about 10 per cent by 
employing a value of the solar motion 7=19 km. 

The Mount Wilson results of Table IX seem to indicate, if 
interpreted directly, that among the very distant stars the change 
of velocity with spectral type is slight, and Campbell's results, 
except perhaps in the case of the M stars, point to the same con- 
clusion when allowance has been made for the effect of the large 
number of relatively near stars included among his F- to M-type 
spectra. This would be in agreement with the hypothesis put 
forward by Eddington in 191 1, 1 but later entirely disproved, as he 

1 British Association Report, 191 1. 



192 



WALTER S. ADAMS 



considered, by the evidence of the A stars, 1 that the relation between 
velocity and spectral type might be a relation between velocity and 
distance, the stars nearest the sun, which are mainly of types 
F to K, moving more rapidly than the distant stars. The evidence 
which Eddington regarded as conclusive in disproving this hypothe- 
sis was provided by an analysis according to proper motion of the 
A- type stars for which velocities had been published. Xo increase 
of radial velocity with proper motion was indicated by the results. 
It has already been stated in this communication that such a con- 
clusion is by no means tenable in the case of the K stars, for which 
Kapteyn has found from the Lick and Mount Wilson values an 
increase of velocity of from 10.9 km for stars having an average 
proper motion of about o''o2o to 26 . 7 km for stars with a proper 
motion exceeding o?30. The following evidence derived entirely 
from the Mount Wilson observations for the other types of spectra 
will be of interest in this connection. The effect of stream motion 
has not been eliminated. 2 

TABLE XI 



No. Stars 


M 


d' 


Xo. Stars 


k 


-/ 


B 


61 


o."oi6 


8.2km 


52 


o!'o4i 


9.6 km 


A 


55 


o.oiq 


10.0 


104 


0.067 


10.7 


F 


20 


O.OII 


10. 1 


45 


°-53 


24.6 


G 


63 


0.013 


10.6 


6o 


0.67 


24.9 


M 


27 


0.015 


12.6 


12 


0.17 


17.6 



The agreement of these results with those obtained from the 
K-type stars is surprisingly close, and suggests that the empirical 
law connecting proper motion and radial velocity derived by Kap- 
teyn may be applied to the other types of spectra quite as well. 
Only a few A-type stars of very large proper motion have been 
observed at Mount Wilson. Of those for which n exceeds o''20, 
two have velocities exceeding 150 km; one has a velocity of 87 km; 
and the average for the other six is 20 km. 

The main feature of interest resulting from this comparison of 
proper motion and radial velocity is the low average velocity found 

1 Stellar Movements, p. 161. 

2 Velocities exceeding ioo km have been omitted. 



RADIAL VELOCITIES OF FIVE HUNDRED STARS 193 

for the very distant stars of types F to M. The selection of stars 
on the basis of small proper motion means, of course, the selection 
not alone of distant stars but also of those which have small intrinsic 
velocities as well as those whose motion is mainly in the line of sight. 
These factors will affect the results to some extent, especially when 
comparatively small numbers of stars are used. On the other hand, 
the direct comparison of the average velocities of groups of stars of 
greatly different average proper motions means a comparison in 
part between stars of widely different distance, and in part between 
slowly moving stars of one type and rapidly moving stars of another. 
If the rate of change of velocity with spectral type is as gradual as 
seems probable from these results, a very accurate knowledge of 
the stream motions for the different types of stars will be essential 
for a determination of its true value. 

No attempt is made here to discuss the well-known investiga- 
tion by Kapteyn, 1 in the course of which he first analyzed the 
relationship of radial velocities and proper motions to spectral 
types; nor the work of Boss, 2 in which he deduced the linear cross- 
motions of the stars of his catalogue according to spectral type. 
There can, of course, be no doubt that among the stars selected on 
the basis of apparent brightness those of the solar type are moving 
more rapidly than those of types A and B. The question which is 
raised is whether there exists any such marked difference for the 
stars of the solar type with distances comparable to those of types 
A and B. 

The small proper-motion stars of types F to M whose motions 
are considered here are on the average stars of very high absolute 
luminosity. The possible existence of a relationship between abso- 
lute brightness and velocity has been discussed in the communica- 
tion by Kapteyn and Adams, to which reference has already been 
made. The observational material essential to an investigation of 
this question would necessarily be much more extensive than that 
given here, and should be selected with this purpose in view. It 
may, however, be noted in passing that the average radial velocity 
of the stars of very low absolute luminosity is extraordinarily great. 

' Ml. Wilson Contr., No. 45; Astrophysical Journal, 31, 258, 1910. 
2 Astronomical Journal, 26, 187, Xos. 623-624, 1911. 



i 9 4 WALTER S. ADAMS 

Of the stars in the Groningen list of parallaxes with absolute mag- 
nitudes of 8 or fainter (sun =5. 5) sixteen have been observed to 
some extent at Mount Wilson. The average velocity of these stars 
(corrected for the sun's motion) is 36 km; eight have velocities 
exceeding 40 km, although none have been included with values 
higher than 100 km. It is difficult to think of these stars as other 
than stars of small mass, and the results for their velocities would 
be in agreement with the hypothesis suggested by Halm 1 that the 
motions of stars are a function of their masses. 

I am greatly indebted to several of my colleagues at the Observa- 
tory, and particularly to Dr. Kohlschiitter, for much of the observa- 
tional material upon which these results are based. Several of the 
members of the Computing Division have assisted in measuring and 
reducing the photographs. 

Mount Wilson Solar Observatory 
June 1915 

1 Monthly Notices, 71, ('34. 1911. 



THE INFRA-RED ARC SPECTRUM OF BARIUM 

By H. M. RANDALL 

This paper continues work on the infra-red arc spectrum of 
barium, the first results having appeared in 19 n. 1 The barium arc, 
produced by introducing the fused chloride in the positive carbon, 
has always proved most unsatisfactory for bolometric measure- 
ments since these demand for the best results radiant sources of 
constant intensity, while the barium arc on the contrary varies 
greatly in intensity, goes out easily, and shifts erratically about the 
carbons. Work with other materials having shown that large 
currents were sometimes effective in producing steady arcs, their 
effect upon the barium arc was tried. Currents of 70 amperes or 
over from a 220-volt power circuit were found to give arcs relatively 
steady as compared with those produced by currents of 15-25 
amperes. In general, except for this increased steadiness and an 
expected increase in brightness, the arc was of the same type as 
that obtained with smaller currents. At times, however, the 
arc becomes brilliantly white and burns very noisily though it is still 
steady. Under these conditions lines appear which are not obtain- 
able with the usual type of arc characteristic of smaller currents. 
Most of the measurements have been made, therefore, with this 
type of arc. It has not yet been found possible to control these 
two types which change readily the one into the other; although 
in general a large current and a positive carbon well rilled with salt 
and so shaped as to keep the heat in the end seems favorable for the 
maintenance of the noisy arc. Occasionally for considerable periods 
of time it may be thus maintained and settings on lines readily 
made. At other times it appears irregularly and observation 
becomes very tedious and difficult. To the use of this arc, however, 
must be largely ascribed the many new lines now given, as most of 
them are not otherwise observable. 

Fig. 1 shows sufficiently the general arrangement of apparatus. 
The arc is mounted within a water-cooled jacket. A, which is 

1 Annalen dcr Physik, 33, 739, 1910; Astrophysical Journal, 34, 1, 1911. 

i95 



196 



H. M. RANDALL 



provided with a forced draft for carrying the fumes from the room. 
The silvered mirrors M 2 , M 3 have a focal length of 50 cm and are 
10 cm in diameter. The grating G is mounted on the rotating 
table of a large Fuess spectrometer as designed by Paschen. 1 It 
has proved extremely satisfactory. The aluminum grating sup- 
port carries a thermometer for recording the temperature of the 
grating. The angle between the mirrors M 2 and M 3 as seen from 
the grating is about 14 ; the length of the slit S and the correspond- 
ing slit before the linear thermopile T is 14 mm, while the slit- 
width is 0.2 mm. This corresponds to a spectral region at 
10,000 A, of 6 A; at 30,000 A, of 3. 6 A. The entire optical system 
from 5 to T is inclosed within a blackened case. 



M 




Fig. 1 



Two parallel telescopes, one for each eye, enable the observer 
to watch simultaneously the galvanometer scale and the slit S, the 
latter being brought into range by suitably mounted plane mirrors. 
While observing, the operator, with his right hand, rotates the 
grating, using the slow-motion screw of the spectrometer, while 
with his left hand, by one set of pulleys, he can rotate the mirror M 
about a vertical axis and keep the image of the arc upon the slit S. 
By another set he can open and close the arc itself. As he is seated 
directly beside the arc, he is also able to replenish the arc with salt 
when it is required. While this complicates matters for the 
observer, it is not without its compensating advantages, as there 
is little danger of continuing observations with slit poorly illumi- 

1 Giesing, Aiuuiloi der Physik, 22, 333, 1907. 



THE INFRA-RED ARC SPECTRUM OF BARIUM 197 

nated either from want of salt in arc or from shift of arc itself. This 
is of particular importance during the examination of the spectrum 
for lines. 

The galvanometer and linear thermopile are of the Paschen 
type, 1 the galvanometer in fact being the one previously used by 
the writer in Professor Paschen's laboratory in Tubingen. I wish 
here to express my appreciation of Professor Paschen's kindness 
in making possible its removal to the University of Michigan. It 
is a pleasure also to state my indebtedness to Professor Hussey of 
the department of astronomy of the University for the loan of the 
grating employed in the work. This is a 6-inch plane grating 
ruled by Dr. Anderson of Johns Hopkins University, having 
approximately 1 5 ,000 lines per inch . It has proved a very excellent 
grating for this work and has been particularly good in the neigh- 
borhood Of 3 fJL. 

The mercury line 10,140.15- from a Heraeus quartz lamp was 
used as standard line in the calibration of the spectrometer. 
Energy-curves of the first-order lines to left and right were obtained 
by methods already described, which determined their positions 
accurately to within one second. The spectrometer constant given 
by the equation 

A = Csin 6 

was 33, 552. 4 A, and remained constant within the fraction of an 
Angstrom unit, as numerous calibrations at different times showed, 
corrections being made for small temperature changes in the 
grating. A complete check upon the constant so obtained resulted 
when the helium line 10,830. 12 3 was employed, the illumination 
perpendicular to the capillary of the tube being used. 

The entire spectrum between 32,000 A and 11,000 A was slowly 
passed over the slit of the linear thermopile, and spectrometer 
readings, sufficient to locate lines, were taken whenever the galva- 
nometer indicated the passage of a line over the slit. This exami- 
nation, first made with a slit 0.2 mm wide, was repeated with a 

1 Paschen, Annalen dcr Physik, 33, 736, 1910; Zeilsckrift fur Instrumentenkunde, 
13, 17, 1893. 

2 Yolk, Dissertation, Tubingen, 1914. 

3 Ignatieff , Annalen der Physik, 43, 1135, 1914. 



198 H. M. RANDALL 

slit 0.5 mm wide, the second search yielding a number of weak 
lines and a few strong ones overlooked during the search with 
the narrow slit. Lines found in this manner are entirely free from 
any bias on the part of the observer, and only lines so found are 
reported here. 

The measurement of the lines was made with the narrow o. 2 mm 
slit except where otherwise noted. The method of setting on a line 
has been described in detail in the previous paper and will not be 
repeated here. The results given in Table I are the mean of 
several determinations taken at different times. The intensities, 
based upon a slit-width of o. 2 mm, are roughly the means of the 
observed galvanometer throws during the settings on the lines 
while undergoing measurement. The wave-lengths, in Angstrom 
units, are as measured in air according to the Rowland scale. 
The frequencies are the reciprocals of the wave-lengths reduced 
to corresponding values in vacuo. In general the values given may 
be considered correct within 2 A except in those cases especially 
noted. 

The effect of such large currents upon the value of the wave- 
length cannot be stated in the case of those lines which are 
observable only when large currents are used, but where lines are 
measurable with relatively small quantities of salt and current no 
differences have been noticed. This is shown by the values con- 
tained in Table II. 

These values were obtained at different times during a period 
of a year during which the spectrometer had been readjusted several 
times, the mirrors having been resilvered and the grating exchanged 
for another and then replaced. 

A number of the lines given in Table I are superposed by 
higher orders of shorter wave-length lines; in all such cases measure- 
ments were made through suitable screens and shorter wave effects 
eliminated. 

The carbons used gave the K lines 11,689. 1- II -77 I • 1- 15,165 . 8, 
as impurities, the values found agreeing within 1 A of the measure- 
ments of Paschen. No other impurities were present in sufficient 
amount to give measurable effects. All the lines were, however, 
checked by using graphite rods most kindly furnished me by 



THE IXFRA-RED ARC SPECTRUM OF BARIUM 
TABLE I 



199 



Int. 


Wave-Length 


Maximum Vari- 
ation from Mean 


Frequency 


Remarks 




9.S27-3* 


3-5 


10.493 -3 


Starred values those of former 




9,610. 7* 


3° 


10,402. 2 


paper given here for complete- 




9.7I3-4* 


1 .0 


10,292.3 


ness 




9,831- 7* 


2.0 


IO,l68.5 






10,002. 1* 


1 .0 


9,995-3 




60 


10,034.8* 


1 .0 


9,962.6 


10,035 ■ 6 =*= 2 previous value 
10,034 . 1 ± 1 . 5 present value 




10,189. l * 


0.50 


9.811.8 






10,233.8* 


05 


9,768.95 






10,272.9* 


1 .0 


9,73!-7 






10,474.4* 


1 .0 


9,544-5 




So 


10,650.5* 


2.00 


9,386.8 


10,652.4 previous single value 
10,649 - 5 ± 1 present mean value 


20 


10,692.0 


1 .00 


9,35o.3 




40 


11,016.4 


2 .00 


9,o74 9 




IO 


11,116.0 


1 .0 


8,993.6 


Mean of two values; 0. 5 mm slits 


20 


11,304 2 


0.0 


8,843.8 




20 


1 1 ,608 . 1 


05 


8,612.4 


. 5 mm slits 


50 


11,885.7 


2.0 


8,411.2 


Possible error ±3 A 


15 


11,978. 2 


2.00 


8,346.3 


Possible error = fc 3 A 


5° 


12,084.0 


i-5 


8,273.2 


Not Mg line 12,083. 2; strong Mg 
lines lacking 


3° 


12,554-3 


2.0 


7,963 -2 


Possible error ±3 A 


10 


12,814.8 


i-5 


7,8oi.3 




10 


13.057.4 


0.5 


7,656.4 


. 5 mm slits 


40 


13,207.3 


05 


7,569-6 




40 


13,810.5 


2.0 


7,238.9 


Possible error = fc 3 A 


20 


13.956.5 


2-5 


7,163.2 


Possible error ±3 A 


40 


14,077.9 


i-5 


7.IOI.4 




30 


I4.I59-5 


2.0 


7,060.5 




25 


14,211 .4 


1 .0 


7.034-7 




25 


14,325.4 


05 


6,978.8 




40 


15,000.4 


0.5 


6,664. 7 




10 


17,064.8 


2.0 


5.858.4 


0.5 mm slits. Possible error 
=±=3 A 


- 


17.182. 5 




5,8l8.3 


Doubtful, but once measurable. 






0. 5 mm slits 


15 


18,204. 1 


3-o 


5,49i -8 


Possible error ±3 A 


20 


19,074.6 


1 .0 


5,241-2 




25 


19,987.9 


i-5 


5,001.7 




40 


20,712.0 


05 


4,826.8 


Two values also at 20,705 . 7 


15 


21,477.2 


05 


4,6549 






22,220.8 


i-5 


4,499.1 




20 


22,3134 


0.5 


4,480.5 




30 


23,255 -3* 


1 .0 


4,2989 


Former value 23,254.8 
Present value 23,255.7 


50 


2 5-5 x 5 • 7 


0.5 


3.918. 1 




20 


26,221 .4 


i-5 


3,812.7 


0. 5 mm slits 


30 


27.751-1 


0.0 


3,602.5 


Mean of two values onlv 


50 


29,223.9* 


1 .0 


4,3210 


Former value 29,223.4 
Present value 29,224.5 


35 


29,790.6 


0.5 


3,355-9 




15 


30,468.5 


0.0 


3,281 . 2 


Mean of two values; 0.5 mm 
slits 


20 


30,686.9 


0.5 


3,257-9 


0. 5 mm slits 


30 


3o,933 -8 


0.5 


3,231-8 





200 H. M. RANDALL 

Professor Saunders; the barium chloride used was that of 
Schuckert and showed no noticeable traces of impurities. 

As regards series relations the earlier paper suggested a first 
term for the subordinate Series I of doublets which led to a couple 
of combination terms, which in fact were the principle reasons 
for their choice, as the frequency-differences were not very good 
and the wave-lengths somewhat small for this term; the selection 
was called a doubtful one. Shortly after its publication Professor 
Saunders wrote calling attention to the fact that the lines 10,035.6 

TABLE II 

Ci rrext 70-80 Amperes with Large Quantities 
of Salt in Carbon. 0.5 mm Slits 



Intensities 


53 mm 70 mm 60 mm 


X 30,934 -2 29,791.2 29,225.6 
x 30,933 -5 -'0,790.7 29,223.4 


Current 30 Amperes with Small Quantities 
of Salt in Carbon. 0.2 mm Slits 


Intensities 


15 mm 


20 mm 30 mm 


X 30,933 ,7 


29,790. I 


29.224.7 



and 10,652 .4 have a frequency-difference of 575 which characterizes 
the narrow pairs found in the ultra-violet by Lyman and that if 
there were a line at 12,085 the three could make a first term for the 
subordinate Series I of doublets and would strengthen the relation 
apparently existing between the first terms of the wide-pair series 
and the narrow-pair series, already fairly well established in case of 
Ca and Sr. An examination of the original observations showed 
no trace of any such line; neither did a search for it under approxi- 
mately the same experimental conditions as obtained in the original 
work. When, however, the spectrometer readings roughly locating 
the lines found during the first search with large arc currents 



THE IXFRA-RED ARC SPECTRUM OF BARIUM 201 

through the spectral region 32.000-11.000 A were worked out, a 
line at 12,085 appeared among the rest. It is a line not obtainable 
with small current and quiet arc, though always present with the 
other type. The similarities which this triplet and the narrow pair 
series show to the corresponding terms of calcium and strontium 
constitute their principal claim to being considered the correspond- 
ing quantities for barium. While as far as frequency-differences 
are concerned, this group leaves little to be desired, its wave-lengths 
are shorter than might be expected from analogy to the correspond- 
ing ones of calcium and strontium. It is to be noted also that the 
line 12,084.0 does not appear under conditions which readily pro- 
duce the other two, i.e., the quiet arc. A group better meeting the 
requirements of this point of view does not, however, appear in the 
present data, nor was such a group found among the results of a 
preliminary survey of the region 3 fi to 10 // with a coarser grating. 

It should be added that this relationship has been recently chal- 
lenged by Popow, 1 who suggests the group 6498.9, 6143.6, 5855.5 
(X vac.) for the first term of the subordinate Series I of doublets and 
the group 2348.4, 2336.0, 2305.0 (X vac.) as a term of the corre- 
sponding ultra-violet series. The question must remain open await- 
ing further experimental data. 

The group of lines, only two of which were previous!}' found. 



Mean 32,952.6 



2 p 1 


28,472.0 




29-350 4 


29,720. 7 2 


A 


22,313.4 




27.75I- 1 


3o,933 ■ 8 


7 


4.480.4 


877.9 


3,602.5 370.7 


3,2318 


3d" 


32,9524 


32,952.9 


32.952- 5 




181. 5 




181. 5 




A 


23,2553 




29,223.9 




7 


4.298.9 


877.9 


3,42io 




3d' 


32, 77°-9 


32,771-4 






380.8 








A 


25>5i5-7 








7 


3,918.1 








3d 


32.390- 1 





32,7712 



32.390.1 



1 Annalen der Physik, 45, 171, 19 14. 

2 Ritz, Astrophysical Journal, 29, 243, 1909. 



202 //. M. RANDALL 

is characterized by the frequency differences 878, 371, typical of 
the main subordinate Series I of triplets, while the differences 381, 
181 are typical of the series of narrow triplets. It may be regarded 
accordingly as the first term of the subordinate Series I of triplets, 
and is a reversed group. The limits 3d 1 of the narrow triplet 
series are accordingly 32,952.6, 32,771.2, and 32,390.1, on the 
basis of the foregoing values of 2 pi from Ritz. 

In conclusion I wish to express my indebtedness to Mr. E. A. 
Porter for material assistance in recording the observational data. 

Physical Laboratory 

University of Michigan 

June 1915 



Reviews 

Tables for Facilitating the Use of Harmonic Analysis. By H. H. 

Turner. London: Oxford University Press, 1913. Pp. 46. 

is. 
The author's extensive work on sun-spot periodicities has led him to 
develop many useful short-cuts in computing. In these tables he gives 
the coefficients in thirteen Fourier series from nine to twenty-one terms 
in length. The tables are intended for "exploring" work and hence are 
given to two places only. Ample illustration is given of their use, with 
criteria for interpreting the value of any resultant periodicity. The 
compilation should encourage the use of harmonic analysis by anyone 
who is searching for possible periodicities in long series of observations. 

O. J. L. 

The Sun. By R. A. Sampson. Cambridge: University Press. 

1914; Xew York: Putnam. Pp. viii+141, figs. 18. Cloth, 

So. 40, leather, Si. 00. 
This little volume of the "Cambridge Manuals of Science and 
Literature" presents a very acceptable resume of the present state of 
our knowledge of the sun. The inspiring introduction sets forth in 
a telling way the part which the sun has played in the actual march 
of science. "Very many of our theories radiate from it and find in it, 
as in a great physical laboratory, their first and most striking appli- 
cation." Then follow chapters on "Radiation," "The Sun as the 
Mechanical Center of the World," "The Spectroscope," "The Sun's 
Surface," "Periodicity," "Eclipses," and "The Sun as a Star/' which 
pretty well cover the whole of what assiduous research has revealed. 
Inaccuracies are few indeed; there are no serious omissions; it is well 
balanced, and written in attractive, even brilliant, style. A fair sample 
of nicely turned phrase is the characterization of the determination of 
stellar parallax, as "a debt of honor, which since the acceptance of 
Copernicus's theory, science is called upon to pay." 

The volume might very fittingly be used in teaching, to elaborate 

somewhat the chapters on the sun found in the usual textbook. 

P. F. 

203 



204 REVIEWS 

V Astronomic By Marcel Moye. Paris: O. Doin et Fils, 19 13. 
Pp. 382, figs, in text 43, plates 4. Fr. 5. 

Of the projected twenty-nine volumes of the astronomical section 
of the series of publications, the " Encyclopedic scientifique," this is the 
fourth to appear. The earlier volumes — those of Salet, Bosler, and 
Boquet — were of high grade, and the present work in no way departs 
from their standard, though from the very nature of its purpose it is 
radically different in style. It is the first volume of the series, the 
general view of the whole subject, the broad survey; its various phases 
find in the other volumes the technical and detailed presentation. 

American teachers and students will recognize that the arrangement 
of the various chapters, as well as the order of matter within the chapters, 
is similar to that of the various textbooks of Professor C. A. Young, and 
is therefore excellent. The view is modern; the important recent 
advances are generally noted. 

It is to be hoped that the war and the consequent diversion of 
scientific thought will not put an end to, or greatly delay, this useful 
series of publications. 

P. F. 



Slo/ 



THE 

ASTROPHYSICAL JOURNAL 

AN INTERNATIONAL REVIEW OF SPECTROSCOPY 
AND ASTRONOMICAL PHYSICS 



VOLUME XLII OCTOBER 191^ NUMBER 3 



THE REFLECTING POWER OF METALS IN THE ULTRA- 
VIOLET REGION OF THE SPECTRUM 

By E. 0. HULBURT 
INTRODUCTION 

Knowledge of the reflecting power of metals in the ultra-violet 
region of the spectrum is far from complete. It was the purpose 
of the present investigation to extend as far as possible into the 
region of shorter wave-lengths the curves of reflecting power for 
metals, and thus to obtain data which might be of service in design- 
ing apparatus for use in ultra-violet work, and which might also 
possess theoretical value. In the present work the reflecting powers 
of metals, for an angle of incidence of 18 , have been measured 
throughout the region 3800 to 1800 A by a direct method. 

HISTORICAL 

In 1902 Hagen and Rubens 1 published the results of their 
measurements on six of the more common metals — silver, gold, 
platinum, copper, nickel, steel — and on four alloys, in which the 
curves of reflecting power were carried out as far as wave-length 
2500 A. The method used was a direct one, and consisted in 

1 Annalen der Physik, 1, 352, 1900; 8, 1, 1902. 

205 



206 E. O. HULBURT 

observing the incident and reflected intensities of a monochromatic 
beam of light by means of a sensitive thermo-couple. Their table 
has stood as the final word on the subject. 

Beyond wave-length 2500 A there have been within the knowl- 
edge of the present writer no direct determinations at all of the 
reflecting power of any substance. 

In 1903 Minor 1 made katoptric measurements on four metals — 
copper, steel, cobalt, and silver. He used a photographic method, 
and was able to get measurements for two points beyond 2500 A, 
namely, at 2313 and 2265 A. The reflecting powers were calculated 
by means of Drude's well-known formula connecting the reflecting 
power, the refractive index, and the absorption coefficient of the 
metal. 

In 1 9 10 Meier, 2 using a method similar to that employed by 
Minor, determined the reflecting powers from katoptric measure- 
ments down to wave-length 2500 A for gold, nickel, iron, platinum, 
bismuth, zinc, selenium, and for several alloys. 

The results of these three investigations comprise our total 
knowledge on this subject, for the observations of other experi- 
menters have contributed nothing new. 

METHOD 

The principle of the method employed in the present investiga- 
tion was very simple. Light from a source rich in ultra-violet light 
was resolved into a spectrum, and a small, nearly monochromatic, 
beam was isolated by the slit B, Fig. 1, of the spectrograph, and 
passed into the metal chamber shown in Fig. 1. The intensity of 
the direct beam was measured by a photo-electric cell F connected 
with an electrometer. The intensity of the beam when reflected 
was measured by the same cell. This was effected by swinging both 
the cell and the mirror from their original positions M and F to the 
new positions M' and F' respectively. The length of the optical 
path from the slit to the cell was kept constant for the two positions. 
Consequently the ratio of the two measurements gave the reflecting 
power of the mirror. 

1 Annalen der Physik, 10, 581, 1903. 2 Ibid.. 31, 1017, 1910. 



REFLECTING POWER OF METALS 



207 



APPARATUS 

The spectrograph. — This consisted of the usual Rowland mount- 
ing of a very fine concave speculum metal reflecting grating (C, 
Fig. 1) of 50 cm focal length. The grating had a ruled surface 
6X9 cm, and was ruled in this laboratory especially for the purpose 
of this investigation. Slit A, Fig. 1, back of which the source of 
light was placed, was fixed on a movable brass arm CD. This arm 
was constrained to move by a pin through a slot at end C, and a 
pivoted slot underneath A sliding on a curved brass track BA, so 




40cm 



Fig. i. — Horizontal plan of spectrograph 

that slit A moved on the circumference of the circle whose diameter 
is CB. CB was 50 cm in length. Underneath the brass arm AC 
at D was a nut which worked without play on a steel screw (24 
threads to the inch) ; by turning this screw the brass arm holding 
the slit A could be moved, thus allowing various wave-lengths to 
pass through slit B. Wave-lengths could be recorded by this 
apparatus throughout the region from 3800 to 1000 A. 

The grating was ruled 15,000 lines to the inch by a diamond 
point so selected that the first-order spectrum on one side was very 
bright, and this bright first order was used throughout the present 
work. The spectrum, brought to a focus at slit B, was normal, and 
the dispersion of the grating was such that with slit B o . 5 mm wide 
a beam containing a wave-length range of 16 A passed through. In 
the present work slit A and slit B were both o. 5 mm wide. 



208 



E. 0. HULBURT 



The source. — -An end-on hydrogen discharge tube, such as is 
described by Lyman, 1 was employed as the source of light. The 
tube was of the internal capillary type, equipped with a fluorite 
window and filled with hydrogen at about i . 5 mm of mercury 
pressure. This was excited by a 1 100- volt transformer taking from 
0.5 to 1.5 amperes in the primary, run on 60-cycle, 1 10- volt, 
alternating current. This tube, painted black, and wrapped with 




Fig. 2. — Metal chamber (elevation) 

tin-foil radiators to keep it cool, was clamped in position back of 
slit A. 

The photometer. — The light from the hydrogen tube was brought 
to a focus at slit B, and then passed into the metal chamber shown 
in horizontal section in Fig. 1 and in vertical section in Fig. 2. 
Inside this compartment was placed a photo-electric cell F, which, 
when connected with the electrometer, measured the intensities of 
the incident and reflected beams of light. The metal chamber, 
from which the end hg could be removed, served, when closed, to 
screen the photo-electric cell from all light, except the beam coming 
through slit B, and also to protect the cell and connections from 

1 Astrophysical Journal, 23, 181, 1906. 



REFLECTING POWER OF METALS 209 

electrostatic disturbances. The cell was supported in a brass 
frame 7, rotating around a vertical axis. A second frame M (shown 
in dotted lines in Fig. 2) served as a support for the metal mirror. 
The mirror frame and the photo-electric cell frame were connected 
by a spring, so that when the cell was swung from F to F' the mirror 
swung from M to M' (Fig. 1). This whole shift could be made 
from the outside. The distance from the slit B to the mirror was 
5 cm, and a mirror surface 4X 2 mm was large enough to reflect a 
cone of light of sufficient size to completely cover the window of 
the cell at F' . The photometer consisted of the photo-electric cell 
and electrometer. The spectrum from the hydrogen tube was of 
very small intensity, even when the grating used was one of such 
short focal length and of such large area of ruling. Hence the 
instrument used to measure the intensity of the beam had to 
possess the utmost sensitiveness. 

A cell in which sodium is the active metal is known to be very 
sensitive, and accordingly a method of preparing sodium photo- 
electric cells was developed, 1 and the cell finally selected was 
equipped with a fluorite window 14 mm in diameter and 1 mm in 
thickness. This sodium cell was wrapped in tin foil and placed in 
the supporting frame. The wire to the electrometer led from the 
cell through the jointed copper tube A', Fig. 2, out through sulphur 
supports to the earthing key, and thence to the electrometer. The 
electrical connections are shown in Fig. 2. The earthing key was 
merely a pointed brass rod touching a small brass plate, both made 
of the same piece of brass and filed bright. This gave no trouble 
with contact difference of potential. This type of key is, in the 
author's experience, much better than any mercury or electrolyte 
key, requiring absolutely no attention after it is once made, and 
giving complete satisfaction even for the most delicate work. 

The electrometer was a Dolezalek quadrant electrometer with 
an aluminum needle. The needle was suspended by a quartz fiber 
rendered conducting by a slight coating of platinum put on by 
cathode sputtering, and was charged to no volts from a constant 
potential storage battery. In this work the electrometer had a 
sensibility of 3300 mm per volt difference of potential between the 

1 Hulburt, Astrophyskal Journal, 41, 400, 1915. 



210 E. O. HULBURT 

quadrants (the deflections being observed on a scale four meters 
distant), and in this case the needle had a free period of 21 seconds. 
The electrometer and the wire leading to the photo-electric cell were 
inclosed in metallic shielding made air-tight. 

Through the kindness of Dr. E. Karrer, of the United Gas 
Improvement Company of Philadelphia, the writer secured the use 
of a potassium photo-electric cell which proved of the greatest 
service in the preliminary setting up of this apparatus. 

In taking observations it was found most convenient to use the 
steady-deflection method, rather than a rate-of-drift method. The 
procedure was as follows: The connection to earth was broken, and 
the reading of the position of the electrometer needle recorded; then 
the hydrogen tube was turned on for a convenient length of time, 
e.g., 15 seconds, and the reading taken again after the needle had 
come to rest. If there was a natural drift of the needle — i.e., a 
drift when the cell was in the dark — the final reading was taken one 
minute after the first reading and the drift during the interval sub- 
tracted. During the course of the work there were times when the 
drift was zero and times when it amounted to as much as 10 mm per 
minute. The exact cause of the drift was not found, but the drift 
always increased with a rise in temperature of the room; probably 
this rise in temperature augmented the natural ionization of the air, 
and doubtless also produced effects in the photo-electric cell. The 
current through the hydrogen tube and the time of exposure were 
adjusted to produce deflections of convenient size; whenever pos- 
sible, deflections for the direct beam of 100 to 200 mm were used. 

The intensity of the light from the hydrogen tube fluctuated 
from day to day, but remained very constant for shorter periods of 
time. The changes in intensity were occasioned by changes in 
pressure inside the hydrogen tube, which were produced by the 
absorption and evolution of gases by the electrodes. Also the tube 
became gradually weaker and weaker in the region from 2500 A 
down. This was due to a film being formed on the inside of the 
fluorite window by the discharge; this film was invisible, but upon 
cleaning the window and refilling the tube with hydrogen the origi- 
nal power of the tube was regained. However, a single tube was 
useful for a month. 



REFLECTING POWER OF METALS 211 

The sensibility of the photo-electric cell did not change per- 
ceptibly in several months, and since at all times the intensity of 
the light falling on the cell was very feeble, no evidences of photo- 
electric fatigue were ever observed. 

Measurements made with this apparatus on a polished quartz 
surface gave values of the reflecting power which agreed within the 
experimental error with the calculated values. Also the agreement 
with the results of other observers is satisfactory. Single observa- 
tions varied by as much as 7 per cent, so the final values recorded 
in the work are the means of from two to six measurements. It is 
considered that the final values are correct to two parts in one 
hundred for reflecting powers above 25 per cent, the error increasing 
for lower values of the reflecting power. 

RESULTS 

The results are given in the form of curves, Figs. 3-7. The 
curves are plotted with the reflecting powers as ordinates and the 
wave-lengths in Angstrom units as abscissae. The reflecting pow- 
ers, for an 18 angle of incidence, were measured at intervals of about 
60 A. In all cases where it is possible, comparison tables are given 
between the values for the reflecting powers determined by other 
workers and the values given in this paper; but it is to be noted 
that the reflecting powers found by others are for an angle of inci- 
dence 1-2 , or for normal incidence (when the reflecting power is 
calculated from katoptric measurements), whereas the values found 
in this work are all for an 18 angle of incidence. 

Aluminum (Fig. 6). — Brilliant cathodic films of aluminum were 
produced by sputtering on glass from a freshly scraped aluminum 
cathode in an atmosphere of mercury vapor. It required about 
three hours to deposit an opaque layer of the metal. The curve is 
for an opaque film of aluminum. It is interesting to note that, with 
the exception of silicon surfaces, these films were the most efficient 
ultra-violet reflectors found. 

Antimony (Fig. 4). — The mirror of Curve II was a cathodically 
deposited mirror from the Bureau of Standards, and although nearly 
free from imperfections, it did not seem as white as the aspect of the 
crystals of the metal would seem to indicate. 



212 



E. 0. HULBURT 




2000 



3000 AH Wave-Lengih 




2000 



3000 A.U. Wave-Length 



Fig. 3 



REFLECTING POWER OF METALS 



213 




2000 



3000 A.U. Wave-Lengfh 



Fig. 4 



214 



E. O. HVLBVRT 




2000 



3000 A.U. Wave -Length 




2000 



3000 A.U Wave -Length 



Fig. > 



REFLECTING POWER OF METALS 



215 




2000 



3000 A.U. Wave-LengTh 




2000 



3000 A.U. Wave-Length 



Fig. 6 



A freshly split cleavage surface of a crystal, not perfect, how- 
ever, but crossed by many cracks and crevices, resulted in Curve I. 
This did not deteriorate appreciably after standing for three 
weeks. 



2l6 



E. O. HULBURT 



%Re(l. Power 
50 




2000 



2000 



3000 A.U. Wave-Length 




3000 AU. Wave-Length 



Fig. 7 



REFLECTING POWER OF METALS 



217 



Bismuth (Fig. 6). — This metal was found to sputter readily. 
The brightest surfaces were obtained when the deposition took 
place in an atmosphere of hydrogen. The curve is for an opaque 
film. Table I shows the comparison with results obtained by 
another observer. 



TABLE I 

Reflecting Power of Bismuth 



Wave-Length 


Meier 
Polished Plate 


E. 0. H. 

Cathodic 


2573 


20. 1 
24.8 
3 1 - 2 
36.O 
42.5 


25 
26 


2981 

3255 


29 
34 


3611 


36 







Cadmium (Fig. 6). — This is a very white, soft metal and 
yielded bright films when sputtered cathodically in an atmosphere 
of hydrogen. Care had to be taken, as in the case of chromium, 
not to run the discharge too long at a time; for the yellow oxide 
very readily made its appearance, spoiling the deposit. The film 
was found to come down very quickly, a half-hour discharge being 
sufficient to produce opaque surfaces. These deposits were bright, 
but very soft; even brushing with a powder-puff produced scratches. 

Carbon (Fig. 3). — -Sputtering for four days from a piece of pure 
graphite produced a thin film of carbon slightly more opaque than 
the chromium firm of Curve II (see chromium). In view of the 
fact that silicon possesses such remarkable reflecting properties in 
the ultra-violet, carbon, which is its near neighbor in the periodic 
system and which possesses similar electrical properties, might also 
be expected to show a high reflecting power in this same region. 
It is seen from the curve that the reflecting power of this carbon 
film is very low. 

Carborundum (Fig. 6). — A perfect surface of a crystal was 
measured without further polishing. It was hoped that on account 
of its relation to silicon the carborundum might show peculiar 
reflecting properties. However, the curve for carborundum is of the 
same character as the curve for any dielectric, such as quartz. The 



218 E. O. HULBURT 

value of the reflecting power, 20 per cent at 2000 A, indicates a very 
high value of the refractive index. 

Chromium (Fig. 5). — This metal is very white and is known to 
possess a high reflecting power in the visible region of the spectrum. 
It does not tarnish in air, and is not acted on by the ordinary 
reagents. Metallic chromium at present cannot be obtained free 
from small holes, and it was thought that cathodic films of this 
metal would be very serviceable, if they could be prepared. 

The results are rather disappointing. Curve I is for an opaque 
film of chromium deposited cathodically on glass. The film was 
bright and free from imperfections, but showed a slight brownish 
tinge, which was undoubtedly due to traces of some impurity, prob- 
ably the oxide or carbon. Curve II is for an extremely thin film, 
which, however, did not have the brown tinge, but was a very light 
gray by transmitted light. A solid plate of chromium was polished 
with pitch and rouge. The resulting surface was very bright but 
had many fine holes. The curve for this was practically the same 
as Curve I. 

The curves show that surfaces of chromium are no better 
reflectors than films of many other metals which are much easier 
to prepare. 

A well-defined minimum is noted at 2400, and a maximum at 
2 1 50 A. The alloy stellite also shows this same minimum and maxi- 
mum, due no doubt to the presence of the chromium. 

Chromium deposits extremely slowly and it was found difficult 
to obtain clean white deposits. The best films were obtained by 
sputtering in an atmosphere of hydrogen, running the discharge for 
a minute, and then allowing the cathode to cool for a few minutes. 
It required a week of such treatment to produce an opaque film. 

Cobalt (Fig. 7). — A piece of rolled sheet cobalt was ground with 
emery, polished on pitch and rouge, and finally buffed. The sur- 
face took a good polish, being very bright, but showed many irregu- 
larities and corrugations. The reflecting power was surprisingly 
high, considering the appearance of the surface. Table II shows 
the comparison with results obtained by another observer. 

Copper (Fig. 4). — The electrolytically plated gold mirror men- 
tioned elsewhere was plated with copper from a solution of copper 



REFLECTING POWER OF METALS 



219 



cyanide. This was polished with rouge and chamois, giving a 
bright mirror, free from imperfections. Curve I is for this mirror. 



TABLE II 
Reflecting Power of Cobalt 




Measurements were made on two cathodic films of copper 
deposited on glass, one being more opaque and less red than the 
other. Both gave Curve II, which shows a more pronounced hump 
at 2800 A than other observers have recorded. Table III shows the 
comparison with results of other observers. 

TABLE III 
Reflecting Power of Copper 



Hagen 
Wave-Length and Rubens 
Polished Plate 



23*3- 
2510. 

2573- 
2 749- 
2880. 
2981. 
3050. 
3260. 

3467- 
3570. 



25 -9 



24-3 



25-3 
24.9 



27-3 



Minor 

Electrolytic 



29 





27 
27 


9 

2 


26 


4 




31 


5 



E.O. H. 



Electrolytic 



Cathodic 



29 

27. 
26 
28 
29 
29 
29 
29 
31 
33 



32 
33 
34 
36 
36 
35 
33 
32 
33 
35 



Gold (Fig. 3). — Several films of gold were deposited cathodically 
on glass. These deposits were very soft, and it was found that the 
character of the reflecting power changed after the mirror had been 
allowed to stand for some time in air. Curve I is the result of 
measurements on two different cathodic films of gold; these differed 
only in the thickness of the gold deposit, one appearing opaque and 



2 20 



E. O. HULBURT 



the other quite green by transmitted daylight. They were measured 
a few hours after being made, and gave the same curve, Curve I, 
showing that the gold deposit in each case was thick enough to act 
as an entirely opaque mirror. The curve shows a sharp maximum 
at 3010 and a minimum at about 3700 A. 

A second measurement of the two films two days later gave 
Curve II, and measurements a month later showed no further 
change in the curve. It is seen that the maximum in the curve for 
the older surface is no longer as sharply defined. 

An electrolytic gold mirror was made by depositing gold from 
a solution of gold cyanide on a speculum mirror. This deposit was 
rubbed with rouge and chamois, and a bright surface free from 
scratches was obtained. The curve for this mirror, when new, was 
practically the same as the curves for the old cathodic films. 
Unfortunately this mirror was not kept; hence its behavior with 
time was not recorded. 

The records for gold given by other observers do not agree 
with each other or with the values obtained in the present work. 
Table IV shows the comparison between the results of the various 
observers. Hagen and Rubens have not described how their mirror 



TABLE IV 
Reflecting Power of Gold 



Wave-Length 


Hagen 
and Rubens 


Meier 


E. 0. H. 


Curve I 


Curve II 


25/0 


38.8 


27.6 
27-5 
30.4 
35- 1 
37-7 


25 25 

29 20 


3050 

3260 

35/0 


31.8 
28.6 

27.9 


40 
32 
3° 


33 
30 
29 



was made. Meier measured a mirror of gold deposited electrolyti- 
cally, and in his paper (loc. cit.) called attention to the fact that he 
did not find any indication of the minimum in the curve of reflecting 
power which Hagen and Rubens record at 3570 A. 

Lead (Fig. 5). — This was found to sputter quite readily, the same 
precautions being necessary as were mentioned in the case of cad- 



REFLECT IXG POWER OF METALS 221 

mium. The films are very soft, but come down bright; they soon 
tarnish. The curve is for an opaque film. 

Magnalium (Fig. 7). — -It was not found possible to produce a 
good mirror of this alloy. The specimen was a piece of the alloy 
made in this laboratory, 69 per cent aluminum and 31 per cent 
magnesium. The surface finally measured had many pits and 
scratches, and did not have a high polish. Table Y shows the com- 
parison with other results. 

TABLE V 
Reflectixg Power of Magnalium 



Wave-Length Hagen and Rubens E. O. H. 

2510 : 67 21 



2880 70 

3050 72 

3260 75 

3570 81 



30 
34 
38 
45 



Magnesium (Fig. 3). — A mirror was made of this metal by buff- 
ing and finally polishing with dry rouge and chamois. The resulting 
surface was bright, but had a number of fine scratches and corru- 
gations. 

Molybdenum (Fig. 7). — This was a polished specimen of the 
metal obtained from the Bureau of Standards. The surface was 
bright and free from scratches. The curve shows a small minimum 
at 2500 A. 

Nickel (Fig. 3). — A fine mirror of nickel was obtained by first 
depositing a very thin cathodic film of nickel on glass, and then 
plating this electrically from a solution of nickel ammonium sul- 
phate. This gave a very clean white opaque film, free from imper- 
fections, and was measured a few hours after being made. The 
curve shows a well-marked maximum at 2 no A. Table VI shows 
the comparison with results obtained by other observers. 

Palladium (Fig. 5). — -This metal was deposited cathodically on 
glass, but the films thus made were not absolutely white; all showed 
a dark tinge. Several attempts to produce brighter deposits were 
unsuccessful, and it was decided that the color was due to the 



222 



E. O. HULBURT 



nature of the metal rather than to an impurity or surface film. The 
curve is for an opaque film. 



TABLE VI 
Reflecting Power of Nickel 



Wave-Length 


Hagen 
and Rubens 


Minor 
Electrolytic 


E. 0. H. 


2SIO 

2750 


37-8 


30-9 
37-6 

39-4 
40.4 
41.2 


38 
43 
46 

47 
49 


3050 

3260 

3570 


44.2 
45-2 
48.8 



Platinum (Fig. 3). — An opaque film of platinum was deposited 
cathodically on glass. Table VII shows the comparison with results 
of other observers. 



TABLE VII 
Reflecting Power of Platinum 



Wave-Length 



2510. 

2573- 
2749. 
2880. 
2981. 
3°5°- 
3255- 
3260. 
357o. 
3611. 



Hagen 
and Rubens 



Meier 
Electrolytic 



33-8 



38.8 
'39-8 



41.4 
43-4 



37 
43 


1 
1 


47 


6 


48 


9 





52.4 



E. O. H. 

Cathodic 



42 
43 
46 
48 
49 
49 
50 
5° 
5i 
52 



Selenium (Fig. 5). — This was an old mirror of metallic selenium 
which had been prepared by melting the metal and pouring it on 
glass. For a complete description of the method see Pfund, 
Astro physical Journal, 24, 19, 1906. Table VIII shows the com- 
parison with other results. 

Silicon (Fig. 6). — A solid piece of silicon was ground with emery 
and finally polished with pitch and rouge. The resulting mirror 
was full of pits and had a number of coarse scratches. However, it 
possessed a remarkably high reflecting power. 



REFLECTING POWER OF METALS 



223 



A polished specimen of silicon from the Bureau of Standards was 
measured, and between 3000 and 2000 A it showed a reflecting 
power of 76 per cent (Curve I). The mirror was slightly convex 
and had a number of holes and scratches. A special sample of 
silicon free from holes was obtained from the Carborundum Com- 
pany, Niagara Falls, and was polished by Dr. Anderson. This 
mirror gave Curve II. The reason for the difference between the 
two curves is not known. The two surfaces appeared very much 
alike; the one of Curve II seemed perhaps to have fewer imper- 
fections. 

TABLE VIII 
Reflecting Power of Metallic Selenium 



Wave-Length 

2573 

2749 

2981 

3255 

3570 



Meier 



E. O. H. 



23-3 
25-3 
31-8 

32-5 
30-3 



21 

24 
28 
28 
30 



Curve III is for an opaque cathodic film of silicon. The deposit 
was beautifully bright; its reflecting power for visible light more 
nearly approached that of fresh silver than any of the other metals 
investigated. In the ultra-violet it is seen that its reflecting 
power is somewhat inferior to that of the polished specimen of 
silicon. 

The sputtering from the silicon cathode was performed in an 
atmosphere of mercury vapor, an aluminum anode being used, and 
it is quite possible that the silicon films contained aluminum. The 
curve (Curve III) for such a film also points to the possibility of 
the presence of aluminum, it being lower in the shorter wave- 
lengths and higher in the longer wave-lengths than the curve for 
pure silicon. Subsequent experiment indicated that the percentage 
of aluminum present in these films was small. 

Silver (Fig. 4). — A chemically deposited film of silver on glass, 
polished with rouge and chamois, was measured. The film was 
opaque, and was measured about a day after being prepared 
(Curve I). A three-quarter film of silver, showing a dark 



2 24 



E. O. HULBURT 



gray-blue by transmitted light, gave Curve II. Table IX shows 
the comparison with other observers. 



TABLE IX 

Reflecting Tower of Silver 



Wave-Length 



2263. 

23I3- 

2500. 



Hagen and Rubens 



Fresh 



Old 



Minor 



E.O. H. 
Curve I 



3°5°- 
3160. 
3260. 
338o. 
357o. 



24.1 

21 . 2 
9.1 

4-2 
14.6 

55-5 
74-5 



17 .6 
14-5 



41. 1 



18.4 

19.9 



19.0 

11. 6 
4-2 
9.1 

61 . 7 
75 -3 



32 
33 
33 
33 
25 
17 
6 
18 

49 
67 



Speculum (Fig. 7). — knowledge of the reflecting power of this 
alloy, 68.2 per cent copper and 31.8 per cent tin, is of particular 
interest because Rowland diffraction gratings are ruled almost uni- 
versally on speculum. Curves I, II, and III illustrate the behavior 
of a speculum metal surface exposed to air. These curves were 
obtained from measurements on the same mirror. This mirror 
had a fine surface free from imperfections; it was freshly polished 
on pitch and rouge and was measured immediately, giving Curve I. 
Curve II was taken three days later; Curve III was taken seven 
days after the initial polishing. Table X shows the comparison 
with other observations. 



TABLE X 
Reflecting Power of Speculum 


Wave-Length 


Hagen and Rubens Curve I 


2SIO 

2880 


29-9 37 
37-7 41 
41-7 44 
51.0 60 


3050 

3570 



In this laboratory, gratings are ruled entirely on speculum metal. 
It is the practice before ruling to polish the surface afresh on pitch 



REFLECTING POWER OF METALS 22$ 

and rouge; hence a newly ruled grating finds itself in the condition 
of the mirror of Curve I. In subsequent use the grating either is 
never touched again, or at best is merely cleaned with chalk and 
alcohol. In order to find out definitely the efficiency of the usual 
grating. Curves IV and V were drawn; Curve V is for an old specu- 
lum mirror, with a surface highly polished but covered with a white 
film of tin oxide ; Curve IV is for the same mirror after being cleaned 
with chalk and alcohol, all visible trace of the oxide being removed. 
Both curves show a lamentably low reflecting power, and this is 
undoubtedly due to the presence of the oxide film, which either is 
not entirely removed by the cleansing process, or immediately 
forms again. 

These results show that there are possibilities for great improve- 
ment in the effectiveness of the grating for investigations in the 
ultra-violet. Depositing a thin layer of platinum or nickel on a 
speculum grating would increase its efficiency in the ultra-violet two 
or three times, and a layer of silicon would increase it as much as 
six times ; it is planned to develop a method for doing this. Further- 
more, the effect of a thin deposit on the lines of the ruled surface is 
to increase the brightness of the first order at the expense of the 
other orders. This is an additional advantage in all work in which 
the first order is the only one used, as in Lyman's investigation of 
the Schumann region and in the work recorded in this paper. 

The behavior of a speculum surface in the Schumann region is 
unknown, but it is difficult to believe that the reflecting power 
experiences a marked increase in this region. That a grating yields 
such successful results as were obtained by Lyman in his photo- 
graphic work in the region beyond 1800 A is surprising in view of 
the present record of the reflecting power of speculum. 

Steel (Fig. 5). — The steel mirror was an old one of hardened 
steel, taken from a tuning fork. It had a fine polish with no imper- 
fections, and was cleaned with chalk and alcohol. The comparison 
with other observations is shown in Table XL 

Stellite (Fig. 5). — The mirror was a polished specimen of the 
alloy obtained from the Stellite Works, Kokomo, Indiana. The 
mirror had a fine polish with no scratches. Stellite is an alloy of 
chromium and cobalt with impurities; the exact composition is a 



226 



E. O. HVLBURT 



commercial secret. As was mentioned under chromium, the curve 
for stellite shows a maximum at 2150 and a minimum at 2400 A, as 
do the chromium curves. 



TABLE XI 
Reflecting Power of Steel 



Wave-Length 



2265. 

23I3- 

2510. 
2880. 
3050. 
3260. 
3570. 



Hagen 
and Rubens 
Unhardened 



329 
35-0 
37-2 
4°-3 

45 ° 



Minor 


34-8 


35 


7 


38 


9 


42 


1 


42 


9 


44 


8 


5° 


8 



E.O. H. 
Hardened 



35 
36 
38 
44 

44 
45 
5° 



Tantalum (Fig. 7). — -This was a polished specimen of the metal, 
but the surface finally measured, while having a high polish, was 
marred by fine scratches. The sample was obtained from the 
Bureau of Standards. 

Tellurium (Fig. 3). — This was a cathodic mirror from the 
Bureau of Standards. The film was opaque, bright, and free 
from scratches; it was rubbed with rouge and chamois before 
measuring. 

Tin (Fig. 7). — -An opaque surface of tin was deposited cathodi- 
cally on glass. The mirror was bright and free from imperfections, 
but was measured three days after being made. It is likely that 
the surface became very quickly covered with a layer of oxide, 
which reduced the reflecting power materially. The oxide made 
its appearance unmistakably in a few days, appearing as a white 
film. 

Tungsten (Fig. 6). — The piece examined was a polished speci- 
men of the metal obtained from the Bureau of Standards. The 
surface had a good polish, but was marred by a few holes and 
fine scratches; it was rubbed with rouge and chamois before 
measuring. 

Zinc (Fig. 7). — Bright films of zinc were obtained by sputtering 
in an atmosphere of hydrogen. The curve is for a three-quarter 



REFLECTING POWER OF METALS 



227 



opaque him. Table XII shows the comparison with results ob- 
tained bv another observer. 



TABLE XII 

Reflecting Power of Zinc 



Wave-Length 


Meier 
Polished Plate 


E. 0. H. 

Cathodic 


^573 

2749 

2981 

3255 

3 611 


20.5 
47.6 
60. 2 

68.2 

705 


40 

44 
48 

5i 

52 



DISCUSSION OF RESULTS 

The curves show two general characteristics: (1) in the region 
of the spectrum covered in this investigation the reflecting power 
decreases as the v/ave-length decreases; and (2) the reflecting power 
is never zero. A number of the curves have another characteristic 
in common. Beyond wave-length 2000 A many of them take a 
well-defined steeper slant; that is, the reflecting power begins to 
decrease much more rapidly. That this effect is due to some 
peculiarity of the apparatus is improbable, for the deflections in this 
region are very large, and the determination of the reflecting power 
is accurate even for quite low values of the reflecting power. 
Furthermore, a number of the substances do not show this rapid 
falling off in reflecting power. It may be that this observed 
decrease in reflecting power is a genuine property of the metal, or 
it may be that the air in contact with the reflecting surface plays 
an important part. Air has a strong absorption band which begins 
at 1630 A, and marked absorption starts to set in at 1900 A. It is 
possible that the optical constants of air begin to change rapidly 
from wave-length 2000 A down as the absorption band is neared, 
and this rapid change in the optical properties of the layer of air on 
the surface of the metal may cause a marked change in the reflecting 
power of the metal. 

A certain similarity exists in the curves for copper, chromium, 
nickel, cathodic silicon, and molybdenum, for they all show a shal- 
low minimum, i.e., a region of lower reflecting power, in approxi- 



228 E. O. HULBURT 

mately the same region of the spectrum. There is no evident cause 
to which this may be attributed. That it is due to the presence of 
some common impurity is improbable, because the methods of 
preparation of these five mirrors differed widely. 

The one general conclusion that follows from the results of this 
investigation is that for the metals the reflecting power decreases 
as the wave-length of the light decreases. Whether this same rela- 
tion continues to hold for wave-lengths beyond 1800 A in the 
Schumann and Lyman regions, can be determined only by future 
experiment. Metals, then, have a maximum reflecting power in 
the visible and infra-red regions of the spectrum, and it is concluded 
that the reflecting power diminishes on the short wave-length side 
of this maximum with no indication of ever increasing again. 

Silicon is the one exception to the foregoing conclusion; the 
reflecting power rises to 76 per cent at 3000 A, remains practically 
constant from 3000 to 2000 A, and then beyond 2000 drops rapidly, 
reaching a value of 62 per cent at 1870 A. Future work may show 
that this rapid decrease beyond 2000 A continues until a low reflect- 
ing power is reached, and, if this be so, the elevation in the curve is 
a region of selective reflection. 

% Silicon differs from platinum, copper, etc., in that it is a poor 
conductor of electricity; it is a so-called "metalloid. " The be- 
havior of silicon suggests that perhaps there is a class of substances 
which have the maximum reflecting power in the extreme ultra- 
violet, just as the true metals show a maximum in the region of the 
spectrum of longer wave-length. None of the other substances 
of the metalloid class which were investigated, such as carbon, 
antimony, etc., show characteristics similar to silicon, and perhaps 
silicon is unique in this respect. 

From a practical standpoint the curves show that from all the 
metals investigated (with the exception of silicon) two may be 
selected as being the most serviceable for use in work requiring the 
reflection of light of short wave-lengths: platinum and nickel. 
Optical surfaces of these two metals may be readily prepared by 
cathodic sputtering and by electroplating; these surfaces are quite 
hard, are slow to tarnish in air, and are not acted on by most of the 
common laboratory reagents. 



REFLECTING POWER OF METALS 229 

Those metals which oxidize easily should be avoided. The 
appearance of a white or cloudy film on the surface is almost a sure 
sign of a very low reflecting power in the ultra-violet; on the other 
hand, the good ultra-violet reflectors give very clear white or bluish- 
white reflections in visible light. 

In this connection silicon again deserves special mention. This 
metal possesses in a marked degree all the physical properties 
essential for a perfect reflecting surface; it is as hard as ordinary 
glass without being brittle; it is not attacked by weak or strong 
acids, and of course does not tarnish in air; at ordinary tempera- 
tures the only reagent which acts on silicon is concentrated potas- 
sium (or sodium) hydroxide. The metal takes a high polish by the 
ordinary method of polishing with pitch and rouge, and brilliant 
deposits of silicon can be obtained by cathode sputtering, as has 
been brought out in this investigation. The reflecting power of a 
silicon mirror was found to be 76 per cent in the region from 2000 
to 3000 A (see silicon, Curve I, Fig. 6). The same mirror has been 
measured by Coblentz 1 in the region of longer wave-lengths, and 
its reflecting power in the green was found to be 34 per cent, drop- 
ping to 28 per cent in the infra-red. Hence a silicon mirror, or 
grating, possesses a high efficiency throughout the entire range of 
the spectrum, and the advantages of its use in optical instruments 
are obvious. Thin films of silicon on interferometer plates will 
undoubtedly enable investigations in this field to be extended down 
to 2000 A. 

The preparation of mirrors and gratings upon silicon plates 
depends only upon the possibility of procuring large plates of the 
metal which are homogeneous; for all the large specimens examined 
have been found to be porous, and hence are not suitable for the 
best results. The task of casting silicon pure and in a homogeneous 
state is certainly not an insurmountable one, and is a problem for 
the commercial laboratory rather than for the scientific investigator. 

SUMMARY 

An ultra-violet spectrograph has been set up in which a sodium 
photo-electric cell connected to an electrometer serves to measure 

1 Bull. Bureau of Standards, 7, 217, 1911. 



230 E. O. HULBURT 

the intensity of the light. With this the reflecting powers of 
twenty-eight metallic mirrors have been examined; namely, Al, 
Sb, Bi, Cd, C, carborundum, Cr, Co, Cu, Au, Pb, magnalium, Mg, 
Mo, Ni, Pd, Pt, Se, Si, Ag, speculum, steel, stellite, Ta, Te, Sn, 
W, Zn. 

The curves of reflecting power have been drawn throughout the 
region 1800 to 3800 A, and it has been shown that the reflecting 
power for light of wave-lengths shorter than 3000 A is rarely above 
50 per cent, with one noteworthy exception, silicon, which shows a 
reflecting power of 76 per cent in the region 2000 to 3000 A. 

It has been shown that brilliant opaque films of silicon can be 
prepared by cathode sputtering. 

In conclusion I wish to express my hearty thanks to Professor 
Ames for his interest throughout the course of the work. 

Dr. Pfund has been especially helpful; it was at his suggestion 
that the work was undertaken, and his advice and assistance at 
every stage have been invaluable. I am deeply indebted to Dr. 
Anderson for his kindly interest and many helpful suggestions. 

Dr. W. W. Coblentz, of the National Bureau of Standards, has 
kindly allowed the use of several mirrors of the more uncommon 
metals. 

Johns Hopkins University 
June 1915 






A STUDY OF THE POLE EFFECT IN THE IROX ARC 1 

By CHARLES E. ST. JOHN and HAROLD D. BABCOCK 
I. INTRODUCTION 

In the investigations made at this observatory upon the deter- 
minations of standards of wave-length and upon the relation 
between laboratory and solar spectra, it was early found that a 
detailed study of the iron spectrum would be required as a pre- 
liminary to further definite progress. 2 

The measurements by different observers of the wave-lengths 
of the iron lines that serve as standards in the international system 
show discrepancies which far exceed the limit of precision attainable 
with a grating spectrograph of high dispersion, and the interpreta- 
tions of sun-arc displacements may be illusory and lead to diverse 
conclusions, if the presence and influence of lines of certain types 
are unrecognized. The divergent results were found to depend 
upon conditions in the arc, its length, the current-density, and the 
portion of the arc from which the light is taken, and to inhere in 
those types of lines that show more or less dissymmetry under 
varying pressure and line intensity and that appeared to have large 
or abnormal pressure displacements. 3 

The purposes in view in undertaking the investigation of these 
sensitive and unstable lines were: (i) to determine whether the 
variations in wave-length observed with different arc conditions 
are real or fictitious, that is, whether there are actual displacements 
of the maxima of the lines; (2) to determine whether there are 
general pressure differences in the arc sufficient to account for the 
displacements; (3) to examine some other conditions in the arc 

1 Contributions from the Mount Wilson Solar Observatory, No. 106. 

2 Mt. Wilson Contr., No. 75; Astrophysical Journal, 39, 9-14, 1914. 

3 Alt. Wilson Contr., No. 61, pp. 2-5; Astrophysical Journal, 36, 15-18, 191 2; 
Mt. Wilson Contr., No. 75, pp. 5-8; Astrophysical Journal, 39, 0-12, 1914; Mt. 
Wilson Contr., No. 93, pp. 33-36; Astrophysical Journal, 41, 61-64, 1915; Goos, 
Astrophysical Journal, 38, 141, 1913. 

231 



21,2 CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 

which may be effective; (4) to investigate a wide range of the spec- 
trum for the identification and distribution of the questionable 
lines, which must necessarily play an important role in several 
fields of investigation; (5) to indicate working conditions which 
should be observed when lines of this character are to be used as 
standards of reference. 

II. METHODS AND APPARATUS 

Our method has involved an accurate comparison of the spec- 
trum from near the poles with that from the center of the arc. In 
the effort to carry such a comparison of wave-length to the third 
decimal place, difficulty was encountered in obtaining plates free 
from line displacements of small but determinable amounts due 
to instrumental causes or observing conditions. When the problem 
is such that crucial tests can be applied to the results, the difficulties 
involved in obtaining comparison spectra of consistent reliability 
are quite impressive. These were in the end eliminated by making 
the exposures rigorously simultaneous. 

A greatly enlarged image of the arc was thrown upon the slit of a 
plane-grating Littrow spectrograph of 30 feet focus by means of an 
achromatic lens and a large totally reflecting prism above the slit. 
Plate IVa shows an image of the arc as it actually appeared upon 
the slit. The light from the central portion passed directly to the 
slit, at A, Plate IV6, while a system of two small totally reflecting 
prisms, B and C, permitted light to be taken from any desired point 
on the axis of the arc. The spectrum of the light from this selected 
portion of the arc fell between the two narrow spectra of the 
equatorial section. For measurements of high precision, it is of 
great advantage to have the lines of the two spectra of nearly the 
same intensity, and this is particularly important when the lines 
have a tendency to broaden unsymmetrically. The relative expo- 
sure times were controlled by a rotating sector of variable opening 
placed above the first prism in the path of the light coming from near 
the pole of the arc, as shown in Plate TVb. The exposures began 
and ended at the same instant, one being continuous and the other 
rapidly intermittent. In this manner any effect due to slow changes 
of temperature, to flexures of apparatus, or to vibrations reaching 



POLE EFFECT IN IRON ARC 2$$ 

the instrument through the ground was effectively ehminated; 
no part of the instrument was touched during the exposures, so that 
no effects due to mechanical displacements were introduced. Great 
care was used to secure complete illumination of the grating from 
each light-source. A similar arrangement was used in comparing 
arcs with different current-densities and it is applicable to all com- 
parisons where the highest precision is sought. It will be added 
to the reconstructed 6o-foot tower telescope equipment for sun-arc 
comparisons. 

Before the sector was employed the exposures were made of 
unequal length in order to equalize the intensities. They were 
simultaneous during the period covered by the shorter; but, 
though the apparatus is very stable, was not touched during the 
exposures, and has its optical parts in an underground chamber at 
practically constant temperature, there were minute displacements, 
positive on some plates and negative on others, differing even for 
successive exposures on the same plate. It is not a sufficient 
precaution to divide an exposure of a comparison spectrum with 
the thought of detecting an instrumental displacement when the 
quantities involved are of the order of a thousandth of an angstrom. 

The Pfund 1 form of arc, 6 mm long, carrying a current of 6 
amperes, has been found to be a very stable and reliable source. 
In obtaining standards of reference the slit of the spectrograph was 
placed normal to the axis and in the central plane of the enlarged 
image of the arc. Except where otherwise noted the Pfund arc 
has been thus employed for all wave-length comparisons given in 
this paper. 

Some plates in the ultra-violet were taken with a 5-inch concave 
grating of 15 feet radius. On account of astigmatism the arrange- 
ment of prisms and sector described above could not be employed. 
The exposures were therefore not simultaneous, and the use of a 
shutter in front of the plate became necessary. Under these con- 
ditions minute displacements due to instrumental causes appeared 
upon the plates, for the correction of which a series of overlapping 
exposures was made to connect these photographs with those 
obtained by means of the plane grating. 

1 Astro physical Journal, 27, 296, 1908. 



234 CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 

In a valuable paper Eder and Valenta 1 call attention to the pre- 
cautions necessary to obtain reliable photographs of spectra. The 
care that we have given to this question may be seen from the fol- 
lowing details. The 4-inch plane grating (ruled surface 63 X 72 mm, 
42,386 lines) used in the Littrow spectrograph of 30 feet focus was 
ruled by Anderson on the reconstructed Rowland machine. It has 
been shown to yield over 90 per cent of its theoretical resolving 
power in the second order, and is particularly well suited to the 
purposes of this investigation, as it produces bright line spectra 
of a high degree of perfection. In the second order, which was used 
for this work, the diffraction pattern is distinct and symmetrical 
on the two sides of a good line, and when the spectrum is observed 
visually the diffraction fringes of the lines of pressure groups a and b 
remain sharp and distinct even near the poles of the arc. The focus 
for any particular region is read from an experimentally derived 
curve which is accurate to o . 5 mm ; the focal length of the instrument 
is 9. 16 m. The slit-widths were always very nearly four times the 
Rayleigh normal, and give 80 per cent of the resolving power avail- 
able with an indefinitely narrow slit and 77 per cent of the intensity 
given by a very wide one, thus making an excellent compromise 
between opposing conditions. Tests were made to detect a possible 
variation of the gradation-curves of the lines with the slit-width, 
but no effect was found for the widths employed. Great care was 
taken to avoid overexposing the spectrum lines. For the micro- 
photometric measurements with the Hartmann and Koch instru- 
ments no lines were used whose maximum blackness was such as 
to lie in the region of overexposure, as defined by the characteristic 
curve for the plate. On the plates used for filar micrometer 
measurements the exposures were timed to equalize the widths and 
intensities at pole and center. If the strongest lines were possibly 
overexposed, the weakest lines on the same plate were underexposed, 
but among the lines of intermediate strength some must have had 
correct exposures. Lines of all ranges of intensity, however, showed 
the effect. 

For obtaining an independent check upon the magnitude of 
the pressure-effect some photographs were made by means of an 

1 Astropkysical Journal, 19, 251, 1904. 



POLE EFFECT IN IRON ARC 235 

interferometer of the Fabry and Perot type, recently constructed 
in our instrument shop. The plates, by Hilger, are of fused quartz. 
40 mm in diameter and 5 mm thick. Their surfaces are of the 
highest quality and in performance they equal our glass plates 
furnished by Jobin. We have coated them with silver by the 
method of cathodic sputtering in vacuo, obtaining perfect uniformitv 
in the films and a reflecting power so high that more than 60 images 
of the sun can be counted through them. The etalon used is made 
of invar and has a thickness of 10 mm. The rings are projected 
by means of an achromatic objective of 41 cm equivalent focal 
length upon the slit of a 13-foot Littrow spectrograph. The 
auxiliary' dispersion is produced by a 4-inch plane grating having a 
remarkably bright first-order spectrum. 

III. THE REALITY OF THE DISPLACEMENTS 

As the lines exhibiting these variations in wave-length show 
more or less dissymmetry under pressure and are greatly widened 
at the pole, it has been thought by some that the displacements 
in question are only apparent and arise from the difficulties inherent 
in the measurement of lines of this character, and by others that 
they are due to increase of pressure or of vapor-density in the arc. 
The point is not only of theoretical interest because theories of the 
production of spectrum lines must be founded upon detailed study 
of the conditions of emission, but it is also of importance in view 
of the possible employment of these lines in solar and stellar 
investigations, for which their peculiar characteristics promise to 
be of value, provided their properties can be well established and 
the conditions determined under which they may be used. 

To eliminate as far as possible the disturbing effects due to 
dissymmetry, we have made the net exposure times such as to give 
practically equal intensities to the lines from the two parts of the 
source. The lines XX 5424 and 6400 observed in this way are 
shown in Plate Va, with a twenty-eight-fold enlargement. These are 
typical lines, showing displacements toward the violet and red, 
respectively. In order to make the shifts still more apparent 
in the reproduction, fine artificial lines have been ruled through 
the centers of the comparison spectra. For an extreme case, the 



236 



CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 



Center of 

Arjc 
-0.1 80 A 



Vtolet 



Red 



relative exposures were such that the intensity and width of the 
lines in the spectrum from near the negative pole were less than 
for the same lines in the spectrum of the central section of the arc. 
In this case, lines that widen unsymmetrically to the red would not 
show at the pole a displacement toward greater wave-lengths 

having its origin in this quality 

X 6400.02 p ,. .„ 

of dissymmetry. An illustra- 
tion is shown in Fig. 1, which is 
a diagram to scale from measure- 
ments of X 6400 taken under 
these conditions. It is evident 
that if the width of the line, as 
observed near the pole, were in- 
creased by a longer exposure to 
equal that of the same line in 
the spectrum of the central sec- 
tion of the arc, the line would 
still show a distinct displace- 
ment to the red. When such 
lines are of moderate intensity 
upon the photographic plate, an 
experienced observer can make 
micrometer settings upon their 
maxima with surprising consist- 
ency. 

Dissymmetry is not evident 
in the case of every line that 
gives a displacement to the red 
at the pole of the arc as com- 
pared with its position at the 
center. For example, X 5339 is 
apparently as good a line as X5341, though the first belongs to 
group d and the second to group a. On one plate, for illustration, 
the widths of the line at the center and negative pole are o. 106 and 
o . 108 A, respectively, and the measured shift of the latter is o . 01 5 A 
to the red, which cannot be accounted for on the ground of un- 
symmetrical widening when the increase in width is only o . 002 A. 



- PoLe 
0.1 4q A— 

1 
1 



80 JA- 



Centjer of 
Ar|c 



Fig. i. — Persistence of displacement 
when width at pole is less than at center. 



POLE EFFECT IN IROX ARC 237 

In such cases the personal equation of the observer is involved, 
and one may question more or less the possibility of measuring 
lines of this character to the degree of precision suggested. In 
order to eliminate the personal element, measurements have been 
carried out with the Hartmann and Koch microphotometers. 
Fiducial lines were drawn upon the plate, generally one on each 
side and as nearly parallel as possible to the spectrum line under 
investigation. With the Hartmann microphotometer settings 
were made by 0.02 mm steps from one fiducial line to the other, 
across them and the spectrum lines along each of the three divisions 
of the spectrum. The density-curves were plotted to scale and the 
positions of the maxima determined relatively to the fiducial lines. 
Some lines of groups a, d, and e were measured in this manner, 
and in all cases the measurements showed displacements of the 
maxima of the d and e lines to the red and violet, respectively. 
Curves determined by the Hartmann microphotometer are shown 
in Fig. 2 for lines of groups b and d, and in Fig. 3 for lines of groups 
a and e. The results have been confirmed by the photographic 
records made with the Koch form of microphotometer. Both 
instruments show that the displacements of the maxima are un- 
questionable and yield the same values as those found by the usual 
method, but the dissymmetry is much less striking in the graphs 
than was expected from the visual examination of the lines. It 
would seem that the eye is very sensitive to contrast and over- 
estimates the degree of asymmetry. 

An entirely independent test for the reality of the displace- 
ments was made by superposing upon the spectrum of the iron arc 
the absorption spectrum of iodine vapor under low pressure. For 
this purpose the slit was placed parallel to the axis of the arc, the 
prisms and sector being removed, and a spherical glass bulb con- 
taining the iodine was inserted in the path of the light from the arc. 
A number of the iron lines in the green are found to have iodine 
lines superimposed more or less centrally upon them. Plate V6, 
illustrating this, shows the line X 5424 enlarged 6. 7 fold, the upper 
end corresponding to the negative pole of the arc, the lower end to a 
point near the center. On the original plate three iodine absorp- 
tion lines can be distinguished, one of which is seen in the reproduc- 



238 CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 

tion to lie clearly upon the iron line. At the center of the arc it is 
obviously well to the violet side of the maximum of the line, while 
at the pole it is plainly upon the red side. Although the other two 
iodine lines fall upon the violet wing of the strongest part of the 
line, cutting it off sharply and greatly reducing the width of this 




A\ 



\ 



't\ 



/ 



/ 



/ 



X 




I \ \ 



I I \ 



J 



I Line \ 



X 6393 group b X 6400 group d 

Fig. 2. — -Microphotometer curves showing displacement at pole for X6400, 
group d, but not for X 6393, group b. 

portion, the shift of the maximum of the iron line between pole 
and center is clearly apparent. It appears to us that the only 
possible interpretation of this observation is that the wave-length 
corresponding to the maximum intensity of the iron line is 
less at the pole than at the center of the arc. On the original 



POLE EFFECT IN IRON . 1 R( 



239 



negative a smaller shift in the same direction is shown at the 
positive pole. 

The question whether the unsymmetrical broadening of spec- 
trum lines may be accompanied by displacements is an old one. 1 




X 5364 . 8 group c X 5365. 4 group a 

Fig. 3. — Microphotometer curves showing displacement at pole for X 5364.8, 
group e, but not for X 5365 . 4, group a. 

Professor Kayser remarks that the position of a spectrum line is 
determined by the intensity maximum. In measuring these lines, 

1 Kayser, Handbuck der Spectroscopic, 2, 297, 1902; Astrophysical Journal, 26, 
191, 1907; Exner and Haschek, Die Spektrcn der Elemente bei normalem Druck, 1; 
Sitziingsberichte der Wiener Akad., 116, Abt. ILz, 323, 1907; Eder and Valenta, Aslro- 
pkysical Journal, 19, 251, 1904. 



240 CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 

the effort has been to set upon the maximum; a double cross-hair 
in the observing microscope, with the space adapted to the width 
of the particular line under examination, has proved a satisfactory 
device for the purpose. 

There are three points, each of which appears to us to establish 
the reality of the displacements of the maxima of the line between 
pole and center: (i) the persistence of the displacements when the 
intensity and width of the line at the pole are less than for the same 
line produced in the central section of the arc, since the maximum 
is the effective portion of the line when exposure times are shortened ; 
(2) the shift of the intensity maximum when photometrically deter- 
mined; (3) the relative position of the maxima at pole and center 
with respect to the superimposed iodine lines. 

IV. PRESSURE IN THE ARC 

The question whether the pressure differs from point to point 
in the arc sufficiently to account for these displacements was 
investigated by examining the behavior of lines of known pressure- 
shift that remain symmetrical under wide ranges of pressure and 
density. It is a comparatively easy matter to make differential 
measurements of high-dispersion spectra of good lines to the third 
decimal place, but a difficult matter to obtain comparison spectra 
that are reliable to this degree of precision. It was only after 
developing a method of obtaining rigorously simultaneous exposures 
that we were able to convince ourselves that no general pressure 
differences occur in the arc. The data in Table I illustrate the 
relative behavior of the lines of groups a, b, C5, d, and e. At the 
bottom are appended the mean pressure displacements per 
atmosphere for the same groups of lines. 

The displacements of the lines of groups a and b do not exceed 
the limit of error, but the pressure displacement per atmosphere, 
in the case of the b lines, is of a magnitude to show a change of 
pressure of one-tenth of an atmosphere, while to produce the dis- 
placements of the lines of groups c$ and d an increase of pressure of 
one and a half to two atmospheres would be required. The be- 
havior of the lines of group e, on the other hand, would indicate a 
great reduction of pressure. It appears therefore from the data 



POLE EFFECT IN IRON ARC 



241 



that the displacements shown by the lines of groups cj, d, and e are 
not due to a general increase of pressure in the vapors near the pole 
of the arc. 

TABLE I 

Negative Pole minus Center of the Arc 



Group a 


Group b 


Group 05 


Group d 


Group e 


A 


P-C 


A 


P-C 


A 


P-C 


A 


P-C 


| 

A P-C 


5328 
5332 
5341 
5497 
55oi 
55o6 


. 0000 A 

— 0.0002 

— . 0006 

— . 0003 

— . 0004 
+0.0004 


6136 
6137 
6213 
6219 
6230 
6252 


+0.0007 A 
— . 0004 
+0.0003 
+0.0010 
+0.0004 
. 0000 


489O 
4919 
4920 
4938 

4957 
4957 


+0.014 A 

+0.016 

+0.013 

+0.018 

+0.014 

+0.014 


528l 
5283 
5324 

5339 
5393 
5653 


< 

On 00 "O On t-- NO 

000000 
000000 

++++++ 


5364 
5367 
5369 
5383 
5404 
54IO 


— 0.028 A 
-0.025 

— 0.020 
-0.025 
-0.025 

— 0.026 


Mean . 

Displ. 
per 
atm. 


— 0.0002 A 
+0.0036 




+0.0003 A 
+0.0094 




+0.015 A 
+0.0094 




+0.018 A 
+0.0092 




— 0.025 A 
+0.0017 



V. OTHER CONDITIONS IN THE ARC 

Density. — The absence of a general increase in pressure between 
the center and the negative pole led us at first to consider density 
as a possible cause of the pole effect. The concentration of lumi- 
nosity is marked at the poles and is quantitatively indicated by the 
longer exposure upon the center of the arc required to equalize the 
intensities of the pole and center spectra. To test the possible 
effect of density upon the position of these sensitive lines, a pair of 
furnace plates was taken for us by Mr. King with o . 2 g and 2 . o g 
of iron, respectively. The iron deposit upon the walls of the 
graphite tubes showed that in both cases all of the iron was vapor- 
ized, so that the ratio of the vapor densities may be considered 
comparable to the quantities of metallic iron. Neighboring lines 
belonging to group a. the flame lines, were used as standards. 
Their wave-lengths are independent of the current-density and the 
part of the arc serving as a source, and King has found 1 that for 
lines of this type the pressure displacement does not depend upon 
the density of the furnace vapor. Our measurements are given in 



1 A/7. Wilson Contr . No. 60, pp. 21-27; Astrophysical Journal. 35, 203-209, 191 2. 



242 CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 

Table II, and show no increase of wave-length with the increased 
density, though for the same lines the increase in passing from the 
center to the pole of the arc is o. 0195 A. Some lines of manganese 
present as an impurity in the iron poles of the arc show displace- 
ments at the negative pole of the same order as the neighboring 
lines of iron. It does not seem probable that the density of a trace 
of vapor would be very appreciable even at the negative pole. 

TABLE IT 
Lines of Group d under Varying Density and Temperature in the Furnace 



A 


Density 
A HD~ A LD 


Pole Effect 


A 


Temperature 
A HT _A LT 


Pole Effect 


5266 


O 


000 A 


+ 


017 A 


5232 


O 


000 A 


+0 


025 A 


5324 


— O 


004 


+ 


015 


5266 


O 


000 


+ 


017 


5586 


+ 


001 


+ 


024 


5324 


— O 


OOI 


+ 


015 


56l5 


— O 


003 


+ 


022 












Means 


— O 


0015 


+0 


0195 




— O 


0003 


+0 


019 



Temperature. — The effect of a variation in temperature was 
investigated by comparing the wave-lengths of these sensitive 
lines at temperatures in the furnace as widely different as practicable 
(2ioo°-26oo° C). They are high-temperature lines, and hence 
appear strongly only at the highest furnace temperatures, but the 
three given in Table II are measurable at the lower temperature 
and are free from the lines of the carbon flutings appearing so 
abundantly at the highest temperature. With the neighboring 
lines of group a as standards, no increase in wave-length was found 
for a 25 per cent increase in temperature, though between the 
center and the negative pole of the arc the displacement is 0.019 A. 

In vacuo. — -In order to make a preliminary test of the probable 
effect of electrical conditions, a 6 mm arc of the same form as that 
used under normal pressure and actuated by a current of like 
intensity was operated in a vacuum chamber at pressures of o . 5 cm 
and 10 cm of mercury; comparisons were made between the nega- 
tive pole and center with practical equality of intensities for the 
lines under examination. In Table III data are given showing 
the results of measurement for five groups of lines. 



POLE EFFECT IN IRON ARC 



243 



For the lines of groups a and b the measurements show the same 
results as at atmospheric pressure, that is, no pole effect in either 
case; but for these typical lines of groups C5, d. and e the pole 
effects disappear with pressures below 10 cm of mercury, though 
at atmospheric pressure they are +0.012, +0.017. and -0.027 A, 
respectively. 

TABLE III 
Negative Pole minus Center in vacuo 



A 


Group a 


A 


Group b 


A 


Group 05 


A 


Group d 


A 


Group e 


5270 
5328 

533 2 
S34i 
5397 


+ O.OOIO 

— . 0005 
+ O.OO02 

O . OOOO 

— . 0003 


4547 
4592 
4602 
4786 
4789 


O . OOOO 
+ O.OOO5 
+ 0.0002 

O . OOOO 
— O.OOIO 


4607 

461 1 

4736 
4859 
4872 


+ 0.0008 

+ 0.0008 

O . OOOO 

—0.0005 
— 0.0002 


5266 
5281 
5283 
5302 
5324 


— O . OO06 
+ O.OOO5 

— O . OO06 

— . 0004 
+ O.OOI8 


5367 
5383 
54IO 
5415 
5424 


— . 0005 

— 0.0005 
O.OOOO 
O . OOOO 
O . OOOO 


Means 


+O.OOOI 




— O.OOOI 




+0.0002 




+ O.OOOI 




— O.OOOI 



Though the arc in vacuo was of the same type and length and 
carried the same current as the arc under normal pressure, its 
appearance was strikingly different; the luminosity in such a case 
is more evenly diffused over the poles, and does not issue from a 
point source. Though the polar region is brighter than the cen- 
tral zone, the concentration in the core is practically absent. The 
disappearance of the pole effect under these conditions indicates 
that the potential difference plays a minor role, if any, but a more 
definitive investigation is to be undertaken. 

Relation to luminosity. — The observations of Fabry and Buisson 1 
brought out a striking difference of luminosity in the positive and 
negative regions of the iron arc, a difference confirmed by the 
change in the relative exposure times required to equalize the 
intensities of pole and center spectra on our plates. The ratio of 
center to pole exposure is greater for the red than for the violet 
at the negative pole. There is, therefore, a greater apparent change 
in radiation conditions in passing from the center to the negative 
pole in red than in violet light, but the loss of light through scatter- 
ing and absorption in the outer layers of the arc vapor is undoubt- 

1 Journal dc physique (4), 9, 929, 19 10. 



>44 



CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 



edly greater for shorter wave-lengths, and as the negative pole is 
surrounded by a much thicker envelope of cooler vapor than is the 
central portion of the arc, the apparent relative luminosity for 
these parts of the arc should be quite different for widely separated 
spectral regions. At the positive pole the greatest apparent change 
in intensity of radiation between center and pole is in violet light. 
If the pole effect is closely related to these conditions, one would 
expect the displacements for the longer wave-lengths to be greater 
at the negative than at the positive pole, and for the shorter wave- 
lengths the reverse relation to obtain. The observations are given 
in Table IV. 

TABLE IV 

Comparative Displacements at Positive and Negative Poles 





Ultra-Violet 


Green 


o 
as 
O 


a 


Xeg. Pole 
— Center 


Pos. Pole 

— Center 


A 


Neg. Pole 
— Center 


Pos. Pole 
— Center 


d 


332250 
3407-47 
3426.65 
3667. 28 


+ O.OIO 
+0 . 006 
+ 0.004 
+ 0.008 


— O.OOI 
O.OOO 

+0.002 
O.OOO 


5339-94 
5393 19 
556963 
5602.96 


+0.019 
+0.017 
+0.020 
+0.019 


+ 0.004 
+0 . 004 
+0.003 
+0.007 


Means 


+ 0.007 


O.OOO 




+0.019 


+0.004 


e 


3689.46 
3694 00 
3748.96 
3754- 50 


— O.OII 

— 0.014 
—0.014 

— . 008 


— . 004 

— 0.004 

— . 006 

— 0.006 


5367-46 

536996 
5410.90 

54I5-I9 


-0.025 

— 0.020 

— 0.026 
-0.030 


-0.005 

— . 004 

— O.004 

— . 006 


Means 


— O.OI2 


-0.005 




-0.025 


-O.005 



For the region of X 5400 the displacements are largest at the 
negative pole, but the reverse does not hold for the ultra-violet, 
though for the lines of group e the difference between the two poles 
is less for the shorter wave-lengths. The evidence against a rela- 
tionship between luminosity and pole effect is strong in the case of 
the lines of group d, which appear to constitute a homogeneous 
group, since their pressure-shift varies as the cube of the wave- 
length; but the lines in the two sections of group e are not so con- 
nected and upon other grounds seem to be less intimately related. 
Under the reduced pressures used the pole effect disappears for the 



POLE EFFECT IN IRON ARC 245 

lines near X 5400, but persists for the lines in the violet. The 
true pressure-shift for the lines in the green is very near zero, while 
for the violet region these lines show displacements to the violet 
under increase of pressure. A more complete consideration of this 
class of lines will appear in a later paper. 

Local pressure. — In comparing the spectra of the core and the 
flame of the arc. Adams 1 found that the ratio of core to flame inten- 
sity is highest for the lines of groups d and c. and lowest for lines 
of group a. Not only are the lines under consideration relatively 
the strongest in the core when compared to the flame of the arc, 
but they also increase in intensity more rapidly on approaching 
the poles than any other group of lines, so that the energy density 
for them is high in the limited volume of vapor in which they origi- 
nate. This raises the question of a local increase in pressure in the 
core of the arc near the pole, which might produce an effect on those 
lines of which the core is mainly the source, while in the case of 
lines of groups a and b, for which the core plays a less important 
role, the effect may escape observation. In general the measure- 
ments for such lines show a slight indication of displacement, but 
of a magnitude not considered to be within the range of precision 
of our measurements. A possible method of approaching the 
question of a local increase in pressure is to compare the pole effect 
with the pressure displacements for the same lines. We have 
measured the pressure-shift per atmosphere by comparing the 
center of the 6 mm arc under pressures of o. 5 cm and 10. o cm with 
the center of a duplicate arc under normal pressure. Upon this 
point St. John and Ware say: 

Neither the small pressure-changes of about one-fifth of an atmosphere 
taken advantage of in this investigation, nor the high pressures used by Gale 
and Adams are well adapted to the study of lines of this type, and it is purposed 
to examine in vacuo and under normal pressure the behavior of an extended list 
of lines belonging to groups d and e. 2 

The precision which our preliminary measurements give jus- 
tifies the opinion implied in the reference made. Taken in the 
central section of the 6 mm arc in both cases, the lines are of good 

1 .1//. Wilson Conlr., Xo. 40; Astrophysical Journal, 30, 86, 1909. 
- .1//. Wilson Conlr., Xo. 61, p. 21; Astrophysical Journal, 36, 37, 1912. 



?46 



CHARLES E. ST. JOHX AND HAROLD D. BIBCOCK 



quality, and the displacements may be determined with a surprising 
degree of accuracy, but the results show that the pressure displace- 
ments formerly attributed to these sensitive lines are greatly in 
error through pole effect. 

TABLE V 
Pressure-Shift, Pole Effect, and Wave-Lexgth 



Pmll „ No. of 
Grou P Lines 


Mean A A per Atm. 


Pole Effect 


Pressure- 
Increase 


d 

d 
d 

C5 

e 

e 


25 

12 

6 

16 

7 
8 


4085 
5528 
6350 
4766 

3755 
5392 


+0.0048 A 

+0.0089 

+0.0160 

+0.0093 

-00035 

+0.0017 


+0.0099 A 
+O.0206 
+0.0185 
+0.0119 

— . 009 

— 0.026 


2 . i atm. 

23 
1 . 2 

i-3 

2.6 
? 

' 



The results for representative groups of lines are assembled in 
Table V. The increases of pressure on the assumption that the 
effect is due to pressure at the negative pole, given in the last 
column, show variations exceeding the limits of error. 

The pressure displacements for the three sections of group d, 
shown in Table V, are related as the cube of the wave-length, con- 
firming the conclusion of Gale and Adams. 1 The values calculated 
from the weighted equation 

/ A. V 

AA=( - - I 0.00804 
V5000/ 

show residuals as in Table VI. 



TABLE VI 

Agreement with Cube Law 



Mean A 


AA 


Weight 


Observed 


Calculated Obs. — Calc. 


4085 . 0048 A 

5528 0.0089 

6350 0.0160 


0.0043 A +0.0005 A 
0.0108 —0.0019 
0.0164 —0.0004 


25 

12 

6 



Ml. Wilson Contr., Xo. 58, pp. 22-26; Astrophysical Journal, 35, 32-36, 1912. 



POLE EFFECT IN IRON ARC 247 

On taking account of the weights, it will be seen that the small 
deviations of the observed points from the theoretical curve are 
properly distributed; but an examination of the pole effects in 
Table V shows that they do not follow the cube law even approxi- 
mately. Since the pole effects are not so related to the wave- 
length, it is evident that pressure alone does not explain them. 

VI. IDENTIFICATION AND DISTRIBUTION OF AFFECTED LINES 

Between X 2979 and X 6678 we have examined 1570 lines; when 
the negative pole is compared with the center, we find 286 lines 
showing displacements to the red and 80 with displacements to 
the violet; that is, 23 per cent of the lines are affected. In 
Table VII the lines showing displacements to the red are listed, 
and in Table VIII those which are displaced to the violet. The 
first column identifies the lines by their wave-lengths in inter- 
national units to the second decimal place. The present available 
determinations of wave-length show variations of such magnitude 
for the majority of the lines listed that it seems advisable for the 
present to omit the third place. The second column gives the 
intensity and character according to Burns 1 for the fines contained 
in his tables; the others are in general very weak lines. The dis- 
placements, negative pole minus center, are in the third column; 
when followed by I.S., the corresponding lines are international 
standards of the second order. No attempt has been made to 
separate the groups cj and d, nor to indicate any subgroups. This 
is best done by means of the pressure-shifts, which are at present 
under investigation. 

The distribution is shown in Table IX. The regions are so 
selected that the number of affected lines per 100 A is fairly uniform 
in each. From the point of view of one who uses the iron lines as 
standards of wave-length, as reference lines in solar or stellar 
investigations, or as a basis for intensity comparisons, not only is 
the absolute distribution of interest, but also the proportion of 
affected lines in a given spectral region. The sensitive lines are 
numerous in sections of the ultra-violet; they form, however, a 
small percentage of the total number of lines there, but in the 

1 Lick Observatory Bulletin, 8, 27, 1913. 



248 



CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 



TABLE VII 

Fe Lines, Groups cj and d 

Negative Pole minus Center of Arc 

Displacements to Longer Wave-Lengths 



A 
(Int. Units) 


Burns 


P-C 


A 
(Int. Units) 


Burns 


P-C 


2991.65 


4b 


+0.006 A 


3739-54 


ih 


+0.014 A 


3012.46 


2b 


+0.006 


374° 


06 


I 


+0.019 


3048.47 


2H 


+0.007 


3787 


60 




+0.007 


3093 ■ 89 


2b 


+0.006 


3789 


44 


1 


+0.015 


3I54-5I 


2b 


+0.007 


3811 


01 




+0.010 


3188.59 


4b 


+0.004 


3814 


79 




+0.012 


3208.48 


4 


+0.004 


38i7 


65 




+0.030 


3209.33 


4b 


+0.010 


383° 


87 


I 


+0.008 


3211 .69 


4b 


+0.004 


3920 


85 


lb 


+0.008 


33 2 2-5° 


4b 


+0.010 


3928 


09 


ih 


+0.010 


3407 -47 


7l 


+0.006 


3941 


29 


2b 


+0.014 


3410.90 


1 


+0.006 


3947 


00 


2b 


+0.004 


3426.65 


6 


+0.004 


3948 


11 


3b 


+0.009 


343851 


3b 


+0.004 


3955 


36 


2b 


+0.020 


3445 • 78 


2b 


+0.007 


3957 


°3 


2b 


+0.018 


3459-74 


ib 


+0.004 


3963 


11 


2b 


+0.012 


3474-44 


2 


+0.007 


3965 


44 


I 


+0.010 


3518.68 




+0.011 


3976 


62 


2 


+0.004 


3522.27 




+0.004 


4018 


28 


2b 


+0.004 


3532.56 




+0.012 


4024 


75 


2 


+0.013 


3568.98 


4 


+0.010 


4030 


5i 


3b 


+0.011 


3583-67 




+0.013 


4058 


23 


2b 


+0.006 


3586.61 




+0.010 


4065 


40 




+0.006 


3587-25 


2H 


+0.010 


4072 


52 


ib 


+0.008 


3592.66 




+0.010 


4°73 


76 




+0.008 


3599- 13 




+0.012 


4083 


78 




+0.008 


3604 69 




+0.007 


4084 


5i 


4 


+0.007 


3607.55 




+0.008 


4101 


27 


ib 


+0.008 


3612.08 


4 


+0.004 


4104 


13 


2b 


+0.008 


36i3-47 . 




+0.007 


4109 


°7 




+0.004 


3616.32 




+0.009 


4112 


98 


2b 


+0.020 


3620.47 




+0.007 


4118 


90 




+0.010 


3635- 20 




+0.010 


4125 


63 




+0.017 


3636 - 49 




+0.007 


4133 


87 


2b 


+0.009 


3643 ■ 14 




+0.009 


415° 


28 


2b 


+0.018 


3644.81 




+0.009 


4153 


92 


4b 


+0.012 


3655-68 




+0.016 


4154 


82 


3 


+0.004 


3662.85 




+0.014 


4157 


80 


3b 


+0.018 


3664.56 


2 


+0.004 


4158 


81 


2b 


+0.014 


3665.81 




+0.006 


4171 


7° 


2 


+0.007 


3666. 26 




+0.011 


4187 


°5 


6 


+0.008 


3667.28 


4 h 


+0.008 


4187 


81 


6 


+0.010 


3667.99 


2 h 


+0.004 


4191 


44 


6 


+0.010 I.S. 


3676.88 


ib 


+0.006 


4195 


34 


3b 


+0.009 


3688.48 


ib 


+0.005 


4196 


22 


2 


+0.011 


3697 -44 


2h 


+0.006 


4198 


3 1 


6 


+0.010 


3703-7° 


ih 


+0.005 


4198 


64 


2 


+0.009 


3721.51 


1 


+0.005 


4210 


36 


6 


+0.006 


3735-33 


3 


+0.005 


4217 


56 


2b 


+0.008 



POLE EFFECT IN IRON ARC 
TABLE VII — Continued 



249 



A 
(Int. Units) 


Bums 


P-C 


A 

(Int. Units) 


Burns 


P-C 


4222. 22 


5 


+0.006 A 


4938.83 


5 


+0.018 A 


422S 


46 


4b 


+0.004 


4944 


34 




+0.024 


4227 


45 


7 


+0.014 


4946 


40 


2 


+0.024 


4233 


16 


1 


+0.007 


4950 


12 


I 


+0.020 


4233 


61 


6 


+0.010 I.S. 


4954 


11 




+0.016 


4235 


95 


8 


+0.009 


4954 


4i 




+0.029 


4238 


83 


4 b 


+0.011 


4957 


3i 


5 


+0.014 


4247 


44 


5b 


+0.011 


4957 


61 


10 


+0.014 


4250 


13 


7 


+0.010 


4960 


65 




+0.020 


4260 


49 


10 


+0.012 


4966 


10 


3 


+0.017 I.S. 


4264 


21 


2 


+0.006 


4969 


94 


2b 


+0.045 


4271 


17 


7 


+0.010 


4970 


80 




+0.026 


4299 


25 


7 


+0.009 


4973 


11 


2 


+0.018 


4343 


28 


2 


+0.012 


4978 


61 


■> 


+0.018 


4401 


30 


3 


+0.004 


4982 


52 


4b 


+0.026 


4407 


7i 


2 


+0.011 


4983 


27 


3b 


+0.020 


4446 


85 


2b 


+0.012 


4985 


27 


3 


+0.016 


4462 


01 


3b 


+0.020 


4985 


56 


3 


+0.019 


4469 


39 


4b 


+0.008 


4988 


97 


2 


+0.018 


4531 


64 


2 


+0.006 


4991 


29 




+0.030 


458i 


52 


-> 


+0.012 


5001 


88 


5 


+0.023 


4598 


13 


2b 


+0.012 


5002 


82 




+0.022 


4607 


66 


4 


+0.014 


5005 


73 


4 


+0.032 


461 1 


29 


4b 


+0.006 


5006 


13 


5 


+0.016 


4613 


23 


3 


+0.011 


5007 


3i 


2h 


+0.030 


4625 


06 


4 


+0.012 


5014 


96 


4 


+0.022 


4637 


52 


4 


+0.012 


5022 


25 


4 


+0.024 


4654 


64 


3b 


+0.007 


5027 


14 


2 h 


+0.014 


4668 


15 


4 


+0.013 


5039 


27 


2b 


+0.026 


4707 


29 


5 


+0.012 I.S. 


5044 


22 




+0.018 


4709 


09 


2 


+0.011 


5048 


45 


2 


+0.021 


4727 


42 


2 


+0.024 


5068 


78 


4 


+0.030 


4736 


79 


5 


+0.012 I.S. 


5073 


67 




+0035 


4754 


°5 


5 


+0.010 lln 


5076 


28 




+0.022 


4783 


44 


4 


+0.012 Mn 


5090 


79 


3h 


+0.010 


4823 


53 


4 


+0.011 Mn 


5099 


05 




+0.020 


4859 


76 


5 


+0.014 I-S. 


5125 


14 


2b 


+0.020 


4871 


33 


8 


+0.010 


5126 


21 




+0.020 


4872 


15 


8 


+0.014 


5136 


06 




+0.028 


4878 


22 


6 


+0.012 I.S. 


5i37 


39 


3 


+0.014 


4890 


77 


7 


+0.014 


5139 


27 


6 


+0.021 


4891 


5° 


9 


+0.012 


5139 


48 


8 


+0.020 


4903 


32 


5 


+0.009 I-S. 


5162 


32 


5b 


+0.030 


4915 


60 


1 


+0.018 


5165 


43 


2b 


+0.010 


49*7 


20 




+0.012 


5191 


47 


7 


+0.019 


4919 


01 


8 


+0.016 I.S. 


5192 


36 


8 


+0.019 I.S. 


4920 


52 


10 


+0.013 


5208 


61 


4 


+0.020 


4922 


38 




+0.014 


5215 


20 


4 


+0.020 


4923 


94 




+0.046 


5217 


4i 


4 


+0.016 


4930 


33 


1 


+0.015 


5226 


88 


5 


+0.023 


4932 


21 




+0.021 


5229 


52 




+0.019 


4933 


64 




+0.045 


5229 


86 




+0.015 


4934 


02 


ih 


+0 . 005 


5232 


96 


8 


+0.025 I-S. 


4938 


18 


1 


+0.018 


523 6 


19 


1 


+0.020 



250 CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 
TABLE NIL— Continued 



A 
(Int. Units) 


Burns 


P-C 


A 

(Int. Units) 


Burns 


P-C 


5263.32 


5 


+0.020 A 


5655-5I 


2 


+0.016 A 


5266.04 




+0.012 


5658.84 


4 


+0.023 I.S. 


5266.57 


8 


+0.017 I-S. 


5662.53 


3 


+0.018 


5273*8 


3 


+0.014 


5701.47 


4 


+0.010 


5281.80 


5 


+0.019 


5705.48 


1 


+0.031 


5283.64 


7 


+0.018 


5709.40 


3 


+0.024 


5302.32 


5 


+0.014 I.S. 


57II-87 


2 


+0.010 


5324- 19 


6 


+0.015 I-S. 


5712.15 


2 


+0.017 


5339-94 


3 


+0.019 


5715-11 


1 


+0.007 


5353-38 


2 


+0.014 


57I7-85 


3 


+0.018 


538946 


2 


+0.015 


573I-78 


3 


+0.010 


5391-49 


1 


+0.028 


5753 14 


3 


+0.028 


5393 19 


4 


+0.017 


5763.02 


4 


+0.028 


5466.42 


3 


+0.020 


5775-IO 


3 


+0.025 


5472.72 


1 


+0.022 


5782.15 


1 


+0.020 


5473-91 


3 


+0.014 


579I-04 


2 


+0.020 


5476.58 


4 


+0.019 


5809.25 


2 


+0.041 


5480.87 


2 


+ O.OII 


5859-6i 


3b 


+0.025 


5487.78 


3 


+0.036 


5883.84 


3 


+0.024 


5522.46 


2 


+0.013 


5905.68 


2 


+0.007 


55 2 5-55 


2 


+0.010 


5934-68 


4 


+0.028 


5543-94 


2 


+0.018 


5952.75 


4 


+0.021 


5560.23 


1 


+0.025 


5976.8o 


2 


+0.029 


556361 


3 


+ 0.021 


5983-71 


2h 


+0.018 


S56740 


2 


+ O.OI6 


6003 . 04 


3 


+0.020 


5569-63 


5 


+0.020 I.S. 


6008 . 58 


3 


+0.024 


5572.86 


5 


+0.025 


6013.52 


2 


+0.019 ^ n 


5576.IO 


4 


+0.021 


6016.66 


2 


+0.020 Mn 


5586.77 


6 


+0.024 I.S. 


6021 .82 


2h 


+0.018 Mn 


5600. 24 


1 


+0.018 


6141-13 




+0.016 


5602.79 


2 


+0.016 


6180. 22 


2 


+0.011 


5602.96 


3 


+0.019 


6232.67 


2 


+0.017 


5608.16 




+0.021 


6246.34 


4 


+0.020 


5615.66 


6 


+0.022 I.S. 


6301.52 


5 


+0.016 


5618.65 


1 


+0.010 


6302.51 


3 


+0.015 


5624.56 


5 


+0.023 


6336.84 


4 


+0.020 


5633-97 


2 


+0.023 


6400.02 


5 


+0.019 


5638.28 


3 


+0.015 


6408 . 04 


4 


+0.017 


5641.46 


2 


+0.025 


6411.67 


5 


+0.019 


5655 .18 




+ 0.014 


6419.99 


5 


+0.024 



region X 4900-X 5050, for example, there are 34 affected lines. 
Burns gives for this region 24 Fe lines of intensity 2 or stronger; of 
these 20 are sensitive to the pole effect. From X 5500 to X 6000 
they are practically the only lines in the iron spectrum. The lines 
giving displacements to the violet at the negative pole have a 
stronger gregarious tendency showing in the ultra-violet and to the 
red of X 5364. When the ultimate groups of the iron lines are 



POLE EFFECT IN IRON ARC 251 

once determined from their reactions to various physical conditions, 
it may be possible to find definite series relationships even in so 
complex a system as the iron spectrum. 



TABLE VIII 

Fe Lines, Group e 

Negative Pole minus Cexter of Arc 

Displacements to Shorter Wave-Length 



A 
(Int. Units) 


Burns 


P-C 


A 
(Int. Units) 


Burns 


P-C 


3157.88 


4 


— . 004 A 


5074.75 


2b 


— 0.022 A 


3160.65 


6 


— 0.004 


5079 


00 




-0.013 


3205.40 


7b 


— 0.004 


5096 


99 


3b 


— 0.016 


3210.46 


2 


— . 006 


5133 


67 


5b 


-0.045 


3244.19 


1 


— 0.004 


5153 


20 




-0035 


3 2 5I-24 


5h 


— . 004 


5364 


86 


3h 


— 0.028 


35I6.4I 


3 


— . 008 


5367 


46 


3b 


-0.025 


3518.86 




— . 006 


5369 


96 


4b 


— 0.020 


3529.82 


4 


— . 004 


5383 


37 


5b 


-0.025 


353 2 - 10 




— . 004 


5400 


50 


2b 


— O.OII 


3533 00 


4 


— . 004 


5404 


13 


3b 


-0.025 


3549-87 


3 


— O.OIO 


54IO 


90 


3b 


— 0.026 


3582.58 




-0.013 


5415 


19 


4b 


-0.030 


3588.52 




— 0.006 


5424 


06 


4b 


— 0.027 


3594-63 


5 


— 0.004 


5432 


96 




— 0.023 


3604. 28 




— . 008 


5445 


04 


2h 


— 0.020 


3610.15 


5h 


— 0.007 


5462 


96 


2b 


— 0.014 


3616.58 


4 h 


— 0.014 


5463 


27 


4b 


— 0.016 


3633-84 


4 h 


— . 006 


5543 


18 


2 


— 0.014 


36.34.68 




— 0.006 


5554 


88 


3b 


— 0.019 


365003 


3h 


— 0.007 


5565 


78 


3 


— 0.019 


3682. 21 


1 


-0.003 


5594 


66 


2 


— 0.023 


3689.90 


ib 


— O.OII 


5598 


31 


3 


-0.025 


3694.00 


6 


— 0.014 


5686 


53 


3 


— 0.028 


3701.08 


6 


— 0.009 


5693 


64 


2 


— 0.007 


3726.92 


3h 


— . 006 


5705 


99 


2 


— 0.019 


3744 .09 


2h 


— O.OII 


5816 


36 


3 


— 0.026 


374896 


3h 


— 0.014 


5862 


35 


4b 


— 0.018 


3754- 50 


2b 


— . 008 


59*4 


16 


6 


— 0.003 


377369 


2b 


— O.OI2 


5930 


18 


5 


— 0.020 


3797-95 


1 


— 0.012 


5984 


81 


3 


— 0.022 


3845-26 


- 
3 


— 0.007 


5987 


06 


2 


— 0.016 


3966.62 


5b 


— . 004 


6007 


96 


2 h 


— 0.016 


4172.64 




— 0.017 


6020 


18 


2I 


— 0.012 


4200.92 


2 


— 0.007 


6024 


06 


4 h 


-0.015 


4224.51 


2b 


— . 006 


6042 


08 


2 


— 0.012 


4433-22 


2b 


— 0.006 


6055 


99 


3h 


-0.015 


4960.93 




-0.035 


6078 


48 


3 


— 0.022 


4967.89 


2 


— 0.016 


6102 


18 


3 


— O.OIO 


5065.02 


3b 


— 0.029 


6103 


19 


2 h 


-0.015 



2C2 



CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 



TABLE IX 

Distribution of Affected Lines 



Displaced to Red 


Displaced to Violet 


Region 


Total 


Per 100 A 


Region 


Total 


Per 100 A 


3000-3400. . 
3400-3900. . 
3900-4300. . 
4300-4600. . 
4600-4900. . 
4900-5300. . 
5300-5800. . 
5800-6100. . 
6100-6420. . 


10 

47 

■ 54 

9 
20 

• 72 

■ 5o 
13 
11 


2 

9 

14 
3 
7 
18 
10 
4 
3 


3100-3300.. . 
3300-3500. . . 
3500-3800.. . 
3800-4500. . . 
4500-4900. . . 
4900-5200.. . 
5200-5300.. . 
5300-5600. . . 
5600-6200.. . 


6 
O 

25 
6 

8 

18 
17 


3 


8 
1 


3 

6 
3 




286 


80 





VII. WORKING CONDITIONS IN THE IRON ARC 

Aside from the theoretical interest in the changes of wave- 
length considered in this paper, reference may be made to the follow- 
ing practical considerations: 

1. A number of these sensitive lines are included among the 
international standards of the second order adopted by the Inter- 
national Union for Co-operation in Solar Research. 

2. There are regions of the iron spectrum in which few or no 
other lines are available for standards; for example, from X 4900 to 
X 5050 and from X 5500 to X 6000. 

3. In various laboratories there are in progress redeterminations, 
based upon the iron standards, of the wave-lengths in international 
units of the lines of many elements. In these redeterminations 
the instrument most commonly used is the concave grating in the 
usual Rowland mounting, and in practice the slit of the spectro- 
graph is parallel to the axis of the arc and includes the major part 
of its length. The astigmatism under these conditions introduces 
more or less pole effect, and to that degree vitiates results involving 
lines of the character under consideration. The practice of revers- 
ing the current in the arc in order to overcome the tendency to 
produce wedge-shaped lines when the slit and the axis of the arc 
are parallel, obscures, but does not eliminate, the pole effect. 



POLE EFFECT IN IRON ARC 



253 



Since the redeterminations aim at a precision of 0.002 to 0.003 A, 
it is necessary to take the pole effect into consideration. 

4. Lines of the type considered are not limited to iron, but are 
present in the spectra of other elements, the detailed investigation 
of which is necessary before safe deductions can be made from their 
use in astrophysical investigations, or before their wave-lengths can 
be determined with the requisite precision. 

5. The arc lines are often used as a basis for intensity compari- 
sons, and for such purposes reliable results depend upon employing 
suitable arc arrangements. 



TABLE X 

Displacements, Pole Distance, and Current 



Neg. Pole and i mm from Neg. Pos. Pole and 
Center Pole and Center Center 



12— 4 Amperes 7— 5 Amperes 



Group a —0.0005 A +0.0005 A 

Group d +0.021 +0.009 

Group e ! —0.025 —0.014 



— 0.0002 A 
+0.003 

— o . 006 



— o . 0004 A 
+0.007 

— 0.012 



— 0.0002 A 

+0.001 

-0.003 



It is of importance then to determine the practical conditions 
under which these sensitive lines may be used and the limits of the 
precision obtainable. In furtherance of such a purpose we have 
made comparisons between the center of the arc and the positive 
pole, the negative pole, and a point i mm from the negative pole, 
using the Pfund arc 6 mm long, carrying a current of 6 amperes 
under a pressure of no volts; and also between the centers of arcs 
carrying 5 and 7 amperes, and between arcs carrying 4 and 12 
amperes. The data are shown in Table X. For the d lines the 
current. may vary between 5 and 7 amperes without introducing 
errors exceeding the desired precision, and it appears that the 
small changes in current obtaining in practice, when care is taken 
to hold it constant in the standard arc, are without measurable 
effect. A more insidious source of error is the introduction of the 
pole effect by using light from any part of the arc except the middle 
zone, as nearness to the negative pole is accompanied by easily 
measurable displacements. It is important to hold closely to the 
mid-point of the arc, and advisable to approach the positive rather 
than the negative pole if any considerable length of the arc is 



254 CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 

to be employed. In our experience the highest precision and the 
most uniform results are obtained by keeping the slit normal to the 
axis at its mid-point in a greatly enlarged image of the arc. The 
necessary conditions for high precision are difficult to realize in the 
classical mounting of the concave grating without some arrange- 
ment for rotating the image of the arc. The ultra-violet plates 
for this investigation were taken with a concave grating in a Row- 
land mounting arranged in a vertical plane and with the slit normal 
to the axis of the arc. 

The effects arising from differences in arc conditions and types 
of spectrographs employed are, as has been mentioned, manifest 
in the determinations of the tertiary standards by different ob- 
servers. They are also apparent in other lines of work. We 
wished to compare our results for the pressure displacement of these 
lines with those taken under the widest range of pressure, and turned 
to Duffield's interesting paper. 1 He worked with pressure differ- 
ences of 3 to ioo atmospheres, and used the ordinary mounting of 
the concave grating with the slit parallel to the axis of the arc, the 
slit and the image of the arc being of the same height. His proce- 
dure involved the pole effect in somewhat varying degrees, as he 
changed both the length of the arc and the current-strength, and 
at high pressures the exposures were made by a series of flashes, 
a process that intensifies the effect of the polar influence. From 
his Tables I and II the lines showing pole effects are selected, and 
the pressure-shifts per atmosphere, deduced from the pressure differ- 
ences used, are given in Table XL Unreversed lines only are con- 
sidered and the means of his two sets are taken. In the last column 
are shown the displacements for one atmosphere found by us for some 
of the same lines of group d in passing from a vacuum to atmos- 
pheric pressure. Duffield's results vary from 0.033 A P er atmos- 
phere, determined from the pressure difference of 3 atmospheres, 
to o . 006 A, deduced from the pressure difference of 80 to 100 atmos- 
pheres. These discrepancies are explicable as pole effect. At low 
pressures a larger proportion of its influence would appear as an 
increment to the pressure-shift, while with increasing pressures the 
pole effect would play a decreasing role. For the lines of group a 

1 Phil. Trans., A, 208, 111, 1908. 



POLE EFFECT IN IRON ARC 



255 



no pole effect is shown by our measurements. There are in Duf- 
field's tables two lines of this group. The pressure-shifts per atmos- 
phere deduced from pressure differences of 10 and 80 atmospheres 
are 0.0022 A and 0.0015 A respectively, an agreement in striking 
contrast to the results for lines showing pole effect. 

TABLE XI 
Pressure-Shift per Atmosphere — Duffield 



Atmospheres 



So 



St. John and 
Babcock 



4299. 
4236. 

4233- 
4227. 
4222. 
4210. 
4191. 
4187. 
4187. 



•0330 
•0377 
.0287 
.0300 



0.0128 
0.0126 
0.0172 
O.0240 
O.OljO 
0.0134 
0.0162 



0.0147 
0.0163 
0.0125 
0.0151 
o . 0090 



.0067 

.0083 

.0060 



.0060 

.0082 



.0034 

• 0057 



.0040 
.00 



0.0407 

0.0353 



0.0123 



.0060 

.0086 

.0064 



.0048 
.0064 



.0046 

■ 0057 

.0090 



0.0019 
0.0027 

. 003 2 

o . 0038 



Means 



0.0326 I 0.0146 



.0135 0.0060 j 0.0061 ! 0.0064 



o . 0044 



The pole effect appears also in the interferometer determina- 
tions of Xatm. — X in vacuo by Fabry and Buisson. 1 We have 
measured the values of Xatm-.— Ami vacuo for the lines used by 
them, both with a grating spectrograph and with an interferometer. 
The respective results are given in the fourth and fifth columns of 
Table XII. The differences between the values of Fabry and Buis- 
son and the means of our two determinations appear in the sixth 
column. 

For the arc at atmospheric pressure Fabry and Buisson used a 
current of 3 amperes, while we used a current of 6 amperes. They, 
say: ''For the unsymmetrical lines the displacements would have 
been much greater if the intensity of the current had been stronger " ; 
but the displacements observed by us are smaller than those found 
by them. A comparison of the differences in the sixth column with 
the pole effects in the seventh leaves no doubt that the large values 
obtained by them were mainly due to pole effect. As the maxima 

1 Astro physical Journal. 31, 112, 1910. 



2<6 



CHARLES E. ST. JOHN AXD HAROLD D. BABCOCK 



of the interference fringes correspond to the maxima of the emission 
lines, the measurements show actual displacements of the maxima 
under varying arc conditions, even when determined by the inter- 
ferometer. 

TABLE XII 

X atm. minus X in vacuo for Sensitive Lines 









St. John and Babcock 


Fabry and 




s 


A 


Fabry and 
Buisson 






Buisson minus 
St. John and 


Pole Effect 


o 






O 






Grating 


Interferometer 


Babcock 




d.. 


4187.05 


+0.011 


+0 . 004 


+ 0.004 


+O.007 


+0.008 




4191.44 


+0.010 


+ O.O03 


-0.005 


+0.006 


+ 0.010 




4227.45 


+0.020 


+ 0.006 


+ 0.009 


+0.012 


+ 0.014 




4233.61 


+0.012 


+ 0.006 


+ 0.006 


+0.006 


+0.010 




4235-95 


+0.011 


+ 0.006 


+ 0.005 


+0.005 


+0.009 




4250.I3 


+0.013 


+O.O05 


+0.007 


+O.007 


+0.010 




4859.76 


+O.017 


+0.008 


+ 0.005 


+0.011 


+0.014 




4871-33 


+O.010 


+0.013 


+ 0.008 


0.000 


+ 0.010 




5415-19 

5424.06 




+ O.OOI 




— 0.016 


— 0.025 




— 0.017 


+ O.OOI 


O.OOO 


— 0.017 


— 0.026 



There is also evidence that in the furnace spectra studied by 
King 1 the positions of these sensitive lines are affected by the 
phenomenon under consideration; for when their pressure dis- 
placements are compared with those of the stable lines in the same 
spectral region the furnace displacements exceed by o . 007 A those 
of the stable lines given under the same conditions, while those 
obtained from our arc determinations exceed the mean given by 
the stable lines under like conditions by 0.0026 A. Moreover, as 
shown in Table XIII, a striking agreement appears between the 
differences, furnace minus arc, and the pole effects given in the 
fourth and fifth columns respectively. 

So much emphasis has been placed upon the differences between 
various determinations of pressure-shift that it may be well to call 
attention to the fact that the lines showing marked discrepancies 
are those catalogued in our Tables VII and VIII. and that among 
the iron lines examined by us some 1200 are free from pole effect 
and will normally yield definite values for pressure-shift. For 
example, in Table XIV we compare our interferometer determina- 

1 Ml. Wilson Contr., No. 53; Astro physical Journal, 34, 37, 191 1. 



POLE EFFECT IN IRON ARC 



257 



tions with the pressure-shift per atmosphere deduced from the 
displacements for 8 atmospheres found by Gale and Adams for 
lines of group a. Those lines of group b which we have measured 
in this way also show differences smaller than the errors of observa- 
tion. 

TABLE XIII 

Displacements per Atmosphere in Furnace and Arc 
Fe Lines, Group d 



A 


Furnace Arc 


F-A 


Pole Effect 


4187.05 

4187.81 

4i9!-44 

4I98.3 1 

4210.36 


+0.012 
+0.013 
+0.013 
+0.014 
+0.013 


+ 0.0038 
+ 0.0033 
+ 0.0027 
+0.0113 
+0.0019 


+0.008 
+0.010 
+0.010 
+ 0.002 
+ 0.011 


+0 . 008 A 

+0.010 

+0.010 

+0.010 

+0.006 


Mean 


+ 0.013 


+0.0046 


+0.008 


+0.009 A 



The agreement for lines of this type, shown in Table XIV, is in 
strong contrast to the consistent difference for lines of group d. 
For the lines given in Table XII, the mean pressure-shift per atmos- 
phere deduced from the displacement for 8 atmospheres found by 
Gale and Adams is -f 0.011 A, while, from our measurements based 
upon the lines as produced in the central zones of 6 mm, 6 ampere 
arcs, its mean value is +0.006 A, the difference being referable 
to the pole effect introduced by the short arcs used by them. 



TABLE XIV 

Definite Pressure-Shift for Stable Lines 
Group a 





Gale and Adams St. John and Babcock 


4376 

5371 

5397 

54o6 

5429 


+ 0.0022 +0.0020 
+0.0036 +0.0031 
+ 0.0036 +0.0029 
+ 0.0034 +0.0045 
+ 0.0036 +0.0033 
+ O.0039 +0.0030 
+ 0.0036 +0.0035 


5447 








+ 0.0034 


+ 0.0032 



258 CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 

A remarkable agreement appears between the pressure displace- 
ments found for this group of sensitive lines by Fabry and Buisson 
(arc and interferometer), Gale and Adams (arc and grating), and 
King (furnace and grating), namely, 0.013, 0.011, and 0.013 A, 
respectively, while our measurements give only 0.006 A. It 
seems probable that some common factor was effective in producing 
these larger values, and a comparison of the excesses with the pole 
effect points to it as the operating cause. 

It is a matter to be considered, whether the differences in 
wave-length between the center of the arc in vacuo and in air, 
as we have used it, are wholly due to pressure, or are still measurably 
influenced by pole effect. One way of approaching the question is 
to compare our results with those given by Duffield's data. As our 
value for the pressure-shift is 0.0044 A, and that deduced from the 
pressure differences of 100 atmospheres used by him is 0.006 A. 
it appears that under the conditions of our arrangement we are 
approaching closely, if we have not actually reached, the true 
pressure-shifts for lines subject to pole effect. This is further indi- 
cated by their varying as the cube of the wave-length, a relation 
shown by Gale and Adams to hold for the iron lines of groups a 
and b, which are free from pole effect. If the displacements found 
by us are complicated by the presence of another effect, not follow- 
ing the cube law, such a close agreement between observed and 
calculated values would be a remarkable coincidence. Another 
reason for thinking the 6-ampere arc, 6-7 mm in length, is prac- 
tically free from the pole effect in the central plane is found in the 
way the displacements vary with current. Combining with ours 
some of Royds's 1 data for the differences between the centers of 
arcs carrying different currents, we find for the following current- 
changes the corresponding increases in wave-length: 

5 to 7 amperes +0.001 A 

4-5 " 9-5 " +0.003 

4 "12 " +0.007 

1 During the progress of this investigation Dr. Royds's interesting paper appeared 
(Bulletin No. 40, Kodaikanal Observatory) . The two investigations have proceeded 
along some common lines, and where the same ground is covered by the observations 
they are mutually confirmatory. 



POLE EFFECT IN IRON ARC 259 

These indicate approximately displacements of 0.001, 0.002, 
and 0.004 A Ior 2-ampere increments to currents of 5, 7, and 10 
amperes, respectively, and that decrease of current below 6 amperes 
is not necessary for the elimination of pole effect in the iron arc 
employed. 

VIII. DISCUSSION 

Though our observations show that displacements of the 
maximum intensity of certain types of lines occur between the 
center and pole of the iron arc, the cause of the displacements is not 
evident, nor is the mechanism plain that produces the unsymmetri- 
cal broadening which characterizes lines of these types, and with 
which the displacements are more closely related than with the 
pressure-shifts. Dr. Goos 1 attributed such displacements to differ- 
ences of pressure in the arc. We do not find pressure differences of 
the order necessary to produce them. It may be said that probably 
all data relative to the pressure displacements of these sensitive 
lines are more or less affected by pole effect, and cannot serve for 
the accurate determination of pressure differences. Dr. Royds 2 
considers density the predominating influence in producing the 
displacements. The fact that a tenfold change in vapor density 
in the furnace is without effect upon the position of the maximum 
is opposed to the density hypothesis, but the conditions obtaining 
in the furnace and in the arc are not strictly comparable. Exner 
and Haschek 3 suggest variability in the intensity of the components 
of a complex line under varying excitation as an explanation of 
displacement of the maximum. This would mean that in 18 per 
cent of the lines examined by us a close-lying satellite to the red 
of the principal component given by the central zone of the arc 
increased in relative intensity on approaching the negative pole, 
and that in 5 per cent of the lines the component of increased 
relative intensity was to the violet. More observational data than 
are now available are necessary to determine the probability of such 
a behavior of complex lines. The possibility of the occurrence of 
such variability is evident, but the observations of Nutting do not 

1 Loc. cit. 2 Loc. cit. 

* Sitzungsberichte Wiener Akad., 116, Abt. Ha, 323, 1907. 



260 CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 

indicate it in the case of iron. 1 Neither of these points of view seems 
to us to offer a satisfactory explanation of the phenomenon, nor 
until definite results are obtained from investigations now in prog- 
ress and to be undertaken do we wish to offer any further sug- 
gestion, as we are inclined to sympathize with Nutting when he 
says: "In conclusion, I wish to enter a plea for a simpler and 
broader basis for spectroscopy and a basis as free as possible from 
either assumption or speculation."- 

Though we have not satisfied ourselves as to the explanation 
of the main phenomenon considered in this investigation, we feel 
that the data should be accessible to other investigators, particu- 
larly in view of the employment of the iron arc as a standard in the 
redeterminations in progress, and as a basis of sun and arc compari- 
sons in the discussions bearing upon pressure, motion, anomalous 
dispersion, and Einstein effect in the solar atmosphere, as it is 
evident that the iron lines given in Tables VII and VIII, and lines 
of other elements behaving in a similar way, must be given separate 
consideration, and conclusions based upon them accepted with 
great caution. 

We have suggested the term ''pole effect," not only as a con- 
venient designation of the phenomenon, but also as an indication 
of its dependence upon nearness to the pole. The effects due to 
increase of current appear to us a projection of the polar influence 
to a greater distance from the pole, while a shortening of the arc 
simply brings the central zone nearer to the pole. 

We take this opportunity to express our appreciation of the 
assistance given us by various members of the staff; we are under 
particular obligation to Miss Ware for her able and unwearying 
help in the difficult measurements. 

IX. SUMMARY 

i. A combination of totally reflecting prisms and a rotating 
sector furnishes a means of making rigorousl}- simultaneous 
exposures upon different sources. 

1 Astrophysical Journal, 22, 7, 1906. 

2 Astro physical Journal, 28, 70, 1908. 



POLE EFFECT IN IRON ARC 261 

2. Displacements of the maxima of certain unsymmetrical iron 
lines in passing from the center to the negative pole of the arc are 
shown by the persistence of the displacements when the widths of 
the lines at the pole are less than at the center of the arc, by the 
shift of the intensity maxima of the photometric curves, and by the 
relative position of the maxima at pole and center with respect to the 
superimposed iodine absorption lines. 

3. Observations upon symmetrical lines with large pressure- 
shifts do not show a general increase of pressure in passing from the 
center to the negative pole sufficient to produce the observed dis- 
placements. 

4. The wave-lengths of these sensitive lines are not affected 
by a tenfold change in the density of the iron vapor in the furnace. 

5. Their wave-lengths are independent of a change in furnace 
temperature over the range of our observation, 2ioo°-26oo° C. 

6. Except in a very few special cases, the pole effect disappears 
in vacuo and in so far appears independent of electrical conditions. 

7. It does not appear to be intimately related to the differences 
in luminosity between the positive and negative poles. 

8. The variation of pole effect with wave-length does not follow 
the same law as pressure displacements. 

9. Therefore an increase of pressure localized at the pole and in 
the core of the arc, where a greater proportional contribution is 
made to the total intensity of these lines than to any other groups, 
does not alone explain the displacements. 

10. Between X 2979 and X 6678, of 1570 lines examined 286 
show displacements to the red and 80 to the violet. 

n. The affected lines are not distributed with any degree of 
uniformity, but show rather a tendency to cluster in certain regions. 

12. In extensive regions of the spectrum, X 4900-X 5050, 
X 5500-X 6000, nearly all the lines are of this character. 

13. An investigation of the limits of the working conditions 
in the 6-ampere, no-volt, 6 mm iron arc of the Pfund form shows 
that the small fluctuations in current occurring in practice may be 
neglected, but that even when the arc is running steadily only a 
narrow equatorial zone is practically undisturbed by the pole 
effect. 



262 CHARLES E. ST. JOHN AND HAROLD D. BABCOCK 

14. Our study of the behavior of iron lines under different con- 
ditions furnishes additional ground for regarding the classification 
suggested by Gale and Adams as resting upon a real physical 
basis. 

15. Emphasis is placed upon the necessity of considering the 
pole effect when the arc is used in comparisons of intensity, in re- 
determination of wave-lengths, and in astrophysical investigations. 

Mount Wilson Solar Observatory 
May 1915 



STELLAR PARALLAX WORK AT THE McCORMICK 
OBSERVATORY 

By S. A. MITCHELL 

It has seemed advisable at the present time to publish the first 
measures of stellar parallaxes obtained by photography at the Uni- 
versity of Virginia. It was generally conceded by the Clarks. 
while they were alive, that the 26-inch refractor was one of the 
best that they had ever made. Certainly the definition is excel- 
lent, with an almost utter absence of stray light. 

Photographs were made with a yellow color-filter and Cramer 
isochromatic plates. The star images are small and clean-cut 
and lend themselves to accurate measurement, as the following 
results show. The plates, 5X7 inches, were measured on the 
Repsold measuring machine, which was kindly loaned by Columbia 
University. The methods of exposure, measurement, and reduc- 
tion were substantially the same as those explained in this Journal 
by Schlesinger in Vols. 32, 33, and 34, and by Slocum and Mitchell 
in 38, 1. 1913. 

70 Ophiuchi (i8 h o m , + 2°3i') 

This system has a very large proper motion, if 13 per year. 
It has a period of 88 years, and has completed one revolution since 
its discovery. This star was put on the parallax program because 
it was on the Yerkes program, 1 and because it was desirable to see 
how accurately measures could be made on such a pair. The com- 
ponents are of magnitudes 4.3 and 6.0, and the present distance 
about 4". As the scale of the photographs is 1 mm=2o!8, the 
stars were separated by 0.2 mm. A rotating sector was used to 
cut down the brightness of the two stars. The sector was opened 
so that the fainter star was nearly of the same brightness as the 
comparison stars. This, of course, made the principal star brighter 
than would ordinarily be used for parallax determinations. The 

"Slocum, Astrophysical Journal, 41, 237, 1915. 

263 



264 



S. A. MITCHELL 



two stars were well separated when definition and guiding were 
both good. 

The measures and calculations were carried out to o. 1 micron. 
The final values we turned into angle by multiplying by the value 
1 mm=2o!8. 

The details of the plates follow. 

TABLE 1 

Plates of 70 Ophiuchi 



No. 



Date 



Hour Angle 



Observers 



Quality of 
Images 



13 
216. 



225. 
249. 
336. 

353 
365- 

1 1 19. 

1 1 20. 
1178. 



1203. 
1213. 



19 14 May 2 
May 9 
May 9 

May 10 
May 11 
Sept. 9 

Sept. 13 
Sept. 15 
Sept. 28 

Sept. 30 
Oct. 1 

1915 Mar. 27 

Mar. 27 
Apr. 11 
Apr. 1 2 

Apr. 14 
Apr. 15 



+ o h 4 
—0.4 
+0.2 

+03 
-i-5 

+ 1.1 

+0.6 
+0.6 
+ 10 

+i-3 

+ 13 
— 1.2 



-0.9 
-0.9 



M 
M 
M 

M 
M 
M 

M, G 

M 

M 

M 

M.Ol 

G 

G 
A 

M 

A 
M 



Good 

Fair-good 

Good 

Fair-good 
Fair-good 
Fair 

Poor 

Fair-good 

Fair 

Fair-good 
Fair 
One good 

Good 

Fair 

Fair 

Good 
Fair-good 



M = S. A. Mitchell; Ol = Charles P. Olivier; A = Harold Alden; G=P. H. Graham. 



COMPARISON STARS 



No. 



Diameter 



A' (Right 
Ascension) 



Y (Declination) 



Dependence 



2 

3 

4 

Principal star 
Companion . . 



13 



mm 
-41 
-35 
+36 

+39 

+ 3 

+ 3 



-23 
+35 
-29 

+ i7 
+ o 
+ o 



+0. 212 

.240 

263 

+0.285 



STELLAR PARALLAXES 



265 



Plate 



TABLE 2 
Reductions for 70 Ophiuchi, Principal Star 



Solution 



Weight 
iP) 



Parallax 
Factor (P) 



Time in 
Days (/) 



Residual 

(v) 



Vp-v 
in Arc 



6 

7 

10 

13 

216 

225 
249 

33t> 

353 
365 

1 1 19 

1 1 20 
1178 
1 183 

1203 
1213 



- o . 0490 

- .0486 

- 0492 

- .0500 

- 0474 

- .0578 

- 0582 

- 0582 

- . 0600 

- . 0600 

- .0624 

- 0449 

- 0442 

- 0471 

- .0468 

- 0432 

- 0.0418 



0.9 



09 
0.9 
0.6 

0.4 

0.9 
0.7 



0.7 



0.9 



+0 

+ 

+ 

+ 
+ 



+ 

+ 
+ 
+ 

+ 

+ 



752 
670 
670 

657 
644 



990 
995 



994 
992 
992 

992 
942 
929 

917 



-145 
-138 

-138 

-137 
-136 

- IS 



+ 

+ 
+ 



+ 184 
+ 199 

+ 200 

+ 202 
+ 203 



mm 
+ 0.0006 

— .0003 
+ .0003 

4- .0010 

— .0017 

— .0017 

— .0014 

— .0014 
4- .0005 

4- .0005 
+ 0030 
+ . 0007 

.0000 
4- . 0026 
4- .0022 

— .0014 

— 0.0029 



+o''oi 
+ 



+ 



The normal equations are : 

13.9C+ 3.155 n+ 3. 7591*-= -0.7018 

+ 28. 2249 /EX— J— 4.8637*"= — O. II04 

+ 10. 7958^ = — o. 1 184 

from which 

c=-o. 05255 

H = +0.00075 = +0T0157 

tt= +0.00699= +o''i45 ± o''oo7 

Probable error corresponding to unit weight = 
= = t =o':fo2 2. 



O.OOIO: 



266 



S. A. MITCHELL 



TABLE 3 
Reduction" for 70 Ophiuchi, Companion 



Plate 



Solution 
(m) 



Weight 
(P) 



Parallax 
Factor (P) 



Time in 
Days (/) 



Residual 
(») 



yp.v 

in Arc 



6 

7 

10 

216 

225 

336 

353 

365 

1119 

1 1 20 
1178 
1 183 

1203 
1213 



+0.0768 

+ .0808 

+ .0777 

+ .0762 

+ -0772 

+ .0678 

+ .0726 

+ .0682 

+ .0726 

+ 0694 

+ .0681 

+ .0896 

+ .0928 

+ .0935 

+ 0919 

+ 0934 
+0.0925 



0.9 
0.9 
0.6 



0.4 
0.9 
0.7 

0.9 
0.7 

0.7 



+0 

+ 

+ 


752 

670 
670 


+ 
+ 


657 

644 
980 


— 


990 

995 

998 


+ 


994 
992 
99 2 


+ 
+ 
+ 


992 
942 
929 


+ 
+0 


9i7 
908 



-H5 
-138 
-138 

-137 

— 136 

- 15 

— 11 

- 9 

+ 4 

+ 6 
+ 7 
+ 184 

+ 184 
+ 199 
+ 200 

+ 202 
+ 203 



mm 
+ O.OOI2 

— . 003 2 

— .OOOI 

+ .0014 
+ .0003 
+ .0014 

— 0034 
+ .OOII 

— .0028 

+ • 0005 
+ .0018 
+ .0027 

— 0005 

— .OOIO 
+ 0005 

— .OOIO 
— O.OOOI 



+oTo2 

- .06 

.00 

- 03 
+ .01 

+ -02 

- .04 

+ .02 



+ .01 

+ -03 

+ -05 

— .01 

— .02 

+ .01 

— .02 
0.00 



The normal equations are : 

13.9 c-\- 3.155 /x + 3.759i7r=+i.ii93 

+ 28.2249^+ 4. S6377T= +0.3895 

+10. 7958^= +0.3955 

from which 

c =+0.07752 

/a = +0'' 00377 = +CK0782 

7r= +0.00794= +0'' 165 = o''oo7 

Probable error corresponding to unit weight =•= 0.00105 
= = ! =o''o22. 

The equations for 70 Ophiuchi might have been solved by allow- 
ing for the orbital motion. The above-described photographs. 
however, were all taken w-ithin a year, and in this interval of time 
it was assumed that the orbital motion w r as linear, or in other 
words, proportional to the time. Orbital motion is, therefore, 
included in the determination of /x, the proper motion in 100 days. 



STELLAR PARALLAXES 
Other determinations of the parallax of this system are: 



>67 



Authority 



Method 



Principal Star 
A 



Center of Gravity 
AB 



Krueger. . . . 

Schur 

Jewdokimov 

Flint 

Slocum 



Heliometer 

Heliometer 

Meridian circle 

Meridian circle o".iq± o''o29 

Photography o''2i2±o''oc>7 



+o''i56=fco''oio 
+ .286* .0,31 
+ .279* .105 



Cygni 6 (iqV, +4Q°37') 
This is a system of the 61 Cygni class with nearly common 
proper motion of 0T65 per year in position angle 344 . The stars 
are of type K, and of magnitudes 6 . 6 and 6.8. The rotating sector 
was used. According to Adams and Kohlschutter. 1 these stars, 
though separated by nearly 10", undoubtedly form a physical 
system, since they have radial velocities of —41 and —39 km 
respectively. The values of the parallaxes below and their common 
proper motion confirm this notion. 

TABLE 1 
Plates of Cygxi 6 



Plate 



Date 



Hour Angle 



Observers 



Quality of Image 



53 
58 

59 
212 

237 

278 
279 
291 

292 
346 

1 184 

1 185 
1196 
1204 

1205 



1914 



May 30 
May 30 
May 31 

May 31 
Sept. 7 
Sept. 14 

Sept. 21 
Sept. 21 
Sept. 22 



Sept. 22 

Sept. 29 

19 1 5 Apr. 12 

Apr. 1 2 
Apr. 13 
Apr. 14 

Apr. 14 



-0^8 



-0.4 



-i-3 



-0.9 



M 
M 
M 

M 

M 

M,A 

M 
M 
M 

M 

M 
M 

M 
01 
A 



Fair-good 

Good 

Fair 

Good 
Good 
Good 

Good 
Good 
Fair-good 

Good 
Good 

Fair 

Good 
Good 
Good 

Good 



1 Aslrophysical Journal, 39, 346, 1914. 



268 



S. A. MITCHELL 
COMPARISON STARS 



No. 



Diameter 



X (Right 
Ascension) 



Y (Declination) 



Dependence 



3 

4 

5 

Parallax star, 7r x 
Parallax star, tt. 



mm 

. 20 
. 10 



o. 16 



mm 

-55-3 

-251 
+ 9-6 
+ 10.0 
+60.8 
+ 1.9 
+ 2.1 



-27.8 

+41.2 

-32-7 
+32.6 

-13-3 

— 1.2 

- 0.9 



+0. 192 
+ .185 
+ .209 
+ .196 
+0.218 



TABLE 2 

Reduction for Cygni 6 (Seq). Brighter Star 



Plate 



Solution 



Weight 
(P) 



Parallax 
Factor (P) 



Time in 
Days (/) 



Residual 
(f) 



yp-v 

in Arc 



52 
53 
58 

59 
212 

237 

278 
279 
291 

292 

346 

1 184 

1185 
1 196 

1204 

I2CK 



mm 

— O.O032 

— .0020 

— . 0008 

— OO35 

— .OO94 

— .0082 

— . 0094 

— .0103 

— .0103 

— .0116 

— .0081 

— . 0080 

— .OII2 

— .0116 

— 0115 

— 0.0120 



0.9 



0.9 



0.7 



+0 

+ 
+ 

+ 



+ 

+ 
+ 

+ 



608 
608 
595 

595 
852 
906 

948 
948 
952 

952 
978 
990 

990 



+0.986 



-137 
-137 
-136 

-136 

- 37 

- 3° 

- 23 

- 23 

- 22 

- 22 

- i5 

+ 180 

+ 180 
+ 181 
+ 182 

+ 182 



mm 
+0.0007 

— .0005 

— .0017 

+ .0010 
+ . 0004 

— .0012 

— .0003 
+ . 0006 
+ . 0006 

+ .0019 

— .0019 

— . 0030 

+ .0002 
+ .0006 
+ . 0004 

+0.0009 



+o'roi 

— .01 

- 03 

+ .02 
+ .01 

— .02 

— .01 
+ .01 
+ .01 

+ .04 

- .04 

- °5 

.00 
+ .01 
+ .01 

+0.02 



The normal equations are: 

15.2C+ 1.897 /*+ 0.3689^ = — o. 1271 
+ 22.5665 /«.+ 7. oi627r= —0.0655 
+ 11. 9135*-= +0.0053 



from which 



Probable 
= =to!oi8. 



c— —0.00805 

fi= —0.00299= — o''o622 

7r= +0.00245 = +o''o5i ± o''oo6 
error corresponding to. unit weight 



: o . 00086 



STELLAR PARALLAXES 



269 



TABLE 3 
Reduction for Cygni 6 (Pr). Fainter Star 



Plate 



Solution 
(m) 



Weight 
(P) 



Parallax 

Factor 

(,P) 



Time in 
Days 



Residual 



yp'f 

in Arc 



52 
53 
58 

59 
212 

237 

278 

279 
291 

292 

346 

1 184 

1185 
1196 
1204 

120^ 



mm 
+ O.0541 



+ 
+ 

+ 
+ 
+ 

+ 
+ 
+ 

+ 

+ 
+ 

+ 

+ 
+ 



0543 
0588 

0570 
0508 
0475 



04Q9 
0481 
0482 

0474 
05I3 
0468 

0452 

0446 
0432 



O.q 
I .O 
0.7 

1 .O 
1 O 



0.9 



I O 
I .0 



+ 

+ 

+ 

+ 



+ 0.0446 



608 
608 

595 

595 
852 
906 



952 
978 
990 

990 



4-0.986 



-137 
-137 

-136 

-136 

- 37 

- 3° 



948 - 23 

948 - 23 
952 



— 22 

- 15 
+ 180 

+ 180 
4-i8i 
+ 182 

+ 182 



mm 
+O.OO18 

4- .0016 

— .0021 

— .0012 

— .0012 
+ .0018 



+ -0015 

— .0027 

— . 0020 

— .0004 
+ .0002 
+ 0015 

4-0.0001 



+o"o4 
+ -03 
- .05 



+ 



— .0009 j — 
+ .0009 j + 
+ .0007 j + 



+ 



+ 



The normal equations are: 

15.2 c+ 1.897 /"•+ 0.3689^= +0.7499 

+ 22.5665 /A+ 7. Ol627T= +0.0230 

+ ii.9I35tt=+o.oi3o 

from which 

c =+0.04975 
/i.= —0.00370= —o".0"iO 
7r= +0.00173 = +o''o36±o''oo7 

Probable error corresponding to unit w r eight =* 

= ±0?022. 



: o. 00107 



70 



S. A. MITCHELL 



Various determinations of the parallax of this system have been 
as follows: 



Authority 



Method 



Brighter Star 
A 



Fainter Star 
B 



Center of Gravity 
AB 



Ball. 
Ball. 
Ball. 



A. Hall 

A. Hall 

A. Hall 

Chase 

Kostinsky . . . 

Russell 

Flint 

Jewdokimov . 



Equatorial (dis 

tance) +0*504 

Equatorial (pos. 

ang.) 
Equatorial (dist. 

and pos. ang.) 
Equatorial (AS) 
Equatorial (AS) 
Equatorial (Aa) 
Heliometer 
Photograph) 
Photography 
Meridian circle 
Meridian circle 



: o . 000 



+ 0.383^0.13 

+o.482±o.o54 
— 0.094 ±0.025 
-0.137^0.017 
+0.023 ±0.000 



+0.040= 
— 0.011 = 



03 
.049 



— 0.02; 

+0.05 
+0.07: 



=0.039 
= 0.03 
= o . 063 



+0.04 



o45 = 
.094 = 



.021 
055 



Parallax work at the Leander McCormick Observatory was made 
possible, in as large quantities as was attempted during the past 
year, by the award to the writer by Columbia University of the 
Ernest Kemp ton Adams research fellowship. Grateful acknowl- 
edgment is hereby expressed. Appreciation is also due to the 
members of the observatory staff. Dr. Charles P. Olivier, Mr. 
Harold L. Alden, and Air. P. H. Graham, for their hearty co- 
operation, and to Mr. R. C. Lamb, student in the University, 
for aid in computation. 

Leaxder McCormick Observatory 

University of Virginia 

May, 1915 



NOTE OX THE DENSITIES OF SECOND-TYPE STARS 1 

By HARLOW SHAPLEY 

During the last few years our knowledge of stellar densities 
has been considerably increased through the acquisition of specific 
values for the mean density of certain classes of double stars; and, 
at the same time, there has been a growing need in studies of stellar 
development for more definite information regarding this as well 
as other physical properties of stellar bodies. From the study of 
eclipsing variables it is found that the average density of the first- 
type stars is one-tenth or two-tenths that of the sun. Moreover, 
the range of values is apparently limited, for from a total of some 
fifty carefully investigated binaries, no star of spectral type B or A 
is known to have less than one-hundredth the solar density. Among 
the second-type systems a number are known to be denser than 
the white stars; but, on the other hand, there are also solar- type 
stars of remarkably low density — so rare, in fact, that with solar 
mass their volumes must be hundreds of times that of the sun. 
This result has been stated in various recent articles, but only in a 
more or less summary fashion; and, as the existence of such low 
densities and the bearing they may have on current astronomical 
problems is not generally admitted, it is the object of the present 
communication to give the data upon which the conclusion depends 
in a manner sufficiently detailed to permit an easy inspection and 
consideration of its validity. 

The point is of some importance in determining the order of 
stellar evolution. Admitting that stars in growing older contract 
and become denser, the stars of least density must obviously be the 
youngest; and, if we suppose that the order of evolution is uni- 
formly that represented by the spectral sequence B, A, F, G, K. 
and M, we must expect the densities of second-type stars always 
to be greater than those of the first. In other words, second-type 
stars of low density find no place in this scheme of stellar evolution 
except by the assumption that these particular bodies, in spite of 

1 Contributions from the Mount Wilson Solar Observatory, Xo. 107. 



272 HARLOW SHAPLEY 

gravitation, expand as time goes on. There may be some other 
explanation of such small values — we might hypothecate the 
existence of important counter-gravitative forces, or deny the 
whole of the eclipse theory, or, regardless of the evidence, propose 
that these are exceptional bodies which do not develop in the 
normal manner or are preceded by as yet undiscovered whiter stars 
of still greater volume, rarity, and luminosity. 1 But otherwise, if 
the existence of the abnormal densities is proved, it would seem that 
the conventional order of the evolutionary stages must be modified. 

The existence of many second-type stars of great intrinsic 
brightness is not questioned — for instance, Capella, the Cepheid 
variables, and the bright yellow stars in the Hyades group. With 
any reasonable assumption as to the surface brightness of these 
stars, the inevitable conclusion is either that they have enormous 
masses, or, if the masses are within the limits found in double-star 
systems, that the mean densities are extremely low. In some cases 
the dimensions must be so large that there can be no middle-ground 
adjustment that will keep both mass and density within the limits 
generally admitted in stellar studies. To account for the great 
size of the second-type stars of high luminosity, the choice between 
large mass or small density is generally made in favor of the former 
in order to maintain a late epoch in stellar development for these 
objects. But this implies for these stars, when earlier in their 
history they were of spectral type A or B, still greater dimensions 
than they now possess; and this circumstance, coupled with the 
much greater intrinsic light-emitting power of the whiter stars, 
would demand the presence of giant white forerunners of a magni- 
tude, both absolute and apparent, not at present to be found. 

This possible, though apparently improbable, interpretation of 
the great volume of isolated giant red and yellow stars contributes 
nothing to the question of whether the first-type stars are denser, 

1 In this connection it is well to keep in mind the group of B-type spectroscopic 
binaries whose periods exceed ioo days. We have as yet no assurance that their 
densities may not be peculiarly low. Xone of them is known to be an eclipsing 
variable. Of the second-type spectroscopic binaries, however, one-third have periods 
longer than the longest of the B's, so that, if length of period is to be the criterion for 
density, here again the white stars have intermediate values (Mt. Wilson Conlr., No. 99; 
Astrophysical Journal, 41, 291, 1915). 



DENSITIES OF SECOND-TYPE STARS 273 

in the mean and individually, than some of those of the second type; 
but, for valuable evidence, recourse may be had to the data of 
eclipsing binaries in which the mean density of each system can be 
determined independently of the mass. 1 

The questions to be answered are, first: Do these extremely low 
densities certainly exist ? and secondly : Are the stars considered 
certainly those with the redder spectra ? Since the evidence so far 
presented is by no means to be considered overwhelming, nor per- 
haps even incontrovertible, a specific record of the data is desirable 
in order to indicate the present status of the argument. 

The equations giving the density in terms of the orbital elements 
have been developed in various forms, and results for 20 stars, which 
seem certainly to be of the second type, have been published. 
Some of these densities are abnormally low, but the fact that their 
derivation has been involved with the rather complicated orbital 
theory of binary systems perhaps detracts something from the con- 
viction that the results would otherwise carry. There is. however, 
a simple relation which gives the upper limit of the mean density of 
an eclipsing binary without hypothesis as to the depth of the minima 
or the relative size or brightness of the components — in fact, in a 
circular orbit or one of small eccentricity the limit involves only 
the period and the duration of one eclipse. As the results from 
this relation are of the same order as those previously found, the 
conclusion as to the existence of very low densities is freed from the 
orbital theory and given a very direct derivation. 

Expressing the period, P, and the semi-duration of eclipse, /, in 
days, and the mean density, d , in terms of that of the sun, we have 
(as shown in the supplementary note) 



. 2irt (i) 

P 2 sin 3 — 

Table I contains data relative to five eclipsing systems of low 
mean density. The upper limits in the fifth column were derived 

1 The assumption that isolated stars and binaries are physically comparable is 
necessary, of course, in applying to the general aggregate of stars the conclusions 
reached in the present case; but there seems to be no reason at present to doubt the 
validity of this assumption. 



274 



HARLOW SHAPLEY 



by the foregoing relation. The remaining data are from Contri- 
butions from the Princeton University Observatory. No. 3, pp. 82 ff., 
INS- 
TABLE I 
Densities and Dimensions of Five Eclipsing Systems 



Star 


Spec- 
trum 


Period 


Semi- 
Dura- 
tion OF 
Mini- 
mum 


Upper ' CoMPUTED Density 
Limit 


Hypothetical Longest 
Radius 


Mean 
Density Bright 
Star 


Faint 
Star 


Bright 
Star 


Faint 
Star 


Relative 
Orbit 


SX Cass. . . 
RX Cass-. . . 
RZ Oph . . . 
RT Lac. . . . 
W Crucis. . 


G 3 

Ko 
F8 
G 5 
Gp 


36 d 572 
32.316 

261 .9 
5074 

198.5 


2 d 5 

2-5 

8.0 
0.4 

22.0 


O.OO05 0.0004 0.0002 
0.0005 0.0005 '0.OOO4 
O . OOOl 20.OOI . 00003 
0.02 0.013 O.OIO 

. OOOO S . C0O0O2 O . OOOO 2 t 

1 1 


15-3 
14.8 
IO. 1 
4.6 
94- 


18.6 

14.8 

33-5 
4-6 

36. 


59- 

53- 
217 . 

15.6 
180. 



Only for W Crucis are the observations adequate at present to 
give a curve and orbit of the first grade; the periods, however, are 
accurately known in all cases. To indicate how closely the dura- 
tion of the eclipse can be ascertained, as well as to show how closely 
the variation of these stars resembles that of typical eclipsing 
binaries of shorter period, the computed light-curves are given in 
Figs. 1, 2. 3, and 4. That for W Crucis has already been published 
in this Journal; 1 the peculiarities of its spectrum and the small 
distance separating the components may entitle it to diminished 
weight in the present discussion. 

The sources of the observations for the other four systems are 
as follows: 

SX Cassiopeiae. — The measures are visual estimates by Luizet ; 
the open circles represent points of low weight. Normal magni- 
tudes are printed in Contributions from the Princeton University 
Observatory. No. 3. p. 132 (1915), and the orbit, ibid., p. 86. The 
curve is computed from the uniform orbital elements. 

RX Cassiopeiae. — Observations are by Wendell using a Harvard 
polarizing photometer, each point representing the measures of a 
single night. The curve is computed from the uniform elements 
(ibid., pp. 86, 135). 



1 36, 148, 1912. 



DENSITIES OF SECOND-TYPE STARS 



275 



RZ Ophiuchi. — Only one-half of the curve is shown. The #'s 
are normal points from observations made at the Laws Observatory 
by Seares and Haynes; the dots define co-ordinates of the observed 



S M 6 



8.8 



9.0 



9-4 



9.6 



+4' 1 4-8 d + i2 d +16' 1 +2o d +24' 1 +28 d +32 d 



-V f- — -\ v^~ — 

\ 0/ \ / • 



Fig. 1. — The light-curve of SX Cassiopeiae 
_ 4 <i o' 1 +4 d +8 d +I2 d + i6 d +20' 1 +24 d 



8 J1 t> 














• 


• • 




















1 


* 5^" 














• »^\ 


8.8 










• 








• s 
















• / 


/• 










• \ 


i» 




• • 


90 




•\ 






































































• \ 








9.2 






















































94 






























1 

















Fig. 2. — The light-curve of RX Cassiopeiae 

curve by Nijland. The curve is computed from the darkened ele- 
ments (ibid., pp. 86, 157); the orbit is discussed in Astronomische 
Nachrichten, 194, 225, 1913; see also Laws Observatory Bulletin, 
No. 16, 1908. 



276 



HARLOW SH A P LEY 



RT Lacertae. — The x's represent normal magnitudes by Enebo; 
the dots, normals by Luizet (black squares have quadruple weight). 
The curve is computed from the darkened elements, the uniform 
solution being impossible (Contributions from the Princeton Uni- 
versity Observatory, No. 3, pp. 17, 26, et passim). 

One other variable similar to these — e Aurigae — might be added 
to the list, but its marked peculiarities of spectrum make the inter- 
pretation of its light-curve uncertain. 1 Similarly f3 Lyrae must be 
considered anomalous. 2 



9 M 6 



10.4 



10.6 



40" 



> 


2 x 


X 






1 * 




\ J 




( 








I X 
















X 


\ f 




1 




















1 
















L. 


1 1 
J 



































Fig. 3. — The light-curve of RZ Ophiuchi 



The faintness of the stars in the table has made the classification 
of the spectra difficult. 3 To make certain, however, that they are 
definitely of the second type, three independent and accordant 
classifications of their spectra were kindly made at the writer's 
request at Harvard by Miss Cannon. 

The tabulated semi-duration of the eclipse, which is used to 
compute the upper limit of the mean density, was read directly 

1 Contributions from the Princeton University Observatory, No. 3, pp. 20, 84, 94, 



1015- 



2 Ibid., pp. 71 ft". 

3 For the spectrum of W Cruris see Astrophysical Journal, 36, 153, 1912. 



DENSITIES OF SECOND-TYPE STARS 



277 



from the plot of the observations. For all but RZ Ophiuchi 1 the 
position and shape of the observed secondary minimum is sufficient 
to show that the orbital eccentricity is so small that the formula for 
the limiting density is valid. The depths and shapes of the 
secondary minima also show that the components must be of 
approximately the same dimensions, so that the mean density of 
the system also indicates the mean density of each component. 
This is not the case, however, for RZ Ophiuchi, where the steepness 



8*0 


o c 






I 


i 






i 






3 


i 


4 


1 






■ • 


X 


• * 


• 


i 


X 

- • 


• 

X 




x 




— *— _• 




\ 






X 


*— 


A 


• / 


> 


- x» • 


X 


X 


9.2 


\ 










V 












\ 










\ 










9-4 


\ 










\ 










9 .6 












\ 






















X? 








9.8 






















































































10. 2 


> 


: 



















Fig. 4.— The light-curve of RT Lacertae 



of the curve at primary eclipse shows that the component whose 
spectrum is classified as F8 is the smaller and brighter one for 
which the actual density, as computed from the orbital elements, 
is ten times the mean density; the second component is doubtless of 
a redder spectral type. 

The computed densities in the fifth and sixth columns were 
derived from a discussion of the orbital elements and have been 

1 The deviation of the observation near the secondary minimum suggests a deeper 
secondary eclipse than computed, but one of the comparison stars used for this part 
of the curve at the Laws Observatory is suspected of slight variation. Graff's meas- 
ures of the maximum light show no trace of a conspicuous secondary minimum (Astro- 
nomische Nachrichten, 176, 79, 1907). A deeper secondary minimum would give a 
lower mean density for the brighter component. Data are now available for a revision 
of the orbit, which will be undertaken soon. 



278 HARLOW SHAPLEY 

adjusted for polar flattening and probable irregular division of 
masses between the components in each system. They are close 
to the true values of the mean densities of these individual stars, 
but of course do not pretend to represent accurately the average 
density of the giant second-type stars as a whole. For a first-type 
star the lowest recorded density is 0.012, computed from a pro- 
visional curve for RZ Scuti, type B3; it is likely that further obser- 
vation will tend to increase rather than diminish this value. The 
next lowest value is o . 01 7 for UZ Cygni, type A. 1 

Fig. 5 gives a diagrammatic representation of four of the fore- 
going low-density systems, the major axes of the several stars and 
orbits being taken from the last three columns of Table I. For 
convenience the linear dimensions of SX Cassiopeiae and RX 
Cassiopeiae have been divided by two, those of RZ Ophiuchi by 
four, and those of W Crucis by eight. (The tabulated dimensions 
for RT Lacertae show that it is intermediate between the giant 
systems and the sun.) The diagram shows not only that these 
binaries are typical in their relative dimensions, but also that the 
components are distinctly separated. If the components were in 
contact, as is probably the case with /3 Lyrae and RR Centauri, 2 
we might expect the existence of a gaseous envelope that would 
give rise to spectral peculiarities; or, of more importance to the 
present problem, we might question the meaning of the computed 
densities, as Jeans 3 has done, because of possible interactions 
through a connecting neck of gas. But in these giant systems we 
find the stars as definitely and distantly separated as the average 
eclipsing and spectroscopic binary. The sun is drawn to scale 
(with the linear dimensions of the binaries reduced as mentioned 
above) on the assumption that each component of all the systems 
has solar mass. The masses are more likely to exceed the sun's than 
to be less. If each component is 8 times as massive as assumed. 

1 Stebbins has just announced that the mean density of 5 Ononis (type B) is 0.006 
(Science, N.S., 41, 811, June 4, 1915; see also Astrophysical Journal, 42, 144, 1915). 

2 Monthly Notices, 63, 537, 548, 1903. Roberts finds the components to be actu- 
ally overlapping in their lines of centers. The computed density, however, is 
entirely normal for a dwarf F-type system. 

3 Astrophysical Journal, 22, 93, 1905. 



DENSITIES OF SECOND-TYPE STARS 



279 



the sun should be drawn one-half as large; if but one-eighth the 
solar mass, its diameter should be doubled. The true dimensions 
of the stars relative to the sun are probably well within these limits. 
For the purpose of comparison, the two eclipsing systems of highest 
known density, which are also of the second spectral type, are 






o 





00 



o 

The Sun 



OO 

/ 



Fig. 5. — Eclipsing binaries of low and high density. The mass of each compo- 
nent is assumed equal to that of the sun. 

a) SX Cassiopeiae; period 36^572; spectrum G3. Reduced to one-half. 

b) RX Cassiopeiae; period 32 d 3i6; spectrum Ko. Reduced to one-half. 

c) RZ Ophiuchi; period 261^; spectrum F8. Reduced to one-fourth. 

d) \Y Crucis; period 198"? 5; spectrum Gp. Reduced to one-eighth. 

e) W Ursae Majoris; period 0^334; spectrum G. 
/) U Pegasi; period 0^375; spectrum F? 



280 HARLOW SHAPLEY 

included in the diagram, thus affording a fair illustration of giant 
and dwarf stars. 

SUPPLEMENTARY NOTE ON THE DERIVATION OF EQUATION (i) AND 
SIMILAR RELATIONS 

The equivalent of equation (i) has been given by Russell; 1 
expressions for the lower limit of the mean density of a binary, 
involving only the period, have been given by Stebbins 2 and others. 
On the basis of what is now known of the elements of eclipsing star 
orbits the range can be much narrowed, and it may be of value to 
derive both of the limits from the beginning. The resulting simple 
relations will then give with considerable accuracy the mean 
density of an eclipsing variable from the two most easily observed 
quantities, namely, the length of the period and the duration of 
minimum. 

Selecting the appropriate units of time, length, and density, we 
derive readily from the equation for elliptic motion the following 
expression for the mean density of a binary system: 

_o_oi34__ 0.0134 /x 

°° P*(rl+rl) Pfa+r&X' {) 

in which 

r\+rl 



X = 



(r t +r 2 )* ' 



and P. r 1} r, are the revolution period and the radii of the component 
stars, relative to the distance between their centers. The ratio X 
has its maximum value, unity, when one of the radii is zero; its 
minimum, \, corresponds to r I = r 2 . Hence. 



Upper limit of d = _ / , . (stars equal) 
P 2 {ri-\-r 2 y 

Lower limit of d = ■=-}■ — r~^r, (one star a particle) 
2*(ri+r a ) 3 



(3) 



The stellar radii are determined only by a solution of the orbit, but 
in the above limiting expressions we may substitute quantities that 
are determined directly from the light-curve. 

1 Astro physical Journal, 10, 316, 1899. 2 Ibid., 34, 105, 1911. 




(5) 



DENSITIES OF SECOND-TYPE STARS 281 

For a circular orbit 1 

(ri+r 2 ) 2 = cos 2 i cos 2 0'+sin 2 6' , (4) 

where i measures the inclination of the orbit to the plane per- 
pendicular to the line of sight and 6' = 2irt/P. t as before denoting 
the semi-duration of eclipse. For any given value of 6 f 

(r I -\-r 2 ) 2 = i (maximum) for i= 0° 

(r x +r 2 ) 2 = sin 2 0' (minimum) for i — go° 

Hence, 

o°S37 
Maximum upper limit d = r=- — . „ ,. 
FF P 2 sin 3 6' 

,,. . • ,. . , 0.0=537 

Minimum upper limit d = — =^ — 

,, . , .. . , 0.0134 

Maximum lower limit d = — — : — „, 

P 2 sin 3 v 

^ r - ■ 1 i- • 7 0.0134 

Minimum lower limit d = — j^- 

r 2 

The first of equations (5) is equivalent to (1). 

If the stars are just in contact, $t=P, so that B'=ir/2 and 
(ri-\-r 2 ) 3 = 1 for all values of i. The limits then become independent 
of the inclination and 

Upper limit d = ° ° 5 2 37 (r I =r 3 ) 

i- • 0.0134 , . 

Lower limit d = — ^r— (r 2 = o ) 
r 2 

With the aid of known values of the orbital inclinations we can, 
in practice, raise the lower limits of do as given by the last two of 
equations (5). Substituting (4) in (2) we obtain 

, > 00134 rM 

°~P 2 (cos 2 i cos 2 0'+sin 2 0') 3/2 ' 

which becomes an equality for one star a particle. 

The average value of cos i for ninety eclipsing systems, all with 
ranges at primary eclipse in excess of 0.4 mag. (except /3 Aurigae ; 

1 The necessary modifications of computations of density because of orbital eccen- 
tricity have been noted by Roberts {Astro physical Journal, 10, 311, 1899) and others. 
In most cases the changes would be negligible for the present work. 



282 HARLOW SHAPLEY 

range o. i mag. and cos £ = 0.23), is o. 112. On the average then 
(6) becomes 1 

■^ OOI 34 / \ 

0> ^(0.013+0.987 sin 2 0y/> • {1) 

For three systems only does cos i exceed o . 4, and in but one excep- 
tional case is the inclination less than 6o°. A very safe limit, 
therefore, is cos i^o. 5. and then we have finally 

0.108 , . 

0> P 2 (i+ 3 sin^') 3/2 " 
In equations (1) and (8) we have pretty close limits for the 
mean density which depend not at all on orbitaj elements. If on 
the basis of the depths and character of primary and secondary 
eclipses we can assume equal components, then X=\ and the 
right-hand member of (8) may be multiplied by four; and, at any 
rate, since only in the exceptional case of /- 2 <o.25/'i is X greater 
than one-half, this limit of density may be safely doubled in 95 
per cent of the eclipsing systems. 

Mount Wilson Solar Observatory 
May 1915 

1 Similarly the average value of (1) may be derived, and is found to be just four 
times as large as (7). 



Reviews 

Dialogues concerning Two New Sciences. By Galileo. Trans- 
lated from the Italian and Latin into English by Henry Crew 
and Alfonso de Salvio. With an introduction by Antonio 
Favaro. New York: Macrnillan, 1914. Pp.300. S2.00. 
"For more than a century English-speaking students have been 
placed in the anomalous position of having Galileo constantly referred 
to as the founder of modern physical science, without having any chance 
to read, in their own language, what Galileo himself has to say." With 
this pertinent remark Messrs. Crew and De Salvio preface their truly 
excellent translation of The Two Xew Sciences. In this, the last and 
greatest of his works, Galileo laid the foundations of two new subjects — 
strength of beams and uniformly accelerated motion. The book is in 
the form of dialogues between Salviati, a student of Galileo, the Academi- 
cian, and Sagredo and Simplicimus, the one a broad-minded seeker after 
truth, the other an uncompromising Peripatetic. The dialogues are 
divided into four days, after the manner of chapters, but so numerous 
and delightful are the digressions, ranging over the broad field of physics, 
that the whole seems rather a conversation, naturally developed, than a 
carefully worked-out treatise. 

Salviati undertakes to explain why similar machines, of the same 
material and with parts of proportional dimensions, cannot bear pro- 
portional strains. This leads to a consideration of cohesion, of vacua, 
of rarefactions and condensations, of resistance of media to falling bodies, 
of the laws of the pendulum ; and the day closes with a digression on the 
laws of vibrating strings. The Aristotelian hypothesis that, in a given 
medium, heavy bodies fall with speeds proportional to their weights 
is disproven by reason as well as by experiment. Suppose two bodies, 
one much the heavier, be tied together. If the old idea were correct, then 
the lighter would retard the heavier. But this would mean that the two 
together, though heavier than the heavy one alone, would fall more slowly 
than the heavy one alone — a conclusion contrary to the hypothesis. 
Therefore the assumed hypothesis is false. By actual experiment it is 
found that bodies fall with very nearly equal speeds, and the theory is 
advanced that these inequalities are due to resistance of the air. Two 
methods are mentioned for determining the weight or specific gravity of 

283 



284 REVIEWS 

the air. One is especially simple. Water is forced into a vessel until the 
imprisoned air is under considerable pressure; the vessel is weighed; 
the imprisoned air is allowed to escape; the vessel is again weighed. 
Then the difference in weight is the weight of a volume of air equal to 
the volume of water in the vessel. 

The second day's discourse is confined to strength of beams. The 
elements of this subject are established by simple geometrical reasoning 
from the law of the lever. 

On the third and fourth days is read and discussed a book on Motion, 
written by the Academician Galileo. The first part treats briefly of 
uniform motion, and more at length of uniformly accelerated motion, 
which is for the first time precisely defined. The laws of falling bodies are 
demonstrated by means of inclined planes and a water clock. Then 
follows a geometrical treatment of motion on inclined planes, the essen- 
tials of which are found almost unchanged in the textbooks on physics 
of today. 

The second part of this book deals with trajectories. Resistance 
to the air is disregarded as relatively slight and uncertain. The resultant 
of a uniform horizontal motion and the uniformly accelerated motion of a 
falling body is shown to be a semi-parabola. In the motion of pro- 
jectiles, the horizontal component of velocity is measured by the height 
from which a body must fall to attain that particular velocity and is 
called the "sublimity." Tables are computed, giving the amplitudes, 
altitudes, and sublimities of trajectories for a given muzzle velocity and 
varying angles of elevation. 

The dialogues afford an intimate acquaintance with conditions of 
the days of Galileo. Geometry was the mathematical instrument, and 
in the hands of a Galileo did surprising service. Nomenclature was 
obscure, ideas confused, and, above all, the experimental method was 
new. By a nice adjustment of literalness and freedom, the translators 
have retained the contemporary atmosphere without in any way sacrifi- 
cing clearness. 

The book is further enriched with an introduction by Antonio Favaro, 
of the University of Padua, editor of the Italian national edition of 
Galileo's works; with an excellent portrait of Galileo, as a frontispiece; 
and with a facsimile of the title-page to the Elzevir edition of 1638. 
Large print and good paper add materially to the book's attraction. 

E. P. Hubble 

Yerkes Observatory 
Williams Bay, Wis. 



THE 

ASTROPHYSICAL JOURNAL 

AN INTERNATIONAL REVIEW OF SPECTROSCOPY 
AND ASTRONOMICAL PHYSICS 



VOLUME XLII NOVEMBER 191^ NUMBER 4 



THE VISIBILITY OF RADIATION IN THE RED END OF 
THE VISIBLE SPECTRUM 

By EDWARD P. HYDE and W. E. FORSYTHE 

It has long been recognized that the sensibility of the average 
eye for radiation varies with the wave-length, the sensibility being 
a maximum in the yellow-green region of the spectrum and falling 
off to quite small values at each end of the spectrum. If the total 
radiation, measured in energy units for the wave-length interval 
whose center is at X, be denoted by J\, and the luminous intensity 
measured in light-units for the same interval by 7a, then the sensi- 
bility of the eye for the same interval is 

J A 

The determination of the ratio V K , termed the visibility of radia- 
tion, has been made in a number of investigations among which 
may be mentioned particularly those of Konig, 1 Langley, 2 Bender, 3 
Ives, 4 and Nutting. 5 

The methods used to obtain the value of 7a in this ratio may be 
divided into two classes. One involves a direct comparison, as in 

1 Konig, A., Ges. Abhandlungen. 2 Amer. Jour. Set., 36, 359, 1888. 

3 Annalen der Physik, 17, 105, 1914. See also Thurmel, ibid., 33, 1139, 1910. 

4 Phil. Mag. (6), 24, 853, 191 2. 5 Ibid., 29, 301, 1915. 

285 



286 EDWARD P. HYDE AXD W. E. FORSYTHE 

the ordinary "equality of brightness'' photometer, of the illumina- 
tion produced by light of successive wave-lengths in the visible 
spectrum with that produced by another source taken as a standard. 
The other method involves the use of the flicker photometer in 
which the criterion of equality is the disappearance of flicker. In 
either case the light from the comparison source may be kept con- 
stant in color, or the step-by-step method may be employed, in 
which case the color of the comparison source is changed at those 
points where the color difference exceeds a predetermined amount. 

The direct-comparison method was used by Konig and by 
Langley, while Ives, Bender, and Nutting have used the flicker 
method. Although much work has been done on the subject, there 
seems to be some doubt as to whether these two methods give the 
same result for very great color differences; indeed, it has been 
shown that in certain cases they do not. 1 The measurements have 
extended from 0.4 n to o. 7 fi, though the data near these limits as 
determined by Nutting, who has carried his measurements farther 
than anyone else, are given only to one significant figure. 

The great difficulty in the way of determining the visibility 
relation far out in the red or blue end of the spectrum is the small 
amount of light available. When it is realized that the sensibility 
of the eye varies by a factor of about 48,000 in going from the posi- 
tion of maximum sensibility to about 0.77/x, as may be seen by 
considering the results of others in conjunction with those given 
below, it will be evident that a source that would be very luminous 
taken as a whole would be quite weak if only a small interval of 
wave-length were taken in the deep red. The same considerations 
apply to the deep blue. 

In connection with a problem in optical pyrometry recently 
investigated in this laboratory, 2 it was important to know the 
visibility-curve somewhat beyond o . 7 \x and to be certain of the 
value to a reasonable degree of accuracy. To this end the present 
investigation was undertaken, making use of an adaptation of the 
arrangement employed in the Holborn-Kurlbaum optical pyrom- 
eter. The advantage in using the method of optical pyrometry is 

1 Luckiesh, Electrical World, 67, 621, 1913. Physical Review (2), 4, 1, 1914. 

- Astrophysical Journal, 42, 294, 191 5. 



VISIBILITY OF RED RADIATION 287 

twofold. In the first place, and in general, may be mentioned the 
availability of greater brightness, which permits the extension of the 
measurements farther into the red end of the spectrum; and in 
the second place by this method the sensibility-curve is obtained 
under conditions as to size of field and method of making the 
measurements very similar to those of the problem that was being 
investigated. Although, in accordance with the present needs, 
measurements were confined to the red end of the spectrum, the 
method might be employed also in extending the visibility-curve 
in the region of short wave-lengths. 




Fig. i. — Arrangement of apparatus 

In Fig. 1 is shown the arrangement of the apparatus used. The 
spectrum of a broad vertical carbon filament (A) is formed by means 
of a Hilger constant-deviation spectrometer in the focal plane of 
the object-glass of the telescope, in which plane is placed the horizon- 
tal filament of a second lamp (F). A lens (H) projects an image of 
this filament and of the background spectrum on a narrow vertical 
slit (/), in the focus of the eyepiece (K). By rotating the drum- 
head of the spectrometer, any spectral region of (A) may thus be 
brought into the field of view and compared in brightness with the 
pyrometer filament operated at a constant current. The brightness 
of the lamp filament (^4) was kept constant for the entire determina- 
tion. After the brightness of the lamp filament (F) that would 
apparently equal that of a region far out in the red end of the 
spectrum of the filament (A) had been determined, this lamp 



288 EDWARD P. HYDE AND W. E. FORSYTHE 

filament (F) was maintained at that constant brightness, and differ- 
ent spectral regions of filament (-4) were compared with this bright- 
ness. This was accomplished by reducing the apparent brightness 
of the lamp (A) by means of rotating sectored disks placed between 
the carbon filament (A) and the collimator slit (C) of the spectrome- 
ter and quite close to the latter, and then finding the position 
of apparent equality by turning the drumhead. The filament of 
lamp (A) was about 1.6 mm wide and about 0.3 mm thick, re- 
quiring 9 . 6 amperes for a black-body color-match temperature of 
1940 K., a temperature which was used throughout. This lamp 
was matched in color with a standard lamp several times during 
the course of the observations and, as closely as could be determined, 
it remained constant. The collimator slit (C) was for the greater 
part of the work kept at an opening of o . 5 mm. As a magnification 
of about one and one-half was used with the lens (B), it can be seen 
that the slit was at all times much more than filled. The lamp fila- 
ment (F) was of tungsten, 0.06 mm in diameter. The brightness 
of the filament (F) used for the most part corresponded to a color- 
match with a black body at about 1300 K. Determinations were 
also made with this lamp filament at about one-half, twice, and four 
times this brightness. These four determinations all checked well 
within the limits given below. The eyepiece slit was maintained 
at an opening of o. 2 mm because if wider eyepiece slits were used, 
variations across the slit could be noticed. Before and after each 
set of observations the calibration of the spectrometer was tested 
by means of known spectral lines. 

The energy-curve of the lamp (A) was determined by compari- 
son with a black body. Using the temperature thus obtained the 
energy-distribution was calculated from Wien's equation, taking 
C 2 equal to 14,500. In reducing the observed luminosities, correc- 
tions were made for dispersion, slit-widths, selective absorption of 
the lenses and prisms, and scattered light. It has been shown 1 that 
in certain cases an error may be made owing to diffraction of the 
light around the pyrometer filament. This error depends upon the 
size of the pyrometer filament, the angle of the incident radiation, 
and the wave-length. In the present investigation the size of the 

1 Physical Review (2), 4, 163, 1914. 



VISIBILITY OF RED RADIATION 289 

filament and the incident angle were large enough to make this 
error negligible over the range of wave-lengths used. In correcting 
for the scattered light, two methods were used. First, the bright- 
ness of the scattered light was measured as follows: the field of the 
spectrum was limited in height by a diaphragm in front of the slit 
(C) and the filament (F) moved up above the spectrum so that it 
could be compared with the brightness of the scattered light alone. 
By varying the current through the lamp filament (F) the brightness 
of this scattered light could be compared with that of the direct 
radiation plus the scattered light. Inasmuch as the lamp filament 
(F) was moved out of its position, the brightness of the scattered 
light that was compared may have been somewhat different from 
that at the center of the spectrum. However, results by this 
method check very closely with those of the method described below. 
The second method of correcting for the scattered light was to use 
before the eyepiece (K) a red glass of known transmission which 
would absorb all the more luminous parts of a scattered radiation. 
These two methods gave results for the scattered light that 
amounted to about 20 per cent at X=o. 76 p. for a particular length 
of slit (C). The illumination of the retina was well beyond the 
region where the Purkinje phenomena are effective, as indicated by 
the data given above, and the size of the field was extremely small 
for the comparison source, corresponding to the filament (F) 
(diameter o . 06 mm) magnified six times by the eyepiece, giving in 
angular units a field of about 0.4 degrees. 

As has been shown by the work of Ives 1 and others, it would be 
expected that the Purkinje effect would be very small even for low 
illuminations with this small field. As the same results were 
obtained with lamp (F) at one-half, at twice, and at four times the 
mean intensity used, it is seen that conditions were well outside of 
those in which the Purkinje effect is found. 

Measurements were made by nine observers whose final results, 
reduced to a common value at X=o.64ju, are shown in Table I. 
Each observer made determinations with at least two intensities of 
lamp (F) and also check-settings at these intensities, yielding for 
each observer at least four separate determinations on different 

1 Phil. Mag. (6), 24, 173, 1912. 



290 



EDWARD P. HYDE AXD W. E. FORSYTHE 



days. In making a single determination, observations were made 
with nine sectors and check-readings were made with at least live 
sectors. In working up the data, curves for the two intensities 
were made equal for the region where they overlapped. From a 
number of readings of the ordinates of the two curves, the mean 
ratio was calculated, giving the constant by which the luminosities 
differed. The variation of this ratio from a constant value was 
used in part to determine the accuracy of the work. The values 
given in Table I are the mean of the values read from smooth curves 
thus obtained, made equal to 100 at X=o.64 jj.. 



TABLE I 
Visibility Data on 9 Subjects in the Red End of the Spectrum 



Wave 


(1) 


(2) 


(.3) 


(4) 


(s) 


(6) 


(7) 


(8) 


(9) 


Length 


s E.P.H. 


W.E.F. 


F.E.C 


A.G.W. 


ML. 


C.F.S. 


R.G.B. 


WAV. 


H.M.J. 


O.620 


• 245° 


245 -O 


255 ° 


21 1 .0 


265.O 


252.O 


297.O 


291.O 


237-0 


.630 


. 164.0 


163.0 


155 


151 .0 


171 .0 


I590 


178.O 


174.O 


161 .0 


.640 


. 100. 


IOO. 


100.0 


100.0 


100.0 


100.0 


100.0 


100.0 


100.0 


.650 


• 59 


56.0 


59 


59 


570 


59 


53 


56.0 


61 .0 


.660 


■ 3 2 ° 


31.0 


29.0 


32.0 


26.0 


32.0 


27.0 


30.0 


32.0 


.670 


. 16.8 


153 


15-8 


16.3 


14.4 


16.8 


13 -7 


15.6 


16.6 


.680 


• 8.3 


7-5 


7-8 


8.0 


7-i 


8.2 


6.8 


8.1 


7.8 


.690 


■ 4-i 


3-6 


3-8 


4.0 


3-5 


4-i 


3-4 


4.0 


3-7 


. 7O0 


■ 2.05 


i-73 


1.87 


1 .96 


1.77 


1.86 


1. 61 


1 .90 


1.88 


• 7 IQ 


1 .01 


0.86 


0.92 


0-95 


0.86 


0.94 


0.86 


093 


0.90 


. 720 


0.49 


0.42 


0.46 


0.48 


0.41 


0.46 


0.42 


0.46 


0.44 


• 730 


0.24 


0.21 


0. 22 


0. 24 


0. 21 


0. 22 


0. 20 


0.23 


0. 21 


.740 


O.I2 5 


O. IOg 


O.II.S 


0. n 7 


0. 10, 


0. 1 : 2 


0. IC, 


0. u 4 


0. io 7 


750 


o.o6j 


0.052 


0057 


0.05s 


0.053 


o°5s 


0.05 


0.056 


■ °5> 


.760 


0.03, 


0.026 


0.030 


0.030 


0.02 7 


0.02 7 


0.02 9 


0.028 


O.O2 


0. 770 


O.OI 7 


OOI3 


OOI 5 


0.016 


O.OI 4 


O.OI2 


O.OI 4 


OOI 2 


O.OI 4 



To show the relative values of the sensibility of the individual 
observers in the red end of the spectrum Table II is given. In ob- 
taining these data, both lamp (^4) and lamp (F) were kept constant, 
(F) being at the average brightness used, and settings were made 
by each observer. Data were thus obtained in the form of curves 
from which could be computed the relative values of the sensibility 
of different observers at X=o.75 fx. It will thus be seen that the 
values given are for the relative sensibility of the different observers 
when comparing the brightness of the particular spectral color with 
the brightness of lamp (F). As previously stated, the values given 



VISIBILITY OF RED RADIATION 



291 



in Table I are also relative. It will be seen from a comparison of 
Tables I and II that, though there was a great variation in the values 
given by the individual observers to the luminous intensity in the 

TABLE II 

Relative Value of the Sexsibility of the Different Observers for 

Light at A = 0.75/*. When Compared with That from 

a Black Body at about 1300 K. 

E.P.H II3 

W-E.F IS7 

F-E.C I?0 

A.G.W IQ2 

->LL 123 

CF.S I25 

R-G.B 7 8 

W.W I22 

H.MJ 84 

extreme red, the relative values do not vary so widely. The aver- 
age results of the nine observers, together with the values obtained 
in previous determinations, are shown in Table III. For compari- 
son the values of the previous determinations have also been 



TABLE III 
Visibility Data in the Red End of the Spectrum 



Wave-Lengths ' Mean Visibility 
of g subjects 


Mean Values 
Given by Nutting 


Mean Values Given 
by Ives 


Konig's Values 


O.620 

•630 

.640 


252.0 

164.0 

100. 

58.0 

30.0 

15-7 
7.6 

3-8 

1.87 
0.91 

o.45 
0. 22 

O. II r 

055 
0.02 9 
O.OI 4 


227.O 

164.0 

IOO. 

62.O 

34-0 

18.6 

8.0 

4-7 
1-3 


221 
156 

IOO 

59 
39* 
25* 
15* 


189 
143 


.650 


61 


.660 


.670 


33 


.680 


z 5 


.690 




.700 






■7IO 






.720 








• 73° 








•74o 








•75° 








. 760 








0.770 

















* Extrapolated values. 



202 EDWARD P. HYDE AND W. E. FORSYTHE 

reduced to ioo for X=o.64^t. The average results of the nine 
observers were computed by taking the arithmetical average of the 
values given in Table I. As the relative values differed by such a 
small amount, this method will give approximately the same results 
as the method of reduction to equal areas. 

In determining the accuracy, consideration has been given first 
of all to the necessary corrections together with the accuracy with 
which they could be obtained; secondly, to the error which the 
different observers made in setting the drum of the spectrometer 
for a match of brightness in the different parts of the spectrum; 
thirdly, to the agreement of observations taken on different days; 
and, fourthly, to the agreement of the data obtained with different 
intensities of the lamp (F). From a consideration of all the fore- 
going it would seem that the accuracy of the resulting sensibility- 
curve ranges from about 5 per cent at 0.62 n to about 15 per cent 
at 0.76^. How nearly the final curve could be classed as an 
average curve is a question. The observations are those of nine 
men, and, as can be seen, the different observers have quite a range 
of sensibility. It will be noticed that observer 4 is quite sensitive 
to red radiation, while observer 7 is very sensitive to the blue-green 
part of the spectrum. It is doubtful if multiplying the number of 
observers would change the curve by a very great amount. To 
make this point certain it would be necessary to have quite a num- 
ber of observers, and at the time this was not feasible. All of the 
observers with the exception of the last two have had considerable 
experience in photometric work and with instruments of similar 
optical character. These two have had much to do with optical 
apparatus, but have not had so much photometric experience. 

The agreement as shown in Table III between the values given 
and those obtained by other investigators within the common region 
is as good as might be expected. The agreement in the present 
work among the different observers in measurements in the red is 
probably better than that attainable in the more luminous region 
of the spectrum where the color differences are much more pro- 
nounced. It should be remembered that the agreement referred to 
pertains to the relative visibility in different wave-lengths of the 
red region rather than to the visibility in the red region compared 



VISIBILITY OF RED RADIATION 293 

with the visibility of white light, which was shown to be markedlv 
different for different observers. Emphasis should be laid on the 
fact that the data given have been obtained with a small field. It 
is probable that the same result would be obtained with larger 
fields. 

SUMMARY 

Data have been given for the visibility-curves for 9 observers 
from 0.62 n to 0.77/i, together with the relative values for the 
sensibility of the individual observers when comparing light at 
o . 75 fx with that from a black body at about 1300 K. These results 
have been compared with the results of other determinations in 
the common region. 

Nela Research Laboratory 

National Lamp Works of Gexeral Electric Co. 

Nela Park, Cleveland, Ohio 

April 19 1 5 



THE EFFECTIVE WAVE-LENGTH OF TRANSMISSION 

OF RED PYROMETER GLASSES AND OTHER 

NOTES ON OPTICAL PYROMETRY 

By EDWARD P. HYDE, F. E. CADY, and W. E. FORSYTHE 

A. THE EFFECTIVE WAVE-LENGTH OF TRANSMISSION OF RED 
PYROMETER GLASSES 

In working with any optical pyrometer it is in general sufficient 
to use an approximately monochromatic screen between the eye 
and the pyrometer filament or other comparison source in order 
that the latter may apparently match in color the source studied. 
The glass or screen used must be much more nearly monochromatic 
for studying sources at high temperatures, as it is in this region that 
the differences in color of the various sources are more noticeable. 
An optical pyrometer can be so calibrated and so used as to make 
unnecessary a knowledge of the extent to which the screen is mono- 
chromatic. To do this it is necessary to use in calibrating the 
pyrometer a black-body furnace that can be operated at various 
temperatures up to the highest temperature for which the pyrom- 
eter is to be used. However, if an attempt is made either to 
calibrate the pyrometer by the aid of a black-body furnace held 
at a single temperature, 1 as for instance the melting-point of palla- 
dium, or to extend the temperature measurements beyond that of 
the standard furnace by means of absorbing glasses or rotating 
sectored disks, a knowledge of the effective wave-length for the 
screen used is necessary. In attempting to check the calibration 
of a Holborn-Kurlbaum optical pyrometer using a black-body 
furnace, differences much greater than could be ascribed to errors 
of observation were encountered. Pyrometer readings were made 
with the black body held at the temperature of melting palladium, 
using various rotating sectored disks. The scale thus obtained was 
tested by direct comparison with the same furnace held at the 
temperature of melting gold, and found to be in error by several 

1 C. E. Mendenhall, Physical Review, 33, 74, 1911. 

294 



NOTES ON OPTICAL PYROMETRY 295 

degrees. In this case the value for the effective wave-length of 
the red screen used was obtained with a spectrometer as outlined 
below. An investigation of the causes of the error led to the follow- 
ing study of the effective wave-length of transmission of the red 
glass used. 

Various definitions have been given to this effective wave- 
length. It has been identified 1 with the maximum of luminosity 
as determined with a spectrometer. This maximum of luminosity 
is determined by so mounting the screen with respect to the spec- 
trometer that a direct observation of the wave-length of maximum 
brightness of the transmitted light can be obtained for any par- 
ticular spectral distribution. It has also been defined 2 as the 
center of gravity of the luminosity as transmitted through the 
screen, this center of gravity being determined in various ways. 
Further, an attempt has been made to associate it with a definite 
distribution, 2 i.e., a definite temperature of the incident radiation, 
the value of the wave-length being determined by computation. 

The foregoing definitions and methods will not in general give 
the effective wave-length; in fact it can be shown that in nearly 
all cases they will not give the wave-length which must be used to 
calculate temperatures. The wave-length that should be used is 
one such that for any definite temperature interval for a particular 
source the ratio of the radiation intensities for this wave-length 
shall equal the ratio of the integral luminosities through the screen 
used. This is evident when it is remembered that the quantities 
which are actually compared are the integral luminosities as 
observed through the screen, and therefore, in computation, a 
wave-length should be used for which the ratio is the same. Defin- 
ing the effective wave-length in this manner leads to the same 
result for the given temperature interval as would be obtained if 
the screen used were absolutely monochromatic in this wave- 
length. 

The screens furnished with optical pyrometers are not mono- 
chromatic. Among the glasses commonly used for red screens are 

1 Waidner and Burgess, Bulletin Bureau of Standards, 3, 163, 1909; see also 
Mendenhall, he. cil. 

2 Pirani, Verh. der deutschen physikalischen Gesellschaft, 15, 826, 1913. 



296 EDWARD P. HYDE, F. E. CADY, AND W. E. FORSYTHE 

Jena '"Kupferrubin" glass No. F-2745 and Jena "Rotfilter" No. 
F-45 1 2 . The transmission of a specimen, 2 . 9 mm thick, of what was 
furnished by the makers as "Rotnlter" glass No. F-45 12 is shown 
in curves A and A ' in Fig. 1 . Three methods have been employed 
to obtain the transmission of the red glass: (1) the spectropho- 
tometry, (2) the spectral pyrometric, and (3) the spectrobolometric. 



0.6 


M O 


8 


1 





I 


2 


I 


4 


I 


6 


1 


8 


2 





2 


.2 


2 


4 


2 


.6 


2 


.8 


3 





3 


.2 


3 


■4 


3 


.6 


90 
































































-A 




























































80 


*" 




























A' 
































f 




















































































































































































60 




































































































































1 






















































5° 








\ 
























C 






































\ 


/ 




















































40 










/ 






























































\ 




















































J u 








I 














































































































































































































































































































\i 






V 

























































o.6om .62 .64 .66 .68 .70 .72 .74 .76 

Wave-length scale for curves A', B, and C 

Fig. 1. — Transmission of red pyrometer glasses 

A Transmission of single piece F-45 12 re d glass 

A' Same as A; larger wave-length scale 

B Transmission double thickness of same glass 

C Transmission of single thickness of red pyrometer glass, probably F-2745 

The agreement of the three methods can be seen from curve A, 
Fig. 1, where the transmissions obtained by the different methods 
are marked differently. The transmission of two thicknesses of 
the glass (5.8 mm) in the visible spectrum is given by curve B. 
In curve C is shown the transmission of what is supposed to be 
" Kupf errubin " glass No. F-2745. This is a piece of the same 
sample of red glass as has been used 1 in a comparison of the tem- 
perature scale based on the Wien radiation law as applied to an 
optical pyrometer and a scale based on the Stefan-Boltzman law. 

1 Mendenhall and Forsythe, Physical Review (2), 4, 62, 1914. 



NOTES ON OPTICAL PYROMETRY 297 

It is seen that the transmission band is rather broad, though the 
apparent breadth, as observed with a spectrometer, is much less, 
owing to the limit of vision. It has been recognized by Waidner 
and Burgess, 1 Pirani, 2 and others that, owing to the breadth of the 
transmission band, the effective wave-length is subject to change 
with changes in spectral distribution of the incident radiation, as 
occasioned by changes in temperature of the radiating sources 
under investigation. In fact, Waidner and Burgess have attempted 
to show how this wave-length changes with the change of the 
temperature of the source by the use of the spectrometer as out- 
lined above. In this way they found that the effective wave- 
length seemed to become longer at higher temperatures, a result 
quite contrary to expectations. 

The importance of knowing in accurate measurement in pyrom- 
etry the effective wave-length for different ranges of the temperature 
is evident. It was desired to determine the effective wave-length 
for the red glass for the interval between two definite temperatures 
of a black body and to determine how this effective wave-length 
changes as this interval is changed. Two methods were employed: 
(1) that of direct measurement, and (2) that of computation, 
assuming a knowledge of the visibility-curve of the eye. An elec- 
tric incandescent lamp at two arbitrary currents, corresponding 
in energy distribution to the black body at 1600 K. and at 2000 K. 
respectively, was selected as the source, and measurements were 
made with the best or most nearly monochromatic glass in our 
possession, viz., that for which the transmission-curve is given 
in Fig. 1 (curve A) and of the kind known as Jena "Rotfilter" 
No. F-4512. A double thickness of glass (5.8 mm) was used, as 
this is about the thickness of glass generally employed. 

By the first method, the ratios of intensities of emission of the 
source for a number of wave-lengths at the two temperatures were 
measured, and these ratios compared with the ratio of integral 
luminosities of the radiation from the source observed through the 
double thickness of glass. These measurements were carried out 
with two distinct sets of apparatus. In one set of measurements 
the ratios of the intensities of radiation were measured with a 

1 Op. cit. 2 Op. cit.; see also ibid., 17, 47, 1915. 



298 EDWARD P. HYDE, F. E. CADY, AND W. E. FORSYTHE 

spectrophotometer, and the ratio of the integral luminosities was de- 
termined with a Lummer-Brodhun photometer having the double 
thickness of red glass in the eyepiece. In the other set of measure- 
ments the ratios of the intensities of radiation were determined with 
a spectral pyrometer 1 and the ratio of the integral luminosities was 
measured by the use of a laboratory form of the ordinary Holborn- 
Kurlbaum pyrometer having two thicknesses of the red glass in 
the eyepiece. 

By the second method the integral luminosities through the 
red glass at the two chosen temperatures were computed from a 
knowledge of the spectral energy-curves (computed from Wien's 
equation), the transmission-curve for the glass (Fig. 1, curve B), 
and the sensibility-curve of the eye. Inasmuch as the best pub- 
lished visibility data extend only to o . 7 /jl and are given only to one 
significant figure in this neighborhood, which is most important 
in the present investigation, a preliminary investigation of the 
sensibility of the eye in this region was undertaken. 2 The data 
obtained in this preliminary investigation were used in the present 
computations. 

The results obtained by the two methods, direct experiment 
and computation, are given in Table I. 

TABLE I 

Effective Wave-Length of Monochromatic Transmission for Two 
Pieces of Red Pyrometer Glass No. F-4512, 5.8 mm Total Thick- 
ness, for the Interval between the Temperatures 1600 K. and 
2000 K. 

Direct experiment, using spectrophotometer 0.664 /^o.ooi /j. 

Direct experiment, using pyrometer 0.6635 ±0.001 

Computed value o . 6638 

Mean o.6638/x ± o.ooi p. 

The next point of interest lies in the variation of this effective 
wave-length with change in temperature of the source studied. 
These variations can be determined most accurately by the method 
of computation, and as the changes in effective wave-length are 

1 Henning, Zeitsclirift fitr Instrumentenkimdc, 30, 61, 1910. 

2 Astrophysical Journal, 42, 285, 1915. 



NOTES ON OPTICAL PYROMETRY 



299 



small it is unnecessary to give the value for more than a few tem- 
perature intervals. In Table II are given the results of these 
computations, assuming the effective wave-length between i6oo°K. 
and 2000 K. to be the mean value given in Table I. Because of 
interest in the paper already referred to in connection with some 
work by C. E. Mendenhall and one of the authors, the changes in 
the effective wave-length of transmission of the red glass used 
in that work have been computed. These results are also given 
in Table II. 

TABLE II 

Computed Changes Due to Variation" in the Temperature Interval in the 

Effective Wave-Length of Two Samples of Red Pyrometer 

Glass Using Two Thicknesses of Each 



Temperature Interval 



i336°-j6oo° K 

i336°-i822° (gold to palladium) 

i336°-3 IO °° 

i6oo°-i82 2° 

l822°-2400° 

l822°-3IOO° 

240o°-3ioo° 



Glass No. 

F-4512 Total 

Thickness 

5 .8 mm 



0.664, 
.6646 
.6634 
.664j 
.662, 
.662 4 

o.66i 7 



Glass No. 

F-2745 Total 

Thickness 

6 . 7 mm 



O.6671 
.666 7 
.6646 
.666, 
.6636 
.662 7 

0.661, 



Observations made on other pieces of glass used with the 
Holburn-Kurlbaum and other pyrometers indicate quite appre- 
ciable deviations from the particular specimens studied in the 
present investigation. As obviously it would be most incon- 
venient to subject every sample of glass to such an investigation 
as that recorded here, it appears desirable to find a simple way 
of calibrating glasses in terms of the specimen already investi- 
gated. This can be done readily, by determining the ratio of the 
apparent candle-powers of a standard lamp at two definite cur- 
rents, using the glass under investigation in the eyepiece of a 
Lummer-Brodhun or other suitable photometer, and comparing 
this observed ratio with the known ratio as determined with the 
known sample of glass in the eyepiece of the photometer. If the 
ratio with the test glass is found to be, say, 1 per cent greater than 
the given ratio for the standard glass, then the effective wave- 



300 EDWARD P. HYDE, F. E. CADY, AND W. E. FORSYTHE 

length for the temperature interval corresponding to the two 
currents through the lamps must be shorter than the accepted 
wave-length of the standard glass by an amount readily computed 
from Wien's equation and from the known black-body color- 
match temperatures of the lamp at the two currents. Until the 
standardization of glasses may be undertaken by the Bureau of 
Standards, Nela Research Laboratory will be glad, for the con- 
venience of other investigators, to calibrate red glasses in terms 
of our standard; or else will, if desired, furnish at cost lamps cali- 
brated between two definite currents, giving the black-body color- 
match temperatures and the ratio of apparent candle-powers as 
determined with the standard red glass in the eyepiece. 

Using a sample of red glass (No. F-4512) slightly thicker than 
the standard sample here investigated, the ratio of the intensities of 
the radiation through the glass from a black body at the tempera- 
ture of melting palladium and at the temperature of melting gold 
has been determined. In determining this ratio four different 
pyrometer lamps have been used, three of tungsten and one of 
carbon. Four different black-body furnaces have been used. 
At times the same furnace was used for the two points and at other 
times different furnaces. As a final result of ten determinations 
extending over a year and a half, 76.9 was obtained for this ratio. 
Using this value, 76 . 9, the effective wave-length for this tempera- 
ture interval for the red glass employed together with the two 
temperatures, C 2 of Wien's equation may be computed. Thus 
C 2 was found to be 14,460, a value that checks well with the latest 
determinations. 1 

By computation, as shown above, the effective wave-length 
can be determined for any range of distribution of radiation, that 
is, any range of temperature. In some work it is very desirable to 
know the effective wave-length as a certain temperature is ap- 
proached. If the effective wave-lengths are computed for the 
intervals 1500 K. to 1300 K., 1500 to 1700 , 1500 to 1800 , etc., 
and these values are plotted as a curve between effective wave- 
lengths and temperature difference from 1500 K., this curve would 
pass through the 1500 point and could be used to obtain the 

1 Coblentz, Bulletin Bureau of Standards, 10, 1, 1914. 



NOTES ON OPTICAL PYROMETRY 301 

effective wave-lengths for 1500 K. By computing a series of such 
limiting effective wave-lengths the data given in Table III were 
obtained. 

TABLE III 

Limiting Value of Effective Wave-Length as Different Temperatures 

Are Approached 

Temperatures Limiting Effective 

Wave-Lengths 

1300 K O . 665 5 /A 

I 500° 6648 

I JOO° 664j 

I9OO -6635 

2300 662., 

2700 66u 

3100° 0.661, 

As a test of the correctness of the value of the effective wave- 
length obtained and its variation with the temperature interval, 
a pyrometer lamp was carefully calibrated, using rotating sectors, 
against a black-body furnace held at the temperature of melting 
palladium. This same furnace was held at two temperatures lower 
than this temperature, and its temperature was determined by the 
application of Wien's equation, going down from the temperature 
of melting palladium and also up from the temperature of melting 
gold, as determined for the same furnace. The results are given in 
Table IV. For the temperature interval between 182 2° K. and 

TABLE IV 

Temperatures of Black-Body Furnace as Determined by Computation 
from Two Fixed Points 

Temperatures from Temperatures from 

Palladium Point Gold Point 

I72I°K. I 7 20°K. 

1625° 1625° 

1336 K. the effective wave-length for this interval given in Table 
II has been used, and for C 2 the value given above. A reference to 
Table II will show that there is a very small change in the effective 
wave-length for smaller intervals within this same interval. 



302 EDWARD P. HYDE, F. E. CADY, AND W. E. FORSYTEE 



B. THE TEMPERATURE COEFFICIENT OF TRANSMISSION OF RED 
PYROMETER GLASS 

In connection with the investigation described above it was 
observed that the transmission of the red pyrometer glass, pre- 
sumably made with copper oxide, and dependent for the color on 
a colloidal solution, is subject to a large change with temperature. 
This has not been investigated thoroughly, but observations were 

made at two temperatures, 
2o° C. and 8o° C, by immersing 
the glass in water heated to 
these two temperatures. The 
results are given in Fig. 2. 
Curve A is the transmission of 
the glass at the lower tempera- 
ture 20 C.j and curve B the 
corresponding curve at the 
higher temperature 8o° C. The 
transmission is shown to de- 
crease with increase in tempera- 
ture, the coefficient of change 
of temperature being greatest 
in the shorter wave-lengths. 
The change is such as to make 
the transmission band appear 
to shift to longer wave-lengths 
as the temperature is increased. 
A further investigation of this 
should give data with which to test the theoretical formula of 
Mie 1 for colloidal solutions. 

A test was made of the effect of this temperature-shift of the 
transmission band on temperature-measurements when the red 
glass was used as a screen before the eyepiece of the pyrometer. 
The temperature of a broad carbon filament lamp operated at an 
apparent temperature of 1900° K. was measured with the red j 
glass used as a screen before the eyepiece of the pyrometer. It was J 
so arranged that the red glass could be used at room temperature I 
1 Annalen der Physik, 25, 377, 1908. 

































<JU 






















A 






































So 




R 






























































/<J 












/ 




















60 












1 






























































1 




















5" 










\ 


/ 




















































4" 










f 






















































i^ 










































, 






























































I 


/ 





























































*i 





I 























o.6om .62 .64 .66 .68 .70 .72 
Wave-length 
Fig. 2. — Transmission of single thick- 
ness of glass F-4512: A at 20 C; B at 
8o° C. 



NOTES ON OPTICAL PYROMETRY 303 

and also when heated to about 8o° C. The temperature of the 
lamp was measured using a 2 sectored disk, as this would give 
a larger effect than a sector with greater transmission. It was 
found that there was a decrease of 5 C. in the temperature obtained 
when the glass was heated to 8o° C, over that obtained with the 
glass at room temperature. From this it will be seen that for all 
ordinary temperature changes the effect would be negligible. 

C. INFLUENCE OF POSITION OF ROTATING SECTORED DISK IN USE 
WITH THE HOLBORN-KURLBAUM TYPE OF PYROMETER 

If a rotating sectored disk is used with an optical pyrometer 
to reduce the intensity of the source, care must be taken as to the 
location of the disk. There is a very marked difference in the 
results of temperature measurements, depending upon whether 
the sector is located near the projection lens or as near as possible 
to the pyrometer lamp. There is also a difference depending upon 
the relative position of the openings in the sector and the source, 
providing the source is a lamp filament. If a sector of small trans- 
mission is mounted near the lens and so placed that the openings 
of the sector are parallel to the axis of the filament when passing 
across the center of the lens, the definition is very bad, while if the 
openings of the sector are turned through 90 so that they are per- 
pendicular to the axis of the filament, the definition is apparently 
quite good. When the rotating sector is located near the pyrom- 
eter lamp the definition is good and practically independent of the 
position of the openings of the sector. If a very large source, as 
for example a black body, is used, no such effect is to be noted. It 
would appear that the rotating sector as used with the optical 
pyrometer 1 has at times been placed in a position which would lead 
to uncertainties. 

If a lamp filament used as a background be set so that it has 
the same brightness as a black body at i822°K. (the temperature 
of melting palladium), as determined by the optical pyrometer 
using red glass before the eyepiece, and this background again set 
at the brightness corresponding to the melting-point of gold as 
indicated by the black body, the relation between the brightness of 

1 C. E. Mendenhall, loc. cit. 



304 EDWARD P. HYDE, F. E. CADY, AND W. E. FORSYTHE 

the lamp at the two temperatures, as determined by the rotating 
sector if placed near the lens, is not the same as that for a black 
body or other large source over the same range. Thus it was 
found that with the rotating sector located near the projection 
lens the error amounted to about 8° for this interval. The disk 
was so mounted that the openings made an angle with the axis 
of the pyrometer of about 45 when crossing the lens. The fila- 
ment of the lamp used as a background was about 0.3 mm in 
diameter. However, if the sector be located very near the pyrom- 
eter lamp the ratio as found checks very closely with that for a 
black body. 

SUMMARY 

Data have been determined for the effective wave-length for 
Jena "Rotfilter" No. F-4512 and Jena " Kupf errubin " glass No. 
F-2745 for the interval corresponding to a black body at tempera- 
tures 1600 K. and 2000 K. The effective wave-lengths for different 
temperature intervals have also been computed for these two glasses. 
In connection with the work a determination of the constant C 2 of 
the Wien radiation law has been made. 

It has been shown that care must be taken as to the location 
of the sectored disk when it is used to extend the temperature 
measurements with the optical pyrometer, and that the trans- 
mission of red glass used in such pyrometers is subject to change 
with change of temperature, although this effect does not lead to 
appreciable errors under the conditions ordinarily encountered. 

Nela Research Laboratory 

National Lamp Works of General Electric Co. 

Nela Park, Cleveland, Ohio 

April 19 1 5 



OX SOME PECULIARITIES OF THE RESIDUAL RADIAL 
VELOCITIES OF STARS OF DIFFERENT SPECTRAL 
CLASSES AND THEIR RELATION TO THE SOLAR 
MOTION 

By C. D. PERRIXE 

While investigating the relation between radial velocities and 
magnitudes, I noticed in some of the classes what appeared to be 
a tendency of the velocities in some regions to differ systematically 
from those in other regions. Further examination confirmed the 
earlier suspicions and led to an examination of all of the classes. 

It is the purpose of the present paper to point out some of the 
peculiarities found. 

As the stars of Class B have such a strong preference for the 
Milky Way, they were examined first, as showing more readily 
peculiarities in widely separated and distinct regions of the sky. 

The mean residual velocities and mean inherent velocities of all 
these stars were first grouped in quadrants as in Table I. 

TABLE I 
Stars of Class B 



No. 



Residual Vi 



Mean V, 



2I h_ 3 

3~9 
9 "IS 

15 -21 




The velocities used are from Campbell's catalogues, of Class B 
stars in Lick Observatory Bulletin, No. 195, of Class A in Bulletin 
No. 2ii, and of 915 stars of Classes F, G, K, and M in Bulletin 
No. 229. 

These results indicate a systematic tendency, both in the general 
mass motions and in the average inherent velocities. 

The average radial velocity (mean V 2 ) appears to be a minimum 
not far from the solar antapex and a maximum near the apex — 

3°5 



306 C. D. PERRINE 

the velocities midway between these points being approximately 
the same and a mean between the maximum and minimum values. 
The significance of any such eccentricity of velocity, if confirmed, 
would be very great indeed. 

The stars in the different classes were then cleared of the solar 
motion upon a common hypothesis for all. 

An examination of the velocities and constant errors obtained 
by Campbell 1 shows an apparent relation between the solar motion 
and the K-term which will be referred to later. He concluded, 
however, that for all of the classes (all stars) the value of V© (—19.5 
km) was indifferent to the inclusion or exclusion of the constant 
error K. This was assumed, therefore, as a basis for intercom- 
parison of the different classes. The individual stars of the six 
classes were cleared of the solar motion, using the value of —19.5 
km for V Q , neglecting K and assuming the position of the apex 
at a= 270 , 5= +30? There is perhaps a doubt about the assump- 
tion of this apex, but in the absence of any definite knowledge it 
seems justifiable to use it. 

Campbell finds a very consistent tendency of the radial veloci- 
ties to place the apex about 8° south of that found from the proper 
motions. He also concludes that the velocities of the stars are 
greater in the plane of the Milky Way. It seems not improbable 
that the greater velocities in the Milky Way will be found to 
explain the difference in the positions of the apex. As soon as the 
solar velocity and the velocities with respect to the galactic and 
non-galactic regions become better known and more observations 
available it should be possible to test the matter more fully. 

Groups of all classes of stars were selected with respect to the 
apex, antapex, and the two regions at right angles to these having 
distances from the apex between 70 and uo° and being between 
22 h and 2 h and between io h and 14 11 . 

The results are given in Table II. 

Attention may be called to the peculiar progressions in the 
group velocities at right angles to the direction of solar motion 
shown in Table V. These progressions resemble similar ones in the 
values of the solar motion and constant term K. 

1 L. 0. Bulletin, No. 196, p. 127. 



RESIDUAL RADIAL VELOCITIES 



307 



The number of stars concerned in these groups is not large, and 
abnormal individual velocities probably affect them to some extent, 
especially in the stars of the middle and later types. 



TABLE II 

Residual Velocities 



Apex 


Antapex 


22^—2^ 


io h -i4 h 




No. 


Mean V 


No. 


Mean V 


No. 


Mean V 


No. 


Mean V 


B 

A 


22 
28 

24 
21 

31 
J" 

\io* 


km 
+ 2-4 

+ 2.1 

— 4. 2 
+ 1-3 
-4-3 
-6.2 

— O. 2 


36 
21 
18 
12 
39 

fl2 

\ll* 


km 
+ 6.2 

- 2.0 

- 2.3 

- 7.o 
+ 2.6 
+ 6.2 
+ 11. 5 


18 
20 
15 

21 

43 
16 


km 

+0.7 
+5-0 
+8.0 

+ 2.6 

+5.9 

+ 2-5 


27 
19 
II 

15 

28 

13 


km 
+ 5-4 
-3-i 
— 0.8 


F 


G 


-3-6 
+ 2 I 


K 


M 


+7-3 













* Rejecting one large value. 

There is probably also some effect still remaining of an}- differ- 
ences between the corrections applied for the solar motion and 
the true ones; but as the true ones must be considered unknown 
for the present, we have no other recourse. 

The general character of these peculiarities is believed never- 
theless to represent real conditions. However this may be, whether 
due to a single physical cause or only to groups of abnormal veloci- 
ties, any such conditions will affect the solar- velocity and constant- 
error terms derived from data containing them. 

The peculiar relations between the solar motion and constant 
errors are exhibited in Table III. 



TABLE III 





^0 


K 


Vq+K 


MeaniJ 


FQ+Mean R 


B 

A 

F 


km 

— 20. 2 
-16.8 
-15.8 

— 16.0 

— 21.2 
-22.6 


km 

+4-Q7 
+°-95 
+0.06 
— 0. 20 
+ 2.82 
+3-93 


km 
-16. 1 
-15-8 • 
-15-7 
— 16. 2 
-18.4 
-18.4 


km 

+4-3 
-0.4 

-03 

0.0 

+3-5 
+5-1 


km 

-15-9 
— 17.2 
-16. 1 


G 

K 


— 16.0 
-17.7 
-l7o 


M 



3 o8 



C. D. PERRINE 



Column 5 of Table III contains the mean residual of all of the 
stars after correction for solar motion on the basis of V© = — 19. 5 
and A=o. These are seen to follow closely the value of A' found 
by Campbell and may be considered to be essentially the same 
quantities. 

Campbell concludes 1 that the elements of the solar motion are 
apparently indifferent to the inclusion or omission of the term K. 

That appears to be true so far as the mechanical solution is 
concerned, but how are we to explain the peculiar relation of Vq 
and this constant term indicated in Table III ? Notwithstanding 
the fact that this constant error was determined along with Vq 
and therefore that Vq ought to be free from any such effect, we 
find the values of Vq varying systematically in such a way that 
the algebraic sum of Vq and A (but closer still of mean R and Vq) 
is a nearly constant quantity. The conclusion seems justified that, 
notwithstanding its apparent elimination, at least a part still re- 
mains, or that its real significance is other and that an entirely 
different explanation must be sought. 

It is not necessary to give the details of all the tests applied, 
but the two tables following show the values of the solar motion 
obtained from hemispheres around the apex and the antapex (Table 
IV) and for different portions of these hemispheres (Table V) 
as they came accidentally in the tabulations for solution. No 
attempt was made to form them into groups according to region 
of sky", although in a general way this has resulted from taking the 
stars in the order of right ascension. A' was omitted. 

TABLE IV 





B 


A 


p* 


G 


M 




No. 
Stars 


V Q 


No. 
Stars 


^0 


No. 
Stars 


V Q 


No. 
Stars 


^© 


No. 
Stars 


^0 


Apex 

Antapex. . . 
All 


90 

1-33 
223 


km 

-11. 5 

-27-3 
— 21.9 


ill 

IOI 

212 


km 
-17.4 
-15-2 
— 16.4 


103 

93 

196 


km 

-16.3 
-18. 1 
— 17.2 


63 

74 
137 


km 1 
-17-7 38 

— 18.O 42 

— 17.9 80 


km 

- 8.0 
-30.I 

— 20.1 



* One star of very large velocity was omitted in Class F . In Class G all stars having velocities of 
50 km and over were omitted, as the solar velocities from all stars were abnormal, —34.6 km from the 
apical region and — 37 .1 km from the antapical region. The effect was traced to the fact that practically 
all of the great velocities were negative in the apical and positive in the antapical regions. Here we have 
unequivocal evidence of the possible effect of systematic velocities on the solar motion. 

1 L. 0. Bulletin, No. 196, p. 127. 



RESIDUAL RADIAL VELOCITIES 



3°9 



The foregoing results seem to me to point to the necessity of 
looking for other effects as well as for constant error depending 
only on spectral class, probable as such an error seems. 



TABLE V 





B 


A 


F 




No. Stars 


V Q 


No. Stars 


v O 


No. Stars 


^O 


Apex 


45 
46 


km 

-i S . 8 

-22.3 


44 
43 
24 


km 

-14.4 
-18.2 
-I3-I 


50 
53 


km 
-l8.5 
-16. I 










Antapex 


42 

44 
48 


-18.9 
-23.1 
— 17.6 


44 
43 
14 


-19.7 
-12.4 
-15-3 


5° 
45 


-IS© 
— 20.0 







The explanation for this constant error has for its basis a 
physical cause which should produce a nearly uniform effect among 
the stars of the same spectral class, whereas we find large discord- 
ances among groups of such stars in different regions of sky. 

The range of about six kilometers which exists between the 
velocity of the solar motion derived from the different spectral 
classes seems entirely too large to be explained by accidental errors 
or velocities alone. 

CONCLUSIONS 

1. The values of the solar motion derived from the different 
spectral classes separately show large and systematic variations. 

2. The values of the solar motion, the residual motions, and 
the mean velocities show wide variations in different regions of the 
sky and within the same spectral class. 

3. The constant error, and the solar motion, derived from each 
spectral class, vary in such a way that the algebraic sums of these 
two quantities are in very good agreement. This gives rise to 
the suspicion that these quantities are still related. 

4. Discordances appear to be too great to be represented 
wholly by the assumption of a mere constant error within any 
spectral class. 



3io 



C. D. PERRINE 






5. It is believed that the chief cause of the discordances noted 
is to be found in systematic or semi-systematic motions of the stars 
and that until some degree of success has been obtained in the 
determination and elimination of such motions the true value of 
the solar motion must be considered to be uncertain. 

It is yet to be seen whether the star streams already known are 
competent to account for the peculiarities observed. The pecul- 
iarities observed indicate that at least some modifications will be 
required. 

Since the above was prepared I have been able to represent the 
observed radial velocities of the stars of Classes A and B better 
upon the assumption of general preferential motions of the stars 
themselves. The resulting values of the velocity of the solar 
system are much better harmonized also by such an assumption. 
It was found necessary, however, to limit the stars used to those 
in and near to the Milky Way. 

The assumed vertex of preferential stellar motions was right 
ascension o h and declination +6o°. Preliminary solutions based 
upon this vertex and apex of the solar motion at i8 h , +30 yield 
the following results: 







The residuals for the solutions, including the V s term and 
omitting it, are as follows: 





Including 
V s Term 

M 

100 


Omitting 
V s Term 

M 
100 


No. of Groups 
in Solution 


Class B 


56 
39 


139 
51° 


6 


Class A 


8 







The improvement in the case of the stars of Class B is not so 
marked as in the stars of Class A. This is perhaps to he expected 



RESIDUAL RADIAL VELOCITIES 311 

from the smaller value found for the preferential stellar velocity 
in the former case. 

These solutions can only be considered as approximate. 
Whether a larger number of stars would confirm the results 
obtained and whether all of the spectral classes will show similar 
peculiarities may be questioned, of course. There is reason to 
believe, however, that some such preferential general motions 
will be found to be real, although their magnitudes and char- 
acteristics may be considerably altered. 

The value of the solar motion from the new solutions appears 
to confirm that derived by Campbell from all of the classes together. 

The numerical value of the K term for stars of Class B remains 
practically unchanged. 

There are strong indications here also that the B8 and B9 
stars should be grouped apart from the earlier stars of Class B. 

Observatorio Nacional Argentino 

Cordoba 

May 25, 1915 



THE ORBITAL ELEMENTS OF THE ECLIPSING 
VARIABLE SX DRACONIS 

By W. VAN B. ROBERTS 

The observations used were those published in the Annates de 
VObsercatoire Royal de Belgique, 13, II, 1914, and the Publications 
of the Vassar College Observatory, No. 3. 

After an approximate period from Belgian observations had 
been obtained and a rough light-curve plotted, this curve was 
applied to the observations on various nights to get the best value 
of the time when the star was of the eleventh magnitude, or fifteen 
"degres" on the Belgian scale. Several of the Belgian comparison 
stars were identified with the Vassar comparison stars for which the 
magnitudes on the Harvard scale were given. By means of these 
stars and by comparing the magnitude of the variable when at 
constant light in the two systems, the following formula was found 
for converting degres to magnitudes: 

mag. = 11 .7 — o.09i4(d — 5.8) 

The period finally determined from the combined Belgian and 
Vassar observations was 5. 16935 days and the epoch of middle of 
minimum determined from the mean curve was J.D. 2418683.409. 

Observations of nearly equal phase were then combined into 
normals, then normals of nearly equal phase before and after the 
middle of minimum were combined, giving a table of " super- 
normals" which was used to draw the light-curve. 

Using this curve and following the method, due to Professor 
H. N. Russell, 1 it was found that the assumption of a total eclipse 
of a bright spherical star by a larger and fainter companion, both 
showing disks of uniform brightness, would reproduce the observed 
variations in light, provided we have the following relations : 

Light of bright star =0.862 of the total light. 
Radius of bright star = 0. 137 of the radius of orbit. 
Radius of faint star = o . 360 of the radius of orbit. 
Inclination of orbit plane = 78°oc/ 

1 Astro physical Journal, 35, 315, 1912; 36, 54, 239, and 385, 1912. 

312 



ELEMENTS OF SX DRACONIS 313 

for, on calculating the light-curve of such a system, it was found 
to coincide within the limits of error with that obtained from the 
Belgian observations. 

On the other hand, if we assume a system like the foregoing 
in nature, with the exception that in the new system the stars show 
disks completely darkened at the limb, it would also reproduce the 
observations, provided that 

The radius of bright star = o. 1957 of the radius of the orbit. 
The radius of faint star =0.321 of the radius of the orbit. 
The inclination of orbit =84°45'25". 

Since either of these two hypothetical systems would account 
equally well for the observations, we are in doubt as to the real 
nature of the true system. The second hypothesis, however, seems 
the more likely considering the evidence of the sun, which is dark- 
ened at the limb. 

The observations made at Vassar seemed from the magnitude 
of the residuals to be affected by large accidental errors and yielded 
a curve that could not be represented by the eclipse hypothesis. 

If we assume the masses of the two components equal, the 
formula, density = o . 00672 P~ 2 r~ 3 , gives for the uniform case a den- 
sity of the larger star= o . 0054 and of the smaller = o . 098, while for 
the darkened stars we get densities 0.0076 and 0.0335. It is shown 
by Harlow Shapley in Contributions from the Princeton University 
Observatory, No. 3, that in such a system as this it is probable that 
the brighter star is also the more massive. Using his equation for 
the probable mass of the brighter star, knowing what proportion 
of the total light of the system the bright star gives, we find that 
we must change the densities in the darkened solution to 0.00433 
and 0.0478. 

By a method described by Russell and Shapley 1 we may make 
an estimate of the probable distance of the star, known as the hypo- 
thetical parallax. The variable has a spectrum of type A, and by 
means of its spectral type, density, and our assumptions as to its 
mass and surface brightness we can make an estimate of its absolute 
magnitude. Comparing this with the observed magnitude we find 

1 Astro physical Journal, 40, 417, 1914. 



314 



W. VAN B. ROBERTS 



the parallax is o'' 00087, which means that the star is 3750 light- 
years away. Its galactic latitude is + 26 , so that its distance from 
the galactic plane is 1650 light-years, which is one of the greatest 
known distances of a variable star from the galactic plane. 
Table I gives the normals, supernormals, and residuals. 

TABLE I 
Residuals for Darkened Solution and Uniform Solution 



Normals 


Supernormals 


Phase (in Days] 


Degres 


o-c 

(Dark- 
ened) 


Uniform 


Phase 


Degres 


o-c 

(Dark- 
ened) 


Uniform 


—0.326. . . . 

.280 

.262. . . . 

.212. . . . 
.176. . . . 

.166 

.153 

.137 

.123 

. IO7. . . . 
. I02. . . . 
.078 

- .038.... 

+ .002. . . . 

.045 

.074 .... 
.076. . . . 
. Ill .... 
.140. . . . 

.148 

. 172. . . . 
.I8 5 .... 

.203 

.230 

.251 

.262. . . . 

.280 

- 295 

.315 

+ O.344 


24.9 
23.2 
22.3 
20.4 
18.2 
15-8 
13-3 
"•3 
10.4 

10. 
8.1 
6.9 
5-3 
6.6 

6-5 

4.0 

6.9 
6.7 

10. 1 
12.2 
14.0 
17.6 
19.9 
21.8 
23.0 
24.6 

25-7 
27.0 
28. s 
30.1 


- O m 2I 

- -15 

- -14 

+ .04 
+ .18 

+ .05 

- .02 

- 04 
+ .03 

- .01 
+ .03 
+ .08 

- .04 
+ .07 
+ .06 

- .08 
+ .09 

- .16 

- -17 

- .07 

- .16 
+ -03 
+ .05 

- .01 

- .01 
+ .06 
+ .07 
+ .12 

+ -IS 
+0.20 


- o M 23 

- .17 

- 15 

+ .04 
+ .18 

+ .05 

- .02 

- .04 
+ .02 

- -03 
+ .01 
+ .07 

- .04 
+ .07 
+ .06 

- .09 

+ .08 

- -17 

- -17 

- .07 

- .16 
+ .03 
+ -05 

- .02 

- .02 
+ -o 5 
+ -05 
+ .11 
+ .13 
+0.18 


O.043 

.078 

. 107 

130 

•149 

. 169 

.181 

.208 

•239 

.262 

.283 

0325 


5-7 
6.7 
8.8 
10.9 
12.0 
14.9 
17.9 
20. 1 
22. 1 
23.2 
25-0 
26.9 


— o¥oi 
+ .004 

— .01 

— .004 

— .01 

— .04 
+ .09 
+ -03 

— .02 

— -05 

— .01 
-O.03 


— o¥oi 

- .006 

- -03 

- .01 

- .01 

- .04 
+ .09 
+ -03 

- -03 

- .06 

- -03 
-O.05 



The foregoing computations were made with the kind assistance 
and supervision of Professor H. N. Russell throughout. 



Princeton University Observatory 
June 2, 1915 



ORBITAL ELEMENTS OF THE ECLIPSING VARIABLES 

T\V ANDROMEDAE, TU HERCULIS, AND 

RS VULPECULAE 

By JOHN Q. STEWART 

The right ascensions and declinations of these stars for the year 

1900 are: 

TW Andromedae: 23 h 53 m i +32°i7(3 

TUHerculis: 17 9.8 +3050.0 

RS Vulpeculae: 19 13.4 + 22 16 

The light-curves of TW Andromedae and TU Herculis were 
derived from the eye-estimates of L. Casteels and the photometric 
observations of G. Van Biesbroeck. 1 Only eye-estimates were 
available for TU Herculis. These were made by the Argelander 
method; the brightness of the variable is stated not in magnitudes 
but in "degres." The brightness of some of the comparison stars 
of TW Andromedae is given in photometric magnitudes as well. A 
consideration of these stars showed that the relation between 
degres and magnitudes is approximately linear: 1 degre = 0.095 
magnitude. The following transformation equations were found 
to hold: 

For TW Andromedae, 0.095 (degres— 2. 2) = 10. 76— mag. 

For TU Herculis, 0095 (degres— 2.0) = 11 .70— mag. 

The phases of the observations (which are not published in 
the Belgian Annates) were calculated; and observations of nearly 
equal phase were grouped into normals. These are given below. 
In the case of TW Andromedae the photometric observations were 
assigned double weight. It was found unnecessary to. change 
Van Biesbroeck's periods, but for each star it seemed advisable to 
shift his epoch of middle of minimum. This correction, for TW 
Andromedae, amounted to — o d oo7, for TU Herculis it was +o d oo6. 
The corrected values are: 

TW Andromedae : J.D. 24i8629 d 267+4 d i229 E. 
TUHerculis: J.D. 24i883i d 44o+2 d 267i3 E. 

1 Annates dc VObservatoirc Royal de Belgique, 13, II, 1914. 

3i5 



3i6 



JOHN Q. STEWART 



The solution of TW Andromedae presented no difficulty. The 
maximum brightness is well determined by fifty visual observations. 
There appears to be no sensible secondary minimum. At the 
middle of the primary minimum there is a distinct, constant, total 
phase. Application of the methods of Professor Henry Norris 
Russell showed that the observed light-curve could be fitted very 
well on either the "uniform" or the "darkened" hypothesis. 1 

TABLE I 
TW Andromedae — Normals 



Phase* 



No. OBS.t 



Obs. Mag. 



O-C 



+ 



.149- 
.130. 

.108. 
.091. 
.066. 
• 058. 
.047. 

■°39- 
.021 . 
.002. 
.019. 
.044. 
.044. 
.052. 
.063. 
.083. 
. 104. 
.132. 
o. 166. 



5 
5 
5 
4 
4 
4 
4 
5 
o 

15 
o 



9.27 
9.46 
9.67 
9.92 

10. 14 

10.4s 

10.66 

10.73 

10.72 

10.78 
10.77 

10.75 
10.81 
10.77 

10. 70 

10.56 
10.28 

9.98 
965 
9.40 



mag. 
+ O.OI 
.OO 

— .02 
.OO 

+ -03 
+ -04 

— .02 

— .OI 
+ .04 

— .02 

— .01 
+ -OI 

— .06 

— .02 
.OO 
.OO 
.OO 

+ -OI 

— .02 
+ 0.02 



♦The phases given are corrected to the revised epoch of middle of minimum, 
f P indicates photometric, E, eye-estimates. 

All the residuals in each case are so small that it seemed only worth 
while to publish the calculated "darkened" curve. There is 
nothing especially remarkable about this star, except the large 
color-index noticed by Harlow Shapley at Mount Wilson. 2 He 
finds a photo-visual range of 1.63 mag. and a photographic range 
of 2.04 mag.; the brighter component he gives as type F3, and 
the fainter as G4. 

1 See preceding paper by W. Van B. Roberts for references. 

'Publications of the Astronomical Society of the Pacific, 26, 156, 1914. 



ORBITS OF ECLIPSING VARIABLES 



3*7 



The light-curve of TU Herculis heretofore always has been 
drawn with a flat-bottomed minimum — indicative of total (or 
annular) eclipse. The orbital elements derived from such a curve, 
however, show that the eclipse is just partial. Nevertheless it 
comes so near totality that the method of solution for a totally 
eclipsing variable suffices to give the elements with quite satis- 
factory accuracy. The round-bottomed minimum necessitated 
by the partial eclipse represents the observations as well as, or 

TABLE II 
TU Herculis — Normals 



Phases 


No. Obs. 


Obs. Mag. 


o-c 


— O d I36 

• 063 

•033 

.016 

.008 

4- .007 


5 
5 
5 

2 
1 
2 


9-75 
10.49 

"•35 
11.69 

"■59 

n 6n 


mag. 

— 0. 14 
+ .10 

.00 

— .01 
+ .08 

— .02 


.022 


3 "SO 

5 1 1 ■ 06 
5 10.65 
5 10.28 
5 10.03 
5 9-94 
5 0.78 


+ .04 
.00 

— .01 

- .06 
+ .05 
+ .01 
+ -04 
+ .02 


■ 045 

.062 

.082 

.091 

. 100 

.Ill 


.127 


5 
3 


9.67 
9.60 


c 141 


— O.02 



* Phases corrected to new epoch of middle of minimum. 



better than, the fiat one. The maximum percentage area of the 
smaller star obscured by the larger (a ) is 0.998 by the ''uniform" 
solution and 0.995 by the " darkened." 

The constant maximum brightness of the variable is determined 
by thirty-six closely agreeing eye-estimates. Its value in magni- 
tudes is somewhat uncertain, but was assumed to be 9.50 mag. 
This uncertainty does not in the least affect the accuracy of the 
solution, which depends only upon the range in brightness. None 
of the observations are of the proper phase to give information 
concerning the existence of a secondary minimum. The spec- 
trum of TU Herculis is unknown; the hypothetical parallax 
was calculated on the assumption that it is of type A. Both 



3i8 



JOHN Q. STEWART 



the "darkened" and the " uniform" curves closely represent the 
observations; only the "darkened" residuals are published. 

For RS Vulpeculae, the final variable considered in this paper, 
the visual observations of Mentore Maggini were used. 1 His 
brightnesses are in magnitudes, corrected to the Potsdam scale. 
Before drawing the light-curve, the thirty-three normals given 
by him (each of which represents five observations) were com- 
bined into supernormals. The epoch of middle of minimum is not 

TABLE III 
RS Vulpeculae — Supernormals 



Phase* 



No. Normals 



-0?40i . 
.280. 
.244. 
.215. 
.178. 

■135- 

. 101 . 
- . 006 . 
.112. 
.163. 
.229. 
0.286. 



Obs. Mag. 



O-C 



mag. 

O.OO 

+ 02 

.00 

+ .02 

— .OI 

— .02 
.OO 
.OO 

— .OI 

— .02 
.00 

-O.05 



* A correction of —0.097 was applied to Maggini's phases. 

well determined, on account of the scarcity of observations during 
increasing light. Assuming Maggini's period, it comes at 
J.D. 2419652*963+ 4 d 4773 2 5 E - 

A long period of total eclipse is indicated. It was found neces- 
sary to use a special method in solving for the elements. The usual 
process, when applied to some parts of the light-curve, led to a 
negative radius for the smaller star, and, for other parts, made 
it appear that the smaller star was the larger of the two. By 
the use of the following simple method, however, all difficulties 
were eliminated, and a light-curve was calculated which satisfies 
all of the observations. The light-curve gives sin 2 as a function 
of a (following Professor Russell's notation). But we know that 
sin 2 is a linear function of \f/(k,a). When sin 2 0, taken from the 

1 Astronomische Nachrichten, 200, 54, 1915. 






ORBITS OF ECLIPSING VARIABLES 



3*9 



light-curve for various values of a, was plotted as ordinate against 
the corresponding values of \f/(k,a) as abscissae for different 
arbitrarily chosen values of k, it was found that a straight line 
passed through all the points k— constant only for k = o. 20. This 
same value of k was found in both solutions ("uniform" and 

TABLE IV 

Table of Elements 



TW Andromedae 



TU Herculis 



RS Yulpeculae 



Maximum 

Depth of primary . 



mag. 
8.99 
1.77 



mag. 

9-5° 
2. 19 



mag. 
7-30 
0.81 



"Uniform' 



"Dark- 
ened" 



"Uniform" 



'Dark- 
ened 



"Uniform' 



"Dark- 
ened" 



Depth of secondary 

Semi-duration of entire 

eclipse 

Semi-duration of total 

eclipse 

Light of brighter star {Lb) 
Radius of brighter star (r*) 
Radius of fainter star (r/) . . 
Cosine of inclination (cos i) 
Ratio of surface brightnesses 



Density of bright star* Q>*) 
Density of faint star (p/) . 
Radii in term of sun 



r/ 

Spectrum 

1000 ?r" 

Galactic latitude (/3) . . . 

r sin ^ 

r cos /3 (in light-years) . 



mag. 
O.044 



5 n 47 n 
o h ;8 E 



mag. 
O. IO 

6 h I2 n 



mag. 
O.036 

4 h 9 m 



mag. 
0.070 



mag. 
0.021 



mag. 
0.021 



0.804 



0.866 



o. 124 
0.248 
o. 107 



16.4 
o. 29 
0.016 

1 .69 

3-38 



0.155 

o. 232 

0.054 



9.1 
0.15 

0.020 

2. II 
3.l6 



o. 146 
o. 299 

0.155 



26.9 
0.61 
0.02; 



0.189 
0.278 
0.098 



14 

0.28 
0.032 



A 

2 "o 1 "6 

-29 
I —IOOO 

I 1800 



i-34 1-73 

2 • 73 2 . 54 

A: 

2 To 1*1 



+33° 



+ 1600 
2500 



1 49 

0.090 
0.450 
0.346 



27.7 
0.47 
0.0036 

1.30 

6.50 



0.526 



o h 58 r 



0.0932 

0.466 

0.368 



27.7 

o.43 

o . 003 : 

i-34 
6.70 



+4° 



9.1 

+ 25 
360 



*The densities are corrected for brightness (see preceding paper by W. Van B. Roberts). 

"darkened"). The slope of the straight line was taken as B, 
and the intercept on the axis of sin 2 6 as A . The trouble with the 
ordinary method of solution in this case was that the two points on 
the light-curve taken as standard in constructing the tables of 
\[s(k,a) were nowhere near their correct position. 

The value of k (the ratio of the radii of the two components) 
found for RS Yulpeculae is the lowest yet discovered in an eclipsing 



320 JOHN Q. STEWART 

system. This star is further remarkable in being among the 
nearer eclipsing binaries (if the computed hypothetical parallax 
is to be trusted). In addition, the star is a bright one, and the 
period of total eclipse long, so that the color-index of each com- 
ponent could easily be determined. Further observations would 
certainly be valuable and might be of the greatest theoretical 
interest. The elements deduced here doubtless are not altogether 
accurate; they are far from agreeing with those calculated by 
Shapley 1 from the light-curve of Professor Nijland. 

I take much pleasure here in thanking Professor Russell for his 
many suggestions, and for the great interest he has taken in these 
calculations. 

Princeton, N.J. 
June 7, 1915 

1 Contributions from the Princeton Observatory, No. 3. 



AX ADAPTATION OF THE KOCH REGISTERING MICRO- 
PHOTOMETER TO THE MEASUREMENT OF THE 
SHARPNESS OF PHOTOGRAPHIC IMAGES 1 

By ORIX TUGMAN 

A photometer for measuring the brightnesses of small areas has 
been desired for some time in the study of the intensities of spectral 
lines and in the investigation of the properties of photographic 
plates. The Hartmann microphotometer has served this purpose. 
But the most recent apparatus of this kind is the Koch 2 registering 
microphotometer, which eliminates visual observation by register- 
ing on a photographic plate the readings of the instrument. This 
paper gives an account of the adaptation of this apparatus to the 
measurement of the sharpness of photographic images and a state- 
ment of the limitations and necessary corrections which have been 
found in using Koch's photometer in the investigation of photo- 
graphic resolving power. 

The Koch registering microphotometer was originally designed 
to measure the densities of the developed photographic images of 
spectral lines, but as the apparatus was used by Koch, and by King 
and Koch, 3 no attention was given to the resolving power of the 
apparatus. In many cases inattention to this point will lead to 
incorrect conclusions drawn from the shape of the registered curve. 
This apparatus has been adequately described in the papers referred 
to above, but a brief description here may not be out of place. 

The developed negative is passed under an illuminated slit over 
which is an objective of a microscope which carries a second slit 
in the focal plane of the objective as shown in Fig. i . The current 
generated by the incident light in the photo-electric cell C charges 
the silvered quartz fiber Q of a string electrometer. The movements 
of the quartz fiber are registered on a falling photographic plate by 
throwing an image of the fiber on the photographic plate by means 

Communication Xo. 27 from the Research Laboratory of the Eastman Kodak 
Company. 

2 A)inalcn der Physik, 39, 705, 1912. * Aslrophysical Journal, 39, 213, 1914. 

321 



322 



ORIN TUGMAN 



of a microscope and a cylindrical lens. A clockwork moves the 
original negative under the illuminated slit and simultaneously 
drops the registering photographic plate at a constant speed. One 
source of light serves to illuminate cell d and at the same time cell 
C 2 , which affords an adjustable leak to earth for the current charging 
the quartz fiber. 



Zoo v 



QUACTZ flBRE. 



\-<W 





PJ-ATE. QLAJ/ 



Fig. i 



By assuming that the movement of the quartz fiber is propor- 
tional to its potential, an equation is obtained giving the relation 
between the distance moved and the intensity of the illumination 
on the photo-electric cells. Under the working conditions of the 
apparatus it is assumed that the current through a photo-electric 
cell is proportional to the intensity of the illumination on the 
photo-electric surface and the difference of potential between that 
surface and the sealed-in electrode. This is in accord with known 
facts. 

Let V x , F 2 ,'and V be the potentials of cell i, cell 2, and the quartz 
fiber respectively, and let L Y and L 2 be the respective illuminations 



SHARPNESS OF PHOTOGRAPHIC IMAGES 



323 



on the cells 1 and 2. In a state of equilibrium the current through 
cell 1 is equal to the current through cell 2. Therefore, we may 

write 

K l L I (V+V I ) = K 2 L 2 (C-V 2 ), 

where K t and K 2 are constants. It is seen that when L x is zero the 
potential of the fiber V is V 2 , which is the potential acquired by the 
photo-electric surface when illuminated. 

The relation between the distance x moved through by the 
quartz fiber and the potential V was determined experimentally by 





































































































































































































































































































2. 




* 




1 


l o 


1 





1 


' 


" 




1 


U 





Potential of quartz fiber volts 
Fig. 2 



illuminating cell C 2 and applying different potentials to the quartz 
fiber. This relation is shown graphically in Fig. 2. Obviously, 
there is not a linear relation between the movement of the quartz 
fiber and the intensity of the illumination on the cell C. 

The use to which the Koch registering microphotometer was put 
in the Research Laboratory of the Eastman Kodak Company was 
to measure the sharpness of photographic images in an investigation 
of resolving power of photographic plates. A carefully ground 
knife-edge was placed on a photographic plate and the whole 
exposed to a beam of parallel light. The developed negative was 
passed through the Koch photometer to obtain a curve giving the 
falling off in density from the edge of the image. 



324 ORIN TUGMAN 

On an ordinary photographic plate the distance at the edge of 
such an image between maximum and minimum density is less than 
50 fx and in many cases not over 10 yu. It was necessary, therefore, 
to use a microscope of greater magnifying powers than that supplied 
with the Koch apparatus. The upper slit of the microscope should 
not cover more than one-fifth of the total width of the image of the 
photographic edge. Accordingly, a 4 mm objective was placed in 
the microscope and the upper slit was adjusted to cover 10 ju of the 
object. In this arrangement the lower slit under the objective was 
not used. It was found, however, that the apparatus was not 
sufficiently sensitive on account of insufficient light on the cell d. 
To overcome this difficulty the Nernst filament was replaced by an 
arc light, and a microscope condensing lens was placed under the 
plate carrying the negative. A condensing lens in front of the arc 
cast a parallel beam on an inclined mirror under the microscope 
condenser. In this way a powerful beam of light was concentrated 
on the object. A water cell in front of the arc prevented burning 
of the emulsion film. A piece of plain glass in the path of the paral- 
lel beam reflected sufficient light on the cells C 2 and C 3 . With this 
arrangement the photo-electric cells operated the quartz fiber across 
its complete range of movement. 

After these alterations it was found that the relative motion of 
the registering photographic plate and the negative under measure- 
ment was too small. It was necessary to alter the clock mechanism 
so the registering plate could have a maximum speed of one thou- 
sand times the speed of the plate carrying the negative. 

With the apparatus so altered and the slit in the microscope 
adjusted to cover 10 /x of the object, it was considered necessary to 
determine the correction due to the width of the slit. This point 
has not been discussed in the previous papers published on the 
Koch photometer. 

Obviously, the best method of measuring the slit-width correc- 
tion is to make a record of a sharp knife-edge. A Gillette razor 
blade fastened by soft wax to a microscope slide was passed under 
the microscope, care being taken to set the razor edge parallel to 
the edge of the slit. It is easy to predict the shape of the record 
under such circumstances. The record should be a straight line 



SHARPNESS OF PHOTOGR.APHIC IMAGES 



325 



across the plate at an angle depending on the relative speed of the 
registering plate and the razor edge. If the slit covers 5 ll and the 
movement of the edge is multiplied one thousand times, one end of 
the straight line on the record should be displaced just 5 mm farther 
along the plate than the other end. This should be the result inde- 
pendent of the amplitude of the motion of the quartz fiber. The 
kind of record actually found is shown in Fig. 3. 




Fig. 3 



Under the conditions named above with a 5 fx slit the record 
made with a razor edge had a slope much greater than calculation 
would indicate. A record was made with the slit covering 2 . 5 /x and 
also covering 10 /*. In all three cases the straight-line slope was 
constant, when first consideration would indicate that the slope of 
such a curve should vary inversely as the width of the slit. When 
the width of the slit covered about 15 fx, the slope of the line began 
to change as the slit-width increased. Thus, the maximum slope 



326 ORIN TUGMAN 

of the line was such that one end was 0.15 mm farther along the 
plate than the other. 

A search for the cause of these results revealed that a pinhole 
image was being formed on the photo-electric surface by the slit in 
the microscope barrel. That this is a fact could be demonstrated 
by holding a piece of ground glass above the microscope and moving 
the razor edge under the microscope objective. An image of the 
razor edge could be seen moving out from both sides of the slit, 
one evidently being that cast by the objective on the slit, and the 
other image being that made by the slit on the screen. One might 
expect this pinhole image of the last surface of the objective to be 
formed by the slit. Then a decrease in the intensity of the light 
falling on the photo-electric surface would begin as soon as the 
razor edge began to pass under the objective and would continue 
until the objective was entirely covered. But the effect of the pin- 
hole image is small compared to the passing of the objective image 
across the slit, and it is only when the slit is small that anomalous 
results appear. 

It will be seen that a serious error is introduced if measurements 
are made on a density-gradient which extends over a distance of 
only about 30 n, that is, about twice the width of the slit in the fo- 
cal plane of the objective. During the time the slit is being covered 
and until the slit is completely covered, the record cannot be a true 
register of the density-gradient. Also, when the maximum density 
of the negative begins to pass, the record is erroneous. It is only 
when the slit is completely covered by the image that a true record 
is possible. Moreover, any irregularities of breadth less than 15 /x 
in the density-slope will be incorrectly registered. The curve for 
a very fine spectral line would be too narrow at the points of maxi- 
mum density. If the density-slope is long compared to 15 /a, the 
error grows less. This applies, however, only to the case where a 
4 mm objective is used. 

The difficulty mentioned above comes from the absolute value 
of the slit-width. If the magnification is less, the width of the slit 
cannot be less in actual measure because of the pinhole image 
formed. With the 4 mm objective giving a magnification of 50 the 
actual width of the slit was 0.75 mm, covering 15 /j. of the object. 



SHARPNESS OF PHOTOGRAPHIC IMAGES 



327 



Therefore, with a magnification of 25 the slit would still be o. 75 mm 
wide and cover 30 n of the object. The resolving power of the 
apparatus is limited by the magnification of the microscope objec- 
tive and not by reducing slit-width to less than o. 75 mm. 

As was pointed out above, the top and bottom of a registered 
curve will be in error over a distance depending on the slit-width d, 
magnification m, and relative speeds of the registering plate and the 

negative under measurement. This may be ^____ 

expressed 



R= 



ds 
m 



R is the actual distance parallel to the verti- 
cal side of the registering plate, through 
which the curve is in error. 

For a registered curve of a density- 
gradient extending over narrow limits the 
corrections are such that their application 
becomes laborious. In such cases it is 
doubtful if the record is sufficiently accurate 
to admit the correction. Consider a slit, 
Fig. 4a, and a wedge passing under, cutting 
off light from below. Suppose the light 
transmitted by the wedge is some function 
f(x) of x, where x is measured from the point of the wedge 
light L passing through the slit is 



b 

Fig. 4 
Slit and wedge 
Curve for light-trans- 
mission of wedge 



The 



jp 



Lo=P(A-x)+ \f(x)dx. 

The equation L 1 — fi(A — x) applies for opaque edge passing the slit 
if light diffracted around the edges is neglected. (3= constant. 







L —L= I f(x)dx 

is an equation giving the total light transmitted by the wedge at 
any position. After reducing the ordinates of the registered curve 
by (A — x) and plotting another curve, the true light-transmission 
of the wedge can be obtained by taking the difference of any two 



321 



ORIN TUGMAN 



adjacent ordinates and dividing by the difference in abscissae, as 
shown in Fig. 4b. 

Calibration of the electrometer scale was made by passing under 
the microscope, while the registering plate was in motion, a photo- 
graphic negative bearing a series of densities. The record made 
was an irregular stair-step trace on the registering plate. Fig. 5 
shows a type of the calibration-curve. Obviously, the slope x and 
shape of this curve will be altered by changing the tension of the 



1.6 

1 4 

1 . 2 
0.0 
0.8 
0.6 

0.4 

O. 2 











































































































l\ 










































































































































































































-* 































































































































> 20 30 40 50 60 70 8 

Fig. 5. — Calibration-curve 
I. Density measured by spectral transmission 
II. Density measured by diffuse transmission 



90 



fiber, the adjustment of the electrometer plates, and relative illu- 
mination of the photo-electric cells. However that may be, it is 
most essential to know how the densities used for calibration are 
measured. It must be remembered that a photographic negative 
is a light-diffusing medium and the value of the measured density 
of such a material depends on whether the measurement is made 
with diffuse or specular light. The beam of light passing through 
a negative into the microscope of the Koch instrument is practically 
all due to specular transmission. Furthermore, the percentage of 
diffusion produced by a negative is a function of the size and num- 
ber of silver grains in the gelatine layer. It is necessary, therefore, 



SHARPNESS OF PHOTOGBLAPHIC IMAGES 329 

for correct calibration that the calibrating densities be from the 
same emulsion as the negative being measured, and also that the 
densities be measured by specular transmission. The calibration- 
curves when made from densities measured by diffused and specular 
light are seen in Fig. 5. There is very nearly a constant ratio 
between the two curves throughout the entire range, but this con- 
stant ratio would not be the same for all kinds of negatives. 

The shape of the calibration-curve shows that for high densities 
the accuracy of measurement is greatly decreased. This feature of 
the apparatus is a disadvantage in investigating the sharpness of 
photographic images of high density. Koch claimed in his original 
paper on this apparatus that the relation between movement of the 
quartz fiber and the density of the negative was nearly linear within 
a limited range. The curves here verify that statement. 

Measurements on the relative energies of the spectrum lines 
were made by King and Koch with this registering photometer. 
The negatives were made with an exposure which did not produce 
a density too great for the apparatus to register with reasonable 
accuracy. The area of the curve obtained was taken as a measure 
of the energy of the line. 

The use of photographic plates for recording the distribution of 
energy of a spectrum line was investigated by Koch. 1 He calibrated 
the Hartmann microphotometer with a series of densities made with 
a known series of exposures. A method more in line with the sys- 
tem usually adopted in measuring the light-sensitiveness of photo- 
graphic plates has been outlined by Mees. 2 

In the system of sensitometry of photographic plates developed 
by Hurter and Driffield, 3 the density is plotted against logarithm 
of exposure, and the curve obtained is in general like Fig. 6. Here 
density is defined by the equation 

L = I Q (io)- D , 

where I is incident light on the negative and I t is transmitted light. 
With different periods of development the straight part of the curve 
will swing about a point on the axis of log E indicated by producing 

1 Annalen der Physik, 30, 84, 1909. 2 'Knowledge, 33, 417. 1910. 

3 Jour, of Soc. of C hem. Industry, May 1890. 



33° 



ORIN TUGMAN 




the straight line until it cuts the axis of log E. The slope of this 
straight portion increases with development up to a maximum value 
depending on the character of the emulsion. The maximum slope 
for any plate is different for different wave-lengths of light. More- 
over, the other points of the curve will have a shape depending on 
wave-length of exposing light. 

After the ordinates of the registered curve of the Koch micro- 
photometer have been reduced to densities, the exposure required 
to produce these densities can be determined from a sensitiveness- 
curve such as is shown in Fig. 6. 
This can be done only if the 
sensitiveness-curve and the origi- 
nal negative are made from the 
same kind of plate exposed to the 
same monochromatic light and 
developed in the same developer 
for equal periods. Inasmuch as 
the maximum density which can 
be correctly registered by the 
Koch instrument is not much 
over 1.5, an important part of 
the exposure must be down on the toe of the curve and off the straight 
part. This destroys the complete linear relation between the 
deflection of the electrometer fiber and the logarithm of exposure. 
The area of the curve made by the Koch instrument cannot, there- 
fore, be a measure of the energy of the spectral line. However, 
within the straight part of the sensitiveness-curve and also within 
the straight part of the calibration-curve of the Koch photometer 
the deflections of the electrometer fiber are proportional to the 
logarithm of the intensity. 

From the foregoing paragraphs it is seen that this registering 
microphotometer is a useful instrument only for certain classes of 
work where the corrections do not apply. It is hoped that the 
foregoing account will be of service to others interested in micro- 
photometry and in the properties of photographic plates. 

Research Laboratory, Kodak Park 

Rochester, N.Y. 

July 16, 1915 



Log exposure 
Fig. 6. — Sensitiveness-curve 



THE RESOLVING POWER OF PHOTOGRAPHIC PLATES 1 

By ORIX TUGMAN 

The resolving power of photographic plates has hitherto been 
investigated by methods which have been suggested by general 
definitions. The distance between two closely adjacent images 
when developed being a measure of resolving power, it has been 
considered sufficient for a practical test to photograph the reduced 
image, formed by a highly corrected lens, of some fine-lined structure 
and determine what lines are resolved. For this purpose Mees has 
devised a fan-shaped test-object having alternate black and white 
sectors of about ten degrees in angle. The photograph of the 
reduced image is examined with a microscope to determine the 
resolution. In this test the accuracy of the measurement rests 
upon personal judgment of the separation of two lines. 

From theoretical considerations Wadsworth 2 arrived at the 
conclusion that two lines can be resolved if the distance between 
their centers is four times the diameter of a silver grain in the 
emulsion. It is evident that Wadsworth did not take account of the 
lateral spreading of the light in the emulsion and of the raggedness 
due to the random distribution of the silver grains. As a result 
the statement applies only to a non-diffusing medium whose light- 
sensitive material is in the form of discrete particles distributed 
at random. But such a non-diffusing medium does not exist. 

Wadsworth's theory and the scattering of light by different 
emulsions has been investigated by Mees. 3 The resolution of the 
plate was measured by photographing the reduced image of a black 
and white line grating and examining the plate to determine what 
lines were resolved. The scattering of the light at different expo- 
sures was shown by photographing an illuminated slit covered with 
a black wedge which admitted light varying in intensity from one 
to sixty along the length of the slit. The image of the slit was 

1 Communication No. 28 from the Research Laboratory of the Eastman Kodak 
Company. 

2 Astrophysical Journal, 3, 188, 1896. * Proc. Roy. Soc, 83 A, 10, 1909. 

33i 



332 ORIN TUGMAN 

reduced about twenty-two diameters. At that end of the image 
which received the most light there is the greatest amount of 
spreading. This makes the developed image of the form of a tad- 
pole. The conclusions drawn by Mees are: "The resolution of a 
photographic plate is dependent upon the amount of irradiation 
displayed by that plate. The irradiation is not directly propor- 
tional to size of grain, but is caused by two different forms of scatter 
arising from reflection and diffraction. The resolving power is 
likely to be much smaller than that indicated by the theory of 
Wadsworth." 

The rate of spreading of a photographic image has been investi- 
gated by Scheiner, 1 who showed that the increase of the size of an 
image increased as the logarithm of the exposure. Later, Mees 2 
obtained similar results. The reduced image of an illuminated pin- 
hole was photographed and measured. This general method has 
been followed by Goldberg, 3 who made contact prints through 
conical holes in a metal plate. The holes were made and arranged 
so as to insure good contact with the emulsion surface. 

Goldberg represented his measurements by a set of curves, 
reproduced here for discussion (Fig. i ) . The increase in diameter of 
the circular image is plotted against the exposure measured in 
threshold units. The curve so obtained is called the turbidity- 
curve and the slope at any point the turbidity-factor. The experi- 
ments demonstrated that the turbidity-curve is not dependent 
on development or size of the opening through which the print is 
made but is dependent on the physical characteristics of the plate. 

It is seen that the slope of the curves changes with exposure, 
indicating that the turbidity-factor increases with exposure. 
However, the slope is not consistent with the relation between 
spreading of the image and exposure found by Scheiner and Mees. 
A few readings upon the curves will show that the increase in diam- 
eter is not proportional to the logarithm of exposure. The increase 
in diameter plotted against log exposure is not a straight line, as it 
should be if the logarithmic law is true for a wide range. 

1 Photographic dcr Gestirne, Leipzig, 1897. 

2 Astrophysical Journal, 23, 81, 1911. 

3 The Photographic Journal, November 191 2. 



RESOLVING POWER OF PLATES 



333 



Goldberg's results are in accord with those of previous investi- 
gators, in that he finds the spreading of the image does not depend 
on the size of the grain of the plate. However, he finds that a grain- 
less Lippmann plate shows no measurable increase whatever of the 



16 



14 



2 10 

















































































k 
















A 
















4 / 












A 


























^% 














J— 







I IO IO 2 IO 3 IO 4 IO 5 IO 6 IO 7 

Exposures in threshold values 
Fig. 1. — Drawn from Goldberg's curves {The Photographic Journal, 36, 1912) 
1. Lippmann plate 4. Portrait plate 



2. Transparency plate 

3. Sigurd moment-plate 



5. Double-coated plate 

6. Bromide paper 



334 ORIN TUGMAN 

diameter, while the coarse-grained, highly sensitive portrait-plate 
exhibits strong spreading. But the very fine-grained bromide 
paper and the high-resolution plate of Wratten and Wainwright, 
chemically developed, spread the imprinted disk very greatly 
indeed. 

The turbidity-factor was identified by Goldberg with the recipro- 
cal of the light-gradient measured laterally from the image. Let 
x be the distance of any point a short distance from the edge of the 

— dx 
disk and / the intensity of the light. Then, 8 is defined 5= jr. — =... 

by differential calculus. If D is photographic density, then the 

dD 

photographic factor y = -jr. y\ > which is the slope of the curve of 

sensitiveness obtained by plotting densities against log exposure. 

The factor of sharpness S is defined as the slope of the curve made 

by plotting density against distance out from the edge of the image, 

— dD 7 

and that 5=—, — . Therefore, he has 5=t. "In words, the 
dx 8 

sharpness-factor is equal to the development-factor divided by the 

turbidity-factor." 

Now the question arises: Is Goldberg's turbidity-factor as 

*— * «0T) the — - the ^ " hk -bidity-curve 
A little consideration will show these two definitions to be incon- 

dx 
sistent. In general, when -tt\ jx , the reciprocal of the light- 
gradient, is large, the rate of spreading will be large for plates of I 
equal sensitiveness. But the light-gradient cannot be a function of . 
the time of exposure, as is indicated by one of the two definitions ? 
of the turbidity-factor. When the exposure begins, the light dis- 
tributes itself through the emulsion in all directions in a manner iji 
depending on the physical structure of the emulsion. During the li 
exposure this distribution of light must remain unchanged. So 
far as we know the exposed grains do not reflect or scatter any 
more or less light than unexposed grains. Therefore, there is no 

dx 
reason to argue that the turbidity-factor as defined by jr. p. 



RESOLVING POWER OF PLATES 335 

changes with exposure. In fact, the slope of Goldberg's turbidity- 

dx 

curve and the factor -jr. ^ are not identical. 

d(\og I) 

According to Goldberg's statement the edge of the enlarged 
disk is not sharp, and there is a gradual shading off of density. 
This makes the determination of the diameter a matter of difficulty. 
If. however, one measures out to a constant density on all the images 
the rate of spreading could be measured. Now, suppose this is 
done. Let us write the function f(x) giving the relation between 
log / and distance x from the edge of the opening 

log /=/(*). (1) 

Our relation between density D and exposure for the straight part 
of the Hurter and Driffield sensitiveness-curve is 

D=\ogI+B. (2) 

We can therefore write 

D=f(x)t+B= Constant. (3) 

If we measure out along the diameter to the same density in all the 
images on the same kind of plate and plot a curve between exposure 
land x, the slope of the curve is given by differentiating x with 

1 respect to t in (3) 

dx_ f(x)dx 
Jt~~ df(x)t ' 

which is the slope of Goldberg's turbidity-curve. 

It is obvious, therefore, that Goldberg's method of measuring 
Ithe spreading of an image does not give a measure of the light- 
jgradient. 

Besides the discrepancy between Goldberg's theory and results 
there are objections to the circular aperture used by him. With a 
:small circular hole the light is spreading out radially, and conse- 
quently the spreading of the image is not under the conditions which 
would be imposed by a straight-edge. However, the use of a 
circular aperture would impose the conditions experienced in photo- 
graphing stellar images, but would not compare with conditions in 
photographing fine-lined structures. Moreover, reflection of light 
from the sides of the conical opening in the metal plate would be a 






336 ORIN TUGMAN 



source of error. The image of a straight-edge would represent more 
general corrections, but with the disadvantage of not permitting 
the exact location of the edge on the image. 

The use of a straight-edge in investigating resolving power of 
photographic plates has been described by Nutting. 1 He found 
that by- care fully cleaning and setting a steel blade on the surface of 
an emulsion all traces of diffraction under the edge could be elimi- 
nated. The photographic images obtained were examined under 
a microscope and the density-gradient plotted. For densities less 
than unity there was a raggedness of the edge due to the random 
distribution of the silver grains. The shading off became more 
apparent with densities greater than i, and at about a density of 
2 the density-gradient appeared to reach a fixed value. In general, 
the density-gradient increased with decrease of the size of the silver 
grains. In cases where this rule did not apply, that is, with fine- 
grained emulsions and least diffusing, yet showing low density- 
gradients, the photographic gradient was also low. Those plates 
having a long, low slope in the sensitiveness-curve made by plotting 
density against log of exposure show a low density-gradient. 
Nutting pointed out that density-gradient can be written 
dD_ dD d{\og E) 
dx\ d(\og E) dx 

by simple differentiation, where E is exposure. 



Inasmuch as - , is independent of development and 

is the slope of the Hurter and Driffield sensitiveness-curve, 



d(\ogE) 

which becomes steeper with development, it was argued that 
density-gradient should increase with development at the same 

rate as -jf, — f\ • The experimental work described in this paper 

was a measurement of the density-gradient for the purpose of deter- 
mining, if possible, the relation between the other factors of the 
equation. 

The straight-edge used for the photographic images was made 
by cutting a secant strip from a nickel cylinder and carefully grind- 

1 Photographic Journal, June 1914. 



RESOLVING POWER OF PLATES 



337 



ing the edges. A cross-section of the metal strip is shown in Fig. 2, a. 
This edge was placed on a strip of plate about one inch wide and 
the plate exposed to a parallel beam of monochromatic light. After 
exposure the plate was cut in two strips and each part developed 
for a different time. It may be noted here that all plates were 
well backed before exposure. 

The Koch registering microphotometer was used to measure the 
density-gradient as described in the paper on that instrument 
published in this Journal.* The difficulties encountered were such 
as to necessitate the use of some other apparatus. 





Fig. 2 

a. Cross-section of metal strip 

b. Polarization photometer 

On account of the number and uncertainty of the corrections 
which are necessary to the curve registered by the Koch micro- 
photometer it was considered necessary to seek for other means 
of measuring the density-gradient. For this purpose a Konig- 
Martens polarization photometer was adapted. A sketch of this 
apparatus is shown in Fig. 2, b. This instrument was used to measure 
the image of the photographic edge thrown by a microscope on a 
piece of flashed opal glass placed over the holes h, h. On the opal 
glass on the side next to the microscope was a metal screen having 
two small parallel slits. Each slit passes over a diameter of one 
of the holes //, h. The photometer was mounted on a carriage 
which could be shifted by means of a micrometer screw in a plane 
at right angles to the axis of the microscope. The magnification was 
adjusted to suit the case by changing the distance between pho- 
tometer and microscope or by changing the lens system of the micro- 
scope. A coarse-grained negative required a low magnification, 

1 This number, p. 321. 



338 ORIN TUGMAN 

because otherwise the photometer would be measuring the density 
of the individual grains. 

This apparatus avoids the complication arising from the pin- 
hole image found in the Koch instrument. Also, the resolving 
power of the Konig-Martens photometer can be adjusted within 
wide limits, so that the correction for slit-width is practically nothing 
in all cases. However, there is one difficulty which was also found 
in the Koch microphotometer. The readings for densities which are 
above i . 5 are erroneous, in that the instrument gives the same read- 
ings for all densities about F5. But below this value a calibration 
showed the instrument to be correct within the limits of observa- 
tion. The trouble undoubtedly comes from light scattered in the 
microscope system. 

The results of these measurements are shown in Figs. 3, 4, 5, 
and 6. The maximum density is indicated in Fig. 3. This was 
obtained by measuring the density on a Konig-Martens photom- 
eter without the microscope attachment and continuing the curve 
to the proper value. In the other curves this maximum density 
is not indicated, because the curve as made gives sufficient length 
to determine the slope. Each pair of curves was made from differ- 
ent exposures and each member of the pair was given a different 
development. 

An explanation of the departure of this result from that expected 
from theory may be found in the penetration of the developer. 
The top layer of the emulsion is developed first and as development 
proceeds the layer of reduced silver becomes thicker. The photo- 
micrographs in Plate VI, a and b, show the penetration of a metol- 
hydrochinon developer. These sections were swelled out with water 
before photographing. The density-gradient, therefore, for long 
development would extend over a greater distance but would not be 
steeper than for short development. 

The variation of density-gradient with wave-length of exposing 
light may be explained by the difference in optical opacity of the 
emulsion for different wave-lengths. The variation of photo- 
graphic gradient is not enough and not in the right direction to' 
account for the variation of resolving power with wave-length 
In general, the sensitiveness-curve of a plate exposed to green light 



RESOLVING POWER OF PLATES 



339 



is steeper than the curve of the same emulsion exposed to violet 
light. Also, the depth of penetration of green light is greater than 
that of shorter wave-length. Therefore, if the optical opacity 
for the long wave is less than for the short waves the lis;ht-o;radient 




i division =10 microns 

Fig. 3. — Seed "Process" plates exposed to green light. Equal exposure, but 
varying development, i.e., 

1, developed 2 minutes 
1 -A, developed 5 minutes 



in the emulsion him will be less steep for green light than for violet 
light, and, consequently, there will be more spreading of the image 
made by green light. The larger value of the photographic gradient 
is overbalanced by the lower value of the light-gradient. This 
explanation assumes that the scattering of the light by the silver 



34Q 



ORIN TUGMAN 



halide grains does not vary appreciably with wave-length. This 
assumption is justified by the fact that it is the short waves which 
usually are scattered most by heterogeneous media and on this 
account the resolving power of a photographic plate should be 
greater for long waves than for short waves. Further evidence 
that the opacity of the emulsion is a more important factor in the 
light-gradient than the diffusion is given in the curves 4, 4 A of 
Fig. 4. A "Process" plate was immersed in a yellow dye and 




1 division = 10 microns 

Fig. 4. — Seed "Process" plates exposed to violet light. Equal exposure, but 
varying development, i.e., 

1, developed 2 minutes 
1 -A, developed 5 minutes 
4 and 4-A, plates bathed in yellow dye previous to exposure 



exposed to violet light. In this case the diffusion could not be 
changed, but the opacity was increased with a corresponding 
increase of resolving power. 

The curves in Figs. 3,4, and 5 are all from images exposed and 
developed within the range of ordinary working conditions. A 
long exposure will show the distribution of the light in the emulsion 
as explained in the first part of this paper. The curves for long 
exposures are in Fig. 6. Here there is a decided change in the 
density-gradient with development. If the exposure could be 
timed just right, a density-gradient could be obtained showing 






RESOLVING POWER OF PLATES 



34i 



the very beginning of the curve to grow steeper with long develop- 
ment. It appears, then, that in ordinary exposure the lateral 
spread of exposure is not sufficient to permit the density-gradient 
to become steeper with prolonged development. 

A cross-section of the emulsion film (Plate VI, c and d) at the point 
where the edge of the image occurs shows the distribution of the 













































































































































































































// 




or /-a 




cfl 




2- A 





























0.8 
1 ° 6 

0.4 



1 division = 10 microns 
Fig. 5. — Seed "30" plates 

1 and 1 -A, exposed equally to violet light, but developed 2 and 5 minutes 
respectively. 

2 and 2-A, exposed equally to green light, but developed 2 and 5 minutes 
respectively. 



grains at this point. It is seen that the greatest spreading occurs 
at the top of the film. This distribution suggests that the intensity 
of the light in the emulsion at any point is given by the equation 

J =Ioe -Hx+y) 

where x is the distance down through the emulsion and y is the dis- 
tance out from the image and measured from the region of uniform 
exposure. The validity of this equation is supported by previous 



342 



ORIN TUGMAN 



investigations on the absorption of light in heterogeneous media. 
The logarithmic character of the law of light-absorption in such 
media was shown theoretically by Nutting 1 and experimentally 
by the writer. 2 

A study of these overexposures opens a way for the determina- 
tion of the exposure-gradient. Goldberg's investigation was essen- 



































































































>> 
























"53 

c 

P 












































































/T-i 


i 






























I 



































i division = io microns 

Fig. 6. — Seed "30" plate, over-exposed to violet light 

1, developed 2 minutes 

1 -A, developed 5 minutes 






tially a study of overexposures, but his methods failed to reveal 
the nature of the factor desired. On some points, however, the 
investigation will be similar to Goldberg's procedure. 

It was pointed out above that exposures do not affect this dis- 
tribution of light in the emulsion and that spreading of the image 
results from the diffused light having time to expose the adjacent 
sensitive material. If the exact position of the knife-edge on the 
emulsion can be located and the density is measured at a given 

1 Phil. Mag. (6), 26, 423, 1913. 2 Tugman, Photographic Journal, June 1914. 



RESOLVING POWER OF PLATES 343 

distance from that edge for various exposures and developments, 
the true value of the exposure-gradient can be found by referring 
these densities to a sensitiveness-curve of the emulsion being 
investigated. Two parallel knife-edges placed at a known distance 
apart on a photographic plate would permit an exposure over a 
rectangular area. The density-curve taken across such an exposed 
area would show the falling off of density on both sides and the 
position of the knife-edges with respect to the exposed area. This 
is a subject for further experimental work. 

The writer is indebted to Dr. C. E. K. Mees and Dr. P. G. 
Nutting for their interest and suggestions in this investigation. 

Rochester, N.Y. 
July 22, 1915 



THE VARIATION WITH TEMPERATURE OF THE 

ELECTRIC FURNACE SPECTRA OF 

COBALT AND NICKEL 1 

By ARTHUR S. KING 

The treatment in this paper of the electric furnace spectra of 
cobalt and nickel follows the method previously used for the 
spectra of iron, 2 titanium, 3 vanadium and chromium, 4 the lines 
being classified according to the temperature at which they first 
appear and their rate of increase in intensity as the temperature 
rises. The range of wave-length covered extends from below 
X 3000 to about X 7100. 

APPARATUS AND METHODS 

The operation of the tube resistance furnace in vacuo has 
been described in former papers. The spectrum was photographed 
with a 15-ft. concave grating in the vertical spectrograph. 5 The 
second order (scale 1 mm= 1 . 85 A) was used as far as X 5200, and 
the first order from this point to X 6700, a few lines at the red end 
being recorded on films taken with a 1 -meter concave grating. 

The three temperatures on which the classification of spectrum 
lines is based were given by a Wanner pyrometer as 2000-2 ioo° C. 
for the low-, about 2300 C. for the medium-, and 2500-2600 C. 
for the high-temperature plates. A meager spectrum, consisting 
of the stronger low-temperature lines of both elements, mainly 
in the blue region, was obtained as low as 1850 C. 

The metallic cobalt and nickel used in the furnace were highly 
purified preparations by Kahlbaum, each of them showing but a 
trace, spectroscopically, of the other element. As the furnace tubes 
were of regraphitized Acheson graphite, there was little disturbance 

1 Contributions from the Mount Wilson Solar Observatory, Xo. 108. 
- ,1//. Wilson Contr., Xo. 66; Astrophysical Journal, 37, 239, 1913. 
3 .1//. Wilson Contr., Xo. 76; Astrophysical Journal, 39, 139, 1914. 
4 Ml. Wilson Contr., Xo. 94; Astrophysical Journal, 41, 86, 1915. 
s Ml. Wilson Contr., Xo. 84; Astrophysical Journal, 40, 205, 1914. 

344 



FURNACE SPECTRA OF COBALT AND NICKEL 345 

from impurity lines, the main trouble from this source being the 
strong carbon bands given at the higher temperatures. 

EXPLANATION OF THE TABLES 

Wave-lengths. — The wave-lengths in Tables I and II are those 
given by Exner and Haschek 1 for the arc spectrum, supplemented 
occasionally by those of Hasselberg, 2 designated by "H" usually in 
cases where close doublets were not resolved by Exner and Haschek. 

An asterisk after the wave-length denotes that an explanatory 
remark for the given line is to be found at the end of the table. 

The sign f indicates that the estimates of intensity for the line 
in the furnace spectrum are disturbed by the presence of a band 
spectrum, this being usually one of the heads of the "Swan spec- 
trum" of carbon, though a banded structure farther in the red, 
whose origin has not been definitely fixed, interfered with a few 
lines. 

Arc intensities. — These were estimated by the writer from spec- 
tra given by the purified cobalt or nickel in the carbon arc, the 
exposure being timed to produce as distinct intensity contrasts as 
possible. Nebulous lines, occurring for the most part in the nickel 
spectrum, are indicated by "n" after the intensity value. The 
letters "R" and "r," both for arc and for furnace lines, indicate 
complete and partial self-reversal, respectively. 

Furnace intensities. — The columns devoted to the intensities 
of furnace lines give the relative strength as estimated for each 
temperature, a line distinctly outlined on the plate being given 
the intensity " 1," a fainter appearance being indicated as a trace, 
"tr". There is usually a decided difference in appearance between 
lines in the furnace at different temperatures, and also between 
furnace lines and those of the arc, but the relative change of differ- 
ent lines with increase of temperature is shown in the tables. 

Classification. — -The method of assigning lines to the classes 
given in the last column of Tables I and II is the same as for the 
spectra previously treated. Class I lines are relatively strong at 

1 Spektren dsr Elemente bei normalem Dritck, Leipzig, 1911. 

2 Kgl. svenska vet. akad. hand!., 28, 1896; see also Kayser, Handbuch dcr Spectro- 
scopic, 5, 310; 6, 172. 



346 ARTHUR S. KING 

low temperature and strengthen slowly at higher temperatures. 
Class II lines appear at low temperature, but strengthen more 
rapidly than those of Class I as the tube becomes hotter. The lines 
of Class III are absent or faint at low temperature, appear at 
medium temperature, and are usually considerably stronger at 
high temperature. Class IV lines appear at the highest furnace 
temperature, sometimes faintly at medium temperature; while 
those of Class V are usually absent in the furnace, or if present 
are faint compared with the arc intensity. Arc lines below a 
certain minimum intensity are not entered in the tables unless 
they appear also in the furnace. 

The use of "A" after the class number indicates that the line in 
question is relatively weak in the arc, being usually not more than 
half as strong as in the high-temperature furnace. 

LEADING CHARACTERISTICS OF THE FURNACE CLASSES 

Class I. — The lines of this class are of a well-defined and fairly 
uniform type. With few exceptions, the scale adopted gives them 
nearly the same intensity at the three furnace temperatures and 
in the arc, while the lines of other classes decrease with varying 
degrees of rapidity from high to low temperature. A large pro- 
portion of the Class I lines are of moderate strength and unreversed. 
These are very similar in appearance at all furnace temperatures. 
A considerable number, however, reverse at high and sometimes 
at medium temperature, while at low temperature the lines are 
sharp but still strong. A few lines of this class maintain their 
strength at low temperature to an unusual degree, these coming 
out strongly at the lowest temperature at which the vapor radiates. 
In general, however, the higher temperatures do not seem to be at 
a disadvantage in producing the low-temperature lines, the rule 
prevailing that a line strong at low temperature is strong at all 
temperatures; though in the case of Class I A lines it may be 
weak in the arc. The question arises whether, when the furnace 
is operated at high temperature, the Class I lines may be radiated 
chiefly by the cooler vapor which is doubtless present near the ends 
of the tube. This seems improbable since the ratio of exposure 
times for high and low temperature is of the order of 1:50, so that 



FURNACE SPECTRA OF COBALT AND NICKEL 



347 



TABLE I 

Temperature Classification of Cobalt Lixes 



Arc 



Furnace 



S 
30R 

2 

i2r 
3 

4 



2or 

5 

5 

1 

6 
15* 

3 

5 
i2r 

2 

4 

3 
1 
10 
4 
3 
3 



High 
Temp. 



I5R 
I5R 

tr 
tr 
5r 
2 
1 or 
3 

15R 

2 

3 
1 
6r 



1 or 
30R 

1 
12R 

2 

5 

5 

1 

20R 

? 

5r 

tr 

5r 
15R 

3 

5 
12R 

2 

3 
15R 

3 

3 
10R 

4 
4 
3 
2 
10R 



Medi- 
um 
Temp 



Low- 
Temp. 



i or 


5 


1 or 


5 


3 


2 


1 




6r 


2 


2 




1 




ior 


3 


1 




2 


tr 


tr 




4 


2 


2 




1 




.Sr 


2 


20R 


ior 


8r 


3 


1 




3 


2 


3 


tr 


tr 




15R 


Sr 


3 


2 


4 


2 


4 


3 


i2r 


6r 


2 




4 


2 


10R 


5r 


1 




2 


tr 


12R 


6r 


1 




1 




Sr 


4 


2 




2 




2 




1 




8r 


4 


1 





Class 



III 
II 
II 
IV 

IV 

II 

III 

II 

III 

III 

II 

III 

III 

III 

II 

III 

III 

IV 

II 
II 

IV 

II 

III 

II 

III 

III 

II 

II 

II 

IV 

I 

II 

III 

II 

II 

III 

III 

II 

III 

III A 

II 

III 

III 

III 

III 

II 

III 

III 

III 



(ExNER AND 

Haschek) 



3104 
3106 
3106 
3107 
3107 
3109 
3110 
3110 
3111 
3113 

3«8 
3H8 
3121 
3121 
3126 
3126 
3127 
3129 
3129 
3i3i 
3132 
3136 
3137 

3137 

3137 
3HO 
3HO 
3145 
3147 
3149 
3ISO 
3I50 
3152 
3*54 
3154 
3*57 
3158 

3159 
3161 
3168 
3169 
3173 
3174 
3175 
3177 
3179 
3180 
3182 



Arc 



10 

10 

I 

4 
7 
3 
3 



/10 

\ 3 
4 



3 
10 



Furnace 



High 
Temp. 



5 
3 
3 

3 

I 

3 
3 

4 
1 
6 
8r 

4 

12R 
12R 

1 

3 
8r 

5 

3 

1 

6r 

6r 

1 
10R 

3 

4 
12R 

2 

3 
15R 

8R 



5 
3 
5 
1 
12R 
8R 

4 
8 

5 



Medi- 
um 
Temp. 



4 
tr 

4 

5 

3 

ior 
1 or 



i2r 
6r 



5 

tr 
i2r 
6 
3 
4 
4 
tr 
tr 

3 
2 



Low 
Temp. 



tr 



tr 



I 




6 


5 


5 


2 


1 




6 


3 


3 


2 


tr 




8r 


5 


1 




2 




1 or 


S 


tr 




1 





tr 



Class 



tr 



III 

II 

III A 

III 

IV 

III 

III 

I 

III 

III 

II 

II A 

II 

II 

IV 

III 

I 

II 

III 

IV 

II 

II 

III 

II 

III 

III 

II 

IV 

III 

II 

II 

V 
V 

III 

III 

II 

III 

II 

II 

III 

III 

III 

III 

III 

III 

III 

IV 

III 
III 



348 



ARTHUR S. KIXG 
TABLE I — Continued 



Furnace 



(Exner AND 
Haschek) 



Arc 



3186.05, 

3186.46. 

3188.50. 

3189.87. 

3I9I-44- 

3I92.35. 

3I9330. 

3198.79- 

3I99.44. 

3203. _ 

3206.00. 

3210.35. 

3210.96. 

321546. 

3217- 

321931 

3223.30. 

3224.80. 

3227.15. 

3227.93. 

323430. 

323569. 

3237. 

3243-70. 

3243.99. 

3247-13 

3247-32 

3250.17. 

325360. 

3254-37. 

3258.16. 

3258.58. 

3260.99. 

3263.35 

3264.96. 

3265.49. 

3268.15. 

3269.04. 

3270.35. 

327192. 

3276.60. 

3277-44. 
3277-80. 
3278.23. 
3278.96. 

3279.39. 
3281.75. 
3282.23. 
3282.37. 
3283.49. 



3n 



6 

1 
12 

4 
1 

9 

4 



High 

Temp. 



tr 
I 
8R 

3 
4 



4 
10R 

7 

3 

6 

8r 

tr 



Medi- 
um 
Temp. 



Low 
Temp. 



2 




tr 




5 


4 


3 


tr 


2 




1 




4 


2 


3 


1 


8r 


4 


1 




6 


3 


2 




6 


3 


5 


4 


9 


6 


3 


tr 


tr 




5 


2 


2 




5 


4 


2 




tr 




5 


2 


1 




3 


tr 


tr 




4 


1 


3 


1 


5 


3 


tr 




1 





Class 



III 

I 

III 

I 

II 

III 

II 

II 

I 

I 

IV 

III 

IV 

IV 

III 
II 

III A 

III 

III 

II A 

IV 

II 

II 

III 

II 

III 

II 

II 

IV 

II 

III 

III 

II 

II 

I 

III 

IV 

III 

IV 

II 
III 
III 
III 

IV 

III 
II 

I A 
IV 

III 
III 



(Exner and 
Haschek) 



3283 
3283 
3286 
3287 
3287 
3292 
3293 
3294 
3294 
3298 
3304 
3304 
3304 
3305 
3305 
33o6 
3307 
3308 
33o8 
3312 
3312 
3313 
3314 
3314 
3315 
33i8 

3319 
3319 
3320 
3322 
3322 
3325 
3326 

3327 
3328 

3329 
3329 
3333 
3334 
3337 
3338 
3339 
3341 
3342 
3342 
3344 
3346 
3347 
3348 
335i 



Arc 



3or 



Furnace 



High 
Temp. 



tr 



Medi- 
um 
Temp 



tr 



I 


tr 


5 


3 


2 


1 


4 


3 


2 


1 


1 


1 


8 


5 


6 


6 


4 


2 


5 


3 


1 


tr 


1 


tr 


3 


1 


8r 


8 


30K 
8r 


8 


1 


tr 


5 


3 


4 


2 


4 


2 


ior 


6 



Low 

Temp. 



tr 



tr 



FURNACE SPECTRA OF COBALT AND NICKEL 
TABLE I — Continued 



349 



Arc 



3 

4 

20 

3 

2 

6 
3 
3 
3 
6 

5? 
6 

4 
3 

4 

2 

3or 
io 

7 

4 

5 

2 

5 
3 
5 

4 

2 

4 
25r 



3or 



4or 



4 
150R 

2 
6or 
80R 
80R 

5 
5°r 



Furnace 



High 
Temp. 



I 
? 

20R 

2 



3 
6 

3? 
4 
2 
1 

5 
2 

30R 

ior 
6 



25R 
tr 

tr 
30R 



40R 



tr 



150R 

? 

60R 
80R 
80R 
6 
50R 



Medi- 
um 
Temp. 



I5R' 



20R 



40R 
30R 
50R 
6 
35R 



Low 
Temp. 



tr 



Class 



tr 




6 


2 


tr 




1 




4 


tr 


1 




1 




20R 


15 






20R 


is 


tr 




4 


1 


tr 




1 




30R 


20 


tr 




tr 




tr 




2 




tr 




100R 


60R 



2or 
3or 
40R 

6 
20 



III 

III? 

II 

III 

III 

III 

III 

III 

III 

III 

III 

III 

III 

IV 

III 

III 

II 

I 

III 

III 

III 

III 

II 

III 

III 

III 

III 

III 

II 

IV 

IV 

II 

III 

III 

III 

III 

II 

III 

III 

IV 

III 
III 
III 

II 

IV? 

II 

II 

II 

I 

II 



(exner and 
Haschek) 



3417-84 




34i 7 -93 




3420.64 




3420.95 




3421.77 




3422.63 




3423-03 




3424-67 




3426.60 




3427.90 




3428.34 




3428.89 




3429.82 




343I-76 




343 2. 46* 


e 


3433 18 




3437 10 




3437-83 




3438.83 




3439-OS 




3441.28 




3443 06 




3443-31' 




3443 ■ 79 




3445 • 29 




3446.21 




3447 43 




3448 . 49 




3449 • 26 




3449 • 54 




3452.44 




3453-66 




3455-33 




3456.58*.. 


3457 05. • 


3458.16 




3460 . 86 




3461.33 




3462.94 




3463.62 




3465 96 




3467.37 




3468.74 




3469.11 




3471-53 




3472.34 




3473 ■ 60 




3474- 17 




3474-40 





Arc 



5or 

3 
60R 

3 
6n 

4 

5 

2 

4or 

5 
80R 

1 

12 

3 

4 
60R 
60R 

3 
200R 

25r 

/ 1 

\ 1 

9 

3 

4 

15 

6or 

3 
100R 



100R 
6 



Furnace 



High 
Temp 



tr 
5oR 

3 
60R 

1 

3 

5 

2 

tr 
40R 

? 
80R 

1 

4 

tr 

1 
50R 
60R 

1 
200R 

25R 

tr 
tr 

8r 

4 

5 

4 
60R 

3 

100R 
1 
tr 

1 

4 
tr 
1 
100R 
? 



Medi- 
um 
Temp. 



35R 

2 
40R 

tr 
1 

3 
tr 



30R 

? 
60R 

1 



Low 
Temp, 



tr 

40R 
SOR 

I 

125R 

20R 



6 

3 
40R 

2 

80R 



tr 



tr 



60R 

? 



3or 



3 or 
3or 



80R 



4 
tr 
3or 



60R 



Class 



4or 
? 



Ill 

I 

II 

III 

III 

IV 

III 

II 

III 

IV 

III 
III 

IV 

II 

III 

II 

III 

III 

III 

IV 

IV 

II 

III? 

II 

III 

III 

IV 

III 

II 

II 

III 

II 

I 

IV 
IV 

I 

III 

I 

III 

II 

III 

II 

IV 
IV 

III 
III 

IV 

III 

II 

? 



35° 



ARTHUR S. KING 
TABLE I — Continued 



(exner and 
Haschek) 



3474 

3476 
3478 
3478 
3478 

3479 

3480 

3483 
3483 
3485 
3485 
3487 
3489 
349° 
3491 
3492 
3495 
3496 
3496 
3496 
3502 
3502 
3S°3 
3504 
350S 
35o6 
35io 
35io 
3512 

3513 
35i6 
35i8 
3S20 
352i 
3521 
3523 
3523 
3523 
3526 
3526 
3528 
3529 
3529 
353° 
3533 
3534 
3537 
3543 
3543 
3546 



Arc 



Furnace 



High 
Temp. 



68 


... 6 


5° 


... 511 


00 


... 4 


60 


... 8 


90 


... 7 


•74 


1 


■17 


... 6 


•29 


2 


■58 


. . . 2or 


■5i 


... 15 


■85 


... 4 


•84 


... 8 


•57 


. . . 6or 


.89 


... 10 


■49 


... 15 


. 12 


••• 3 


■83 


... 5or 


. 20 


••■ 3 


.80 


... 15 


■90 


... 6 


■45 


. . . 100R 


.80 


. . . 2or 


•85 


••• 3 


.89 


••• 5 


■29 


••■ 3 


•47 


. . . 80R 


.00 


... 5or 


•59 


... 3or 


.80 


... 60R 


.61 


... 50R 


■78 


1 


•50 


.. 50R 


•23 


... 15 


•73 


... 3or 


•85 


■•• 5 


.00 


... 4 


•55 


... 25r 


•83 


... 7 


.00 


•■■ 3 


■97 


. . . 100R 


.09 


•■• 5 


.19 


... 3or 


.96 


. . . 80R 


.70 


... 1 


•5i 


... 25r 


.91 


... 4 


•85 


1 


•!5 


2 


■43 


■ •■ 15 


■85 


.... 6 



20R 

6 

4 

6 
40R 

8r 
20R 

50R 

15R 

6 

100R 

20R 

3 

4 

2 
80R 
40R 
30R 
50R 

5°R 

1 
40R 
20R 
3°R 

5 

1 
20R 

5 

4 
100R 

2 
30R 
80R 

25R 
4 

1 

5 
8 

5 



Medi- 
um 
Temp 



20R 

4 

3 

5 
30R 

8 
20R 

tr 
40R 

tr 

I2T 

3 
60R 
20R 



I 
50R 
30R 
30R 
40R 
40R 

I 
20R 
20R 
3 0R 

5 
tr 
20R 



80R 

1 
25R 
50R 

tr 

25R 

2 
tr 

5 



Low 
Temp 



Class 



15 



25 



40R 

20 



3or 

25 
25 
25 
3°r 



15 



20 
2 

50R 



3°r 



I 

IV 

III 

III 

II 

III 

II 

III 

I 

III 

II 

II 

II 

I 

I 

III 

II 

III 

I 

III 

II 

I 

III 

III 

III 

II 

II 

I 

II 

II 

III 

II 

II 

I 

I 

III 

I 

II 

III 

II 

III 

I 

II 

III 

I 

III 

III 

II A 

II 

III 



(exner and 
Haschek) 



3548.6o 
3550.78 
3SSI-84 
3552.90 
3553-16 

3553-31 
3558.93 
3559-75 
3560.47 
3561.03 
3562.25 
3563-09 
356431 
356509 
3568.56 
3569-59 
3570.57 
3575 13 
3575-53 
3577-39 
3577-82 
3578.21 
3579-04 
3579-15 
3582.02 

3584-94 
3585 -33 
3585 -94 
3586.20 

3587-3° 
359 x -9i 
3595 03 
3596.67 
3600.97 
3602. 22 
3604.62 
3605.17 
3605.52 
3608.45 
3609 . 94 
3611.89 
36i5-54 
3618.15 
3620.56 

3624.54 
3625.18 
3626. 20 
3627.98 

363 !• 59 

3632.12 



7 
2or 



12 

1 

5 
2or 

6 

7 

4 
25r 

2 
80R 

411 
25r 
6or 

3 

2 

6 

6 

6 

4 
15 
25R 

4 

3 
70R 

4 
50R 

5 

3 

40R 

4 

5 

2or 

3 
4 
10 
6 
4 
5 
5 



25* 
2or 



Furnace 



High 
Temp 



7 
20R 



1 or 

6 

1 
i2r 

tr 

6 
20R 

6 

9 

2 

25R 

2 
70R 

3 

25R 
60R 

4 



Medi- 
um 
Temp 



6 
20R 



5 
6 

4 

15R 
25R 

4 

2 

60R 

3 
50R 

5 

4 
40R 

1 

6 
20R 



7 
9 
5 
7 
i2r 

4 
25R 

25R 



50R 

2 
20R 
50R 

3 



Low 

Temp. 



10 


10 


6 


2 


tr 




12 


10 


3 
20R 


15 


3 
6 


2 


1 




25R 


20 


1 





3 

4 

5 

2 
i2r 
20R 

3 

1 
40R 

2 
40R 

3 

3 
30R 

1 

5 
i5r 



6 

5 

7 

3 

4 

9 

2 
20R 
25R 







FURNACE SPECTRA OF COBALT AND 


NICKEL 


351 






TABLE I- 


— Continued 










A 
(EXNER AND 


Arc 


Furnace 


Class 


K 

(EXNER AND 


Arc 


Furnace 












Medi- 




Class 


Haschek) 




High 


. e 1- 


Low 




Haschek) 




High 


Low 








Temp. 


Temp. 


Temp. 








Temp. 


um 

Temp. 


Temp. 




3633 O 1 • 


• 7 


5 


3 


tr 


III 


3750.07. . 


• 9 


6 


6 


3 


II 


3633 


49... 


2 


1 


1 




III 


3751-75- • 


• 5 


8 


4 


1 


III 


3634 


86... 


7 


5 


3 


tr 


III 


3754-47- • 


• 4 


2 


1 




III 


3636 


84... 


. 6 


6 


5 


2 


II 


3755- 60. . 


10 


IO 


7 


3 


II 


3637 


44- • • 


4 


3 


2 




III 


3759-83-- 


■ 3 


2 


1 




III 


3638 


50... 


1 


1 


tr 




III 


3760.53. . 


■ 4 


5 


4 


2 


II 


3639 


60... 


. 10 


10 


8 


5 


II 


3774- 75- • 


8 


IO 


6 


2 


II 


3641 


94... 


6 


7 


4 


3 


II 


3777-25- • 


1 


I 


tr 




III 


3643 


35- •■ 


9 


8 


6 


4 


II 


3777-68.. 


6 


8 


5 


1 


III 


364s 


34- • • 


• 5 


6 


4 


1 


III 


3805.94. . 


2 


2 


1 




III 


3645 


60... 


■ 3 


3 


2 


tr 


III 


3808.25.. 


10 


10R 


ior 


12 


I 


3647 


23 ••• 


• 5 


5 


3 


tr 


III 


3811.23.. 


• 5 


7 


6 


5 


I 


3647 


56... 


1 


1 


tr 




III 


3812.62. . 


■ 4 


4 


3 


tr 


III 


3647 


85... 


. 12 


15R 


15* 


15 


I 


3S14.62. . 


• 5 


5 


4 


1 


III 


3648 


26... 


• 3 


2 


1 




III 


3816.48.. 


• 15 


6 


5 


4 


I 


3649 


49- •• 


. 8 


8 


4 


tr 


III 


3816.61.. 


• 15 


6 


5 


4 


I 


3651 


41. .. 


4 


5 


4 


1 


III 


3817.01. . 


5 


5 


3 


1 


II 


3652 


70. . . 


• 15 


20R 


20R 


20 


I 


3820.08.. 


4 


5 


3 


1 


II 


3654 
3657 


59- •• 
10. . . 


• 5 

• 7 


6 
8 


5 
8 


2 
10 


II 

I 


3823.66.. 
3841.60. . 


1 
5 


tr 

4 






IV 


4 


4 


I 


3658 


06... 


2 


1 


1 




III 


3842.21. . 


• 3° 


20R 


15* 


10 


II 


3662 


32... 


12 


8 


7 


4 


II 


3843-85-. 


4 


4 


3 


tr 


III 


3668 


80... 


1 


1 


tr 




III 


3845.60. . 


. 60 


60R 


40R 


30R 


II 


3670 


20. . . 


3 


3 


2 


tr 


III 


3850.27.. 


5 


4 


3 




III 


3676 


72... 


. 12 


10 


5 


1 


III 


3851-09. • 


4 


1 or 


8 


8 


I A 


3683 


22. . . 


20 


20 


15 


10 


II 


3852.00. . 


2 


2 


1 




III 


3684 


63... 


. 10 


12 


6 


1 


III 


3856.94- ■ 


4 


2 


2 




III 


3685 


11 . . . 


2 


2 


1 




III 


3861.31.. 


. 20 


20R 


15* 


15 


I 


3686 


62... 


2 


1 


tr 




III 


3863.75.. 


2 


1 


tr 




III 


3690 


91... 


7 


6 


4 


2 


II 


3870.66.. 


4 


3 


1 




III 


3693 


29... 


8 


8 


8 


5 


I 


3873-23- - 


. 60 


60R 


40R 


30R 


II 


3693 


53H. 


2 


2 


1 




III 


3874.09. . 


• 40 


40R 


30R 


20R 


II 


3693 


63... 


. 8 


6 


7 


5 


I 


3877.01. . 


. 20 


20R 


J 5r 


15 


I 


3699 


IS... 


211 


1 






IV 


3882.06. . 


• 25 
10 


20R 


18R 


t cr 


I 


3702 


39- •• 


. 12 


8 


5 


1 


III 


3884.70-- 


8r 


8 


6 


I 


3704 


22. . . 


■ 25 


30R 


20 


20 


I 


3885.45.. 


6 


6 


6 


4 


I 


3707 


62... 


6 


5 


4 


2 


II 


3890.18.. 


2 


2 


1 




III 


3709 

37" 


00. . . 
83... 


12 
3 


9 

2 


8 
2 


5 
tr 


II 
III 


3891.85.. 
3892.30. . 


2 
■ 3 








V 


2 


1 




III 


3712 


35 ••• 


. 6 


5 


4 


1 


III 


3893.20. . 


2 


1 


1 




III 


3726 
3728 


79... 
96... 


5 
3 


6 
2 


4 
1 


1 


III 
III 


3893-45- • 
3894-25. • 


2 
. 60 








V 


50R 


30R 


20R 


II 


3730 


63... 


20 


15 


12 


8 


II 


3895-I5- • 


. 20 


20R 


15R 


8 


II 


3731 


42. . . 


2 


2 


2 


tr 


III 


389854.. 


- 4 


5 


5 


1 


III 


3732 


59- •■ 


20 


15 


12 


12 


I 


3904 . 23 . . 


2 








V 


3733 


65... 


12 


10 


8 


5 


II 


3904 . 94 . . 


3 








V 


3734 
3736 


30... 

08... 


• 7 
. 12 


7 
12 


5 
9 


2 
4 


II 
II 


3905-70. . 
3906.46. . 


2 
10 








V 


i2r 


i2r 


10 


I 


3740 


34- •• 


5 


4 


3 


1 


II 


3910.13. . 


• 15 


20R 


20R 


15* 


I 


3745-65... 


• 25 


3°R 


2or 


20 


I 


3917.80.. 


8 


6 


5 


2 


II 





























352 



ARTHUR S. KING 
TABLE I — Continued 



(exner and 
Haschek) 



3920 


32... 


3920 


75- •• 


3920 


90... 


3921 


27... 


3922 


90... 


3925 


33- • • 


3929 


43- •• 


3934 


07. .. 


3934 


85... 


3935 


44. . . 


3936 


13... 


3939 


00. . . 


3939 


21 . . . 


394i 


06 ... . 


394i 


91. ... 


3942 


84.... 


3945 


07. .. . 


3945 


51.... 


3946 


75---- 


3947 


26. .. . 


3952 


46.... 


3953 


10. . . . 


395« 


10. . . . 


3961 


IS-- 


3965 


IS---- 


3965 


37- ■■■ 


3968 


7S---- 


3969 


28.... 


3972 


69.... 


3973 


31... . 


3974 


90. . . . 


3975 


45---- 


3977 


34- ••• 


3978 


78.... 


3978 


99.... 


3979 


67.... 


3987 


25.... 


3990 


45- ■•■ 


3991 


68*... 


399i 


83*... 


3994 


70. . . . 


3995 


45 • ■ ■ • 


3998 


09 ... . 


4003 


85.... 


4008 


07. . . . 


401 1 


25.... 


4014 


09 ... . 


4016 


95. ... 


4019 


45 ■ ■ ■ • 


4021 


07. . . . 



Arc 



3° 
3 



3 
3 

10 

4 

10 
6 
6 

4 
6 
6 

(.0 

40 

2 



Furnace 



High 
Temp 



30R 



i2r 
20R 
tr 

tr 

15* 

2 

3 
8r 

25R 
15R 

4 
2 

4 



10 

I5R 

2 

3 

ior 

15R 

8 

5 

2? 

8? 

6 
60R 
40R 



20R 



Medi- 
um 
Temp 



I 




3 


1 


8 


7 


tr 




tr 




6 


6 


tr 




1 





I5R 



ior 
15* 



i5r 

i2r 
2 



4 
tr 

10 

i2r 



15R 

8 

4 
tr 
6 

5 
40R 
20R 

1 

tr 
4 
5 



15R 



Low 
Temp 



7 
12 



3 
12 
tr 
tr 
9 



5 
20R 

15 



Class 



III 

III 

II 

IV 

I 

III 

III 

I 

III 

III 

II 

V 

V 

I 
II 

IV 
IV 

I 

II 

II 

I 

II 

II 

II 

II A 

II A 

II A 

III 

III 

II 

I 

III 

III 

I 

V 

I 

I 

II 

IV 

I 

I 

II 

II 

III 

III 

IA 

II 

V 

I 

I 



(exner and 
Haschek) 



4023 


55- •■ 


4027 


18... 


4035 


74... 


4040 


95 ■•• 


4045 


5 6... 


4053 


10. . . 


4054 


08... 


4057 


10. . . 


4057 


36... 


4058 


36... 


4058 


76... 


4066 


56... 


4068 


72. . . 


4069 


71. . . 


4076 


30. . . 


4077 


56*.. 


4081 


64... 


4082 


75- •■ 


4083 


78.... 


4086 


49- •• 


4088 


45 • • • ■ 


4092 


56.... 


4093 


03 ... . 


4093 


22. . . . 


4096 


11 ... . 


4104 


57- ... 


4104 


91 


4110 


70. . . . 


4118 


96.... 


4121 


52.... 


4122 


43 


4132 


00. . . . 


4132 


30.... 


4139 


60. . .. 


4150 


62.... 


4158 


59 • ... 


4162 


32.... 


4179 


34- •• • 


4187 


46.... 


4190 


88.... 


4195 


03 ... . 


4225 


28.... 


4234 


IS*--- 


4237 


50. ... 


4241 


69.... 


4242 


03 ... . 


4245 


70. ... 


4248 


30.... 



Arc 


Furnace 


High 


Medi- 


Low 




Temp. 


Temp. 


Temp. 


4 


4 


4 


I 


10 


i or 


ior 


IO 


8 


3 


1 




2 


2 


2 


tr 


20 


20R 


15* 


15 


3 


1 


1 




1 
2 
5 


1 










8r 


8 


8 


8 


ior 


10 


10 


6 


6 


6 


2 


15 


i2r 


10 


10 


8 


7 


6 


3 


1 
3 


tr 

8 






8 


7 


1 2 


2 


1 




I 2 
2 
2 














5 


5 


4 


1 
15 


1 
15 






12 


6 


1 


8 


8 


6 


25 


20R 


15* 


15 


3 


2 


1 




2 
2 
2 














2 


2 


tr 


4 


3 


2 


tr 


25 


20R 


151 


15 


50 


50R 


30k 


15* 


60 


60R 


40k 


2or 


2 


1 


tr 




3 
4 








6 


6 


4 


3 


3 


2 


tr 


2 


4 


4 


2 


4 


1 


1 




2 
2 


1 
1 






tr 




4 


4 


4 


2 


20 


20R 


2or 


25 


1 


1 


tr 




2 


2 


2 


tr 


f 2 


4 


4 


6 


I 2 


4 


4 


6 


1 


1 


1 




2 
2 








2 


1 




2 
2 





















FURNACE SPECTRA OF COBALT AND NICKEL 
TABLE I — Continued 



353 



(ExNER AND 

Haschek) 



Arc 



.61. 
.92. 

.41 

■58. 

•43- 
.80. 

■ 3it- 
$1. 



2QT. 
78. 
II . 
.09. 

.86. 
.08. 
■55- 
• Si- 
.79. 
. 22. 
.90. 
.09. 

■75- 

76. 
.00. 

■So- 

. 11 . 
.94. 

■ 35- 

.26. 

■95 

.08. 



.99. 
i' 

8( 
.79. 
. 20. 

•34- 

.80. 

.90. 

.82. 

. 10. 

.91 

.58. 

.6of. 

55t- 
■ 361". 

S6f. 



S 
4 
3 
1 

3 
3 

5 
4 
3 
2 

4 

10 

IS 
5 
1 

4 
3 
2 



2 
3° 
7 
6 
1 
10 

15 
2 

4 
20 
1 
4 
5 
2 

15 
12 

9 
6 



Furnace 



High 
Temp. 



tr 

4 
6? 



12 

tr 



IS 



8? 

? 
? 
? 



Medi- 
um 
Temp 



3-' 



tr 



tr 



4 
4? 



Low 
Temp 



is 

10 



tr 



Class 



I 

III 

I 

I A 

V 

IV 

III 

III 

IV 

III 

III 

III? 

Ill 

III 

III A 

III 

III 

III 

III 

III 

IV 

III 

III 

III 

III 

III 

III 

III 

IV 

IV 

III 

III 

III 

II 

III 

III 

III 

III 

III 

IV 

I A 

III 

IA 

IV 

IV 

III 

III 

III 

III? 

IV? 

IV? 



(exner and 
Haschek) 



4728 


61... . 


4735 


Olf... 


4737 


92.... 


4749 


89.... 


4 7 54 


60.... 


4768 


26. ... 


477i 


30. ... 


4776 


si.... 


4778 


42 


4780 


20. . . . 


478i 


64.... 


4793 


10. . . . 


4796 


06 ... . 


4796 


60.... 


4813 


70. . . . 


4814 


22. . . . 


4816 


09 ... . 


4840 


50 


4843 


68.... 


4868 


08.... 


4882 


89.... 


4899 


70. . . . 


4904 


38.... 


4912 


58.... 


4920 


40 


4928 


47 


49S3 


32*. . . 


4966 


72. . . . 


4972 


09 ... . 


4988 


10. . . . 


5067 


73t- - • 


5077 


57t-.. 


5087 


97... . 


5095 


i3t... 


5 1 09 


02f. . • 


5 1 13 


39t-- 


5122 


93t-- 


5124 


apt-.. 


512s 


84t-.. 


5126 


3 6f... 


5133 


60... 


Si4S 


63L. 


5146 


8 9 t-. 


5149 


2lf.. 


5i49 


93t- ■ 


Si 54 


2of. - 


Si 56 


49t- • 


5158 


57t-. 


5159 


ooj . . 


Si 65 


3°t- • 


516b 


27. .. 



Arc 



3 
2 

2 

10 
3 
5 
6 



1 
:o 

2 

1 
25 

3 
25 

2 



IS 



Furnace 



High *gf 
Temp -| Temp. 



5 

3 

3 

IO? 



IO 

5 
tr 
tr 

5 
tr 
8 
tr 

5 
tr 

4 
2 



Low 
Temp 



tr 



IO 

7 



Class 



I A 
III? 

II A 
III 
III 
III 
III 
III 
IV 
III 
II A 
III 
V 

II A 
III 
III 
III 
III 
III 
II 
III 

III A 
III 
IA 
III A 
III 
IA 
IA 
IV 

I A 

IV? 

III? 

V 

III 

V 

IV? 

IV? 

IV? 

IV? 

IV? 

V 

IV? 

IV? 

IV? 

II 

IV? 
IV? 
IV? 
IV? 
IV? 
V 



354 



ARTHUR S. KING 
TABLE I — Continued 



Furnace 



(Exner AND 
Haschek) 



Arc 



High 
Temp. 



5176. 
5192. 
5210. 
5210. 
5211. 
5212. 

5219- 

5222. 

5230- 
5235- 
5248. 
5250- 
5254. 
5257- 
5264. 
5266. 
5266. 
5266. 
5268. 
5276. 
5280. 
5283. 
5287. 
5288. 
530I. 
5312. 
53l6. 
5321. 
5325- 
5326. 
5326. 
5328. 
533* ■ 
5332. 
5333- 
5335- 
5336- 
5339- 
5341- 
5342. 
5343- 
5347- 
5349- 
5352. 
5353- 
5359- 
5359- 
5362. 
5369- 
538i. 
538i. 



S3- 

20. 

97- 
91. 

85- 

26. 

67. 

40 

32- 

02 . 

12. 

78. 

75- 

40 

00. 

Si H« 

71 H* 

70.. 

32-- 

80.. 

60.. 

78H. 

02H. 

20. 

So. 

90. 

89. 

40. 

06. 

39- 

20. 
62. 

85. 
82. 

oj . 

3° ■ 

61. 

34- 
89. 

58. 

63- 

23- 

3°- 

69. 

16H. 

41H. 

95 •• 

83.. 

92.. 



20 
4 
3 
3 
3 

25 



15 

15 

7 



4 
10 

25 



20 
4 
3 
5 

tS 



10 

4 
3 
2 

15 
5 
5 
6 

3 

4 

7 

So 

20 

4 

4 

20 

25 
2 
6 

15 
20 

5 
6 



15 



IS 
12 

15 



ti 



15 



tr? 

tr 
15 



tr 



15 



15 

5 



Medi 

um 

Temp. 



10 
12 



I? 
[2 
2 

3 



tr 



4 
4 

1? 
1 
15 
4 



Low 
Temp 



tr? 



Class 



III 

V 

IV 

IV 

IV 

III 

V 
IV 

II 
II 
II 

V 
IV 

III 

IV 
V 

II? 

II 

III 

V 

III 

V 
V 
V 

II 

III 

III 

V 

III 
III 

IV 
V 

II 

III 

III 

V 
V 
V 
V 

III 
III 

V 
V 

III 
III 

IV 

III? 
Ill 
I 
III 

V 



(Exner and 
Haschek) 



539° 
5402 

5407 
5408 

5413 
5431 
5434 
5437 
5444 
5452 
5454 
5469 
5470 
5477 
5483 
5484 
5489 
5495 
5523 
5525 
553° 
5546 
5559 
559° 
5636 
5637 
5640 

5647 
5659 
5688 
577o 
5830 
5846 
5881 
5890 
5915 
5935 
5946 

5984 

5992 

6000 
6006 
6007 
6049 
6070 
6082 
6086 
6093 
6108 
6117 



62f 

20. 
70. 
35t 
43- 
22. 

72t 
i7t 
80* 

53 
81 

40 
69 

3° 

59 
19 

Sit 

90 f 

Sit 

23- 
99. 

6of 

02f 

99 

So 

9' 

22 

47 
36 
82 
62 
32 
78 
S- 
7i 
74 
61 

73 

40 ; ' 



SO 
85 

34 

So 
67 
8 4 f 
35 

1 2 
20 



Arc 


Furnace 


High 
Temp. 


Medi- 
um 
Temp. 


Low 
Temp. 


2 
3 
5 
2 


1? 
















2? 


I? 




2 
2 

2 

3 

20 














3? 
1? 

? 


2? 
I? 
? 




3 
20 

4 

4 

5 

40 

10 

5 
2 
8 

4 

10 

2 

2 








1 
8 






7 


I 








20 
tr 
2? 
1? 
4? 


20 


20 


1? 

1? 
3? 


2? 


12 
2? 

2? 


10 

? 

? 


6 


10 


10 


10 


3 


3 
3 

1 














2 


1 


tr 


12 


10 


10 


3 


3 
2 
2 

4 
2 
2 
12 
10 
6 


4 
3 


3 

2 


2 

1 














3? 
8 
8 
6 


3? 
8 
8 
6 


3? 
2 

2 

1 


5 

/ 3 

1 3 

20 


2 

2 

2 

20 


1 
2 
1 

20 


? 

? 
4 


5 
5 
5 
6 
2 

15 
7 

10 


3 

1? 


3 


3 


















3 

4 

12 


2 

3 
10 


1? 
8 


2 
8 








10 


8 


7 



FURNACE SPECTRA OF COBALT AND NICKEL 
TABLE I — Continued 



355 



(exner and 
Haschek) 



6l22 9O. 
6189. 20. 

62ii.34f 
6231 . 20* 
6232.70. 
6249. 70. 
6257. Sif 
6273.28! 
6282.89 
6320.62 
6348 . 00 
6351.66 
6305-4O 
6396.71 
6417.99 
j 6421 .91 
6430. 10 

643Q-5 1 
6444 . 89 



Arc 



6 

4 

40 



Furnace 



High 
Temp. 



30 



Medi- 
um 
Temp 



15 

? 



10 
6 



tr? 
20 



Low 
Temp 



7 
2? 



tr 



Class 



IV? 

II A 

IV? 

Ill 

IV? 

II 

III 

III? 

I 

IV 

V 

V 

V 

V 

III 

V 

III 

V 

V 



(exner and 
Haschek) 



6450-51- 
6451.38. 

6455-30. 
6478. 10. 
6490.50. 
6551.69. 
6563.61. 
6596.17. 
6617.30. 
6617.70. 
6624.00* 
6632.69. 
6679.03. 
6771 . 29* 
6815.20* 
6872.62* 
7016.82* 
7053.11* 
7085.25* 



Arc 



80 

3n 
40 
10 

6 

3 
40 
12 

6n 

3n 

2 
15 

4 
20 

15 



l S 



Furnace 



High 
Temp. 



60 

4 



7 
4 

20 



5 

20 

15 

10 



Medi- 
um 

Temp. 



5° 

3 



6 

4 

20 



3? 

8 

4 



Low 
Temp 



SO 



4 

2 
15 



Class 



I 
V 
III 
V 

III 
III 
II 

V 
V 
V 

II? 
I 

I 



REMARKS ON TABLE I 

A 

3062 . t,^ Concealed at high temperature by X 3061 . 94. 

3104. 12 Probably double. 

3137.47 Doublet, just resolved. 

3140.08 Close doublet. Companion makes reversal unsymmetrical. 

3168. 19 and 3344.36 Both probably double. 

3354-34 Concealed by reversal of A. 33 54 . 5 1 . 

3361 . 72 Coincides with strong Ni line. 

3409. 05 Furnace line may be concealed by X 3409. 29. 

3432.46 Probably double. 

3443 .31 Concealed by adjacent lines. 
3474.40 Concealed by reversal of A 3474. 17. 
3991 . 68 and 3991 . 8^ Blend at high temperature. 

4077. 56 Doublet in arc. Only violet component appears in furnace. 

4234. 15 Close doublet, not fully resolved. 

49S3-3 2 Blend with Ni. Furnace line probably all Co. 

5266. 51 and 5266. 71 Close blend. 

5444.80 Very weak in furnace if present. 

5881 .32 Furnace line may belong to band spectrum. 
5984.40 Doublet. Disturbed by band at low temperature. 
5992 . n May be close doublet. 

6231 . 20 Low-temperature line may belong to band. 

6624.00 Furnace line may belong to band. 

6771 . 29 to 7085. 25 Photographed with i-meter concave grating. 



356 



ARTHUR S. KING 



TABLE II 

Temperature Classification of Nickel Lines 



(exner and 
Haschek) 



2983 

2984 

2991 

2992 

2994 

3002 

3°°3 
3012 
3019 
3029 
3031 
3038 
3045 
3050 
3054 
3057 
3064 
3066 
3080 
3097 
3099 
3101 
3101 
3105 
3107 
3"4 
3116 
3129 
3134 
3145 
3145 
3iSi 
3154 
3159 
3164 
3165 
3170 
3176 
3181 
3183 
3183 
3184 
3191 
3195 
3197 
3199 
3200 
3202 



Arc 



20R 

4 
12R 

4 
20R 

25R 

100R 

60R 

75R 
20R 

3 

ior 
60R 
ior 
100R 
50R 
50R 

2SR 

3 
20R 

iSr 
i2r 
100R 
40R 
i5r 

4 
20R 

2 

7 
60R 



4n 



Furnace 



High 
Temp. 



6 

ior 
3n 
5 

5 



20R 

2 
12R 

2 
20R 

25R 

100R 

60R 

75R 
20R 
1 
ior 
60R 
ior 
100R 
50R 
50R 

25R 

1 
20R 

15R 
i2r 
100R 
40R 
15* 
3 
20R 



4 
60R 



Sr 



Medi- 
um 
Temp. 



8r 



6 
ior 



15R 



15R 
15R 
75R 
40R 
30R 
i*R 



5 

40R 

6 

75R 
30R 
30R 
20R 



i5r 

i2r 

8 

60R 

25R 

ior 

2 
i2r 



3 
40R 



Low 
Temp 



4 

Sr 



8r 



8r 

8r 

40R 

20R 

iSr 

8r 



20R 

3 
40R 

15R 
15R 

ior 



7 
6 

4 
30R 

i5r 

5 
2 



3 
20R 



tr 



Class 



II 

III 

II 

II 

II 

II 

II 

II 

II 

II 

IV 

II 
II 
II 
II 
II 
II 
II 

IV 

II 

II 

II 

II 

II 

II 

I 

II 

V 

I 

II 

I 

II 

V 
IV 

I 

IV 

I 

IV 
IV 

II 
III 
II 
II 

V 

II 
II 

V 

II 

IV 



(exner and 
Haschek) 



3207.05. . . 
3210.00. . . 

32I3-53- ■■ 
3214.17. . . 
3216.93. . . 

32I7-93- • ■ 
3219.92. . . 
3221.41. . . 
3221 .81. . . 
3223.66. . 
3225.19. . 
3227.11. . 
3233-o6- 
3 2 33-28*. 
3234.00. . 
3234-78. • 
3235-86.. 
3243.20. . 

3245-47- • 
3248.56. . 

3249.55. • 
3250.90. . 
3264.56. . 
3268. 21. . 
3269.08. . 

3271-25. • 
3282.03. . 
3282.81.. 
3282.96. . 
3284.56. . 
3287.08.. 
3287.36. . 
3305-IO. . 
33°7-l6. . 
3309 • 56 ■ • 
3310.35. . 

33I2.49. • 
33I3-I5-- 

33I5-82.. 
3320.42. . 
3320.92. . 
332I.36- • 
3322.50. . 
3326.80. . 
3327.52. • 
3328.85.. 

333^-3^- ■ 
3335-72. . 
3337-15- • 



Arc 



411 

5 

5n 

7 

5 

8 

3 

5 
ior 

3 
ior 

5 
25R 

4 

2 
ior 

4 
25R 

411 

8 

6 

9 

211 
411 
211 
10 

5 

8 

5 
4 



211 

5 
10 

4 
30R 
20R 

6 

2 
15* 

4 

4 

5 

6n 

211 

4 



Furnace 



High 
Temp. 



tr 



tr 

15R 

1 

12R 

7 
25R 



12R 

4 
25R 



Medi- 
um 
Temp. 



ior 

5 
ior 



ior 

tr 



30R 
20R 
tr 



15R 



tr 



4 
20R 



3 
20R 



Low 
Temp. 



25R 
I5R 



5 

3 

i5r 



5 
3 



i2r 
8r 



FURNACE SPECTRA OF COBALT AND NICKEL 
TABLE 11— Continued 



357 



Furnace 



Arc 



3 
411 



20R 

6 

4 

5 

15* 
20R 

IO 

8 
8oR 
i5f 
i5r 
15 

2n 

4 
8oR 

i5r 
3 

5oR 

iooR 

6 

8 



25R 
I i2r 
150R 

5 

7 

4 

4 
50R 
70R 

2 
30R 

5 

4» 

211 



High 
Temp. 



20R 

5 
tr 

tr 

I5R 

20R 

2 

8r 
80R 
15R 
15R 

3 



SoR 

15R 

4 

50R 

100R 



12R 

25R 

15R 

150R 

6 



50R 
70R 

30R 



100R liooR 



40R 

125R 

125R 

12 

4 

15 

70R 



40R 
125R 
125R 

12R 



15R 
70R 



Medi- 
um 

Temp. 



3 
15R 



1 or 

15R 

1 

6 
60R 
i2r 
i2r 

2 



50R 

i2r 

4 
40R 
70R 



tr 
1 
1 or 
20R 
i2r 
100R 

5 

tr 



30R 
50R 

25R 

tr 



60R 

25R 
70R 
70R 

8 



1 or 
40R 



Low 

Temp. 



Sr 
4 



6 
8r 



5 
30R 



25R 

8 

3 

20R 
40R 



50R 

4 



I5R 
30R 
tr 
15R 



35R 



Class 



III 

V 

IV 

II 
II 
I 
rv 

IV 

11 

11 

in 

11 

11 

11 

11 

11 

Y 

Y 

II 

II 

I 

II 

II 

V 

III 

III 

II 

II 

II 

II 

I 

III 

V 

Y 

II 

II 

II 

II 

III 

V 

V 

Y 

II 



15R II 
40R II 



45R 

6 


II 
II 
Y 
II 
II 


8 
20R 



(ExNER AND 

Haschek) 



3476.80 
3478.00 
3478.42 

3479 36 

3480.30 

3483.98 
3485-25 

3486 . 09 

3488.43 

3493 11 
3496.47 
3501.02 

3502.73 
35°7-85 
35io.52 
351176 

3514. 10 
35I5.2I 

3516.33 
3518.80 

351997 
3S23.23 
352361 
3524.68 
3526.67 
3528.13 
3528.70 
3530.73 
3548.32 
355I.7I 
355364 
3560.05 

356190 
3566.51 
3572.02 
3576.o8 
357736 
3588.07 
3597-86 
3602.41 
3604.41 
3607 . 00 
3609.48 
3610.61 
3612.90 
3619.52 
3624.89 
3630.03 
3635.1° 
3641-75 



Furnace 



Arc 



2n 

2 

3 

3 

4 
25R 

2n 
10 

2 
150R 

5 
25R 

8 

8 
80R 

2 

15 

150R 



20R 

4 

10 

200R 

3 
15 

3 

4 
2or 

8 

7 

2 

10 

100R 

50R 

2 



50R 

15 

1 

4 

15 

60R 

30R 

150R 

15 

5 
12 

4 



High 
Temp 



tr 



25R 



150R 
tr 

25R 

8r 

8r 

SoR 

2 

15R 
150R 



20R 

4 
ior 

200R 



15R 



1 
20R 

8r 
6 



ior 

100R 

50R 



Medi- 
um 
Temp. 



20R 



100R 



20R 

6 

6 

50R 

1 

ior 

100R 

1 

15R 

4 

8r 

125R 



ior 



15R 

7 
5 



5 
i2r 

50R 

i5r 
3 



60R 
40R 



i5r 
60R 
30R 
150R 
i5r 



ior 
40R 



ior 

50R 

15R 
SoR 



Low 
Temp. 



60R 



i2r 

5 

5 
25R 



60R 



8r 

4 

6 

SoR 



6 
30R 
20R 



4 

7 

2sR 



30R 

ior 

50R 

6 



Class 



V 

Y 

IY 

Y 

Y 

II 

V 

II 

V 

II 

Y 

II 

I 

I 

II 

III 

II 

II 

III 

III 

II 

I 

II 

II 

V 

II 

V 

III 

II 

I 

I 

Y 

II 

II 

II 

V 

I A 

II 

II 

II 

III A 

V 

II 

II 

II 

II 

II 

V 

I 

I 



358 



ARTHUR S. KING 
TABLE 11— Continued 



(exner and 
Haschek) 



3642 
3644 
3 6 47 
3657 
3662 
3664 
3666 
3668 
3669 
367O 

3674 



3689 
3694 
3697 
3713 
3715 
3722 

3724 
373° 
3736 

3739 
3739 
3744 
3749 
3772 
3775 
3778 
3783 
3792 
3793 
3807 
3831 
3833 
3858 



3909 
3912 

3913 
3944 
3962 
3970 
3972 
3973 
3974 
3984 
3994 
4006 
4017 



07 



Arc 



j 11 

2 



20 
/I0 

Us 



15 

4 

4 
15 
10 

3n 

5 

8 

6 
3 or 

5 
3or 

5 
8 

35r 
20 

S 
4or 

15 
8n 
8n 

5 
1211 

3" 
ion 
10 

25 
ion 

8n 

3n 

3 

6n 



Furnace 



High 
Temp 



6 
20R 



i2r 

20R 

8? 

i5r? 



lr 



15R 



5 
15R 



6 
30R 

5 
30R 

5 
8 

35R 
20R 

5 
40R 

5 



6 
20R 



Medi- 
um 
Temp. 



6 
i2r 



I2T 

8? 



I2r 
6 



5 

10 



6 
iSr 

5 
i5r 

5 

7 
20R 
i2r 

5 
30R 

3 



5 
ior 



Low 

Temp. 



5 
10 

5 
6 

i2r 
6 

5 
20R 



Class 



V 
V 

II 

V 

I 

II 

III 

V 

II 

II 
I 

II 
II 

V 

I 

V 

IV 

V 

II 

V 

I 

II 

I 

V 
V 

I 

I 

II 

I 

II 

I 

I 

II 

II 

I 

II 

II 

Y 
V 

I 

V 
V 
V 

I 
II 

V 
V 

V 
V 
V 



( exner and 
Haschek) 



4064.55. 

4075 . OO . 

4164.80* 

4I95-72. 

4200.60* 

4201 .89* 

4231.19 

4284.84 

4288.15 

4296.05 

4325-52 

4325-78 

433° -90 

433I-83 

435 6 07 

4359 -76 

4368.47 

4384.70 

4390-05 

4398.80 

4399 -78 

4401 .02 

4401.75 
4410.66 

4437-15 
4437-78 
4459 19 
4462.63 
4470 . 64 
4520.15 
4547" 
4547 38 
4592.72 
4600.56 
4605.17 

4606 . 38 
4648.85 

4667. I2f 
4667.92 

4686 . 39 
47OI.7O 
4703-97 

4714. 6of 

47i5-95t 

473i-98t 

4732-63 

4752-59 

4754-92 

4756.70 

4762.82 



Arc 


Furnace 


High 


Medi- 


Low 




Temp. 


Temp. 


Temp. 


2 

2 








5 


4 


2 


1 


6 


5 


2 


4 
5 








1 


1 


I 


5 


1 


1 


I 


5 
6 

15 

8 
2 
6 
2 
12 








tr 
tr 






















tr 










8 


6 


3 


3 


6 


3 


1 


10 
2 
5 
3 
3 
3 
3 

30 


1 
1 






































8 


4 


tr 


4 


1 


tr 




5 

2 

20 


tr 












6 


3 




10 


2 


1 




15 


4 


2 




4 


4 


3 


1 


5 


1 


tr 




3 
10 








2 


1 


tr 


6 
12 


tr? 

3 






1 




3 
15 








3 


2 


tr 


2 


? 


1? 




3 

5 








2 


1 




3 

4 

25 














6? 


4? 


2 


8 


2? 


1? 


tr 


3 
3 
4 


? 












1 


1 




3 
10 








4 


2 




3 


6 


4 


2 



FCRXACE SPECTRA OF COBALT AXD NICKEL 
TABLE II— -Continued 



359 



Arc 



37 

.90. 



59- 



.62. 
.61. 

19. 



•45- 
.62. 

■3& 
.50. 

•34 
•31- 

.40. 

•Si- 

.64. 
• 73t. 

.48. 

■52 

•37 

.00. 

.70. 

,29. 



. 3 8t. 
•55- 
•93 
23- 
•43 
.91. 
.61 

3i 
.90. 
.81. 



15 
2 

10 
2 

4 
10 
2 
3 
4 
2 

4 
4 
2 

3 
2 



4 

2 

10 

3 
12 

4 

4 

3° 



4 
5 
3 
8 

3 

10 

12 

4 

9 

6 



F URN-ACE 



„• , Medi- 
H'gh um 
Tem P' ( Temp. 



tr 



tr 



tr 



Low 
Temp. 



tr 



Class 



III 

II 

III 

III 

III 

III 

V 

V 

III 

IV 

III 

V 

III 
III 

V 

III 
III 
III 

IV 

III 

IV 
V? 
V 

III 
III 
III 
III 
III 
III? 

IV 

III 

V 

V 

III 
III 
III 

V 

V 

V 

V 

IV? 

V 

V 

I 

V 
V 
V 
V 
V 

III 



(ExNER AND 

Haschek) 



5176. 12 

5184.78 

5192.66 
5197-35 
5216.58 
5220.30 
523561 
5268.52 
5353-6o 
537i- 60 
5411-41 
5424-87 
5436 • 08 
5462.69 
5477-12 

5495 15 
55io. 2of 
5553-93t 
5578.94 
5588.09 

5589 -58f 

5592-49 

5593-99 

5615 01 

5625.52 

5637-33 

5649.89 

5664.23 

5682.42 

5695 i9t 

5709.76 

5712.10 

57I5-2Q 

5748.58 

5754-89 

5761.03 

5805.40 

5831.82 

5858.00! 

5893- 11 
5997.02 
5997.80 
6007 . 54 
6053.91 
6086.53 
6108.36 
6111. 22 
6116.35 
6163.60 
6175.69 



Arc 



3 

4 
4 
4 
5 
4 
50 

2 

4 

2 

5 

5 



3n 
211 

3 

2 

5n 

8 

2n 

6n 

5n 



Furnace 



High 
Temp. 



tr 



1? 
12 



Medi- 
um 
Temp. 



Low- 
Temp. 



Class 



V 

IV 

V 

V 

V 

V 

V 

V 

II? 

IV 

V 

II 
II 

V 

I 

V 

IV? 

rv? 

1 
1 

IV? 

II 
III 

V 
V 
V 

V 
V 
V 

IV? 

I 
II 

V 

II 
II 

IV 
V 
V 
IV? 

II 

V 
V 

II 

V 
V 

II 

V 
V 
V 
V 



3 6 ° 



ARTHUR S. KING 
TABLE II — Continued 



(exner and 
Haschek) 



6177.OO 
6187.OO 
619I.48 
62O4.78 
6224. l8 
623O.33 
6256.60 
6258.87 
6259.79 
63I4.89 

6327. 7 9 f 
6339-40. 



Arc 


Furnace 


Class 


High 
Temp. 


Medi- 
um 
Temp. 


Low 
Temp. 


12 
2 

12 
2 

3 
2 

15 
2 
2 

15 
5 
7 








V 
V 

I 
III 

V 
V 

I 

V 
V 

II 
II? 

IV 








12 

2 


IO 

I 


8 








15 


12 


IO 








12 
6? 
I 


8 
4? 


6 
2? 







(exner and 
Haschek) 



6366 
6378. 
6483 
6586 
6598. 
6635 
6643 
6767 
6772. 
6914. 
7122. 



61. 

4of. 

08. 

52- 

74- 

32. 

89. 

99* 

55* 

83* 

54* 



Arc 


Furnace 


High 
Temp. 


Medi- 
um 
Temp. 


Low 
Temp. 


4 
5 
5 
6 

3 
3 
20 
20 
5 
3 
5 


tr 

1? 














6 
tr 


4 


2 






20 
15 


20 
12 


20 
IO 


3 


3 


3 









Class 



IV 

IV? 
V 

II 

IV 
V 

I 
I 

V 

I 

V 



3233-28 
3674- 30 

4164.80 

4200.60 
4201.89 

4953-38 

53 53- 60 

6677.99 

to 

7122.54 



REMARKS ON TABLE II 

May be concealed at high temperature by A 3233.06. 
Close doublet. Resolved at low temperature. 
Measured as A 4164. 70 in furnace spectrum. May be due 
to impurity. 

Very unusual type of Class I lines. 

Furnace line probably due to Co. 

Blend with Co at high and medium temperatures. 

Photographed with i-meter concave grating. 



the cooler vapor near the ends of the tube would be very ineffect- 
ive in recording its spectrum during the brief exposure at high 
temperature. 

Class II. — This class includes a large proportion of the stronger 
arc lines. In the region of shorter wave-length, wide reversals of 
these lines are frequent, in some cases the reversal persisting even 
at low temperature. The reversals are usually much wider in the 
furnace than in the arc at moderate current, and the appearance 
of the lines from the two sources is very different. The estimates 
of relative intensity are made independently for arc and furnace, 
the scales being adjusted so that the stronger lines are given the 



FURNACE SPECTRA OF COBALT AND NICKEL 361 

same intensity in the arc and in the high-temperature furnace. 
Lines of Class II usually remain strong at medium temperature 
in these spectra, but weaken at low temperature more than the 
lines of Class I, the distinction between the two classes being often 
based on this feature. 

Class III. — -These lines, whose characteristic is an initial 
appearance at medium temperature, form the most numerous class 
in the cobalt and nickel spectra. A large part of them show but 
slight change of intensity between the arc and the high and 
medium furnace temperatures, but some interesting exceptions 
appear, especially in the nickel spectrum. XX 5080.70, 5081.29, 
5084 . 20 are examples of very strong arc lines which appear only 
faintly in the furnace, but show at both high and medium 
temperature. 

Classes IV and V. — -These high-temperature lines, which are 
faint or absent in the furnace, are much more common in the 
nickel than in the cobalt spectrum. This is due partly to the fre- 
quent occurrence of the nebulous type among the nickel lines, but 
a large proportion of other strong arc lines, especially in the visible 
region, have not appeared in the furnace spectrum. In the cobalt 
spectrum, the lines in Classes IV and V are usually among the 
weaker arc lines which, however, are not given by furnace tempera- 
tures which show other lines as weak as these in the arc. 

Lines relatively weak in the arc spectrum. — -The number of lines, 
designated by "A" after the class number, for the production of 
which the arc appears to be less favorable than the furnace, is quite 
different for the cobalt and nickel spectra, the numbers being 40 and 
6, or 5 per cent and ij per cent, respectively, of the whole number 
of lines listed. This is in harmony with the greater relative rich- 
ness of the cobalt spectrum in the furnace as compared with the 
arc, the proportion of lines in Classes IV and V being much smaller 
than for nickel. 

DISTRIBUTION OF CLASSES ACCORDING TO WAVE-LENGTH 

As the detailed examination of the cobalt and nickel spectra 
covers 4000 A, it seemed of interest to see how the classes are 
divided within successive equal intervals, as of 500 A, throughout 



362 



ARTHUR S. KING 



this range. This is shown in Table III, which gives the percentage 
of each class of the total number of lines within the given 500 A. 

TABLE III 

Division* of Lines in Each 500 A among Furnace Classes 

(The figures give percentage belonging to each class of the total number of 

lines within 500 A) 



Class 


Cobalt 


Nickel 
























I 


II 


III 


IV 


Y 


I 


II 


III 


IV 


V 


A. 
3°00-3500 


7 


28 


5i 


13 


1 


10 


46 


7 


10 


25 


3500-4000 


23 


34 


30 


3 


4 


25 


40 


7 


1 


27 


4000-4500 


22 


9 


46 


9 


13 


7 


13 


17 


3 


60 


4500-5000 


13 


10 


60 


15 


2 





11 


49 


9 


3° 


5000-5500 


2 


9 


28 


27 


34 


5 


8 


20 


10 


5« 


5500-6000 


4 


26 


44 





26 


12 


19 


4 


23 


42 


6000-6500 


18 


6 


24 


14 


38 


9 


17 


4 


13 


56 


6500-7000 


43 


21 


14 





21 


33 


11 





11 


44 



The columns of Table III do not show a regular change in the 
percentages of any class as we pass along the spectrum. In 
each spectrum there is a grouping of Class I lines in the extreme 
red, while at the other end we find a large proportion of the lines 
from X 3000 to X 4000 belonging to the low-temperature Classes 
I and II, the lines of Classes IV and V being in a decided minority 
at the violet end, especially for cobalt. This is in harmony with 
the feature noted for other elements, that the furnace spectrum, at 
least for the medium and high temperatures, is relatively rich in the 
region of shorter wave-length as compared with the arc. The 
greater part of the lines which require arc conditions occur farther 
toward the red. There is a definite tendency in the furnace, as 
in the spectra of other light-sources, for lines exhibiting a similar 
behavior to group in certain regions, this probably resulting from 
series relations which have not as yet been worked out, and the 
occasional preponderance of a single class in a given region may be 
a consequence of such groupings. 

OCCURRENCE OF ENHANCED LINES IN THE FURNACE SPECTRUM 

The behavior in the furnace spectrum of a number of lines listed 
by Lockyer 1 as enhanced seems to render it questionable whether 

1 Tables of Wave-Lengths of Enhanced Lines, Solar Physics Committee, 1906. 



FURNACE SPECTRA OF COBALT AND NICKEL 



>6 3 



these are to be considered as of this class, or at least as a pronounced 
type of enhanced lines. The list follows with the furnace class of 
each line taken from Table I: 



3817 


01 


3843 


85 


3851 


09 


3852 


00 


3863 


75 


3870 


66 


3878 


90 


3898 


54 


3904 


23 


3925 


33 


3929 


43 


3946 


75 



Class 
II 
III 

I A 
III 
III 
III 



A Class 

3947 26 II 

396115 II 

3977-34 HI 

3987-2S I 

4014.09 II 



4023.55. 
4077-56 



III 

| v J (double) 



III 

V 

III 

III 

II 



4i45 
4160 

4244 

44i4 
4569 



31 
86 

42 

09 
48 



In the range from X 3800 to X 4100, the distribution of these 
lines as to furnace class is about what would be expected of the same 
number of lines taken at random, two lines of Class I even being 
found among them; while previous investigations have shown that 
typical enhanced lines, for which the difference between arc and 
spark intensity is large, are among the most difficult lines to obtain 
in the furnace. Exner and Haschek give most of these cobalt 
lines, as far as X 4100, as of the same intensity in arc and spark. 
From the evidence at hand it seems probable that they are not 
enhanced lines of the regular type, but may be similar to a group 
of iron lines discussed in a former paper, 1 which appear in the 
furnace and in the spectra of flames whose temperature does not 
seem to be very high. 

Among the enhanced lines of nickel as given by Lockyer, only 
X 3889.84 appears in the furnace, this being a Class II line, of 
moderate strength in the arc spectrum. 

EXPLANATION OF PLATE VII 

In this plate, the cobalt spectrum from X 3356 to X 3720 is shown 
in two sections for the arc and for three furnace temperatures. 
Leading features are the variations in relative intensity for lines 

1 ML Wilson Contr., Xo. 66; Aslrophysicai Journal, 37, 239, 1913. 



364 ARTHUR S. KING 

of different classes, the numerous wide reversals in the high- 
temperature spectrum, and the general richness of the low- 
temperature spectrum in this region. 

SUMMARY 

1 . The furnace spectra of cobalt and nickel have been examined 
from X 3000 to X 7100 with regard to the temperature at which 
a given line appears and its rate of increase in intensity as the 
temperature rises. The classification of lines on this basis includes 
840 lines in the cobalt spectrum and 423 in that of nickel. 

2. The leading features of the various furnace classes are dis- 
cussed, these being in the main similar to those observed in the 
furnace spectra of other elements. 

3. The number of lines relatively fainter in the arc than in the 
furnace is larger for cobalt than for nickel; while the nickel spec- 
trum shows a large proportion of lines, many of them of nebulous 
type, which require the arc conditions to give them strongly. 

4. An examination of the distribution of furnace classes through 
the spectrum shows a relative richness of the furnace spectrum 
at the violet end, and a tendency for lines of similar character to 
group in certain regions. 

5. A number of lines, especially of cobalt, which have been 
classified as enhanced appear in the furnace spectra, thus indicat- 
ing that they may not be enhanced lines of pronounced type. 

Mount Wilson Solar Observatory 
June 1915 



Minor Contributions and Notes 



NICKEL DEPOSITS ON GLASS MIRRORS FOR ULTRA- 
VIOLET PHOTOGRAPHY 

In the Astro physical Journal for December 1911, I described 
a method for the preparation of the nickel-on-glass mirror which 
I used for the ultra-violet photography of the moon. 

The difficulty in making successful electrolytic deposits of this 
metal on a silver film results from the circumstance that the nickel 
comes down under tension and strips the silver film from the' sur- 
face. I succeeded, however, by the use of a very dilute solution 
of the double sulphate of nickel and ammonium, to which a small 
amount of ammonia was added, in obtaining deposits sufficiently 
thick to answer the purpose. The deposit was not very bright, 
however, resembling a slightly tarnished iron surface. 

Since the publication of the paper above referred to, some experi- 
ments made by Hollard 1 on the behavior of various salts of nickel, 
made it appear worth while to renew the experiments with silvered 
glass mirrors. Hollard found that in the case of electroplating on 
metals very superior results were obtained with a solution of nickel 
fluor-borate, it being possible to obtain much thicker deposits 
without the "flaking-off," than was possible with the solutions 
used in commercial processes. 

I prepared a small quantity of this substance, and obtained 
such superior results on small silvered strips of glass that experi- 
ments on a large scale were at once commenced. The method of 
preparation of the nickel fluor-borate is as follows : A hot solution 
of 350 gm of sodium carbonate in one liter of water is added to a 
lukewarm solution of 600 gm of nickel sulphate in 5.5 liters of 
water. The precipitate thus formed is to be washed until the fil- 
trate shows no reaction (white precipitate) with barium chlorate. 
As it filters very slowly the quickest way to get rid of the sodium 

1 Bulletin Soc. Encouragement (Geneva), 118, 24, 1912. 

36S 



366 MINOR CONTRIBUTIONS AND NOTES 

sulphate is to allow the precipitate to settle for two or three hours 
in tall jars, pouring off the clear solution and then filling up the jars 
again. This process must be repeated three or four times, after 
which the material may be put into the filters, and subjected to 
further washing, until the barium chloride gives little or no reaction. 

Dissolve 130 gm of boric acid in 300 cc of boiling water, heating 
the liquid until the solution is complete. Cool rapidly by immersing 
the beaker in water, stirring constantly. The pasty mass thus 
obtained is put in a wax or gutta-percha beaker (which can be made 
from an old hydrofluoric acid bottle by cutting off the top) and 
250 gm of commercial hydrofluoric acid added. To this solution 
the nickel carbonate is to be added, a little at a time. Owing to 
the great bulk of the latter it is best to pour about 20 cc of the acid 
into a wax dish of, say, 300 cc capacity, and then add the paste until 
a little remains undissolved. The solution can then be poured 
into a glass vessel and a second lot prepared. At the end the 
solution must be distinctly milky, that is, there must be an excess 
of the carbonate. The solution is not yet complete and must be 
stirred rapidly overnight or for, say, fifteen hours by an electric 
motor with a bent glass tube fastened to its axle. It is then fil- 
tered from the undissolved carbonate. In working with the hydro- 
fluoric acid it is necessary to use the greatest precautions. A single 
drop falling on the root of the finger nail, even if washed off instantly 
under the tap, may give rise to a very bad inflammation of the 
whole finger which lasts for ten days or more. If an accident does 
occur, sodium carbonate and not ammonia must be used at once for 
the neutralization. Apparently the frightful nature of the burns 
occasioned by this acid are not generally realized, and the use of 
a pair of rubber gloves cannot be too strongly advised. 

Hollard recommends that the solution be subjected to elec- 
trolysis for an hour with a copper cathode and nickel anode before 
being used for the work desired. In my own case I utilized this 
preliminary run for the preparation of my nickel anode. 

As I happened to have only a sheet of nickel about 20 cm square, 
I decided to make the anode of nickel-plated brass. A thick piece 
of brass rod provided with a binding post was riveted to the center 
of a brass disk 40 cm in diameter. Nickel was deposited on this 



MINOR CONTRIBUTIONS AND NOTES 367 

from the solution, using a current of about 5 amperes. Six dry 
cells were found to be about right for the deposition. Of course 
a nickel disk would be preferable. Preliminary experiments were 
first made on small strips of plate glass silvered by Brashear's 
process. The silver film was dried, and the light deposit of white 
powder wiped from it with a pad of dry absorbent cotton. It was 
found that with two dry cells a firm, hard, and very brilliant deposit 
of nickel could be obtained in about fifteen seconds. Previous to 
the deposition of the nickel the sun's disk could be seen of a 
deep blue color through the silver film. The electrolytic deposit 
rendered the film quite opaque. 

To determine the effect of varying the time of deposition a strip 
was immersed to a depth of 1 cm for five seconds, then to a depth 
of 2 cm for an additional five seconds, and so on until five or six 
patches of nickel of varying thickness had been obtained. It was 
found that the five-second deposit was not nearly so bright as the 
others, it being distinctly brown by comparison. This is rather 
curious, as it is backed by the highly reflecting silver. It seems as 
if a certain definite thickness must be reached before the nickel 
film acquires its full reflecting power, and if we stop short of this 
point the loss due to insufficient thickness is by no means com- 
pletely compensated by the reflection from the underlying film 
of silver. 

Experiments were next made with more dilute solution, and it 
was found that the solution as first prepared (some 2 liters in 
volume) could be diluted with six or eight parts of water and still 
yield perfectly satisfactory deposits. In nickeling my large mirrors 
I have always used the diluted solution. 

A large circular wash-basin of white enameled iron was used for 
the electroplating work, the silvered glass mirror being laid flat 
in the basin, with the film up. Contact with the silver film was 
made by pressing a piece of very thin platinum foil against the 
surface with the finger. The foil was soldered to a copper wire 
which passed through a glass tube. 

At first I used two dry cells, as with the smaller plates, but the 
deposits on the large mirror were very bad. The metal came down 
in irregular patches; some portions of the surface received no 



368 MINOR CONTRIBUTIONS AND NOTES 

deposit at all, and others were colored bright yellow. It was sus- 
pected that the trouble resulted from insufficient current-density. 
Similar deposits were obtained on small plates, if an ordinary carbon 
filament lamp was included in the circuit. 

I then measured the current-density in the case of the small 
plates with a milliamperemeter. 

With an immersed surface measuring 2X3 cm a current of 
33 milliamperes was obtained, or 5 . 6 milliamperes to the square 
centimeter. This current-density gave beautifully bright deposits. 
The area of the large mirrors was then measured, and calculations 
showed that, in this case, a current of about 5 . 6 amperes would be 
necessary, for the radii of the two mirrors were 18 and 20 cm 
respectively. In the case of these mirrors, with two dry cells only, an 
amperemeter showed 1.2 amperes, four cells gave 2.8 amperes, 
while 6 cells gave 5.6 amperes, with a distance of about 3 cm 
between the anode disk and the silver film. Six cells were accord- 
ingly used in all subsequent operations. It was found best to make 
the contact between the platinum foil and the silver film before 
lowering the anode into the solution. If this was not done it often 
happened that the film was destroyed at the point of contact and 
the flow stopped. This resulted from the circumstance that the 
current-density at the first point of contact, formed between the 
platinum and the film, was too great for the latter to carry. Forty 
seconds were sufficient for a good deposit, in the case of the dilute 
solution, and the film was uniformly brilliant over its entire surface. 
In the case of very large mirrors it would be advantageous to have 
a number of contacts around the rim. The deposition can be 
watched by moving the anode from side to side. During the first 
few seconds the metal comes down in small patches of irregular 
form, which are brownish in color. These rapidly brighten, the 
spaces between them fill up, and in twenty or thirty seconds the 
reflecting power appears uniform over the entire surface. The 
anode is then lifted out, the disk removed from the solution and 
washed under the tap. 

The concave mirror which I am now using for ultra-violet 
lunar photography was figured by J. E. Mellish, of Williams Bay, 
Wisconsin. Its focal length is 55 ft., and the definition is perfect. 



MINOR CONTRIBUTIONS AND NOTES 369 

The deposition of the nickel film does not affect the resolving power, 
as far as I can see. 

Some experiments were made on the current-carrying capacity 
of thin silver films, a point which is of importance in the case of 
large mirrors, with but a simple electrode applied to the silver sur- 
face. A narrow strip of glass was silvered with a film of such thick- 
ness that a window backed by a brightly lighted sky appeared of a 
dark blue color through the film. The silver was scraped from the 
middle portion of the plate with the exception of a strip 1 . 5 mm 
in width and 5 or 6 mm in length. It was found that the narrow 
strip carried a current of 1 ampere, but burned out at 1 . 2 amperes. 
If a drop of water covered the strip, the current could be raised to 
2 amperes before the film was disrupted, the final disintegration 
of the film resulting from the explosion of stream bubbles. With 
a circle of contact 1 cm in diameter a current of 20 or 30 amperes 
could probably be delivered to the silver film in the case of the 
electroplating process, which would answer for a mirror very much 
larger than the ones used in the present case. 

It is perhaps worthy of mention that the silver films were 
deposited with a much smaller quantity of the solution than is 
usually recommended for Brashear's process. The 16-inch mirror, 
provided with a rim of paraffin paper, was silvered with but 5 gm 
of silver nitrate and 2 . 5 gm of caustic potash, each dissolved in 
about 70 cc of water. This is less than one-tenth of the amount 
customarily used for a 24-inch mirror. I mention this point, as 
repeated trials may be found necessary before a first-class deposit 
of nickel is obtained. 

These experiments form a part of an investigation now under 
way of the distribution on the moon's surface of the material, 
probably sulphur or sulphur-bearing rocks, which is shown only 
in photographs made with ultra-violet light. 

I have been aided in this work by a grant of $200.00 from the 
Gould Fund of the National Academy of Sciences. 

R. W. Wood 

East Hampton, Long Island, N.Y. 
August 1915 



37° 



MINOR CONTRIBUTIONS AND NOTES 



THE DISTRIBUTION AND SOME POSSIBLE CHARAC- 
TERISTICS OF THE SPECTROSCOPIC BINARIES 
OF CLASS M 

Attention may be called to the distribution of the known binary 
stars of Class M. A comparison with the Cepheid-Geminid vari- 
ables in this and other respects is also of some interest. 

From data available to date ten stars of Class M have been 
found to be binaries or to have variable radial velocities as 

follows : 

(3 Andromedae F Centauri 

+6 5 °36 9 +66°8 7 8 

a Ononis a Scorpii 

r} Geminorum 8 Sagittae 

c Muscae /a Cephei 

With the exception of + 66 8y8, these binaries show a strong 
preference for the Milky Way in contrast to the nearly uniform 
distribution of the other stars of Class M over the sky. 

The average galactic latitude of the nine stars is o°. 

Omitting /3 Andromedae, which is 30 from the central line, the 
average for the remaining eight is less than 7 . 

Three of these stars are variable with small ranges of brightness 
of the order of the Cepheids. These stars have also very small 
proper motions, comparable in this respect with the Cepheids. 

Only two orbits are available, of a Ononis and a Scorpii. 1 As 
both of these stars have very small proper motions, it is interesting 
to compare their orbits with those of the Cepheids, especially as 
one star is known to be variable in brightness. 

The principal elements of the two Class M stars are given 
below: 





ti 


P 


e 


Ctl 


m3 sinn 

(.m+mi)* 


a sin i 


P.M. 


V 




a 


8 




a Orionis. . 
a Scorpii. . 


O.9 
I . 2 


y 
6. 70 

5.8 


O. 24 
0.20 


255° 
289 


0.0029 
0.0020 


70,000,000 km 
60,490,000 


+ 0?OOI9 
- OOS 


+o?oo8 
- .003 


+ 5-4 km 
+6.1 



1 Bottlinger, in Astronomische Nachrichten, 187, ^3^ I0II > called attention to 
Ludendorff's observation of the similarity of the orbits of these two stars. 



MINOR CONTRIBUTIONS AND NOTES 371 

The points regarding these Class M stars to which I would 
direct attention are: 

1 . The strong preference of these binary stars of Class M for the 
Milky Way. 

2. The difference of the angles of periastron of the two orbits 
from the majority of the Cepheids by approximately 180 . 

3. The much larger values of a sin i of the two stars of the 
M-type group and their much longer periods than corresponding 
elements for Cepheids. 

4. The similarity of the two M-type stars to the Cepheids in the 
matter of masses of the secondary bodies. 

5. The generally small proper motions of the M-type binaries. 

6. The generally small radial velocities of these M-type stars. 
The average for the ten is 10 km. Omitting the large velocity of 
yu Cephei, the average for the remaining nine is 7 km. This is 
much below the average for the Class M stars found by Campbell, 
viz.. 17 km. 

There is some uncertainty in the velocities of the systems of 
four of these stars, but it can hardly affect the foregoing conclusion 
greatly. 

It is fully recognized that the data are very meager and sufficient 
only to suggest possible characteristics of the group. There seems, 
however, reason to believe that some of these may prove to be 
characteristics of this class of stars and that efforts in obtaining 
more observations and orbits will be well repaid. 

It seems highly probable that a Scorpii will be found to vary also 
in brightness through a small range. 

C. D. Perrixe 

Observatorio Xacioxal Argextino 

Cordoba 

May 8, 191 5 



372 MINOR CONTRIBUTIONS AND NOTES 

EDITORIAL NOTE 

The attention of contributors and all others concerned is directed to 
the fact that the duties of managing editor of the Astrophysical Journal, 
which have been carried by Mr. Gale for the past six volumes, have been 
resumed by Mr. Frost, beginning with the present volume. 

Manuscripts, proof sheets, books for review, and all editorial corre- 
spondence should be addressed to 

Editors of the Astrophysical Journal 
Yerkes Observatory, Williams Bay, Wisconsin 

Business correspondence should be addressed as heretofore to 

The University or Chicago Press 
Chicago, Illinois 



073. 



THE 

ASTROPHYSICAL JOURNAL 

AN INTERNATIONAL REVIEW OF SPECTROSCOPY 
AND ASTRONOMICAL PHYSICS 



VOLUME XLI! DECEMBER I 9 I J NUMBER 



THE SPECTROSCOPIC DETERMINATION OF THE 
SOLAR ROTATION AT OTTAWA 

By J. S. PLASKETT 
INTRODUCTION 

The value of the solar rotation obtained from plates made at 
Ottawa in 191 1 has already been published 1 by the writer in collabo- 
ration with R. E. DeLury. The present paper gives a summary 
and discussion of the measures of plates obtained in 191 2 and 1913. 
It was deemed desirable, for the sake of homogeneous discussion 
and comparison of the results for the three years, to publish my 
measures separately from DeLury's. which are not yet completed 
and will appear later. It may be mentioned at the outset that the 
differences found to exist between DeLury and myself in the 
measures of the same plates in 191 1 still persist in the same direc- 
tion, though slightly reduced in magnitude. 

The same apparatus and methods used in obtaining the 191 1 
plates, described fully elsewhere, 2 were employed in making the 191 2 
and 1913 plates. The plates of 191 2 were made by DeLury and the 
writer jointly, while those of 19 13 were made by DeLury and 

1 Astrophysical Journal, 37, 73, 1913, and Transactions Royal Society of Canada, 
1912, Sec. Ill, p. 1. 

2 Report of Chief Astronomer, 1910, p. 129, and Transactions Royal Society of 
Canada, 191 1, Sec. Ill, p. 107. 

373 



374 J- S. PLASKETT 

my son, H. H. Plaskett, during my absence at the Solar Union 
Meeting at Bonn. The quality for measurement of the 191 1 plates 
is considerably superior to those of 191 2 and these latter again are 
better than the 1913. This difference is due in the main to a 
change in the emulsion of the plates used, the 191 1 lot being 
especially sensitive and fine-grained, and also, partly, to greater 
care being used in the earlier plates in regard to development to 
obtain the most suitable density for measurement. Furthermore 
a greater number were made in 191 1, and the best of these being 
selected for measurement also tended to a better average of quality. 
It must be stated, however, that equal care and precautions to 
avoid all danger of systematic error were taken in 191 2, and I 
believe in 1913, as in 191 1, that the difference in quality refers 
only to the ease and accuracy of measurement of the plates. As 
will be seen later, the accidental errors of measurement of all these 
plates are small in comparison with the systematic differences 
involved. 

All the 191 2 and 1913 plates were measured on a Repsold 
Measuring Engine, the small differential quantities involved being 
obtained with its eyepiece micrometer, whose run was carefully and 
frequently determined by comparison with the attached calibrated 
scale. The multipliers required to reduce the displacements to 
velocities were obtained by measurements of the spectra with this 
scale. In the 191 1 plates four settings were made on a line in the 
center strip and two each on the corresponding line in the two 
outer strips, and, after all the lines had been measured, the plate 
was reversed on the engine and the measurement repeated. In the 
191 2 and 1913 plates, however, a reversing prism was placed on the 
eyepiece, and, after two settings on the center strip and one each on 
the outside strips had been made, the prism was rotated through 
90 and the same number of settings made on the apparently reversed 
position of the plate, the settings direct and reversed being com- 
pleted on one line before passing to the next. Hence only half the 
number of settings were made on the later plates, thus reducing 
by half the large amount of measuring required. 

The labor entailed in these measurements was further reduced 
by diminishing the number of lines measured. It will be remem- 



DETERMINATION OF SOLAR ROTATION 375 

bered that one of the subjects for investigation decided upon at 
the Solar Union Meeting in 1910 was to determine whether different 
lines or different elements gave systematic differences of velocity, 
and the large number of lines used in 1911, 19 atX 5600 and 15 at 
X 4250, were selected so as to include as many elements as possible. 
However, the results obtained in 191 1 seemed to be so decisive 
negatively, especially at X 5600, that it was not felt worth while 
to continue this investigation. Hence the number of lines measured 
at X 5600 was reduced to 12 in 1912 and still further reduced to 6, 
except in the equatorial plates, in 1913. In the X4250 region, 
however, the 15 lines were measured in 191 2, though this number 
was reduced to 7 in 1913. 

The purpose of thus reducing both the number of lines and 
the number of settings on a line was to enable more plates to be 
measured with the same amount of labor. This reduction was 
justified on the one hand by the failure to find any systematic 
differences of velocity for different elements and on the other by the 
fact that the measures of the 191 1 plates showed that the probable 
error of measurement of a plate, determined from the internal 
agreement of the lines on that plate, was less than one-fifth of the 
probable error of a plate as determined from the agreement of the 
plates among themselves. Hence a determination of the rotation 
obtained by doubling the number of plates and halving the number 
of lines measured on a plate would be of much greater weight. 
Even if no greater number of plates were used, the accidental error 
of measurement of a plate in which the number of lines measured 
was reduced to one quarter would still be less than half the plate 
errors and could not have an appreciable effect on the resulting 
values, while the lessening of the labor of measurement would be a 
decided advantage. 

Of the plates obtained in 191 2, 25 were selected in the X 5600 
region and 25 in the X 4250 region for measurement. On the X 5600 
plates spectra at eight latitudes, o°, 15 , 30 , 45 , 6o°, 75 , 8o°, 
85°, were made and measured, and on the X4250 plates the first 
six of these latitudes only. Of the 1913 plates 20 in the X 5600 
region at the same eight and 17 in the X 4250 region at the same 
six latitudes were measured. 



376 



/. S. PLASKETT 



The lines measured in these plates, the elements to which they 
belong, their intensity in Rowland's tables, and the multiplier to 
reduce the measured double displacement in millimeters to the 
velocities of the observed point on the limb in kilometers per second 
are given in Tables I and II. 

TABLE I 
Lines in X 5600 Region 



No. 


Wave-Length 


Elem. 


Int. 


Velocity 

Constant 


No. 


Wave-Length 


Elem. Int. 


Velocity 
Constant 


1 

2 

3 

*4 

*5.--.: 

*6 


5544- 157 
5560.434 
5562.933 
5569.848 
5576.320 
5578946 


Fe 

a 
it 

a 

Ni 


2 

2 
2 

6 

4 

1 


19. 118 
19.024 
19.OIO 
18.970 

18.933 
18.919 


* 8 

* 9 ... 
10. . . . 
11 ... . 
12. . . . 


5582.198 
5590.343 
5601 . 505 
5624.769 
5638.488 
5658.097 


Ca 
a 

a 

Fe-V 
Fe 
Y 


4 
3 
3 
3 
3 
2 


18.899 
18.852 
18.788 
18.653 

18-575 
18.461 



TABLE II 
Lines in X 4250 Region 



No. 


Wave-Length 


Elem. 


Int. 


Velocity 
Constant 


No. 


Wave-Length 


Elem. 


Int. 


Velocity 
Constant 


1 

2 

3 

*4 

*6 

*7 

*8 


4196.699 

4I97-257 
4216. 136 
4220.509 
4225.619 
4232.887 
4241.285 
4246.996 


La 
C 

Fe 

a 

Fe-Zr 
Se 


2 

2 

I 

3 
3 
2 
2 
5 


26.906 
26.902 

26.745 
26. 710 
26.666 
26.606 
26.502 
26.490 


* 9--. 
*IO. . . 

11 . . . 

12. . . 

13. . . 

14. - - 
IS--- 


4257-8I5 
4258.455 
4266.081 
4268.015 
4276.836 

4290.377 
4291.630 


Mn 
Fe 

Mn 
Fe 
Zr 
Ti 
Fe 


2 

2 
2 
2 
2 
2 
2 




26.400 
26.394 
26.331 
26. 296 
26 . 243 
26.133 
26.122 













In the X 5600 region the 12 lines were used in the measures of 
all the 191 2 plates and in the 19 13 plates at the equator, but in the 
1913 higher latitudes and in repeated equatorial measures of all 
three years only the six starred lines were used. In the A 4250 
region the 15 lines were used in all the 191 2 plates, but only the 7 
starred ones in the 1913 plates and in repeated equatorial measures 
of all three years. 

In the measures of the 191 1 plates two methods of reducing 
the measured values to the actual velocities were used, which, 
however, as was to be expected, gave practically identical results. 



DETERMINATION OF SOLAR ROTATION 



377 



Consequently in the 191 2 and 1913 plates only one of these 
methods has been used, that which was called the first method in 
the earlier paper and which depends upon the projection of the 
observed points to the limb, the obtaining of the corrections by 



TABLE III 
Summary of Measures, 191 2, X 5600 



Plate 
Number 



Date 
G.M.T. 



Velocities in Km per Second at Latitude Regions 



6o° 



898. 

899. 
900. 
901 . 
903- 
907. 
908. 
909. 

923- 
924. 

9 2 5- 

92O. 
927. 
928. 
929. 
930- 
93* ■ 
932. 



June 

5.20 

6.17 

6. 20 

6.24 

8.10 

8.12 

8.24 

13.16 

13.22 

13-35 

13-37 

14.18 

17.19 

17.21 

1723 

26. 21 

26. 23 

26.25 

26.30 

26.32 

26.34 

26.36 

27. 10 

27. 12 

2715 



2.055 
2.019 
2.013 
1-974 
1-956 
2.027 
1.994 
2.041 
2.047 
2.027 
2.043 
1.969 
1.978 
1. 961 
2.013 
2.006 
1.978 
1.997 
2.024 
2.026 
2.023 
2 .026 
2.051 
2.050 
2.060 



1.927 
1925 
1-873 
1.866 
1.882 
1 .890 
1.846 
1 .906 
1.908 
1 .900 
1.874 



1.866 
1.907 
1.852 

1-893 
1.842 
1.782 
1.827 

1.854 
1. 871 
1-851 
1.897 
1.866 



1.648 
1.636 
1.637 

1-637 
1.605 
1.639 
1. 718 
1.659 

1-655 
1.639 

1 .640 
1.628 
1.605 

1 .641 
1 .625 
1.578 

1-579 
1. 601 

1-557 
1-572 
1.603 
1.663 
1. 641 
1.628 
1 .604 



178 

245 
207 

243 
233 
219 

256 
237 
275 
271 
223 

257 
252 

234 
217 
270 
219 
252 
186 
188 
182 
179 
196 
216 
196 



0.766 
857 
831 
827 

835 
799 
831 
808 
807 

795 
806 
702 
804 
681 
725 
794 
796 
818 
898 
754 
833 
937 
806 

813 
764 



1.402 
. 292 
.277 
.326 
.420 
.440 
•405 
■371 
-398 
•397 
•437 
-359 
•385 
•396 
•379 
•332 
.367 
■35° 
•35i 
.318 

■352 
•354 
•396 
•347 
>-35* 



0.286 
•193 
•157 
. 211 
• 236 
.261 
.288 
•223 
.216 
•235 



.230 
.210 

.208 
. 262 

•239 
.246 

■2 75 
-263 
.280 

. 262 

■243 
. 271 
1.231 



094 
148 
132 
116 
141 

117 
120 

"5 
084 

125 
128 
116 
122 
147 
158 
145 
i54 
145 
*33 
149 

155 
145 
116 
144 
157 



Mean linear velo- 
city 

Mean angular ve- 
locity 

Mean latitude . . 

Probable error 
plate 



2 .014 



i4-3i 
o°o' 



1.874 

13-77 
15V 



1.627 

i3°34 
29°59' 



0.803 0.368 



12. 29 

44°58' 



n?38 
59°57' 

0.031 



10.03 

74°57' 



0.026 



0.243 

9°79 

79°5i' 



0.13: 



84?42 



0.022 0.013 



Duner's methods and tables, and the application of a final 
correction, necessary owing to the distance of the observed 
point from the limb, to allow for the change of rotation with 
latitude. 



378 



/. 5. PLASKETT 



MEASURES OF PLATES 



However desirable it may be to publish the individual velocities 
of the lines on the plates, it will be evident that this cannot be 
done here, when it is realized that 222 spectra were measured on 



TABLE IV 

Summary of Measures, 1912, X4250 



Plate 
Number 



Date 
G.M.T. 



Velocities in Km per Second at Latitude Regions 



940. 
942. 
943- 
944- 
948. 
949- 
95° • 
952. 
953- 
954- 
955- 
956- 
957- 
959- 
960. 
961 . 
962. 

9 6 3- 
964. 

965- 
966. 
967. 
968. 
969. 
970. 



October 
5 14 
5 19 
5- 2 3 
5-25 
8.20 
8.23 
8.25 

12. 14 

12. 16 
12.18 
12. 20 
12. 24 
12. 27 
16. 11 
16. 14 

16. 17 
16. 19 
16. 22 
16.24 

16. 26 
16.28 
17.17 

17. 20 
17. 22 
1725 



•95° 
.025 
.030 



2.013 

1-957 
2.022 

1-979 
2.002 
2.081 
2.078 
1.982 

1-974 
2.019 
2.031 
2.058 



.996 
.025 
■952 
.919 
•931 
■934 
.970 



1 .900 

1875 
1.962 
1. 918 
I-93I 
I-9I9 



875 
•952 



1.967 
1 .962 
1. 871 
1.932 
1 .922 
1 .910 
1.948 
1. 914 



1-939 
I-95I 



1 .662 

1-745 
1. 671 
1.672 

1 • 564 
1.562 
1.639 
1 .609 
1.628 
1-633 
I-7I4 
1 . 700 

1-774 
1.697 
1.699 
1 .670 
1.649 

1-634 
1.667 
1.723 
1.729 
1.660 
1.659 
1. 719 
1.748 



1 . 214 
1 . 210 
1. 248 
1.249 
1 . 260 
1 . 207 

1 193 

1 . 269 
1.282 
1.263 
1. 217 
1-235 
1-338 
1. 291 
1. 318 
1 . 270 
1.275 
1234 
1.247 
1. 251 
1. 207 
1.469 
1.390 

1 -341 
1.329 



776 
790 
851 
825 
790 
782 
824 
874 
854 
820 

831 

845 
845 
823 

792 
811 
746 
736 
829 
806 

847 
991 

033 
896 

9°5 



292 
370 
388 
409 
462 
452 
371 
325 
300 

357 
367 
372 
416 
406 
392 
364 
427 

403 
433 
446 
432 
498 
401 
321 
323 



Mean linear velocity . . 
Mean angular velocity 

Mean latitude 

Probable error plate . . 



2.005 

14-24 

oV 

0035 



1. 914 
i4?o6 

I4°55' 
0.024 



1.673 
I3-70 

29°52' 

0.035 



1 . 272 

I2?70 

44°42' 
0.040 



0.832 
n?6 3 

59°2 9 ' 
0.037 



0.389 
9°96 

73°54' 
0.034 



the 1911 plates, 350 on the 1912, and 262 on the 1913, making a 
total of 834 spectra measured and reduced. The total number of 
lines measured was over 11,000 and of settings over 120,000. 

Hence all that will be given here are the reduced velocities for 
all latitudes on all the plates of 191 2 and 1913 with the number 



DETERMINATION OF SOLAR ROTATION 



379 



and Greenwich mean date of the plates. The mean linear and 
mean daily angular velocities at the mean latitudes are given 
at the foot of the columns with the probable errors of single 
plates. 

Table VII contains a summary of the mean values for the differ- 
ent latitudes for the four series in 191 2 and 1913 and also for the 



TABLE V 
Summary of Measures, 19 13, X 5600 









Velocities in Km per Second 


at Latitude Regions 




Plate 


Date 
G.M.T. 


















Number 






















0° 


15° 


3°° 


45° 


6o° 


75° 


80° 


85° 




June 


















979- 




6.30 


2.031 


I.940 


1-645 


I.225 O 


815 


365 


O. 206 


0.125 


985. 




9-23 


1. 961 


I. 841 


I.647 


1-257 


899 


397 


.209 


•113 


986. 




9-25 


1-953 


I.903 


I.678 


1-351 


819 


439 


.218 


.061 


987. 




IO. 20 


2.017 


I.894 


I.560 


1. 167 


823 


39i 


■243 


•135 


988. 




IO. 21 


2. on 


I.879 


I .600 


1 . 206 


788 


39o 


■239 


.178 


989. 




IO.24 


2.017 


1-795 


I.63O 


1 . 226 


840 


408 


. 204 


. 170 


990. 




IO.25 


2.034 


1-905 


I.626 


1-253 


773 


395 


•293 


■145 


992. 




IO. 27 


2.019 


1. 841 


I.628 


1. 176 


795 


35o 


. 219 


. 200 


994- 




IO.3O 


2.008 


1.895 


I .620 


1-234 


753 


322 


.218 


.108 


996. 




IO.32 


2.008 


1 .912 


I .642 


1.249 


740 


377 


-244 


. 146 


998. 




IO-3S 


1.979 


1.887 


I-65I 


1 . 222 


836 


403 


•231 


• T 4 2 


1000. 




IO-37 


1.986 


1.890 


I.674 


1.299 


785 


328 


.246 


.128 


1003. 




13.22 


1.999 


1.940 


I.679 


1-233 


798 


306 


.267 


•105 


1005. 




I3.26 


1-954 


1.880 


I.648 


1.244 


781 


3i3 


■243 


151 


1007 . 




13.28 


1.930 


I-9I3 


1-653 


1. 197 


792 


353 


.283 


.114 


IOII . 




15-23 


1.964 


1.889 


I.580 


1 . 226 


819 


347 


.290 


.117 


1013. 




15.26 


1-939 


1.839 


I-590 


1 . 192 


810 


357 


.278 


. 112 


1015. 




15.28 


1.963 


1.904 


1-554 


1 . 221 


853 


393 


. 201 


.138 


1017. 




15-31 


2.015 


i-9i7 


1-539 


1 . 219 


805 


392 


■275 


.076 


1018. 




I5-3- 1 


1.998 


1.942 


1 567 


1.232 


823 


362 


O.268 


0. 124 


Mean linear velo- 


















city 


1.989 


1. 891 


1 . 621 


1.237 


807 


369 


O.247 


0. 129 


Mean angular 




velocity 


14? 1 1 


13-90 


13-29 


i2?36 1 


[?46 ic 


)°IO 


io?07 


io? 34 


Mean latitude . . . 


o°o' 


1 5°°' 


30V 


45V 6 


o°o' -]l 


1°58' 


79°58' 


84°55' 


Probable error 


















plate . 




0.022 


0.022 


0.030 


0.022 


022 


025 


0.020 


O 020 











two series in 191 1. When each of these values is reduced by the 
final mean formula to the even latitudes and the weighted mean 
for each latitude taken, we have the mean values in the last 
column of the table. The velocities are expressed in kilometers 
per second. 



3 8o 



J. S. P LAS RETT 



DISCUSSION OF VALUES 

In discussing and comparing the values we notice first of all 
that the total range of velocity for any one latitude in any series 
obtained from Tables III-VI is rather higher than would be ex- 
pected, the average total range being 0.157 km per second, the 
smallest being 0.074 and the largest, 0.297. Further, it can be 
seen from Table VII that the mean values for each latitude, except 

TABLE VI 

Summary of Measures, 1913, ^425o 



Plate 
Number 



Date 
G.M.T. 



Velocities in Km per Second at Latitude Regions 



30° 


45° 6 


0° 


1.684 


1.274 ° 


852 


1.669 


1.268 


866 


1.638 


1 . 214 


877 


1-545 


1. 142 


798 


1. 581 


1 . 207 


740 


1.742 


1-275 


782 


1.625 


1. 182 


814 


1-534 


1 195 


823 


1 . 702 


1.223 


847 


1-675 


1.230 


819 


1 .671 


1.284 


846 


1.648 


1.348 


790 


1.644 


1 . 214 


777 


1-593 


1 . 267 


804 


1-738 


1. 218 


876 


1-544 


1. 318 


939 


1.650 


1.286 


816 


1 .64c 


1 . 244 


828 


13-42 


I2?44 1 


[^62 


29°5°' 


44°45' 5 


9>' 


0.042 


0.037 


031 



1030. 
1031. 
1032. 

i°35- 

1050. 

i°55- 
1056. 
1061 . 
1063. 
1065. 

i°73- 
1076. 
1077. 
1078. 
1081. 

109 1 . 
1092. 



June 
25.22 
25 -3° 
27-15 
28.17 
July 
11 . 20 
13.10 

16. 14 
17-35 
18.34 
19.18 
25.18 
26.13 
26.16 
26. 19 
28.32 

August 

11. 15 
II . 20 



1. 971 
I.924 
I.932 
2.00I 

1. 919 

2.089 
2.009 
I.938 
I.979 
I.920 

1-995 
2.009 

1-974 
1-952 
1.929 

1.958 
2.003 



1.942 
1 .906 
1.869 
1.844 



1 .901 

1 -931 
1.839 
1.777 
1.863 
1.882 
1.827 
1.880 
1. 817 
1 .901 

1. 919 



392 
406 
406 
361 

380 
45i 
45° 
375 
336 
343 
438 
367 
385 
408 

35i 

394 

405 



Mean linear velocity . . 
Mean angular velocity 

Mean latitude 

Probable error plate . . 



1. 971 
i4?oo 

°°3' 
0.029 



1.876 
i3?78 
i4°54' 
0.029 



0.391 

IO?22 

74°i4' 
0.023 



the two highest (8o° and 85 ), vary over a total range of between 
0.040 and 0.052, but that these differences do not run regularly: 
the series having high values at the equator may have low values 
at the higher latitudes and vice versa. The run of these differ- 
ences seems to be in the main accidental, and there is no indication 
of any regular or systematic law governing them. 1 It will be 

1 A possible exception to this may be pointed in that the angular values at 8o° 
are systematically considerably lower than at 85 . 



DETERMINATION OF SOLAR ROTATION 



38i 



noticed further that both series in 1913 have lower values at the 
equator than in 191 1 and 191 2, although at the higher latitudes 
this difference is not maintained; for example, in 1912, X 5600 has 



TABLE VII 
Summary of Mean Values 



Year ign 


191 2 


1913 


Mean 


Region ! A 5600 


A 4250 


A 5600 


A 4250 


A 5600 


A 4250 


Values 
Reduced 


Number of Spectra 


19 


24 


25 


25 


20 


17 


Latitude 


Latitude 

Linear velocity . . 
Angular velocity . 

Latitude 

Linear velocity . . 
Angular velocity . 

Latitude 

Linear velocity. . 
Angular velocity . 

Latitude 

Linear velocity . . 
Angular velocity. 

Latitude 

Linear velocity . . 
Angular velocity. 

Latitude 

Linear velocity . . 
Angular velocity. 

Latitude 

Linear velocity . . 
Angular velocity. 

Latitude 

Linear velocity . . 
Angular velocity 


oV 
2.017 
i4?32 

i5°o' 
1.886 
i3?86 

29°58' 
1.652 

13-54 

44°52' 
1.273 

i2?75 

59°46' 
0.809 
n?4i 

74°28' 
0.417 
n?o5 

79°53' 
0.247 

9-98 

8 4 °47' 
0.131 

IO?23 


o°o' 
2.012 
14? 28 

29°59' 
1.625 

13-32 

59°53' 
.788 

11-15 


oV 
2.014 

14-30 

15V 
1.874 
13-78 

2 9 °59' 
1 .627 

i3 ? 33 

44°58' 
1.225 

I2?29 

59°57' 
803 

11-38 

74°54' 

.368 

io?03 

79V 

• 243 
9-79 

8 4 °42' 

.132 

io?i5 


oV 
2.005 
14-23 

i4°55' 
1. 914 

i4?oo 

2 9 °52' 

I 073 
I3-70 

44°42' 
1 . 272 

I2?70 

59°29' 
.832 
n?63 

73°54' 
•389 
9-96 


o°o' 

1.989 

i4?n 

15V 
1. 891 
I3-90 

30V 
1. 621 
I3°29 

45°o' 
1. 231 
i2?36 

6o°o' 
.807 
n?46 

74°58' 
•369 

IO?IO 

79°58' 
.247 
io?07 

8 4 °55 
.129 

io?34 


o°3' 
1. 971 

i4?oo 

i4°54' 
1.876 
13-78 

2 9 °5o' 
1 .640 
13-42 

44°45' 
1.244 
I2?44 

59°36' 
.828 

II?62 

74°i4' 
•391 

IO?22 


oV 

2.003 

I4?20 

15V 

1.889 

13-88 

30V 
1.639 
13-41 

45°o' 

1 . 246 

I2? 5 I 

6o°o' 

.805 

n-43 

75°o' 
•373 

IO?23 

8o°o' 
■ 247 

IO?IO 

8 5 °o' 

.127 

io?34 



values generally lower at the higher latitudes than both series in 
1913, though its equatorial value is considerably higher. 

In order to smooth out these irregularities for each series and 
in the mean, it will be desirable to obtain the formulae connecting 
the change of velocity with latitude. Formulae of the Faye type 



\S2 



J. S. P LAS RETT 



have been generally used, not only for the spectroscopic determina- 
tions, but also in the case of rotation determined from sun-spots, 
faculae, and flocculi. These formulae seem to represent the obser- 
vations within the limiting accuracy of the values obtained. 

In the present case the following forms have been employed, as 
they have the advantage that the a and a' constants give the 
equatorial velocities directly. 

Linear velocity, V= (a—b sin 2 <£) cos <£ 
Angular velocity, i = a! —b' sin 2 cf> 

Owing to difficulty in suitably weighting the different latitudes, 
the angular formulae have been obtained directly from the linear 
by substitution. The constants which are tabulated in Table VIII 
have been obtained by least squares by combining the observations 
in three different ways: 

i. Each of the six series of plates have had independent con- 
stants computed. 

2. The two series in a year have been combined, thus giving 
three yearly constants. 

3. All the observations in the three years have been combined, 
giving the mean Ottawa constants. 

TABLE VIII 
Constants of Faye Formulae 







Linear 


Angular 


\ear 


Region 














a 


b 


a' 


b' 


1911 


X 5600 

X 4250 

Both Regions 


2.0I2 

2.016 
2.0I2 


0.500 
■587 
5l8 


I4?28 

I4-3I 
14.29 


3-55 
417 
3.68 


1912 


X 5600 

X 4250 

Both Regions 


2.002 
2 .C22 
2.0I2 


■558 
•514 
•541 


14.21 
14-36 
14.28 


3-90 
3 64 
384 


!9!3 


X 5600 

X 4250 

Both Regions 


1-993 

1 .980 
1.988 


■SIS 
.470 
.498 


i.4- 14 
14.06 
14. 11 


3-68 
3-34 
3-54 


I9II-I2-I3 


All Plates 


2.006 


O.522 


14.24 


3-71 






DETERMINATION OF SOLAR ROTATION 



3%3 



The differences in the constants above given for the 191 1 plates 
from those previously published are due, in the linear values, to 
limiting the rotation results to those obtained by the first method 
of reduction; and, in the angular values, to substituting from the 
linear constants instead of computing directly. 

Although these constants, especially the b and b' ', may seem to 
vary considerably, we find that they may be altered over quite 
wide limits without appreciably increasing the residuals between 
the observed velocities and those computed by the formulae. 
Table IX gives the residuals between the observed velocity at each 



TABLE IX 
Residuals ix Kilometers from Formulae 







Residuals 






Resdduals 


Latitude 


Observed 
Velocity 












Latitude 


Observed 
Velocity 


Inde- Y 

pendent 












Inue- 
pendent 


Yearly 


Mein 






irly 


Mean 


1911 














iqi2 














A 5600 














A 4250 














0° 2.' 


2.017 


+0 


.005 


+0 


.005 


4-O.OII 


o° 0' 


2.005 


— O 


.017 — O 


.007 


— O 


.OOI 


15 ° 


1.886 


— 


.024 


— 


.024 


- .018 


14 55 


1. 914 


— 


• 005 4- 


.005 


+ 


.009 


29 58 


1.652 


+ 


.017 


- 


.021 


+ .027 


29 52 


1-673 


+ 


• 031 4- 


.044 


+ 


■045 


44 52 


1-273 


+ 


.024 


+ 


.030 


4- .036 


4442 


1 . 272 


+ 


.016 4- 


.032 


+ 


•033 


59 46 


.809 


— 


.016 


— 


.007 


— .001 


59 29 


.832 


— 


.001 + 


.014 


+ 


.Oil 


74 28 


• 417 


+ 


.002 


+ 


.007 


4- .012 73 54 


•389 


— 


.040 — 


.031 


— 


■ 033 


79 53 


• 247 


— 


.022 


— 


.Ol8 


- .018 
















84 37 


•131 


— 


.006 


— 


.005 


- 003 


1913 

A 5600 














IQII 

A 4250 














O O 


1.989 - 


.004 4- 


.001 


— 


.017 














15 O 


I. 891 ± 


.000 + 


.002 


— 


.012 


O O 


2.012 


— 


.004 


=fc 


.OOO 


4- .006 


30 O 


1. 621 - 


.007 + 


.008 


— 


.003 


29 59 


1.625 


+ 


.006 


— 


.006 


± .000 


' 45 


1. 231 


+ 


.007 + 


.002 


— 


.003 


59 53 


.788 


— 


.003 


— 


.026 


- .018 


60 


.807 


+ 


.005 ± 


.000 


zfc 


.000 
















74 58 


-369 


— 


.022 — 


.027 


— 


• 025 


1912 














79 58 


•247 


— 


.013 - 


.016 


— 


.014 


A 5600 
O O 


2.014 


+ 


.012 


+ 


.002 


+ .008 


84 55 


. 129 


— 


.001 


— 


.003 


— 


.002 


15 O 


1.874 


— 


.024 — 


•O34 


- 030 


1913 
















29 59 


1 .627 


+ 


.014 4- 


.OOI 


4- .002 


A4250 
















44 58 


1.225 


+ 


004 — 


.007 


— .011 


3 


1. 971 


— 


. 009 — 


.017 


— 


• 035 


59 57 


.803 


+ 


.010 — 


.002 


— .006 


14 54 


I.876 


— 


.006 — 


.013 


— 


.029 


74 54 


.368 


— 


.018 


— 


.025 


— .027 


29 50 


1 .640 


+ 


.023 4- 


.023 


+ 


013 


79 5i 


• 243 


— 


.014 


— 


.OI9 


— .021 


44 45 


I.244 


+ 


.003 


+ 


.008 


+ 


.004 


8442 


.132 


—0 


.001 


— C 


.004 


- 005 


, 59 36 


.828 


+ 


.003 


+ 


.009 


+ 


.010 
















74 14 


■391 


— 


.027 


— 


.024 


— 


.022 


Means 














Means 
















O O 


2.003 
1.889 
1.639 
1 .246 










- 003 

— .015 


60 O 


.805 

■373 

■247 

0. 127 










— 


.002 


I ? O 






75 ° 
80 









.020 


30 O 
45 






4- .015 
+0.012 









.014 






85 






— C 


.002 













384 /. 5. PLASKETT 

latitude in each series and the velocity computed from the three 
sets of constants, the independent, the yearly, and the general 
mean. It is at once seen that the differences between these are 
relatively very small in each series, and it may safely be said that 
all the Ottawa observations are satisfactorily represented and that 
the law of variation of velocity with latitude is given by the for- 
mulae 

Linear velocity, V= (2.006 — 0.522 sin 2 <f>) cos <f> 
Daily angular velocity, £=14? 24 — t,°.ji sin 2 <£ 

Returning now to the discussion of the differences in rotation 
values for 1913 and 191 1 and 191 2, and the irregularities in the mean 
values for the same latitudes, it was previously pointed out that the 
former consisted chiefly in a diminished value, about 2 per cent, at 
the equator. When the irregularities were partially smoothed out 
by the formulae, this was reduced to about 1 per cent. Table IX 
shows that, although the mean formula represents all the series 
without introducing residuals abnormally large, there still remain 
these residuals and the irregularities in the mean values, as well as 
the large ranges in the individual values, to be accounted for. 

CAUSES OF DIFFERENCES 

These differences and irregularities may be attributed to one or 
more of three causes: 

1. Systematic instrumental errors in the plates obtained. 

2. A change in the habit or personal equation of measurement of 
the observer. 

3. A change or changes in the rate of rotation of the sun. 

1 . Systematic instrumental errors. — This question was quite fully 
discussed in the earlier paper and not much need be added to what 
was there said. The four essential precautions to prevent syste- 
matic instrumental displacements, which were there given and which 
have been scrupulously followed throughout the observations, may 
be here repeated. 

a) The emulsion on the photographic plate must be exactly in 
the focus of the spectrum. 

b) The illumination of the grating from the opposite limbs of 
the sun must be similar and uniform. 



DETERMINATION OF SOLAR ROTATION 385 

c) The solar definition must be good, the image steady, and the 
sky free from haze. 

d) Care must be taken that the reflecting prisms receive light 
from the desired and supposed latitudes. 

The focus was most carefully determined repeatedly both by the 
test and by the Hartmann extra-focal method and could never have 
been sufficiently out to produce any appreciable displacement even 
if condition b was not exactly fulfilled. Nevertheless the reflecting 
prisms in front of the slit were always adjusted before each plate 
was exposed so that the circles of illumination from the two limbs 
were exactly superposed and central over the exposed part of the 
grating surface, which was only about half the diameter of these 
circles. The illumination was always examined after the exposures 
were finished to see that no change had occurred. 

Owing to the large size, 225-230 mm, of the solar image given 
by the Ottawa coelostat telescope considerable advantage so far as 
condition d is concerned prevailed over other observers of the solar 
rotation where the images have been considerably smaller; and the 
ease and accuracy with which the spectrograph can be rotated to 
any desired position angle around the optical axis facilitated the 
exact setting to and determining of the solar latitudes observed. 

Furthermore, the practice, first adopted here, I think, in the 
case of the solar rotation, of placing a narrow strip of spectrum from 
the one limb of the sun between two strips of exactly the same width 
from the other limb, completely eliminates the possibility of error 
arising, in the case of only one strip from each limb, from the 
micrometer wire not being parallel to or remaining parallel to the 
lines of the spectrum. 

So far as can be seen, therefore, the probability of any systematic 
instrumental error in these observations is slight. Independent 
confirmation of this is given by the fact that observations made in 
1910 1 with a different grating and other varying experimental 
conditions gave a mean velocity at the equator for ten plates of 
2. on km per second, almost exactly the same as in 1911 and 1912. 
When a possible change in the habit of measurement is considered 
we have the four years in excellent agreement. 

1 Report of Chief Astronomer, 1910, p. 129. 



J. S. PLASKETT 



2. Personal equation of measurement. — That the same plates 
measured by different individuals may give values differing by 2 
per cent is evident from the previously published paper, where 
Plaskett-DeLury was on the average about 0.040 km per second. 
There were also curious differences in measures of the same plates 
between the Ottawa and Mt. Wilson observers. The rotation value 
is hence uncertain to the extent of the personal equation of the 
measurer and it was felt desirable to carry on further work to 
attempt to clear up this elusive difference. 

Suggestions as to the cause of a personal equation in measure- 
ment have been advanced by H. H. Plaskett 1 who suggests that a 
more or less permanent habit of setting is formed, partly due to 
following the path of least resistance, the method of setting in 
which the least mental energy is required, and partly to a possibly 
unconscious prepossession of the mind looking for a certain result. 
In such a case it is possible that if a sufficient interval elapsed 
between measures the habit of measurement might change. Evi- 
dence of the probability of this in my own case is given below in 
remeasures of all plates at the equator. 

A comparison of the measured values of the 191 2 plates between 
DeLury and myself shows that the differences are in the same 
direction as in 191 1, only slightly reduced in magnitude. Since the 
earlier paper DeLury has measured all the X 5600 plates and all the 
equator spectra in the X 4250 region in 191 1, as well as the 25 plates 
each in X 5600 and X 4250 in 1912. In the following table the mean 
values of the differences for all these measures are given and also 
the differences J.S.P.-H.H.P. for 5 plates, X 5600, in 1912, and the 
20 plates, X 5600, in 1913: 

TABLE X 

DlFFEREXCES IX MEASURES OF SAME PLATES 





Year 


Region 


Xo. of 
Plates 


Observers 


o° 


15° 


3°° 


45° 


6o° 


75° 


8o° 


85° 


1911 . . 


A 

5600 
4250 
5600 
4250 
5600 
5600 


IQ 

24 

25 

25 

5 

20 


J.S.P.-R.E.D. 

" -H.H.P. 
" -H.H.P. 


+0.045 
+ .024 
+ .008 
+ 041 
+ .021 
+0.000 






+0.038 


+0.022 


+0.020 












1912 . . . 


+ .014;+ .009 
+ .0291+ .038 
+ .021;+ .014 
+o.054;+o.oiS 


+ .002 
+ .036 
+ .011 
+0 . 006 


+ .017 
+ -041 
+ .001 
+0.015 


+ .025 
+ .025 
+ .001 
+0.003 


+0.033 


+0.012 


1913- •■ 


+ .019 
+0.004 


— .007 
—0.003 


1 


Joiini 


al R.A 


.S.C., 7, 307, 


1914. 

















DETERMINATION OF SOLAR ROTATION 



387 



These differences, which are in kilometers per second, run in a 
curious way. If we take J.S.P.-R.E.D. we find in 191 1 at X 5600 
a mean difference of +0.031 and at X4250, +0.024. I n I 9 12 a t 
X 5600 the mean difference is +0.015 and at X4250, +0.035, a 
curious reversal of the order of magnitude. The yearly difference 
decreases from 0.028 to 0.025 an ^ the mean of the whole is 
0.027 km per second. The mean differences J.S.P.-H.H.P. in 
1912 is +0.010 while in 1913 it is +0.012. If, however, we 
omit the 15 latitude 19 13, about which there is evidently some- 
thing abnormal in one or both of the measures, the mean differ- 
ence diminishes to +0.006. 

The difference JS.P.-R.E.D., though varying in different 
regions and different years, is persistent and evidently systematic, 
with an average magnitude of +0.027 km P er second. On the 
contrary the difference J.S.P.-H.H.P. is much smaller, diminishes, 
and shows a tendency to vanish altogether. 

These differences and the smaller rotation values for the 19 13 
plates led me to remeasure all the equatorial plates of the three 
years. In order to avoid chance of prepossession, all the X 5600 
plates were arranged at random and the year and number of the 
plate not identified until after the remeasurement, and the same 
procedure was followed with the X4250 plates. Hence a homo- 
geneous and directly comparable set of measures of the 130 equa- 
torial plates were obtained. The mean results are given in the 

following table: 

TABLE XI 

Remeasures of Equator Plates 



A 5600 Region 



A 4250 Region 



Xo. 
Plates 



Original 



Remeas- 
ure 



Diff. 



Xo. 
Plates 



Original 



Remeas- 
ure 



Diff. 



1911 
1912 
1913 



19 
25 
20 



1 .824 
I.848 
I.807 



I.806 

1-835 
I.805 



0.018 
.013 



24 
25 
17 



754 
774 
743 



1-739 

1-755 
1.742 



0.015 
.019 

O.OOI 



This remeasurement was made almost directly after the 
measures of the 19 13 plates, and it will be seen that their measures 
have not changed, but that the remeasured values of the 191 1 and 
191 2 plates average 0.016 km per second lower than the original. 



388 /. 5. PLASKETT 

If a correction of this amount is applied it will bring the plates of 
all four years 1910-13 into remarkably good agreement. A change 
in habit of measurement is hence sufficient to account for the 
difference between 1913 and 1911-12. 

It is not possible to say, when these variations in measures of 
the same plates are present, what to assign as the true value. It 
may be stated as having some bearing that the writer's probable 
error of measurement is somewhat less than H. H. Plaskett's and 
only about half that of DeLury's. It would seem probable, there- 
fore, considering this and the differences in Tables X and XI, that 
his remeasured values are not far from the truth and this would 
make the equatorial rotational value about 2 km per second. How- 
ever, considering that nothing definite can be said, I prefer to leave 
the mean value as obtained above, and given by the mean formulae, 
especially as the differences are evened up in this way and as it 
cannot certainly be said that the remeasured values are superior 
to the original. 

3. Change in the rate of rotation of the sun. — The considerations 
adduced in the last section, which bring all the values at Ottawa 
over four years into remarkably close agreement, form strong evi- 
dence against any general variation of the rate of rotation. In this 
connection it may be useful to give a summary of the values 
obtained by the spectroscopic method elsewhere, consequently they 
are tabulated below. It must be remembered that in some of the 
values tabulated the constants are not given in this form in the 
original papers and have been roughly computed from the data. 
The values may hence in some cases be subject to slight corrections, 
but will, however, serve for comparison. 

The large range shown in these values of the rotation does not 
necessarily indicate a variation in the rate, as they were made by 
different observers with great diversity in instrumental equipment 
and methods of observing and measuring. The measures seem to 
group themselves generally into three sets: (1) high values: Duner, 
Halm, Adams, and Storey and Wilson, averaging about 2.06km 
per second at the equator; (2) low values: Hubrecht and Evershed 
and Royds, with an average equatorial value of 1 . 90 km; (3) inter- 
mediate values: Schlesinger and Ottawa, 2.00km. 



DETERMINATION OF SOLAR ROTATION 



389 



Halm considered that he had discovered a periodicity in the 
solar rotation, but it seems doubtful whether these early observa- 
tions were of sufficient accuracy to permit of definite conclusions. 
The probable errors of Duner's and Halm's visual observations were 
several times greater than Adams' values, the internal agreement 
of which was exceedingly satisfactory. The probable errors of 
Storey and Wilson's, of Hubrecht's, and of Evershed and Royds's 
plates are considerably greater than those given by the Mt. Wilson 
and Ottawa plates, and it seems probable that the exceptionally 
low value of Hubrecht is due to some instrumental or measure- 
mental error. Even excluding the low group, however, there still 

TABLE XII 
Constants of Faye Formulae — Other Observers 



Observer 



Duner 

Halm 

Adams, 1906-07 

Adams, 1908 

Storey and Wilson 

Hubrecht 

Evershed and Royds . 

Schlesinger 

DeLury, 191 1 

H. H. Plaskett, 1913 . 
J. S. Plaskett, 1911-13 



Linear 



Angular 



2.08 

2.05 

2.055 

2.05 

2.08 

1.86 

1.94 

2.00 

1.97 

1.98 

2.01 



remains the difference between Alt. Wilson 2.05 km and Ottawa 
and Allegheny 2 . o km to be accounted for. I do not believe that 
this difference is due to a change in the velocity of rotation of the 
sun, but to plate or measurement errors in one or both of the groups. 

The mean value of the solar rotation as determined from 
sun-spots by Carrington, Spoerer, and Maunder is just midway 
between the Ottawa and Alt. Wilson values, but determinations 
from faculae and flocculi are nearer in agreement to the latter. 
However, the velocity of the reversing layer is not necessarily the 
same as that of these visible phenomena. 

I understand that the rate of rotation is now being redetermined 
at Mt. Wilson with the 150-ft. tower telescope and the 75-ft. grating 
spectroscope. The use of this unequaled equipment, combined with 



39° 



J. S. PLASKETT 



the experience and skill of the Mt. Wilson observers, should give 
values of great weight, and it will be of much interest to see with 
which group of observations they most nearly agree. 

While believing that the general velocity of the reversing layer 
is not subject to change, there seems to be no other means of 
accounting for the large differences in the measured values of plates 
taken under apparently identical conditions, for the high ratio of 
plate error to measurement error, and for the variation in the mean 
values at the different latitudes, than to assume them to be due to 
local movements or eddy currents in the reversing layer of a com- 
paratively transitory character. Such movements are known to 
exist around sun-spots and have been detected in other regions, 
both at Mt. Wilson and Ottawa, of magnitudes sufficient to readily 
account for the observed differences. 



PROBABLE ERRORS 

In Table XIII have been compiled both measurement and plate 
errors for the three years. On the first line we have the probable 
errors of measurement of single lines and on the second the measure- 
ment error of a plate obtained by dividing the foregoing values by 
the square root of the number of lines measured on the plate. The 
last line contains the mean plate errors obtained by comparing the 
plates in each series. 

TABLE XIII 

Probable Errors 





1911 


igl 2 


1913 




A 5600 


A 4250 


A 5600 


A 4250 


A 5600 


A 4250 


Measurement — single line o . 024 
Measurement — single plate .006 
Total single plate . 028 


O.OI5 

.OO4 

O.O26 


O.O3O 

.OO9 

O.O23 


O.O3I 
.008 

O.O34 


O.O4O 

.Ol6 

O.O39 


O.O45 

.017 

O.O32 



We find from the foregoing table by comparing the last two lines 
that the measurement error varies from about one-sixth to one- 
half the total error of a plate, the higher ratios occurring where 
the number of lines and settings had been markedly diminished. 
Indeed it is seen that the total errors are not much different 



DETERMINATION OF SOLAR ROTATION 



39 1 



from the measurement error of a single line and that hence the 
use of only three or four lines on each plate would be amply 
sufficient. 

Some additional information in this direction is given by the 
remeasurement of the equatorial plates of all series, a comparison 
of the total plate errors for each measurement being given in this 
table. 

TABLE XIV 
Probable Errors of Equatorial Plates 



Total Plate Errors 


IQII 


IQI2 


1913 


A 5600 


A 4250 


A 5600 A 4250 


A 5600 


A 4250 


Original measure 

Remeasurement 


O.OI3 
O.O24 


O.OI8 

O.O23 


0.02I 1 O.O3I 
O.O26 O.O29 


0.02I 
O.O28 


O.O28 
O.O24 



Although only 6 or 7 lines were used in the remeasures as com- 
pared with 12 to 19 in the original measures, there is not much 
difference in the plate errors, showing that the measurement effects 
are relatively small and that the cause of the relatively high total 
probable error of a plate as compared with the computed measure- 
ment error is to be sought in differences in the plates themselves, 
caused probably, as previously inferred, by local temporary dis- 
turbances in the reversing layer. 

That the measurement error of a plate determined directly is 
in good agreement with that obtained by dividing the probable 
error of a line by the square root of the number of lines, is shown 
by the comparison of six remeasures of plate 867 of the 191 1 
X4250 series at three latitudes, o°, 30 , 6o°, 12 lines being measured 
on each spectrum, the results of which are given in the following 
table: 

TABLE XV 
Probable Errors of Remeasures of Plate 867 



30 



6o° 



Mean probable error, single line ._ L _ 

Mean probable error, plate = above -^ j 7 1 2 

Probable error, plate from comparison of 6 measures 



=0.018 
.0052 
=0.0057 



±0.024 
.0069 
=±=0.0077 



=0.011 

.0032 
= o . 0034 



392 /. S. PLASKETT 

SYSTEMATIC DIFFERENCES OF VELOCITY FOR DIFFERENT ELEMENTS 

This question was fully discussed in the 191 1 measures where 
the conclusion was reached that no systematic difference for differ- 
ent lines or elements was present. The mean algebraic residual for 
any line was in no case greater than one-third the mean numerical 
residual. The same lines were measured in 1912, X4250, as in 191 1, 
X4250, and the residuals were similarly tabulated with a similar 
result. It was concluded that no difference in velocity for different 
lines or elements, which cannot readily be explained by accidental 
errors of measurement, is present in the Ottawa plates. 

CONCLUSIONS 

The conclusions following from the measures of the Ottawa 
plates 1910 to 1913 by the writer may be summarized as follows: 

1. The value of the solar rotation determined at Ottawa can 
be expressed by the formulae 

V= (2. 006 — 0.522 sin 2 <f>) cos <f> 
$ = i4?24— 3?7i sin 2 ^ 

2. The values for the four years in which observations were 
obtained are in excellent agreement and the values of the constants of 
the foregoing formulae obtained from each of the six series are also 
in good agreement. The differences in the residuals, using the mean 
and separate values of the constants, are negligibly small, and the 
mean constants satisfactorily represent all Ottawa observations. 

3. So far as the interval covered by the Ottawa observations, 
1910 to 1913, inclusive, is concerned the solar rotation is constant. 
The slight decrease obtained in 1913 is shown to be very probably 
due to a change in the habit of measurement. 

4. The total range of mean velocity in each latitude is about 
0.04 km per second. The most probable explanation of such dif- 
ferences is to ascribe them to local motions of the gases in the 
reversing layer. 

5. The errors of measurement of the plates average about one- 
fourth the total errors as obtained by comparison of the plates, the 
average of the latter for a single plate being about o . 03 km per 
second. 



DETERMINATION OF SOLAR ROTATION 393 

6. Personal differences of measurement of different observers 
may be very much greater than the probable measurement error 
of either. The difference J.S.P.-R.E.D. averages +0.027 km P er 
second and J.S.P.-H.H.P. +0.008 km per second. 

7. The personal equation of measurement may change, the 
remeasurement of the equator plates of 191 1 and 1912 giving values 
about 0.015 km P er second lower. 

8. In consideration of the possibility of these personal differ- 
ences and changes, the value of the rotation may be uncertain to 
the extent of one or two hundredths of a kilometer. Such per- 
sonal effects may explain part of the differences in the values 
obtained by different observers. 

9. All the spectroscopic observations of the rotation of the 
reversing layer may be grouped into three sets of values, high, 
medium, and low. High values are obtained by Upsala, Edin- 
burgh, and Mt. Wilson, and average at the equator 2.06 km per 
second. Medium values, obtained at Allegheny and Ottawa, run 
about 2.00 or 2.01 km. Low values, obtained at Cambridge and 
Kodaikanal, average about 1 . 9 km. The cause of such large differ- 
ences in the values can most probably be assigned mainly to 
observational or instrumental errors and secondarily to personal 
differences of measurement. 

10. The large number of plates and measures made at Ottawa, 
much greater than at any other observatory, their close inter- 
agreement over four years' interval, and the care employed in the 
making and measurement of the plates entitle the Ottawa value 
to considerable weight. 

11. No indication of any systematic differences of velocity for 
different lines or elements is given by the Ottawa measures. 

I have much pleasure in expressing my appreciation of the 
readiness of the Director, Dr. W. F. King, to supply the necessary 
apparatus and of his encouragement and interest throughout. 

Dominion Observatory, Ottawa 
June 1915 



THE TRANSPARENCY OF AQUEOUS VAPOR 1 

By F. E. FOWLE 

The chief object of this communication is to treat quantitatively 
of the depletion of energy from the radiation of heavenly bodies 
as it passes through atmospheric aqueous vapor. In earlier com- 
munications 2 the non-selective depletion or scattering was treated; 
in this, the selective depletion or absorption will be considered. 
Further, a summary will be given relating to atmospheric absorp- 
tion in general between the wave-lengths 0.35 /x and 2.00 /x, and 
formulae and data for determining it for any given case. 

THE NON-SELECTIVE SCATTERING 

The non-selective scattering of energy varies continuously with 
the wave-length and is easily expressed as a continuous function 
of the wave-length. In the case of the permanent gases of the 
atmosphere above Mount Wilson on clear days the scattering 
is almost purely molecular and may be computed from the number 
of molecules present in the path. In the case of water vapor, the 
losses are considerably greater than would be expected from purely 
molecular scattering and are apparently caused by grosser particles 
associated with the water vapor. The scattering varies so slowly 
with the wave-length that the coefficients which express it depend 
but slightly upon the purity of the spectrum. Coefficients of 
non-selective depletion, a aK and a w \, for dry, dust-free air and 
water vapor, respectively, have been published. As just stated, 
these vary slowly with the wave-length. In order to know the 
intensity of the energy after transmission through the air, it is 
necessary only to multiply the original intensity of the energy from 
the heavenly body at the wave-length A by a"\a'-".A, where the 
exponents m and w express the length of path and the amount of 

1 Published by permission of the Secretary of the Smithsonian Institution. 
; Astrophysical Journal, 38, 392, 1913; 40, 435, 1914. 

394 



TR.1XSPARENCY OF AQUEOUS VAPOR 395 

water vapor. 1 The transmission coefficients for dry air and 
aqueous vapor will be found in Table I (p. 403). 

The coefficients of transmission for dust will be considered only 
incidentally in this paper. Above an altitude of 1000 meters dust 
is generally negligible on clear days. At sea-level the dust coeffi- 
cients are very variable from day to day. They are probably 
nearly the same for all wave-lengths less than 3 /x. The average 
scattering caused by the dust above Washington on clear days is 
about 9 per cent. On one of the clearest days on which observa- 
tions have been made there it amounted to 3 per cent (February 
15, 1907). 2 

THE SELECTIVE ABSORPTION 

Selective absorption presents a very different case. It exists 
practically only in bands at certain wave-lengths, and within these 
bands varies very rapidly. If absorption or transmission coeffi- 
cients were determined for these bands, as in the earlier case, the 
values would depend greatly upon the purity of the spectrum. 
For instance, in Fig. 1, if ab is an absorption band in a pure spec- 
trum, the transmission would be taken as bc/ac; in an impure 
spectrum for the same quantity of vapor it would wrongly appear 
to be, say, b'c ac. It can be shown, however, that the areas of the 
bands remain nearly the same in the two cases. The areas, being 
nearly independent of the purity, therefore, have been utilized as 
a measure of the absorption. Unfortunately Bouguers formula 
cannot then be used, 3 as with the scattering coefficients, and the 
results must be expressed empirically. 

In each water-vapor band the absorption at first increases 
rapidly with increasing wave-lengths to a maximum, and then dies 
away more slowly. From this lack of symmetry, it results that the 

1 m is taken as unity when the body is in the zenith. It is equal to the secant of 
the zenith distance to within 1 per cent when the zenith distance is less than 70 . 
For greater zenith distances than 70 , Bemporad's air masses for the exponent of aa\ 
should be used, while retaining sec z for the exponent of Ow\ because of the low level 
of the water vapor. See Smithsonian Miscellaneous Collections, 65, No. 4, 1015, and 
Mitteilungen der Grossherzoglichen Stemwarte zu Heidelberg, No. 4, 1904. w is the 
depth in centimeters of the precipitable water in the atmosphere above the place. 

2 Meleorologischc Zeitschrift, 6, 270, 1914; Monthly Weather Review, 42, 2, 1914. 

3 Annals of the Astrophysical Observatory of the Smithsonian Institution, 2, 16, 1908. 



596 



F. E. FOWLE 



equality of areas just considered holds only for radiation in similar 
spectra, that is, from sources of the same order of temperatures. 
Thus, referring to Fig. i, had the energy-curve the slope xy, the 
area of the band would in general have been different, even in a 
pure spectrum, though the amount of incident energy distributed 
over the wave-lengths under consideration were the same. Accord- 
ingly due consideration must be employed in applying the results 
given below to the cases of radiation from bodies at terrestrial and 
laboratory temperatures. The results as here obtained apply with 

their full accuracy only to a 
distribution of radiation-energy 
such as is found in this region 
in the solar spectrum. 

The various atmospheric 
bands, the absorption in which 
will be considered, as well as 
the contour of the solar energy- 
curve, are given in Fig. 2. This 
spectrum lies between the wave- 
lengths o . 65 jj, and 2 . 1 2 ix. The 
coefficients of the general atmos- 
pheric transmission vary so little 
from wave-length to wave-length 
here that the general contour of 
the energy-curve, neglecting the 
bands, scarcely varies from day 
to day, or with the time of the 
day, either without or within the atmosphere. About 95 per cent 
of the radiation sent to us from the sun lies in this region between 
0.30 n and 2.40 fj.} The radiation from a body at the mean 
temperature of the earth, 287 K. = i4° C, lies in quite a different 
region in the spectrum and is affected by entirely different series of 
absorption bands having wave-lengths greater than 2 fx. Quanti- 
tative measures of the absorption by water vapor in this latter 
region are in progress here. For a body at the temperature of the 

1 The selective absorption in the region near the D lines is comparatively small 
and probably nearly wholly taken into account by the general transmission coefficients. 




Fig. 






TRANSPARENCY OF AQUEOUS VAPOR 



397 



Xernst lamp 60 per cent of the radiation lies at wave-lengths 
greater than those of the region treated in this communication. 
There are two quantities the measurement of which is to be 
considered: the amount of water vapor and the corresponding 
absorption of energy passing through it. 



r 
c 


ijoototoco^-oino^rigoj 

D(Or-00CD — O^-tDf-lcO — . 

i d _„-„_ d — — — : — __jc\)c\j 


r 




T\ 


' 




7_ 


p^ 


£ 






































, 


A 


' 




\ 


! / 






































Ba 






III 




N 
















































\ 




































a" 














\ 
















































\ 


v 


















































v\ 


\ 






































fir 




1 


' 


} 


N 


\ 




































1° 




1 








N 


k \ 






































v 
































































<v 


-V 






























$ 








i 














-.,. 




















































■■~-» 












































n 


M 


L z 










II 


0' 


IC 


)0' 


9 


c 


8 


0' 


7 


0' 60' 50' 40' 30' 20' fO' 1 


0' 



Fig. 2. — Contour solar energy-curve, 6o° ultra-violet glass prism. Region of 
atmospheric absorption bands. 

MEASUREMENT OF THE AMOUNT OF WATER VAPOR 

A spectroscopic method for determining the amount of atmos- 
pheric water vapor and the applications of the method have already 
been given. 1 The ratio of the deflection in the bottom of the water- 
vapor bands, p and <i>. to the ordinates of the smooth curve drawn 
across the tops of the bands, was observed with known amounts of 
water vapor in the laboratory. The largest layer of water vapor 
used was equivalent to about 0.6 cm of precipitable water, and the 
curve connecting the ratios for p and <i> with the amount of water 
vapor was produced to about 3 cm precipitable water vapor, 



1 A stt -o physical Journal, 35, 149, 191 2; 37, 359, 191; 



398 F. E. FOWLE 

guided by certain conditions stated in the first of the above- 
mentioned articles. These curves are used to determine the 
amounts of water vapor producing the absorptions treated in this 
communication. For instance, in Fig. 2 the ratio of ab, the inten- 
sity of energy in p, to ac is 0.48 and from curve a in Fig. 3 we find 
this corresponds to 2 . o cm of precipitable water vapor. 

The following results lead to increased confidence in the validity 
of this relationship between the depths of these bands and the 
amount of water vapor. Sounding balloon ascensions were made 
from Avalon during the summer of 19 13 by Mr. Sherry of the United 
States Weather Bureau and Mr. Aldrich of this Observatory. 1 
Avalon is on the Santa Catalina Island, off the southern coast of 
California, about 60 miles to the southwest of Mount Wilson. 
Observations were made spectroscopically on Mount Wilson on 
three days on which balloon ascensions were made and furnish the 
following comparisons : 



Dates 


July 23 


August 3 


August 8 


Spectroscopic values. . 
Balloon values 


1 . 17 cm 
1 .07 cm 


2.06 cm 
2 . 09 cm 


1 .39 cm 
1 .41 cm 



The agreement is very satisfactory considering that the observa- 
tions differed slightly in time and place and that the direct labora- 
tory calibration extended only to o. 6 cm precipitable water, whereas 
these comparisons necessitated the use of the calibration-curve to 
over 6 cm (because some of the observations with the spectroscope 
were made through air masses three times that at the zenith). 2 

1 Monthly Weather Review, 42, 410, 1914. 

2 The estimation of the amount of water vapor, whether right or wrong, intro- 
duces no error into the solar-constant determinations made here. The absorption 
values used in those reductions depend upon the relationship between the measured 
depths of p and the area of the absorption bands which is experimentally determined 
without regard to the amount of water vapor. However, as we have the relationship 
between the depth of p and the precipitable water, the results seem more intelligible 
if the depth of p is eliminated between the two functions, and the absorption expressed 
in terms of the amount of water vapor in the air. In Fig. 3 are given the curves by 
which the deflections in p and* may be interpreted in terms of the precipitable water. 
Curves a and c are for p and <£ with a purity of spectrum such that the bolometer- 
plus-the-slit width is equal to o . 02 2 /*, and curves v and d when it is equal to o . 005 7 p.. 
Linear interpolation between these two curves may be used to construct plots for 
intermediate purities. 



TRANSPAREXCY OF AQUEOUS VAPOR 



399 




Fig. 3. — Curves for areas of bands, etc. 

Curves marked p, 0.8 p., 0, •£, and e: 

Abscissae are precipitable water in cm. 

Ordinates are areas of absorption bands. The first four are for separate bands; 
curve e is the sum of all the bands. The circles are Mount Wilson data; the crosses, 
Washington values with different prism and purity of spectrum, but less accurate 
because of smaller scale. 

Curves marked a, b, c, and d: 

Abscissae are precipitable water in cm. 

Ordinates are ratios of depths of bands to top. 

a and c are for p and <& respectively, slit+bolometer = 0.022 p. 
b and d are for p and 4> respectively, slit+bolometer= 0.0057 p.. 

Curve marked /: 

Abscissae, for cm read air masses. 

Ordinates, number o, 1, 2 in the center of the plot, are the areas of the atmos- 
pheric bands other than those due to water vapor in the same units as curve e. 



400 



F. E. FOWLE 



MEASUREMENT OF THE SELECTIVE ABSORPTION IN CONNECTION WITH 
DETERMINATIONS OF THE SOLAR RADIATION 

The second quantity, the atmospheric absorption of radiation, 
as dependent upon the amount of aqueous vapor, will now be con- 
sidered. At Mount Wilson (altitude 1730 m; barometer 62.3 cm) 
curves are obtained showing how this absorption is distributed in 
the spectrum of the solar energy after this energy has passed 
through the air. There was shown in Fig. 2 the red and infra-red 
end of such an energy-curve, indicating the principal absorption 
bands produced by the constituents of the atmosphere. The follow- 
ing list gives the bands, their wave-lengths, and the constituent of 
the air producing them : 



B . 

a 


0.69 
■72 

.76 

.81 

0-93 


A 

par 



Oxygen 
Water vapor 
Oxygen 
Water vapor 
Water vapor 







M 


* 


I 


13 


*.. . 


I 


42 
89 


ft. . 


I 


w. 


2 
2 


OI 
OS 


U) 2 





Water vapor 
Water vapor 
Water vapor 
? 



Simultaneously with obtaining these curves the pyrheliometer is 
read. Evidently the total area included by these energy- curves, 
suitably corrected for instrumental losses, may be placed equal to 
the number of calories indicated by the pyrheliometer, thus obtain- 
ing the scale or the number of calories per square centimeter of the 
energy-curve or bologram. Whence it would be easy to convert 
the areas of the bands, which represent their absorption, into 
the number of calories absorbed by the atmospheric vapors and 
gases. 

For solar-radiation computations the area included by the 
smoothed energy-curve (i.e., including all the band areas) is 
obtained by adding together the measured ordinates of the 
smoothed curve taken at equal intervals. It would be tedious to 
measure directly the areas of all the bands with satisfactory accu- 
racy; but it has been found feasible to express their total area as 
a function of the depth, or fractional depression from the smoothed 
energy-curve, at p or <p. This quick method requires the assump- 
tion that the form of the smoothed energy-curve in the infra-red 
spectrum region, where the atmospheric bands occur (see Fig. 2), 



TRANSPARENCY OF AQUEOUS VAPOR 401 

should be constant from hour to hour and from day to day. Inves- 
tigation has shown that its small changes of form, which depend 
principally on the variations of atmospheric transparency, do not 
affect substantially the accuracy of the process, as applied to energy- 
curves taken with moderate air masses (less than 5) at Bassour, 
Mount Wilson, or Mount Whitney. 

Accordingly the areas of the bands have been thus determined, 
suitably corrected for instrumental losses, multiplied by the 
reciprocal of the smooth curve's ordinate in centimetsrs at p (ac, 
Fig. 2). 1 They can then be expressed accurately as a simple func- 
tion of the amount of water vapor as measured by the depth of p. 
Several curves showing such results are given in Fig. 3. In the 
upper part of the figure are given the values of the areas for p, the 
'band at o. 8 p for ft, and for $>. Curve e gives the sum of the areas 
of all the bands produced by water vapor. Had the general trans- 
mission in the infra-red been more variable with the wave-length, 
such a simple function of the water vapor would not have been 
right. A set of similar curves would have been necessary for each 
air mass, and had the transmission also varied from day to day, 
even these would not have been sufficient. 

Returning to the energy-curve of Fig. 2, we found from the 
depth of p that the amount of water vapor producing the deflection 
was 2 . o cm. The curve for p and that marked e give, for this 
amount of vapor, for the band p and the total area of all the water- 
vapor bands, areas of 1 . 96 and 1 2 . 3 sq. cm, respectively. Assuming 
that each square of Fig. 2 represents 1 sq. cm, then since the whole 
ordinate at p is 13.4 cm and the scale of abscissae (2 cm to io') is 
twice the standard scale, the corresponding areas for Fig. 2 should 

1 This is in order to reduce to standard conditions which are taken so that the 
smooth curve's ordinate at p = 10 cm. It may be desirable to use the curves for getting 
the absorption in a solar spectrum produced by apparatus of different dispersion. 
In such cases, since the areas of the bands remain the same although the ordinates 
change, it will be necessary to multiply the absorption areas taken from the plots, not 
only by the smoothed-curve ordinate in centimeters atp, but also by the ratio of the old 
to the new dispersion at p. The area of the bands in square centimeters is given in curve 
e, Fig. 3, when the prismatic solar energy-curve (dispersion at /> = o.i2 p- to 10' of 
deviation) is plotted on a scale of 1 cm to 10' of deviation and the ordinate of the 
smoothed curve above p equals 10 cm. The curve connecting the depth of p with the 
precipitable water must be corrected as already indicated for the purity of the spec- 
trum (e.g., bolometer+slit-widths) expressed in microns (m). 



402 F. E. FOWLE 

be 2Xi-34X(i.96 and 12.3), or about 5.25 and 33.0 sq. cm, 
respectively. The scale in calories would be obtained through a 
pyrheliometer reading and the areas of absorption then converted 
into calories. 

ABSORPTION DUE TO THE PERMANENT GASES OF THE AIR 

There is another set of bands which must be taken into account; 
those due to oxygen and those of unknown atmospheric origin. 
These bands all seem to vary only with the length of path or air 
mass (which is very nearly equal to the secant of the zenith distance 
for zenith distances less than 70 ) . Accordingly these bands have 
been measured and reduced to the same standard scale, and their 
sum appears in curve/ of Fig. 3. For use with an observed energy- 
curve, the areas taken for the proper amount of water vapor in the 
one case, and the proper air mass in the other, are multiplied by the 
observed ordinate of the smoothed curve above p. Curve/ is given 
for Mount Wilson. An air mass m x at another altitude where the 
barometer reads x cm is equal to that at Mount Wilson multiplied 
by the ratio of x to 62. 

ATMOSPHERIC LOSSES IN CALORIES AT MOUNT WHITNEY, MOUNT 
WILSON, AND WASHINGTON 

In what has preceded, the selective absorption has been dis- 
cussed as actually determined and used in reducing the solar radia- 
tion holograms made here, at Mount Wilson, and elsewhere. With 
the other atmospheric losses, it will now be given under two 
somewhat different forms: first, as the number of calories absorbed 
from the incoming 1 . 93 calories of the solar radiation under certain 
concrete conditions; secondly, as the fractional transmission of the 
incident energy by water vapor between certain wave-lengths. 

The atmospheric losses from the incoming solar energy comprise 
five parts: (1) that due to the general scattering by the molecules 
of the permanent gases of the atmosphere; (2) that due to the 
general scattering associated with water vapor; (3) that due to 
selective (banded) absorption of the permanent gases of the atmos- 
phere; (4) that due to the selective (banded) absorption of water 
vapor; (5) that due to dust. 






TRANSPARENCY OF AQUEOUS VAPOR 



403 



Table I contains the wave-lengths in /jl, the intensities of the 
solar energy outside the atmosphere, e oK , given on an arbitrary, 
absolute scale of intensities, but on the relative scale from wave- 
length to wave-length of a 6o° ultra-violet glass prism; the atmos- 
pheric transmission coefficients for dry air, barometer 623 mm, 

TABLE I 

6o° Ultra- Violet Glass Prismatic Solar Energy-Curve; Also Dry Air and 
Aqueous Vapor (i cm Precipitable Water) Transmission Coefficients 



X. . 

<?»A. 

X. . 

aa\ 

X. . 
e \. 

aaK 

aii'A 



0.342 
102 

(o.595) 
0.920 

0-503 

907 

0.885 

0.968 



1 45- 7 

586 

0.998 

0.987 



0.350 

130 

(0.626) 

0.926 

O.S35 

1044 
0.898 
0.972 

1.603 

435 
0.999 
0.987 



0.360 

160 

0.655 

o.934 

o.574 

1197 

0.905 

0.970 

1-738 

343 

0.999 



0.371 


0.384 


198 


227 


0.686 


0.713 


0.940 


0.945 


0.624 


0.686 


1334 


1416 


0.929 


0-959 


0.975 


0.981 



1.870 2.000 
262 187 

0.999; 0.999 

0.987 0.986 



0.397 

322 

0.752 

0.949 

0.764 

1435 
0.979 



.123 
123 

•999 



0.413 

437 

0.783 

0-953 

0.864 

143 1 
0.987 



2. 242 

88 

0999 



0.43 1 

5i8 

0.808 

o.957 

0.987 

1306 

0.992 

0.987 

2.348 

74 

0.999 

0.983 



0.452 

681 

0.840 

0.961 

1. 146 

1025 
0.996 
0.987 



o.475 

807 

0.863 

0.964 

1.302 

775 
0.997 
0.987 



altitude 1730 meters, a aK , and the transmission coefficients for 
1 cm of precipitable water vapor, a- d . x . In order to determine the 
absolute "scale," the area of the energy-curve constructed with the 
foregoing e oK data has been placed equal to the mean value of the 
solar constant, 1 . 93 calories 1 per square centimeter per minute at 
the mean solar distance of the earth. Then with use of the formula 

energy-curves have been constructed for various air masses and 
amounts of water vapor, the absorption data of this paper being 
employed. 

Tables II— IV resulted from measures of areas from these curves. 
They have been compared and found to be consistent with energy- 
curves actually observed. The first triplet of lines in each of the 
three tables gives, first, the amount of radiation scattered from the 
direct solar beam by the permanent gases of the atmosphere; 

1 The calorie used is the 15 C. gram-calorie, or the amount of heat necessary 
to warm one gram of water 1° C. at 15 C. 



404 



F. E. FOWLE 






secondly, the amount selectively absorbed by them (B, A, a, co r , co 2 . 
lines) ; and, thirdly, the sum of these two quantities. For the suc- 
ceeding triplets (except for Washington) are given, first, the addi- 
tional amount scattered by the water vapor; secondly, the amount 
selectively absorbed by it (a, par, etc., lines) ; and, thirdly, the totals 
in which for each case are included the totals from the first triplets. 
For the Washington values, in the lines designated "water scat- 



TABLE II 

Mount Whitney. Atmospheric Absorption for Dry Air and Dry Air Plus 
Various Amounts of Water Vapor 

Altitude 4420 m; Barometer 44 . 7 cm . 

Incident solar radiation, 1.93 15 C. -gram-calories per sq. cm per minute 



Air Masses 



Precipitable Water Vapor 



£0 
O 






O 



Oh 



u 

Eg 

o 



2 J 



Cm 



as 
o 






o . 00 cm 

Air scattered. 
Air absorbed. . 
Total lost . . 
o.n cm 

H 2 scattered 
H 2 absorbed 
Total lost . . 
0.25 cm 

H 2 scattered 
H 2 absorbed 
Total lost . . 
o . 50 cm 

H 2 scattered 

H 2 absorbed 

Total lost . 



o. 14 
.01 
•IS 

.01 
.08 
• 24 

.01 
. 10 
.26 



o. 29 



7-3 
°-5 
8.0 



4-i 



0.23 
.01 

•24 

.01 
. 10 
•35 

.02 
.12 
.38 

.04 

•15 

°-43 



n. 9 

0.5 
12.0 

0.5 

5-2 

18.0 

1.0 

6.2 

20.0 

2 .1 

7-8 

22.0 



>-3i 
.01 

•32 

.01 
. 11 

■44 

■03 
■13 
.48 

.06 

.16 

o.54 



16. 1 

°-5 
17.0 

°-5 

5-7 

23.0 

1.6 

6.7 

25.0 

3-i 

8.3 

28.0 



19.7 

0.5 

20.0 



°-5 

6.2 

27.0 



2.1 

7-3 
30.0 

3 6 

8.8 

33-0 



0.44 
.01 

•45 

.02 
. 12 
•59 

.04 

•15 
.64 

.08 

.18 

o. 71 



22.8 

0-5 

23.0 

1.0 

6.2 

310 

2. 1 
7-8 

33° 

4i 

9-4 

37-0 



°-55 
.02 

•57 

.02 
•13 

•72 

•05 
.16 

.78 



0.87 



28.5 

1 .0 
30.0 

1 .0 
6.7 

37-0 

2.7 

8.3 

40.0 

5-2 

10.4 
45-° 



tered," is included the amount scattered by the dust. The amounts 
lost by dust, at the zenith, on the three days included in the table 
are respectively, February 15, 3 per cent, October 4, 9 per cent, and 
May 14, 14=1= per cent (see also Monthly Weather Review or Meteo- 
rologische Zeitschrift, op. cit.). The data for the Mount Whitney 
and Mount Wilson tables have been computed directly from data 
of Table I by means of the formula just given. Except for the first 



TRAXSPAREXCY OF AQUEOUS VAPOR 



4°5 



triplet of lines for dry, dust-free air, a somewhat different procedure 
has been followed for the Washington data. For Washington a 
third coefficient a ( / A would be necessary within the brackets of the 
formula just given to take into account the scattering by the dust. 
Instead of computing for various values a a \ and a u ,^ and a d \, it was 
thought best to make computations using the actually observed 
product of these three coefficients for three days of widely different 
conditions. 1 

TABLE III 

Mount Wilson. Atmospheric Arsorption for Dry Air axd Dry Air Plus 
Various Amounts of Water Vapor 

Altitude 1730 m; Barometer 62.3 cm 

Incident solar radiation, 1.93 15° C. -gram-calories per sq. cm per minute 



Air Masses 


m = i 


m — 2 


m=3 


m =4 


tn — 5 


wi = 7 


Precipitable Water Vapor 


"3 

a i 




60 
€i 


~5 
O ^ 

ss 





to 

C M 

s ° 

■ — 

PL, 


"3 

So 

O 




60 

Ph 


~5 
Eg 


60 






60 

id 

gj 

- 
Ph 


Eg 

O 


6C 
C « 

8 

gt-H 


O . OO cm 

Air scattered 

Air absorbed 

Total lost 

0.33 cm 

H 2 scattered 

H2O absorbed 

Total lost 

0.50 cm 

H 2 scattered 

H2O absorbed 

Total lost 

1. 00 cm 

H 2 scattered 

H 2 absorbed 

Total lost 

2 . 00 cm 

H 2 scattered 

H 2 absorbed 

Total lost 


0.15 

.01 
.16 

.02 
. 11 
.20 

■ 03 

. 12 

•31 

.04 

■ IS 
•35 

.09 

.18 

043 


7.8 

0.5 

8.0 

1.0 

5-7 

150 

1.6 

6.2 

16.0 

2. 1 

7.8 

18.0 

4-7 

9-3 

22.0 


0.28 
.01 
.29 

.02 
• 13 

•44 

•03 
■15 
•47 

.08 
•17 

•54 

•13 

. 21 

0.63 


14-5 

OO 

ISO 

I .O 

6.7 

23.0 

1.6 

7.8 
24.0 

4-i 

8.8 

28.0 

6.7 
10.9 

33° 


O.38 
.OI 

■39 

.04 

• 14 

• 57 

.06 
.16 
.61 

. 10 
.19 
.68 

•19 

•23 

0.81 


I9.7 

0.5 
20.0 

2.1 

7-3 
30.0 

3-1 

8-3 

32.0 

5-2 

9.8 

350 

9.8 

11. 9 

42.0 


0.47 
.02 
•49 

.04 

•15 
.68 

.06 
■17 
•72 

. 12 
. 20 
.81 

. 21 

•24 
0.94 


24.4 

1 .O 

250 

2. I 

7-8 

35-0 

3-i 

8.8 

37° 

6.2 
10.4 
42.0 

10.9 
12.4 
49.0 


o.54 
.02 

•56 

.04 

.16 
.76 

.07 
.18 

.81 

•13 
. 21 
.90 

■25 

•24 

i°5 


28.0 

1 .O 

29.O 

2.1 

8-3 

39° 

3-6 

9 3 

42.0 

6.7 
10.9 
47.0 

13.0 
12.4 
54° 


0.66 
.02 
.68 

■05 

• 17 
.90 

.08 
.19 
•95 

■15 

. 22 

1. 05 

.28 

• 25 
1. 21 


34-2 

1 .0 

35° 

2.6 

8.8 

47.0 

4-i 

9.8 

49.0 

7.8 
11. 4 
54 

14-5 
13.0 
63.0 



These tables show that on the average about half the loss of 
energy in coming through the atmosphere is due to the scattering 
and absorption in the permanent gases of the atmosphere and half 



1 Annals of this Observatory, 2, 112-113, 1908. 



406 



F. E. FOWLE 



TABLE IV 

Washington. Atmospheric Absorption for Dry Air and Dry Air Plus Dust 

and Various Amounts of Water Vapor 

Altitude sea-level; Barometer 76.0 cm 

Incident solar radiation, 1.93 15 C. -gram-calories per sq. cm per minute 



Air Masses 


m = \ 


m = 2 


m=$ 


w=4 


m=s 


m = ^ 


Precipitable Water Vapor 


~5 




0) 

bo 

Oh 


"3 
E 
O 


bo 

cd 

C -ft! 

So 

Ph 


~5 
O 

ES 

O 




bo 

C3 

He 


"3 

Eg 

O 




to 
a 

Ph 


"3 

ES 

O 


bo 


"3 

6S 
O 


bo 

Ph 


O.OO Cm 

Air scattered 

Air absorbed 

Total lost 

. 5 cm February 1 5 

H 2 scattered 

H 2 absorbed 

Total lost 

1 . 8 cm October 4 

H 2 scattered 

H 2 absorbed 

Total 


0.18 
.01 
.19 

.08 
. 12 
•39 

.26 

15 

.60 

.38 
.16 

o-73 


9-3 

0.5 
10. 

4-i 

6.2 

20.0 

13-5 

7.8 
310 

19.7 

8-3 
38.0 


o-33 
.01 

•34 

•15 
• 13 
.62 

.42 
.16 
.92 

.56 

.16 

1 .06 


17. 1 

0.5 
18.0 

7.8 
6.7 

32.0 

21.8 

8.3 

48.0 

29.0 

8.3 

550 


0.44 
.01 
•45 

. 21 

• 14 
.80 

■ 53 

.16 

1. 14 

.67 

• 15 
1. 27 


22.8 

0.5 

23.O 

IO.9 

7-3 
42.0 

27-5 

8.3 

59° 

34-7 

7.8 

66.0 


0-53 
.01 

•54 

.26 
■14 
•94 

.61 

•14 
1 .29 

•74 

• 14 

1 .42 


27-5 

0.5 

28.O 

13 5 

7-3 

49.0 

31.6 

7-3 
67.0 

38.3 

7-3 

74.0 


0.61 
.01 
.62 

■3° 

• 14 

1.06 

.67 

•13 
1.42 

•78 

•13 

i-53 


31.6 

0.5 

32.0 

15-5 

7-3 

55o 

34-7 

6.7 

74.0 

40.4 

6.7 

79.0 


o.73 
.01 

•74 

•37 

•14 

1-25 

■74 
. 11 

i-59 

•83 

.10 

1.67 


37-8 

°-5 
38.0 

19. 2 

7-3 
65.0 

38.3 

5-7 

82.0 


2 . 4 cm May 14 

H 2 scattered 

H 2 absorbed 

Total 


43 -o 

5-2 

86 







is due to similar losses in the water vapor. 1 For the average amount 
of water vapor at Mount Wilson (0.7 cm precipitable water) the 

1 In considering these values of the relative absorption and scattering, a peculiar- 
ity of Bouguer's formula should be borne in mind. We have seen in any case that the 
total energy transmitted is e (a a a™) m . However, if the air gets its share first, the 
amounts of energy transmitted and absorbed by the air and water vapor respectively 

e o a a> e oV- a a)> e o a a- a w> e o a a (l-a w ); 

but if the water vapor gets its share first they are: 

e o( a w a a)' e o a w^~ a J' e o a w> e {x-a w ). 

The final amounts transmitted are the same in each case, but the absorbent coming 
first gets the better chance, other things being equal. The values given in this section 
of the paper assume that the water vapor comes last, but since it extends to a very 
appreciable altitude, its share in the absorption relative to dry air is underestimated. 
The total effect of both together would be the same, irrespective of the distribution. 
These considerations in no way affect the use of the deflection in a band of water vapor 
to estimate the amount of water vapor or the absorptions as expressed in the next 
section, as in both these instances the use of ratios causes the inequalities just noted 
to appear with equal effect in numerator and denominator. 



TRANSPARENCY OF AQUEOUS VAPOR 407 

losses of solar energy due to dry air, the water vapor, and both 
together are on the average when the sun is in the zenith: 

8 per cent (o. 15 cal.); 9 per cent (o. 17 cal.); 17 per cent (0.32 cal.). 

When the sun is about 70 (m= 2 . 9) from the zenith, the correspond- 
ing values become : 

20 per cent (0.39 cal.); 13 per cent (o. 25 cal.); 33 per cent (0.64 cal.). 

For Washington on the driest day (0.5 cm precipitable water) the 
corresponding values are : 

10 per cent (o. 19 cal.) ; 10 per cent (o. 19 cal.) ; 20 per cent (o. 38 cal.) ; 
23 per cent (0.44 cal.); 19 per cent (0.37 cal.); 42 per cent (0.81 cal.). 

(The loss due to the dust at Washington is included with that due 
to water vapor.) The far greater transparency of the air at Mount 
Whitney is largely due to the small amount of water vapor. On 
the days on which spectroscopic observations have been made 
there was never more than 0.1 cm precipitable water above the 
mountain. With this amount of water vapor the corresponding 
values are : 

8 per cent (o. 15 cal.); 4 per cent (0.08 cal.); 12 per cent (o. 23 cal.); 
17 per cent (0.33 cal.); 6 per cent (o. 12 cal.); 23 per cent (0.45 cal.). 

It seems perhaps strange at first sight that with increasing air 
masses the amount of absorption by water vapor (area of the bands) 
may decrease despite the increased amount of vapor in the path of 
beam, even seven fold in the extreme range in the table. This is 
principally due to the increasing air scattering (see last footnote) 
which leaves much less energy for the vapor to absorb. But this 
is continually helped by the decreasing efficiency of the increased 
amount of vapor as an absorber, as shown by the curve connecting 
the absorption with the amount of vapor (Fig. 3, e). 



FRACTIOXAL TRANSMISSION OF ENERGY BY WATER VAPOR 

In general we cannot state what fraction of the radiation from 
an}- body whatever will be transmitted by a known amount of 
water vapor; for this depends upon the distribution of the energy 



4o8 



F. E. FOWLE 



in the spectrum as well as upon the amount of vapor. In a per- 
fectly pure spectrum coefficients of transmission might be deter- 
mined for each wave-length which would probably hold as well in 
this case as for the more slowly varying molecular scattering. But 
this is not feasible. The next best scheme is to divide the spectrum 
into small regions, each containing one of the aqueous vapor bands, 
and to show by empirical curves how the transmission varies with 
the amount of vapor in these regions. The bands and limiting 
wave-lengths and deviations chosen are indicated in Fig. 2 by the 
broken lines at the bottom of the figure and are as shown in Table V. 

TABLE V 



Band 


Range of 
Deviations 


Range of 
Wave-Lengths 


a 


Q2-5-97-5 
82. s 87.5 
70.0 80.0 
55-° 67. s 
35° 54-0 
-7-5 35-° 


0^70 — 0^74 
O.79 O.84 
. 86 . 90 
1.03 1.23 
1-24 i-53 
i-53 2.19 




PCTT . . 


* . . 


*. . 


a 





Curves showing the fractional transmission in these regions as 
varying with the amount of water vapor are shown in Fig. 4. The 
nearer the distribution of energy in the spectrum is solar, the more 
accurately these values apply. Unfortunately the most powerful 
band, 12, is very wide and lies in a part of the spectrum in which 
the distribution of energy varies widely as we pass from bodies of 
solar temperature through the more intense illuminants (Nernst 
lamp, e.g.) to terrestrial sources of radiation. In the case of the 
sun, 12 per cent of the total radiation sent to us lies in the region 
affected by this great band; in the case of the Nernst lamp about 
20 per cent lies within this region, whereas for a source at ioo° C. 
(373° K.) less than a tenth of 1 per cent lies within the whole region 
of wave-lengths less than 2 fx considered in this communication. 



SUMMARY 



The main object in view in the presentation of this communica- 
tion has been to give definite answers to the two questions: How 
much is lost from the incoming solar energy in its transmission 



TRANSPARENCY OF AQUEOUS VAPOR 



409 



through the different constituents of the atmosphere ? What is the 
fractional transmission of energy by dry air and by aqueous vapor, 
and how does it vary as we pass from wave-length to wave-length 
through the spectrum ? 

The first question is answered in Tables II, III, and IV which 
give, for an elevation of 4420 m (Mount Whitney, barometer 



l( 

.9 
.8 
.7 
.6 
.5 

C 


ifi 




Hi- ___ 


































































u 


\ 


S 


























a 


n 




^ 


^J 


























U 






























3a 


































U 






























-± 


n 


\ 




























~P~ 


u 




\ 


























IT 


A 
































u 






























































t 


) r 2 CM - 3 CM 4^ 5 C " 6 CM - 7" I 


CM. 



Amounts of precipi table water 
Fig. 4. — Fractional absorption of energy by water-vapor bands 

44.7 cm), of 1730 m (Mount Wilson, barometer 62.3 cm), and sea- 
level (Washington) , the amounts of heat as calories and percentages 
of the incident energy (1.93 15° C.-gram calories) scattered and 
absorbed at different air masses by dry air and by air containing 
various amounts of precipitable water. 

Further, when we know the amount of precipitable water in the 
air and that the distribution of energy in the spectrum is approxi- 
mately solar, by first reducing our observed curve to certain stand- 
ard conditions we may determine through the curves of Fig. 3 what 



410 F. E. FOWLE 

areas of the energy-curve would be cut out by the water vapor and 
other absorption bands of atmospheric air. 

The distribution of energy in the solar spectrum (outside the 
atmosphere) produced by a 6o° ultra-violet glass prism is given in 
Table I. 

The answer to the second problem, the fraction absorbed from 
wave-length to wave-length, will be found in Fig. 4 and as follows: 
The non-selective scattering due to dry air and associated with 
water vapor will be found in Table I in the lines indicated by a aK 
and a u .\, respectively. These values vary nearly continuously with 
the wave-length, and may be used with the e lines of the same 
table'to find the intensity for any wave-length through the formula 

e=e \a aK -a^\ m , 

where m is the air mass and equal to the secant of the zenith dis- 
tance within 1 per cent for zenith distances less than 70 . This 
formula is for the altitude of Mount Wilson. For other altitudes 
the exponent m must be multiplied by the ratio of the barometer 
reading to that at Mount Wilson (62.3cm). In the spectrum 
regions of selective absorption a further allowance is necessary, 
as shown in the body of this communication. Of course for other 
distributions of energy, other values would be used for e , and m 
would become the length of path. 

For the bands of selective absorption the spectrum has been 
divided into certain indicated regions for which Fig. 4 gives the 
fractional transmission corresponding to definite amounts of water 
vapor. 

It should be remarked that there is no reason to suspect that 
the selective (banded) absorption produced by a given amount of 
water in the form of vapor should be different, whether observed in 
the laboratory or in the atmosphere. However, in the case of non- 
selective scattering, the amount scattered by atmospheric vapor is 
greater than would be expected from the number of molecules of 
water vapor present; hence the use of the expression "associated 
with water vapor." Liquid water scatters what would be expected 
from the number of molecules. 1 

1 Astrophysical Journal, 38, 39J, 1913. 






TRANSPARENCY OF AQUEOUS VAPOR 411 

A comparison between observations of humidity from a balloon 
and nearly simultaneous spectroscopic determinations of the 
amounts of water vapor in the air shows an exceedingly satisfactory 
agreement. 

This paper is the fifth of this series in this Journal discussing the trans- 
mission of radiation through moist and dry air and water vapor. The first 
(35, 149, 191 2) furnished the laboratory calibration, with known amounts of 
water vapor, of the intensity of energy in certain absorption bands the depths 
of which could be very accurately measured bolometrically. The second 
(37> 359> I 9 I 3) gave some applications of the first in the spectroscopic deter- 
mination of the water vapor above Mount Wilson and a comparison of these 
values with determinations by Hann's formula. The third (38, 392, 1913) 
treated of the non-selective scattering of dry air and water vapor for the 
spectrum region between the wave-lengths 0.35 /x and 2.00/x. The fifth 
gives the corresponding selective absorptions. The fourth (40, 435, 1914) 
was concerned with the application of the dry-air transmission coefficients to 
the determination of Avogadro's constant, the number of molecules in a gram- 
molecule of any gas. 

ASTROPHYSICAL OBSERVATORY 

Smithsonian Institution, Washington, D.C. 
August 1915 



THE ELEMENTS OF THE ECLIPSING SYSTEMS TV, TW, 
TX CASSIOPEIAE AND T LEONIS MINORIS 1 

By R. J. McDIARMID 

The following four eclipsing stars have been under observation 
by the writer for three successive seasons with the sliding-prism, 
polarizing photometer, attached to the 23-inch equatorial of the 
Princeton University Observatory. This paper gives the results 
obtained from the discussion of these systems. 

TABLE I 



Star 


Position 1900 


Period in 
Days 


Epoch of 


a S 


J.D.G.H.M.T. 


TV Cassiopeiae 

TW Cassiopeiae 

TX Cassiopeiae 

T Leonis Minoris 


o h i3 m 55 8 
2 37 38 
2 44 24 
9 42 33 


58°35' 
65 18.6 
62 22.4 

33 45-2 


1. 812635 
2-857293 
2.926870 
3.0198965 


2420117. 742 
2419823.432 
2420448.923 
2420573.698 





Star 


Spectrum 


Magnitude 


Eclipses* Duration 




Max. 


Prim. 


Sec. 


Prim. 


Sec. 




TV Cassiopeiae 

TW Cassiopeiae 

TX Cassiopeiae 

T Leonis Minoris 


B 9 
B 9 

B3-B5 
A0-A5 


7.27 

8.29 

9-25 

10.00 


8.32 

8.91 

9.80 

12.46 


736 
8.86 

9-57 
10.04 


6^24 P 

7-54 A 

22. 24 A 

9.28 P 


6^24 P Astbury 

6 . 94 T Leavitt 

22. 24 T Leavitt 

9 . 28 P Leavitt 



*P=partial. T=total. A = annular. 

The periods of TV and TW Cassiopeiae have been determined 
from the writer's visual observations, while the periods of TX 
Cassiopeiae and T Leonis Minoris have been determined by com- 
bining the Princeton visual observations with Harvard photo- 
graphic observations dating back to 1889. The epoch of minima 
for the four stars are all from the writer's visual observations. The 
spectral type of each star was determined by Miss Cannon and 

1 Dissertation presented to the faculty of Princeton University in candidacy for 
the degree of Doctor of Philosophy. 

412 



ELEMENTS OF ECLIPSING SYSTEMS 413 

kindly communicated by Professor E. C. Pickering. The magni- 
tudes were obtained by comparing the variable with stars in the 
same field, whose magnitudes have been determined photometrically 
at Harvard. These results are given in Table I. 

The light-variations of the four systems have been carefully 
observed and are well defined by the respective light-curves. In 
all there have been over 35,000 measures of brightness made, six- 
teen measures constituting one complete observation. In discus- 
sing the observations a system of weights was adopted (maximum 
weight being 5), depending on condition of the sky, presence of 
dew or frost on object-glass, physical condition of the observer, and 
the accuracy of the recorded times. The observations were 
grouped into normals according to phase, each normal representing 
the weighted mean of five complete observations. The observa- 
tions of the first three stars are well distributed throughout the 
entire period of variation. In the case of T Leonis Minoris, 
however, the observations are not so numerous and the normals 
do not all consist of five observations each. 

TV CASSIOPEIAE 

The following discussion is based on 620 observations of 16 
settings made by comparing the variable with B.D.+ 58°29, 
magnitude 9. 94 (the magnitude of B.D.+58°29 was obtained from 
the comparisons with TV Cassiopeiae, five separate determinations 
of whose magnitude at normal light are given in Harvard Annals, 
45). Each point in the curve, with one exception, represents the 
weighted mean of five observations, making 123 normals in all. 
This star has been observed by Astbury and Xijland. For 
Nijland's results, see Shapley's Contribution Xo. j, Princeton Uni- 
versity Observatory. Both observers give the variation at primary 
minimum as one magnitude; no mention is made, however, of a 
secondary eclipse. It was partly for that reason, on Dr. Shapley's 
suggestion, that an extensive study of the system was decided on. 
The Princeton observations indicate a period 5 . 7 seconds longer 
than that given by Astbury; it was found that the primary 
eclipse was nearly i M 05 in depth and that there was a secondary 
eclipse of o M 09. The secondary minimum is slightly displaced, 



414 



R. J. McDIARMID 



coming 17 minutes before mid-period, showing that the orbit is 
eccentric. 

The light between eclipses does not remain constant, showing 
the presence of reflection and ellipticity. These two effects were 
removed from the light-curve in much the same manner as that 
recorded in Russell and Shapley's paper on Z Draconis. 1 From a 
preliminary discussion, values 0=1.003, 6 = 0.040, c= 0.045 were 
obtained. Corrections to these quantities were made from a 
least-squares solution, taking into account depth of secondary 
minimum, as well as the time of secondary. Assumed depth of 
secondary ^=0.104 and time of secondary = 2 i h 24 m . 

The conditional equation is of the form: 

l = a—b cos 6— c cos 2 6— nd-\-e. 

The constants in the equation have the same signification as in the 
foregoing reference. Table III contains the conditional equations 
used in the least-squares solution. 



TABLE II 
Table of Observations. TV Cassiopeiae 

PRIMARY MINIMUM 



Nor- 




Mag. 






Nor- 




Mag. 






mal 


Phase 


Diff. 


o.-c. tt 


°- c d 


mal 


Phase 


Diff. 


o.-c. M 


°- c d 


No. 




(»— a) 




No. 




(v— a) 






1. . 


-4 h 54 m I 


2**641 


+0^025 


+0^025 


20. . 


— O h o6 I ?2 


1^635 


o^ooo 


+o¥oo3 


2. . 


4 19-7 


2.622 


+0.012 


+O.OI2 


21 . . 


+ 10.7 


I.625 


-0.015 


— O.OIO 


3- • 


3 46. 5 


2-577 


— O.OIO 


—0.008 


22. . 


O 25.6 


1. 671 


—0.008 


0.000 


4-- 


3 34-8 


2.578 +0.008 


+O.OIO 1 


23- • 


O 40.4 


1-744 


— O.OIO 


0.000 


5-- 


3 259 


2.497 


-0.052 


-0.054 


24. . 


O 51-3 


1.799 


-0.015 


—0.006 


6.. 


3 14-6 


2.512 


— O.OI2 


-0.015 


25- ■ 


1 02.3 


1. 891 


+0.006 


+0.006 


7-- 


3 04.6 


2.482 


-0.013 


—0.020 


26.. 


I II .9 


1.949 


0.000 


0.000 


8.. 


2 49.6 


2.438 


— 0.012 


-0.015 


27.. 


I 23.2 


1.999 


—0.017 


—0.020 


9. . 


2 31.6 


2.363 


— O.OIO 


— O.OIO 


28.. 


I 36.I 


2.036 


— 0.060 


—0.060 


10. . 


216.7 


2.288 


—0.014 


—0.016 


29.. 


I 48.3 


2.132 


-0.038 


-0.035 


11 . . 


2 02.5 


2. 211 


—0.020 


-0.025 


30. - 


I 59-0 


2.188 


—0.030 


-0.038 


12. . 


1 43-4 


2.163 


+O.OI2 


+0.012 


3i-- 


2 O9.O 


2.244 


-0.034 


-0.034 


13- ■ 


1 26.7 


2.078 


+0.032 


+0.032 


32.. 


2 I9.8 


2.324 


+0.005 


+0.003 


14. . 


1 11. 3 


1-955 


+0.013 


+0.020 


33- • 


2 32-9 


2.385 


—0.004 


—0.006 


I5-- 


058. 5 


1.828 


—0.020 


— O.OIO 


34- • 


2 43-0 


2-437 


+0.008 


+0.005 


16.. 


47.0 


1.782 


—0.003 


0.000 


35- 


2 59-5 


2-535 


+0.045 


+0.040 


17.. 


35-2 


1-738 


+O.OIO 


+0.015 


36.. 


3 19-3 


2.606 


+0.065 


+0.065 


18.. 


27. 7 


1.692 


+0.005 


+O.OIO 


37-. 


3 54-9 


2.646 


+0.042 


+0.052 


19.. 


17.0 


1.682 


+0.020 


+0.023 


38.. 


4 52-5 


2.634 


+0.015 


+0.015 



1 Astro physical Journal, 39, 405, 1914. 



ELEMENTS OF ECLIPSING SYSTEMS 



415 



TABLE II — Continued 

CONSTANT LIGHT AND SECONDARY MNIMUJI 



Normal 
No. 



39- 
4°- 
4i- 

42. 

43- 

44- 



Phase 



-h- -m - 

3 MO 

6 27.8 

6 50.8 

7 22.3 
7 40.3 
7 53-3 



Mag. Diff. 

(B-O) 



45 817-8 

46 856.3 

47 9 15-5 

48 1 10 12.0 



49- 
50. 
Si- 
52. 
53- 



11 16.9 

12 09.7 

12 49.2 

13 10. 1 
13 26.7 



54.. ■ 1342.9 
J 3 59-i 



56. 
57- 



59- 
60. 
61. 
62. 
63. 

64. 
65. 
66. 
67. 

68. 
69. 



73- 

74- 
75- 
76. 
77- 



79- 
80. 



14 21.3 

14 51 r 

16 35-5 

16 55 7 

17 15-5 

17 38.9 

18 17.4 

18 56.6 

19 255 
1946.7 

19 58.3 

20 09 . 1 

20 20.4 
20 35.2 
20 46 . 4 

20 56. 1 

21 02. 2 
21 09 . 1 

21 15.4 

21 21.7 

21 28.1 

21 35-6 

21 42.4 
21 49.7 

21 58.4 

22 04.8 
22 14.5 



2^665 
2.666 
2.653 
2.603 
2.710 
2-653 

2.639 
2.668 
2.615 
2.688 

2.674 
2.713 
2.689 
2.696 
2.660 

2.658 
2.708 
2.709 
2.647 



2.676 
2.668 
2.616 
2.643 
2.586 

2.628 
2.640 
2.602 
2-594 

2-552 
2.632 

2 635 
2.603 

2-599 
2.562 

2-55° 
2-525 
2-53i 
2-555 

2-534 
2.570 
2.602 
2.576 
2-565 



O.-C. 



+0^030 
+0.028 
+0.014 

-0033 
+0.056 
+0.005 

-0.013 
+0.010 

— 0.044 
+0.016 

+0 . 004 
+0.038 
+0.006 
+0.014 

— 0.020 

— 0.022 

+0.027 
+0.027 
—0.024 

— 0.016 

+0.010 
+0.006 

— 0.040 

+0.005 
-0.045 

+0.017 
+0.040 
+0.007 

+0.003 

—0.003 
+0.050 
+0.060 
+0.030 
+0.026 

— 0.003 

— O.OIO 

—0.030 
—0.022 
—0.004 

—0.022 
+0.005 
+0.030 
+0.004 
—0.014 



Normal 
No. 



90 

91 
92 

93 
94 
95 
96 

97 
98 

99 
100 
101 
102 

103 
104 
105 
106 



107 
108 
109 
no 
III 

112 

"3 
114 

115 
Il6 



117 
Il8 
119 
I20 
121 



122 
123 



Phase 



22 h 25™2 
22 36.6 

22 49.9 

23 OI.4 

23 I4.8 

23 29.O 

23 44-5 

24 06.9 
24 29.5 

24 51.6 

25 15-4 
25 40.1 

25 15-3 
25 49-2 

27 18.4 

27 54-9 

28 34.4 

29 03 . 1 
29 22.5 

29 44-9 

30 13-9 
3° 43-6 

31 33-6 

32 07.0 

32 26.4 

32 53-6 

33 20.4 

33 47-8 

34 25.1 

34 54-3 

35 19-7 

35 50-4 

36 20. 2 
36 42.0 

36 55-4 

37 04.8 
37 20.8 
37 33-5 

37 47-5 

38 02.9 
38 16. 1 



Mag. Diff. 
(v-a) 



O.-C. 



2% 1 1 
2.585 
2-55° 
2.633 
2.615 

2.589 
2.637 
2.650 

2-653 

2.661 

2.641 

2.674 
2.644 
2.652 

2.676 
2.650 
2.689 
2.692 
2.688 
2.703 

2.676 
2.685 
2.703 
2.692 

2.679 
2.670 
2.659 
2.618 
2.623 

2.638 
2.677 
2.622 
2.658 
2.631 

2.592 
2.598 
2.581 
2.644 
2.608 

2.603 
2-599 



+ 0' VI 02 2 

— O.O06 
-O.O43 
+ O.O33 
+O.OIO 

— 0.020 
+O.OI5 
+0.020 
+ O.OI2 
+ O.OI2 

-O.OI5 
+ O.O06 

— 0.022 

— O.OI7 

+0 . OO4 

— O.O23 

+ O.OIO 
+ O.OI2 
+0 . OOS 
+ O.O23 

— O.OO4 

+ . OO5 
+O.O23 
+ O.OI8 

+ O.OO4 
+ O.OO3 
+ 0.002 
-O.OI3 

— O.O44 

— O.OI2 

+ 0.028 

— O.OI6 
+0.022 
+0.002 

-O.O36 
-O.O3O 

— O.O40 

+ 0.022 

— O.OIO 

—0.016 
—0.007 



4i6 



R. J. McDIARMID 



TABLE III 
Conditional Equations of TV Cassiopeiae 



8a 


Sb 


Sc 


Sd 


e 


O.-C. 




— O.64 

-0.43 

— 0. 14 
+ O.29 
+ 0-47 
+ O.52 


— 0.41 

— 18 






— 0.026 








+0.005 










— 0.004 




— O 08 






+0.006 










— 0.002 


0.7 


— O.40 


— O.07 


+O.OI 


— . 009 


0.9 


+ O.77 


— O.67 


-Q-45 


+0. II 


— 0.019 


0.9 


+ O.86 


-O.83 


-0.72 


+ 0. IO 


+0 . 004 


1 .0 


+ O.98 


-O.97 


-0.80 


+ O.06 


+0.009 


0.9 


+ O.89 


-O.89 


-0.89 


+ O.04 


+0.026 


0.9 


+O.90 


— O.90 


-0.86 


— O. IO 


— 0.012 


0.9 


+O.90 


— 0.90 


-0.74 


— O.IO 


— O.OOI 


0.9 


+O.89 


-O.89 


-0.63 


-0.08 


+0.007 


0.9 


+O.88 


-O.87 


-0.48 


-0.08 


— 0.004 


0.9 


+ O.86 


-O.83 


-0.27 


-0.05 


+0.005 


1 .0 


+0.91 


-O.74 


— 0.00 


— O.OI 


+0.009 




+O.79 
+O.60 

+0-37 
+O.05 


-O.56 
-O.36 
-0.13 






— 0.021 








— 0.005 








+0.019 








+0.010 




— O.04 






— 0.025 




-O.47 






+0.005 




-O.38 
-O.51 






— 0.020 




— O. 72 






— 0.002 











The'following normal equations were formed: 

+ 22.90080+ 7. 849 S& — 11 . 201 8c — 5.4688c? — o.o86e= —0.0135 
+ 7.849 +11.365 — 7.528 —5.262 —0.083 =+0.0061 

— 11. 201 — 7.528 + 8.708 +5.217 +0.073 =—0.0089 

— 5.468 — 5.262 + 5.217 +4.142 +0.060 =—0.0237 

— 0.086 — 0.083 + 0.073 +0.060 +0.063 =+0.0013 

The adopted values with their probable errors are: 



a = i .002 ±0.003 
b = 0.037 = 0.004 
c = 0.05 2 = 0.009 



d = 0.080= 0.009 
e = 2i h 28 m =7 m 



Probable error of one normal place outside principal minimum : 

:O.Ol6. 

The observations were now ''rectified" by use of the formula 

/ observed -\-b ( 1 +cos 6) 



I rectified = 



( 1 +b) (a -c cos 2 6) 



ELEMENTS OF ECLIPSING SYSTEMS 417 

after which the method of solution for spherical stars equally bright 
on both sides may be applied with slight modification (see Astro- 
physical Journal, 36, 406, 191 2). 

When the star-disks are assumed to be of uniform brightness, 
the value of the function x(£« <*o, i) which defines the form of the 
light-curve for the principal minimum was found to be 1.876. 
With the aid of Table III 1 and this value and the depth of the recti- 
fied primary and secondary minima, the ratio of the radii of the 
stars, k, comes out 0.95 and the percentage of obscuration, a , 
0.628. The other elements were then determined as indicated in 
Astro physical Journal, 36, 406, 191 2. 

For disks darkened at the limb, the observations are represented 
equally well. From the " rectified " depth of primary and secondary 

eclipses and the equation Q(k, a )= _, \ , values of k and a 

were computed; these values for k range from £ = 0.82 to 1.00 
and from <z =o.62 to 0.64. Upon computing %(&, a-o,o),x(k,a ,j), 
and x(k, a , f ) from the observed curve, it was found that the pos- 
sible range of values for k and a was very small. The most satis- 
factory curve was found for a = o. 62 and k — o. 884. The resulting 
light-curve was computed by means of Tables IILr and II#. 

The elements for the two solutions are given in the table of 
results. The residuals for the uniform and darkened solutions are 
scaled from the computed curves and are given in the table of 
observations. The probable error of one normal place in the 
principal eclipse is ±o M oi7 for uniform solution and =±=o M oi7 
for the darkened. Fig. 1 gives the theoretical light-curve derived 
from the uniform solution, and Fig. 2 diagrams of the systems 
resulting from the uniform and the darkened solutions. 

TW CASSIOPEIAE 

This star was discovered by Miss Leavitt on the Harvard plates, 
and has been observed by Munch 2 and Zinner. 3 From the pub- 

1 This and following references are to tables in Astrophysical Journal, 35, 36, 
1912. 

2 Astronomische Nachrichten, 182, 113, 1909. 
*Ibid., 190, 377, 1912; 195, 453, 1913. 



4i 8 



R. J. McDIARMID 



= 



Mag. diff. (v-a) lished note of Munch, the star 

o o 

* was given as an Algol variable 

with a period of 10 days, or 
probably irregular. The range 
of his variation was 8^0 to 
8 M 49. Zinner also thought it 
irregular from early observa- 
tions but later found it to be a 
variable of the Algol type with 
a period of i d io h i6™7 and a 
variation from 8 M 3 to 9 M o. 

The variation of this star 
is well denned by the Princeton 
observations. In all, 820 com- 
plete observations have been 
made on the star by comparing 
it with B.D. 64°343, magnitude 
10.49 ( tne magnitude of which 
was obtained by photometric 
comparison with three stars 
whose magnitudes are given 
in Harvard Annals, 64). The 
observations were grouped in 
the usual manner into 172 
normals. The eclipses have 
been observed five times each, 
in order to define the curve 
precisely. From the plot of 
the observations it appeared 
that the alternate eclipses, 
which had been considered 
similar, were of slightly differ- 
ent depth. The assembling of 
the observations on a period 
double Zinner's and the plot- 
ting of the normals confirmed this suspicion. The period is undoubt- 
edly double that given by Zinner and is confirmed by the following 




ELEMENTS OF ECLIPSING SYSTEMS 



419 




observed phenomena in the light-curve: first, there is a difference 
in depth of the two eclipses of o M o5; second, the interval from 
primary eclipse to secondary is 7.8 minutes longer than from 
secondary to the following primary; third, the two eclipses are 
of different duration, the primary being at least 36 minutes longer 
than the secondary. The last two facts show that the orbit is 
eccentric and in this case, as will be shown later, both the eccentri- 
city and longitude of periastron can be determined from the 
light-curve. The range of varia- 
tion agrees closely with Zinner's 
determination, as the loss of 
light is o M 62 for the primary 
and o M 57 for the secondary. 

The light between eclipses 
remains sensibly constant. In 
this system we have two well- 
defined eclipses of nearly the 
same depths and duration. The 
orbital eccentricity considerably 
complicates the solution, and 
several trials were made before reaching a satisfactory repre- 
sentation of the light-curve, in which, on the hypothesis of 
uniformly bright star-disks, the principal eclipse is annular and 

the secondary total. The value of k was 0.858, obtained from 

j \^ 

the relation 1 — \p-\ 7 — =1, where 1 — X/>= 0.436 and 1 — Xs = 

0.408, the loss of light at primary and secondary eclipse respec- 
tively. From the Table II of the function \f/(ka ) for uniform 
disks, we can compute the light-curve for each minimum separately, 
adjusting the quantities A and B to get the best representation of 
the observations. For primary eclipse ^. = 0.0176, $=0.01430, 
and for secondary, ^4 = 0.01516 and B = 0.00286. Following the 
notation as indicated in Astrophysical Journal, 36, 406, 191 2, the 
radii of the stars from the two minima came out r= 0.183, r = 
o. 157 for the primary, andr=o. i69andr = o. 145 for the secondary. 
It was also found that the semi-durations of the two eclipses differed 
by 18 minutes, the primary being the longer. The difference in 



Fig. 2. — Diagrams for uniform and 
darkened solutions for TV Cassiopeiae. 



420 



R. J. McDIARMID 



TABLE IV 
Table of Observations. TW Cassiopeiae 

PRIMARY MINIMUM 



Nor- 




Mag. 




Nor- 




Mag. 






"mal 


Phase 


Diff. 


°- c -„ 


o.-c, 


mal 


Phase 


Diff. 


°- c „ 


°- c d 


No. 




(a — v) 


u 


No. 




(a—v) 


u 


I . . 


-o'Wu^S 


2 M IOI 


+o M ooi 


+o*'ooi 


18.. 


+O d O h OI n l 1 8 


i M 407 


+0^017 


+0^025 


2. . 


3 59-8 


2.I05 


+0.005 


0.000 


19. . 


OII.O 


1.478 


0.000 


-0.005 


3-- 


3 39-3 


2.074 


— 0.020 


-0.015 


20. . 


O 21 .9 


1.506 


0.000 


0.000 


4-- 


3 °9-4 


2.OI9 


-0.038 


—0.040 


21 . . 


O 32.8 


1.502 


— 0.032 


— 0.028 


5-- 


2 41 .6 


I.998 


0.000 


-0.003 


22. . 


O 43.8 


I.569 


— O.OIO 


— O.OIO 


6.. 


2 15.0 


I .842 


-0.036 


-0.038 


23- ■ 


55-3 


1-615 


— O.OI2 


-0.015 


7-- 


1 54-9 


I.856 


— O.OIO 


-0.015 


24. . 


1 05.4 


1.668 


— O.OIO 


—0.008 


8.. 


1 42.5 


I.83O 


0.000 


0.000 


25- • 


1 17.9 


1 . 702 


-0.025 


—0.027 


9- • 


1 31. 1 


I.829 


4-0.025 


+0.022 


26.. 


1 30.6 


I.790 


0.000 


0.000 


IO. . 


1 20.9 


1-773 


+0.025 


+0.020 


27. . 


1 41 .0 


1-833 


+0.008 


+0.006 


ii . . 


1 11. 5 


1 . 701 


0.000 


0.000 


28.. 


1 53-3 


1.889 


+0.016 


+0.013 


12. . 


57-5 


1.605 


— 0.0301—0.030 


29. . 


2 05 . 5 


I-903 


-0.003 


— O.OIO 


I3-- 


43- 1 


1 .604 


+0.025 


+0.025 


30. . 


2 26.9 


1.968 


0.000 


— . 003 


14.. 


33-7 


1.510 


— 0.017 


—0.018 


3I-- 


3 05.3 


2-053 


+0.004 


0.000 


I5-- 


25.8 


1.492 


— O.OIO 


— O.OIO 


32.. 


3 45-9 


2. II3 


+0.013 


+0.013 


16.. 


16. 7 


1.472 


-0.003 


— O.OIO 


33- • 


4 09.7 


2.072 


—0.028 —0.028 


17. . 


07.9 


1.464 


— O.OI2 


—0.006 


34- • 


4 48.2 


2.I05 


+0.005+0.050 






SECONDAR\ 


mini: 


iUM 




Nor- 




Mag. 






Nor- 




Mag. 






mal 


Phase 


Diff. 


o.-c. 


°- c d 


mal 


Phase 


Diff. 


o.-c. M 


0.-C.4 


No. 




{a—v) 


tt 


No. 




(a—v) 




I . . 


I^OI 1 ^ 


2 M I02 


+ N1 002 


+ M 002 


20. . 


I d IO h 34™9 


i M 5Q4 


— 0^024 


— O^OI2 


2. . 


636.8 


2.068 


— 0.032 —0.032 


21 . . 


10 42.3 


1-539 


+0.003 


+0.015 


3-- 


6 54 


2 . I08 


+0.008 


+0.008 


22. . 


10 50.8 


1-594 


+0.025 


+0.040 


4- • 


7 21 . 1 


2.069 


— O.OIO 


— 0.020 


23- • 


10 59-3 


1.605 


0.000 


—0.008 


5-- 


7 43-4 


2 .022 


— O.OIO 


-0.030 


24. . 


11 06 . 7 


1 .612 


— O.OIO 


0.000 


6.. 


8 02.7 


2.060 


+0.070 


+0.045 


25- • 


11 12.2 


1 .607 


-0.050 


-0.035 


7-- 


8 16. 1 


2.O42 


+0.050 


+0.027 


26.. 


11 20.5 


1.667 


— 0.016 


—0.006 


8.. 


8 33° 


1-925 


+0.030+0.008 


27. . 


11 27.7 


1.723 


+0.003 


+0.002 


9.. 


8 49. 2 


I.83O 


— O.OIO 


— 0.030 


28.. 


11 37.2 


1-745 


— O.OIO 


— O.OI2 


10. . 


904.0 


I. 8l6 


+0.022 


+0.018 


29.. 


11 51-7 


1.843 


+0.023 


+0.015 


11 . . 


9 16.6 


i-753 


+0.006 


+0.013 


30. - 


12 07.6 


1.856 


— O.OIO 


—0.020 


12. . 


9 28.7 


1 .696 


-0.005 


0.000 


3i- ■ 


12 25.1 


1.946 


+0.014 


-0.005 


I3-- 


9 39-6 


1 .609 


— 0.040 


— O.OI2 


32- • 


12 40.4 


2.003 


+0.026 


-0.005 


14. . 


9 48.4 


I-S7I 


— 0.032 


— O.OIO 


33- - 


12 59-9 


2.070 


+0.050 


+0.020 


IS-- 


9 57° 


1 -541 


— 0.020 


—0.008 


34- ■ 


13 23.2 


2.072 


+0 . 003 


+0.006 


16.. 


10 03.9 


I-5I9 


— 0.020 


— O.OI2 


35 •• 


13 51-2 


2.093 


—0.006 


— 0.007 


17.. 


10 10. 1 


1. 561 


+0.028 


+0.036 


36.. 


14 17.8 


2.083 


-0.015 


— 0.017 


18.. 


10 18.7 


1.528 


—0.003 


+0.007 


37- ■ 


1440.5 


2.092 


—0.008 


—0.008 


19.. 


10 27.3 


1-552 


+0.020 


+0.036 


38.. 


15 H-4 


2.096 


— . 004 


—0.004 



ELEMENTS OF ECLIPSING SYSTEMS 



421 



TABLE IV— Continued 

COXSTAXT-LIGHT OBSERVATIONS. TW C.A.SSIOPEIAE 



Phase 



Mag. DiS. 
(a—v) 



-.d r h 



2 NI OQ9 
2. 112 



5 u i4 

5 4i 

6 10.4 ' 2.095 
6 35.3 l 2. 116 

6 54.4 ; 2.076 



7 20.5 

7 40.5 
805.3 

8 432 

9 35-4 

10 14.4 
10 35-3 

10 59-4 

11 28.1 
" 35-4 

12 26.9 

13 28.6 

14 06.4 
14 26.5 

14 47.2 

15 29.6 

15 57-3 

16 19.8 

16 49.4 

17 11. 9 

1/ 37-8 

18 12.2 

19 00.0 
19 249 

19 502 

20 07.5 
20 51.8 

20 55.0 

21 22.6 

21 48.0 

22 02.6 
22 14.4 
22 29.1 

22 51. 1 

23 30.7 

[ 1 09.3 
2 09.2 
2 323 



2. 113 

2 ■ 065 
2. 115 
2. 109 

2. in 

2.069 

2. 112 
2. 118 
2.074 
2.071 

2.084 
2.083 

2. 113 
2. 112 
2.097 

2.092 
2.081 
2.105 
2-095 

2.078 



O.-C. 



— o M ooi 
+O.OI2 

-0.005 

+0.016 

— 0.024 

+0.013 
-0.035 
+0.015 
+0.009 

+ O.OII 

-0.031 

+O.OI2 

+0.018 

—0.026 
—0.029 

— 0.016 
—0.017 

+0.013 
+O.OI2 

— 0.003 

—0.008 

— 0.019 

+0.005 
-0.005 

— 0.022 



2 
2 
2 


143 
093 
082 


+O.O43 

— O.OO7 

— O.OI8 


2 
2 


133 
I08 


+O.O33 

+ O.O08 


2 


078 


— 0.022 


2 
2 
2 
2 


I02 

074 
092 
112 


+ 0.002 

— 0.026 

— 0.008 
+O.OI2 


2 


I02 


+0 . 002 


2 
2 
2 




124 
O9O 
I02 
I08 


+O.O24 
— O.OIO 

+0.002 
+0.008 


2 
2 


079 
122 


-0.031 

+0.022 


2 


no 


+O.OIO 



Normal 
No. 



44 
45 
46 

47 
48 

49 

50 
5i 
52 

53 

54 
55 
56 
57 
58 

59 
60 

61 
62 
63 

64 
65 
66 
67 
68 

69 
70 
7i 
72 

73 

74 
75 
76 

77 
78 

79 

So 
81 
82 
83 

84 
85 
86 



Phase 



I d 2 h 49 I P2 

308.8 
3 28.0 
3 4i-5 

3 53-0 

4 16.5 
4 43-7 

4 58.4 

5 12.5 
5 26.6 

5 38.6 
15 ii-4 

15 35-0 

16 25.6 

16 44.9 

17 08.4 

17 45-7 

18 49.8 

19 13-8 

19 41.2 

20 20.7 

21 06. 7 
21 27.9 

21 54.1 

22 28.8 

23 08.8 
23 48.9 

200 36.3 

1 28.8 

2 16. 1 

3 10.2 

4 05.8 

5 08.6 

5 48.7 

6 19.0 

6 50.7 

7 26.0 

8 13. 1 

8 50.2 

9 26.9 

9 53-4 
10 10.6 
10 30.9 



Mag. Diff. 
{a—v) 



O.-C. 



2^069 
2.082 
2. 117 

2.145 
2.106 

2.089 
2 .090 

2. I02 
2. I05 

2.I08 



— 0^031 

— O.OlS 

+ O.OI7 
+ O.O45 
+O.OO6 

— O.OII 

— O.OIO 

+0.002 
+0.005 
+0.008 



2 


I03 


+0.003 


2 


O96 


— 0.004 


2 


IOO 


0.000 


2 


I02 


+0.002 


2 


IOI 


+0.001 


2 


IOI 


+0.001 


2 


066 


-0.034 


2 


085 


-0.015 


2 


I05 


+0.005 


2 


no 


+0.010 


2 


086 


— 0.014 


2 
2 


124 
126 


+0.024 
+0.026 


2 


078 


-0.032 


2 


112 


+0.012 


2 


116 


+0.016 


2 
2 


096 
106 


— 0.004 
+0 . 006 


2 


118 


+0.018 


2 


087 


-0.013 


2 


109 
096 


+0.009 
—0.004 


2 


103 


+0.003 


2 
2 


058 
080 


— 0.042 

— 0.020 


2 
2 


131 
098 


+0.031 
+0.002 


2 


107 


+0.007 


2 


099 


— O.OOI 


2 


091 


—0.009 


2 


124 


+0.024 


2 


120 


+0.020 


2 


061 


-0.039 



422 



R. J. McDIARMID 
TABLE IV— Continued 



Normal 
No. 


Phase 


Mag. Diff. 
(a-v) 


O.-C. 


Normal 
No. 


Phase 


Mag. Difi. 
(a— v) 


O.-C. 


8 7 

88 

89 

9° 

91 

92 

93 


io h 5o™3 
11 08.5 

11 17-9 
11 30.9 
11 42.9 

11 55-5 

12 07. 2 


2.093 

2. IOO 
2.I08 
2. Ill 
2. I06 

2.069 
2. 112 


— O.OO7 

O.OOO 

+ O.O08 

+ O.OII 

+0.006 
-0.031 

+0.012 


94 

95 

96 

97 

98 

99 


l2 h i9'T , 6 

12 36.0 

13 26-3 

13 53-0 

14 12.3 

15 06.6 


2. 113 
2.087 
2. 121 
2.I08 
2.I07 

2. 115 


+0.013 
-0.013 

+0.021 
+0.008 
+0.007 

+0.015 



the computed radii of the stars, as well as in the duration of the 
eclipses, is due to the orbit being eccentric. 

By means of the equations (30) of Professor Russell's paper 1 

Primary Minimum Secondary Minimum 

rx=r x (l—grj) r " = ri{i+grj) 

cot *! = COt i(l — 2grj) cot ?'" = COt i{l-\-2grj) 

e sin co was determined from the two solutions. The values were 
in good agreement, being —0.0388 from the values of r, and 
— 0.0418 from those of cot i. The remarkable agreement of the 
two separate determinations of e sin co from the light-curve is a 
strong confirmation of the eclipse theory. The quantity e cos co 
was determined from the displacement of the secondary minimum 

6 COS tO = -r- — — . 

P(cosec 2 i-\-i) 

by the use of the equations (32) of the same paper, whence e and co 
were readily determined. The remaining elements of the system 
were computed in the ordinary way. 

In the solution for stars darkened toward the edge, it was found 
that the observations could not be represented with an annular 
and total eclipse. The eclipses were therefore considered partial 
and were drawn slightly deeper, i — \p= 0.440 and i — \s= 0.420. 
The eccentricity resulting from the uniform solution was adopted 
in the preliminary results. It was found that the observations were 
best represented for the stars equal. The values for k of 0.90 and 
0.95 were tried, however, but the results were not satisfactory. 

1 — X^ 1 — As _j (p2—px,)k 



By means of the equations 



<*i 



ak 2 



1, and g-- 



2+{p>+pi)k' 



Astrophysical Journal, 36, 57, 1912. 



ELEMENTS OF ECLIPSING SYSTEMS 



423 



+ 



where 1 — \p, i—\s, k and g are known, 
values of cii and a 2 were found. The curve 
for each minimum was then computed 
separately. It was found that a slight 
increase in the eccentricity would improve 
the agreement. The eccentricity was 
finally adopted as 0.05, and curves were 
computed for each minimum which satisfy 
the observations remarkably well. 

The elements obtained from the solu- 
tion are given in the table of results. The 
residuals for both uniform and darkened 
solutions have been scaled off from the 
computed curves for primary and 
secondary minima and are given in the 

table of observations. The probable error I : •{ I I J „ p 

of one normal place on the uniform 
hypothesis is ±0.015, an d for the 
darkened ±0.013. 

Fig. 3 gives the computed curve for 
stellar disks of uniform brightness, and 
Fig. 4 diagrams of the stars at elongation 
and at primary eclipse. 

TX CASSIOPEIAE 

This variable was discovered by Miss 
Leavitt 1 on the Harvard plates and 
announced as of the Algol type with a 
variation from 8 M 8 to 9 M 4. It has been 
observed by Zinner 2 and was first noted 
by him as an irregular variable; later he 
found it to be eclipsing, and gave its 
period as 2 d 22 h i3™cj. Zinner notes that 
there are two minima, the secondary 
having a flat bottom; eclipses last sixteen g 2 & ° 2> 
hours and the variation is 9^4 to io M c. 

1 Harvard Circular, No. 127. 2 Astronomische Nachrichten, 195, 453, 1913. 



X ~ r "^X 




. 


- 


■ J z[z 










; 




■ 


J 




' 


: . 




L 


-^ 


SJ 


^<^ 


^-Ji 


J w- *"*Lj 


«^> 


~7> 


J-*!**] 


.>"'" 


X _,^ _±_ 


^ X X : 


^X X 


X^ 


' .1 












1 * 








. . 


*, 




.' 












• 










* 














. 


V . 


^ 




"s, 


*"■< 


^-L 


r*^ 


X > 


> 


,-J'" 


^ X4- 


.-*X 


IIT' j_ 




yf m 


* 


it 




i , . 


•. 


:^ , ! XltX 




-ix -lit 


'. 


: 




nx xxxq 




*. 






424 R- J. McDIARMID 

In referring the published Harvard photographic observations to 
these elements, Zinner found they were not satisfied; the interval 
between minima seemed to be of variable duration. He concluded 
that the case was similar to Y Cygni, with the line of apsides in 
motion. 

This star has offered considerable difficulty in the photometric 
study. The period, owing to the nature of the light-variation, for 
a long time was doubtful. The small range of o M 55 for primary 
and o M 32 for secondary, together with the long duration of eclipses 
(over twenty-one hours), made the observing of a complete mini- 
mum at any one time impossible, even during the long nights of 
winter. Through the kindness of Professor E. C. Pickering in 
sending me a long series of Harvard photographic observations of 

this star dating as far back as 
1889, I have been able, by com- 
bining these with the visual 
observations, to establish the 
period very accurately. The 
observations over this interval 
/^^ of twenty-five years present no 

== V'_J' evidence, as suggested by 

, . Zinner, of a motion of the line 

I-iG. 4. — Llongation and primary 

eclipse of TW Cassiopeiae. of apsides. In fact, it was 

found that the two plates 
referred to are not epochs of faintness, but of brightness. The 
star was discovered on these plates by comparison with one where 
the star was faint. After a large number of observations on the 
system had been made, it was found that the comparison star used 
was also a variable of range about o M 2; its light being nearly con- 
stant about half the time with increases of two or three hours' 
duration at apparently irregular intervals of from four to eight 
hours or more. A detailed discussion of this star and the 
methods adopted for correcting the observations will appear in 
a separate paper to be published in the Journal of the R.A .S. of 
Canada. 

The light-variation of TX Cassiopeiae is very well defined by 
the Princeton observations. In all, 585 complete observations were 



ELEMENTS OF ECLIPSING SYSTEMS 



425 



TABLE V 

Table of Observations. TX Cassiopeiae 



Normal 
No. 


Phase 


Mag. Diff. 
(v-a) 


O.-C.rf 


Normal 
No. 


Phase 


Mag. Diff. 
(5—0) 


°-c d 


I . . . . 


— O d i5 h 02 I Po 


0**334 


+ o M oo5 


46... 


d I .h 53 n, I 


0^347 


— 0V010 


2. . . . 


11 59.8 


0383 


— 0.022 


47... 


16 15. I 


0.35I 


— 0.016 


3 .... 


11 39.1 


Q-357 


+0.005 


48... 


18 17.5 


0-339 


— O.OIO 


4 


10 50.0 


0.392 


— 0.012 


49. . . 


18 57-9 


0313 


+0.015 


5 . . . . 


9 °5-4 


0.429 


— O.OIO 


50. • • 


20 49 . 7 


o.333 


0.000 


6.... 


8 34.8 


0.411 


+0.020 


51. . . 


21 20.3 


0.320 


+0.018 


7.... 


7 3°-3 


0.474 


0.000 


52... 


22 16.0 


0-345 


-0.005 


8.... 


6 27.8 


0-5*3 


+O.OI2 


53- •■ 


23 05.4 


0.362 


-0.013 


9.... 


4 54-2 


0.643 


— O.OIO 


54- ■■ 


23 30.2 


0-345 


+O.OIO 


10. . . . 


4 21.7 


0.682 


—0.003 


55 — 


23 53-6 


o-399 


-0.038 


ri ... . 


4 01 . 2 


o.737 


— 0.030 


56... 


1 00 12.8 


0-353 


+0 . 008 


12. . . . 


3 33-2 


0.742 


+0.002 


57- •• 


37-3 


0.364 


+0.005 


13.... 


2 55- 1 


0.796 


— . 004 


58... 


1 11. 3 


0.384 


-0.005 


14 


2 24.6 


0.786 


+0.034 


59- ■ • 


1 31.6 


0.396 


— O.OI2 


15.... 


1 47-3 


0.874 


— 0.020 


60... 


1 47.0 


0.409 


— 0.016 


16.... 


1 12.3 


0.891 


— 0.018 


61... 


2 14.0 


0.386 


+0.014 


17. . . . 


54-2 


0.891 


— O.OIO 


62... 


2 43- 1 


0.443 


— 0.030 


18.... 


— 16.4 


0.882 


+0.005 


63... 


3 35-2 


0.435 


+O.OI2 


19.... 


+0 01 .4 


0.900 


-0.005 


64... 


4 47-3 


0.526 


-0.015 


20. . . . 


021.2 


0.879 


+O.OIO 


65... 


5 40.8 


o.558 


— O.OIO 


21 ... . 


50- 5 


0.883 


+0.004 


66... 


6 00.6 


0-557 


+0 . 008 


22. . . . 


1 11. 5 


0.858 


+O.OI2 


67... 


6 28.8 


0.621 


— 0.032 


23 •■.. 


1 40.6 


0.900 


— 0.044 


68... 


7 05.2 


0.607 


+0 . 008 


24 ... . 


2 15. 1 


0839 


—0.008 


69... 


7 29.5 


0.627 


+0 . 006 


25.... 


2 40.9 


0.828 


— 0.022 


70... 


7 47-i 


0.636 


+0 . 004 


26.... 


2 55-6 


0.782 


+0.008 


71... 


8 09.0 


0.666 


—0.018 


27... . 


3 192 


0. 770 


— 0.006 


72. .. 


8 26.0 


0.665 


-0.015 


28.... 


3 36 2 


0.742 


0.000 


73.. 


8 42.0 


0.648 


+0.005 


29. .. . 


3 58.3 


0.749 


-0.050 


74. . . 


9 00. 2 


0.668 


—0.008 


30. . . . 


4 15-3 


0653 


+0.030 


75- • • 


9 27.2 


0.662 


0.000 


31 •••• 


622.3 


0.498 


+0.033 


76... 


10 09.5 


0.665 


+0.003 


32.... 


7 02. 2 


0.503 


— 0.014 


77. . . 


10 48.4 


0.660 


+0.006 


33- •• ■ 


7 58.4 


0.441 


+O.OI2 


78... 


11 40.8 


0.674 


— . 008 


34- ■ • • 


8 26.6 


0.427 


+O.OIO 


79. . . 


12 17.0 


0.667 


— . 004 


35--.. 


9 20.8 


0.398 


+O.OI2 


80... 


12 42.5 


0.660 


+0.003 


36.... 


10 46.7 


0.366 


+0.014 


81... 


13 01.8 


0.696 


-0.045 


37 •••• 


11 39.8 


0.395 


-0.025 


82... 


13 20.2 


0.660 


— 0.004 


38.... 


12 05.0 


o.35i 


+0 . 008 


83... 


13 37-2 


0.632 


+0.020 


39 ••• 


12 28.7 


0.391 


-0.035 


84... 


13 56 -5 


0.647 


-0.005 


40 


12 51.0 


0-353 


0.000 


85... 


14 48.3 


0.606 


+0.014 


41. . . . 


13 16.5 


o.3 J 3 


+0.035 


86... 


15 39-7 


0.588 


—0.008 


42 


13 36.5 


0.366 


— 0.020 


87... 


16 12.2 


0.542 


+O.OIO 


43 • • • • 


14 15-3 


0344 


0.000 


88... 


16 49.6 


o.539 


—0.018 


44- • • ■ 


15 °9-4 


0.307 


+0.033 


89... 


17 19.7 


0.500 


—0.008 


45 • ■ ■ • 


15 36.1 


0.318 


+0.018 


90.. . 


17 42.5 


o.454 


+0.020 



426 



R. J. McDIARMID 
TABLE V — Continued 



Normal 
No. 


Phase 


Mag. Difi. 
(»— a) 


°- C d 


Normal 
No. 


Phase 


Mag. Diff. 

(v—a) 


o-c-i 


91. ... 

92. ... 
93 ... . 

94. ... 
95. ... 

96.... 
97. ... 
98.... 


O d l9 h 54™I 

20 45-3 

21 46.0 
23 10.6 
23 27.4 

23 50.2 

2 46.0 

1 19-3 


0^393 

0-375 
O.340 
O.367 
0-33I 

0-35I 
0-357 
O.309 


+0**005 
-0.005 
+0.020 

— 0.018 
+0.013 

— O.OIO 

— 0.016 

+0.023 


99... 
IOO. . . 
IOI . . . 

102. . . 

103. . . 

104. . . 

105... 

106. . . 


4 h 22™3 

4 53-5 

5 05.0 
5 19-7 

5 49-0 

612.2 

6 36.0 
6 53-6 


0M341 
O.342 
0.330 
0.34I 

0-357 

0.320 
0.318 
0.369 


— 0**015 

— 0.014 
0.000 

— O.OIO 

— 0.026 

+0.013 

+0.016 
—0.030 



made by comparing the variable with B.D.+6i°493, whose normal 
magnitude, 8 . 92, was determined by reference to three other stars in 
the same field, whose magnitudes are given in Harvard Annals, 64. 
The observations were grouped into 106 normals. The period, 
as determined, is 2 d 22 h i4 m 4i?7. The shape of the curve shows 
that the variation is of the /3 Lyrae type, as it is continuous, indi- 
cating that the stars are sensibly elliptical. 

The ellipticity of the stars was determined by the graphical 
method and it was found that there was also a slight reflection 
effect. The observations were corrected for these and the recti- 
fied light-curve obtained. It was found that in the rectified 
light-curve the secondary eclipse had a constant phase for nearly 
five hours, while the primary eclipse was clearly round-bottomed. 
On account of the long, flat bottom, it is obvious that the eclipse 
at secondary minimum is total. The primary eclipse, from the 
shape of the curve, would seem to be partial, if the star-disks are 
of uniform brightness. For the secondary to be a total eclipse and 
the primary partial, the orbit would necessarily be highly eccentric. 
This, however, is not consistent with the dimensions of the stars, 
as they are large in relation to the size of the orbit. The two 
minima are of the same duration and the secondary comes at 
mid-period. 

When a solution was attempted, assuming a circular orbit 
and uniform disks, with the secondary eclipse total and the primary 
annular, the computed curves for the two minima were not consist- 
ent with the shape of the observed curves. The deviations in 
many cases were several times the probable error of one observation. 



ELEMENTS OF ECLIPSING SYSTEMS 



427 



The assumption of uniform brightness 
in the stellar disks was therefore 
abandoned. 

In the case of stars darkened toward 
the edge, Professor Russell has com- 
puted several light-curves due to annu- 
lar eclipses of darkened stars for 
different values of k (Fig. 1, 
Astro physical Journal, 36, 386, 191 2) 
and has shown that the curves are all 
round-bottomed, since, as it moves in 
front of the larger star, the smaller one 
continues to cut off a brighter area of 
the larger star until the center is 
reached. 

On carrying out the solution for the 
darkened disks, the secondary was con- 
sidered total and the primary annular. 
From the rectified depths of the primary 
and secondary eclipses and the equation 

Q(k,a )= -^-r , where 1— X x = 0.299 

a — (1— Xj) 

and 1 — X 2 =0.171, for total eclipse a = 1 ; 
Q(k, a ) = 0.360. From Table V, for 
the value of function Q(k, a ) = 0.360 
there are possible values of k and a" 
ranging from &=o.552to& = o. 506, and 
a' /= i to a' /= i+.v (where the loss of 
light for central annular eclipse is i-\-x 
times that at internal contact), which 
corresponds to grazing annular and 
central annular eclipse. It was found, 
after several trials (use being made of 
Table ITy) that the primary eclipse was 
best represented by a central annular 
eclipse with value of ^'=1.147 and 
£ = 0.52. The primary curve was then 



Mag. diff. (a—v) 



S 



7- 



a > 



OC rC 



+ 



fs. 



428 



R. J. McDIARMID 



computed by means of Table Iv, while Table TVx was used for the 
secondary eclipse. The computed constant phase for secondary 
eclipse is 4 . 7 hours in duration and satisfies the observations 
perfectly. 

The elements were computed in the usual way and are given in 
the table at the end. The residuals have been scaled off from the 
computed curve and are given in the table of observations. The 
probable error of one normal place is ±o¥on. Fig. 5 gives the 
theoretical light-curve derived from the solution for stars darkened 

toward the edge. Fig. 6 diagrams 
showing stars at elongation and 
at time of primary eclipse. 

T LEONIS MIXORIS 

This variable was discovered 
on the Harvard plates by Miss 
Leavitt and announced as an 
Algol variable with a range of 
2 M o. A note was published by 
the writer in Astronomische 
Nachrichten, 1 concerning the 
variation of the star. The 
period was thought to be within 
a few minutes of 3 d o h 20 m and 
the variation at least 1^7. From later observations, it was found 
that the actual period is 8 m 38 s longer and the variation is nearly 
2^5. The Harvard photographic measures were used, and in this 
case, as in others, have been of extreme value, combined with the 
visual observations, in establishing a definitive period. The series 
of observations covers twenty-five years, and during that interval 
there is no evidence of the period changing. 

The light-curve for this system is not so well defined as in the 
other systems. Weather conditions have been unfavorable, and 
as the star is of the tenth magnitude, observations at the time of 
bright moonlight were rarely taken. In all, 265 observations 
(16 measures each) were made by comparing T Leonis Minoris 




Fig. 6. — Elongation and primary 
eclipse for TX Cassiopeiae. 



1 199, 221, 1914. 



ELEMENTS OF ECLIPSING SYSTEMS 



429 



TABLE VI 

Table of Observations. T Leoxis Mixorls 

PRIMARY MINIMUM 



Nor- 










Nor- 










mal 


Phase 


Mag. Diff. 


°- c „ 


°- c d 


mal 


Phase 


Mag. Diff. 


o.-c.„ 


O.-C, 


No. 








No. 








d 


I . . 


— 5^26?7 


(v-a) o M 3o 


— o¥o6 


— o M o6 


16.. 


-0^5 1 "7 


(a-v) 1 ¥43 


o M oo 


O^OO 


2. . 


4 54-0 


0. 27 


-0.08 


—0.09 


17.. 


O 31-4 


1.77 


— 0.02 


O.OO 


?>■■ 


4 28.1 


0.30 


-0.03 


—0.02 


18. . 


— 11 .6 


2. 10 


-0.03 


— O.02 


4-- 


3 37-1 


0.25 


+0.02 


+0.02 


19.. 


+0 07.5 


1 . 70 


+0.41* 


+O.41 


5-- 


3 28.1 


0. 19 


+0.02 


+0.01 


20. . 


34-5 


1 5° 


+0.09 


— O. IO 


6.. 


3 H-9 


0.18 


+0.07 


+005 


21 . . 


50.0 


1. 14 


+0.16 


— O.16 


7-- 


2 50.8 


0.09 


+0.03 


+0.02 


22. . 


1 05.0 


1 . 11 


+0.05 


+O.06 


8.. 


2 39-4 


(a-v) 0.01 


+0.06 


+0.05 


23- • 


1 29.6 


0.88 


— 0.09 


— O.09 


9.. 


2 26.1 


0. 29 


— 0.07 


—0.09 


24.. 


1 44.6 


o.54 


-O.OS 


— 0.04 


10. . 


2 12.4 


0.34 


-0.03 


-0.03 


25- • 


2 00.8 


°-39 


+O.OI 


+O.OI 


11 . . 


2 01 .0 


o.37 


+0.01 


0.00 


26.. 


2 16.8 


°-34 


—0.06 


— O.06 


12. . 


1 48.9 


°-53 


0.00 


-0.03 


27.. 


2 37-5 


0.18 


—0.09 


— O.09 


13- ■ 


1 33-9 


0.66 


+0.01 


0.00 


28.. 


2 54-8 


015 


— 0. 16 


— O. 17 


14. . 


1 19.4 


0.91 


0.00 


+0.01 


29. . 


3 100 


(v-a) 0. 16 


+0.06 


+ O.05 


IS-- 


1 01 . 7 


1.30 


-0.05 


—0.09 


30- ■ 


3 23.0 


0.25 


+0. 10 


+ 0.09 



* Normal No. 10 half-weight. 



CONSTANT LIGHT AND SECONDARY MINIMUM 



Normal 
No. 



2 
3 
4 
5 

6 

7 
8 

9 

10 

11 
12 
13 

14 
IS 

16 

17 
18 

19 



1 6^26^6 

7 14-5 

10 32.6 

11 15.6 

11 5- 7 ° 

12 12.7 
17 50.6 
23 20.7 

038.7 

7 45-2 

8 46.9 

9 26.0 

9 49-3 
10 16.3 

10 46.2 

11 36.5 

11 59-9 

12 19- 7 
12 39.1 



Mag. Diff. 
(v-a) 



O.-C. 



0'.'29 

o. 26 

0.4s 
0.44 

o. 26 

0.36 
0.43 
0.45 
0.39 

0.30 

0.36 

0.39 
0.31 

0.33 
033 

0.28 
0.36 
0.34 

0.29 



— o¥o7 

— o. 10 
+0.10 
+0.08 
+0.01 

0.00 
+0.07 
+0.09 
+0.04 

— 0.06 

0.00 
+0.03 

— 0.04 

— O.OI 

0.00 

— 0.04 
+0.04 
+0.02 

— 0.04 



Normal 
No. 



23- 
24. 

25- 
26. 
27. 
28. 
29. 

30. 
3i- 
32. 
33- 
34- 

35- 
36. 
37. 
38. 



Phase 



I d l3^28'!'l 
17 32-4 

17 57-7 

18 19.7 
20 52.3 

21 24.9 

21 52.O 

22 21 .O 
22 4O.3 

24 45 -6 

2 812.9 

8 16.5 

9 06. 2 

9 33-9 
10 23.0 

14 48. S 

16 34.2 

17 25.5 

18 16.5 



Mag. Diff. 
(v-a) 



o M 3 6 
0.32 
0.41 
0.40 
o. 29 

o.33 
0-33 
0.30 
o.34 
0-35 

o.37 
o.33 
o.37 
o.34 
o.43 

0.30 

0-39 
0.40 
0.30 



O.-C. 



+o M 03 

— 0.04 
+0.05 
+0.04 

— 0.07 

-0.03 
-0.03 
-0.05 

— 0.01 

— O.OI 

+O.OI 

-0.03 

+O.OI 

—0.02 

+0.08 



+0.03 
+0.04 
—0.03 



43° 



R. J. McDIARMID 



with B.D. 34°2032, magnitude 10.35 (magnitude of B.D. 34°2032 
found with reference to T Leonis, whose magnitude was determined 







photographically at Harvard). These observations were grouped 
into 68 normals of from 2 to 5 observations each according to cir- 
cumstances. Thirty of the normals are in constant light, and make 
T Leonis Minoris 0**357 brighter than the comparison star. At 














































































































/ 






















































\ 


• 














7 








• 


















































■ 














/ 








































































/ 




























































\ 










/ 






























































\ 










/■ 








































































/ 






























































\ 










/ 








































1 
























\ 






| 








































.. 
























































































































































































































































































































































































1 






























































































































































































, 


























1 


: 






































































} 










































































































































































































































































































































































■ 






































































1 
















































LiOl 


























1 ■ 












1 




* 




^- 




1 


s 








1 


; 


7 1 


c J 


1 


- > • 









































— ^— 






























































. ' 








































































































* 1 




r v 


■ 2 


1 


- » 


• > 


• -' 


3 


1 i 


9 


» J 


.' - 


b J 


s 


1 


j t 






:■ 1 


f 


;- -. 




7 Yl 1 




c 


1 


I 


J 


» 


1 < 


t 1 


- 


' ' 



Fig. 7. — Mean light-curve of T Leonis Minoris 

primary minimum T Leonis Minoris is 2^12 fainter, losing 2**48. 
The secondary eclipse has been observed three different times and 
appears to be 0**04 ±0**02 in depth. 

The light between eclipses remains sensibly constant. The 
primary eclipse is evidently partial. For the uniform solution, 
the curve which defines the primary minimum was well represented 



ELEMENTS OF ECLIPSING SYSTEMS 



431 





by a value of the function x(k, a , |)= 1-999- This value gave a 
series of values of k and a ranging from £ = 0.792 to £ = 0.848 
and from a = o.9o to a = 1.00. To represent the observed depth 
of the secondary minimum k must be 0.812 and a , 0.95. The 
light-curve was computed by means of Table Ilia and the equation 
sm 2 d(n) = Co3 2 (n)-\-Du 1 (n) where £=0.0759 and D=o. 03796. 

For darkened disks, from the relation Q{k, a ) = -, — ~— : and 

o. Q — {i — Ai) 

the depths of primary and secondary minima, the values for k and 
a range from o . 537 to 1 . 00 for k and from o . 93 to 1 . 00 for a . To 
represent the shape of the light- 
curve of primary minimum, it 
was found that k must be o. 935, 
whence ^=0.935. The curve 
was computed in the usual 
manner. The residuals for the 
two solutions are given in the 
table of observations. Fig. 7 
gives the theoretical light-curve 
for uniform solution and Fig. 8 
diagrams of the system for the 
two solutions. 

Table VIII gives the elements resulting from the solutions for 
the three stars TW, TX Cassiopeiae, and T Leonis Minoris. 

The table of results contains, besides the elements as computed 
for the various solutions, densities corrected for polar flattening as 
well as for the probable difference of the masses of the brighter and 
fainter components, in accordance with the method outlined by 
Shapley in Contribution No. 3, Princeton University Observatory, 
p. 1 23. The hypothetical parallax, distance in light-years, size with 
respect to the sun, and the ratio of brightness of each system have 
been computed by the method of Russell and Shapley {Astro physical 
Journal, 40, 417, 19 14), using their estimates of the mean mass and 
surface-brightness as a function of the spectral type. The principal 
components of three of the four systems are of quite normal density. 
Their estimated brightness is comparable with that of such stars 
as a Lyrae, and their distances are similar to those estimated for 



Fig. 8. — Diagrams resulting from solu- 
tions for uniform and darkened stars, T 
Leonis Minoris. 



43 2 



R. J. McDIARMID 



most eclipsing variables. T Leonis Minoris, however, appears 
to be situated in space considerably farther from the Galactic plane 
than any of the 90 variables previously investigated. TX Cas- 



TABLE VTI 

Table of Results 



Elements of the System 



TV Cassiopeiae 



Uniform 



Darkened 



Maximum radius of brighter star 

Minimum radius of brighter star 

Maximum radius of fainter star 

Minimum radius of fainter star 

Ratio of radii of the two stars 

Ratio of the axes of the spheroidal stars 
Least apparent distance of centers .... 

Inclination of the orbit 

Eccentricity of the orbit 



Maximum percentage loss of light at 
primary minimum 

Maximum percentage loss of light at 
secondary minimum 

Difference of light of the sides of the 
fainter star 

Light of the brighter star 

Light of the fainter star< ^ \% . ?l 

(raint side . . . 

Ratio of surface-brightness of the bright 
sides of the two stars 

Ratio of surface-brightness of the sides 
of fainter star 

Density of brighter star 

Density of fainter star 

Hypothetical radius of brighter star in 
solar radii 

Absolute magnitude of brighter star. . . 

Brightness compared with sun as unit . . 

Hypothetical parallax 

Number of light-years 



ab 
bb 
af 
bf 
k 

1+** 
cos i 

i 
e sin 03 
e cos w 

a-op 



Probable diameter, sun= 1 . 



Distance in light-years from Galactic 
plane 

Distance projected on Galactic plane 
(in light-years) 



2b 

Lb 
U 

Lf-2b 

Jb/Jf 
L//(Lf-2b) 

Pb 
PS 

A 
M 
Light 

7T 

Distance in 
light-years 

Probable diam- 
eter 



0.301 
0.285 
0.285 
o. 271 

0-95 
1 .052 
0.1783 
79°45' 

-O.OIO 

0.628 



0.074 
0.859 

0.141 
0.067 

6.7 

2. I 

O.Il8 

O.O56 

2.46 

0.3 

IOO 

o''oo3i 
1.030 

3° 
1020 

-53 



0325 
o-3i4 
o. 287 
o. 277 

0.884 
1.065 

o. 2720 
74°iS' 

-O.OIO 

0.640 



0.074 

0.844 

0.156 

0.082 

7.0 



.089 
• 054 



siopeiae is remarkable for its low density, lower than that of any 
other star of spectrum B, except /3 Lyrae; its great estimated 
brightness, which, however, does not exceed that of some of the 



ELEMENTS OF ECLIPSING SYSTEMS 



433 



stars of spectrum B in Kapteyn's group in Scorpius; and its enor- 
mous estimated distance of 10,800 light-years, which, however, 
would be greatly reduced by the assumption of even a small absorp- 
tion of light in space. 

TABLE VHI 

Table of Results — Continued 





T\V Cassiopeiae 


TX Cassiopeiae 


T Leonis Minoris 




Uniform 


Darkened 


Darkened 


Uniform 


Darkened 


ab 

bb 


Ti 0. 176 


0.165 


0.567 

0519 

0-295! 

0.270/ 

0.520 

1 .080 


ri 0.217 


O.218 


af 


7-20.151 


O.165 


r 2 0.266 
0.812 


O.233 


bf 


k 


0.858 


1.00 


0-935 


|i+is) 




cos * 

i 


0.0058 

89V 

1 .00 

1 .00 

6 = 0.040 

w = 274° 


00551 

86° 5 o' 
0.850 
0.869 
0.050 
273° 


0.0442 
82 3 o' 
1. 147 
1 .000 


. 0648 
86°2o' 
0.950 


O.0566 
86°45' 
o.935 


aop 


e sin 1 
e cos wj 
2b 












0.030 
0.829 
0.171 
0.141 

i-5 

1 .2 

0.0068 

0.0214 

5.61 

-31 

1400 

0T0003 
10,800 

9.0 

750 
10,800 






Lb 0.592 

Lf 0.408 

(Lf-ib) | 


0.582 
0.418 


o.945 
0.055 


0.961 
0039 


Jb/Jf 1.07 

Lf/(Lf-2b) 


1-39 


35-7 


28.5 


04 0.167 

PI 0.214 

A 


0.185 
0.185 

1.88 
+0.3 
60 
0*0019 
1600 

2 -5 

170 

1620 


0. 112 
0.018 


0.112 
0.026 

1.98 
+0.3 
60 
of 001 3 
2600 
2.6 

2050 

1600 


M 

Light 

T . . . . 

Distance in lig 
Probable diam 
Distance in lig 

Galactic pla 
Distance proje 

tic plane in 


ht-years .... 

eter 

ht-years from 

ne 

cted on Galac- 
ight-years. . . 



This investigation has been carried out under the direction of 
Professor H. N. Russell, and I am indebted to him for valuable 
suggestions given in the course of the work. 

Princeton University Observatory 
June 29, 1915 



THE STRUCTURE OF THE THIRD CYANOGEN BAND 
AND THE ASSOCIATED TAILS 

By H. S. UHLER and R. A. PATTERSON 

The present investigation forms an essential part of an attempt 
to affirm or deny definitely Thiele's hypotheses concerning band 
spectra. The complete solution of this problem involves two dis- 
tinct kinds of work, (a) experimental and (b) arithmetical. The 
results obtained by a careful study, both qualitative and quantita- 
tive, of the band at X 3883 and of the tails of shorter wave-length, 
as radiated by the direct-current carbon arc in air at atmospheric 
pressure, are recorded in the later paragraphs of this paper. An 
article, by H. S. Uhler, 1 dealing with one phase of the computational 
side of the question has already been published. Historically, the 
experimental data should have been formally presented before the 
theoretical paper, but as the mathematical analysis was independent 
of any particular source of wave-lengths, as Leinen's numerical data 
for the carbon band at X 5165 were used more extensively than the 
wave-lengths recorded below, and as the present account was not 
ready to go to press at the time of completion of the calculations, 
it was thought best not to defer the publication of the theoretical 
article until after the experimental results had appeared in print. 

Formulae for the series lines of band spectra have been proposed 
by H. Deslandres, Kayser and Runge, G. Higgs, J. N. Thiele, A. 
Fabry, J. Halm, and W. Ritz. The equations of Halm, Higgs, and 
Ritz are special forms of the functions given by Deslandres, Thiele, 
and Kayser and Runge, respectively. Since the subject of the laws 
of all kinds of spectra has been presented very clearly and com- 
pletely by H. Konen in a volume entitled Das Leuchten der Gase 
und Dampfe (1913), as well as in Kayser 's classic Handbiich der 
Spectroscopic, it would be superfluous to give bibliographic refer- 
ences and general historic details in this place. Suffice it to say 
that the most comprehensive hypotheses have been advanced by 

1 Astrophysical Journal, 42, 72, 1915. 

434 



STRUCTURE OF THIRD CYANOGEN BAND 435 

Thiele and subjected to experimental tests by their proposer and 
by several later investigators. Because of the general nature of 
these hypotheses and the fact that their validity has been accepted 
by some writers of note and rejected by others, it is a matter of no 
little importance to endeavor to obtain new evidence for them or 
against them. It should also be remarked, at this juncture, that 
the question of the origin of the bands between X 2000 and X 4217 
is not germane to the present work, so that the usual terminology 
of "cyanogen"' bands will be adhered to, notwithstanding the fact 
that W. Grotrian and C. Runge 1 have recently shown experimentally 
that the bands at XX 3360, 3590, 3883, and 4216 are due to nitrogen 
alone and not to a nitro-carbon. Later experiments of the authors, 
who established a direct-current arc between copper electrodes in 
an atmosphere of nitrogen, which had been freed from carbon and 
carbon compounds, were consistent with the results obtained by 
Grotrian and Runge. 

The law for series spectra in general was formulated by Thiele 2 as 

X=/[(»+c) a ] . 

In the case of band spectra this function must embody the following 
characteristics, which are the only ones amenable to direct experi- 
mental investigation and independent of the calculation of the 
series "phase'' c. 

Every series must have a head (n = o) and a tail (« = =*= *> ) . In 
any one series the intervals between successive lines must be finite 
near the head, must increase up to a maximum as the arithmetical 
value of n increases, and then decrease to zero as a limit as the 
extreme wave-length of the tail is approached. In other words, the 
lines should be discrete and theoretically resolvable in the region 
of the head, whereas an infinite number of lines should coincide to 
form the edge of the tail. 

A concrete example of tail bands was first given by Thiele 3 him- 
self, who called attention to the presence on the spectrograms of 
cyanogen, taken by Rydberg, of "certain sudden interruptions of 
the fogged gray background which might be regarded as the tails 

1 Physikaliscke Zeilschrift, 15, 545, 1914. 

2 Astro physical Journal, 6, 66, 1897. 3 Ibid., 6, 67, 1897. 



436 H. S. UHLER AND R. A. PATTERSON 

of the series in this spectrum " Subsequently, A. S. King 1 

determined the wave-lengths of the edges of these bandlike struc- 
tures, three of which are situated just below (on the frequency 
scale) the 3590 band. In addition to these, he recorded thirteen 
above X 3590 and three on the less refrangible side of the 3883 head. 
He concluded that the bands under investigation belong to the 
cyanogen spectrum and constitute the tails of the series emanating 
from the several heads of the groups of bands commencing at 
XX 3590, 3883, and 4216. The particular arrangement of heads and 
tails was established empirically. King did not attempt to deter- 
mine the wave-lengths of the series lines which converge toward 
the tails. 

In the year 1904, the same region of the cyanogen spectrum was 
studied anew by F. Jungbluth 2 in Kayser's laboratory. The main 
object of his investigation was to test the hypotheses of Thiele and 
the conclusions drawn by King. By using greater dispersion and 
resolving power than his predecessors, 3 and by making long expo- 
sures, Jungbluth tried to follow the chief series of the 3883 band 
from this head to one of the tail bands measured by King. The 
attempt did not meet with success because the lines of the series 
ceased, at X 3640, to retain their characteristic, differentiating 
intensity, which is so noticeable for ordinal numbers less than about 
168, and because the spectrum had too dense a structure above 
X 3640 to enable the observer to extend the series by the aid of 
tentative extrapolation. For the same reasons, the second series 
could not be followed beyond the point mentioned, while the third 
and fourth series became indistinguishable at about X 3680. In 
regard to the tails, Jungbluth pairs them with the heads in a differ- 
ent manner from that of King. He made no attempt either to 
verify the wave-lengths given by King, or to analyze the tails into 
series, or to apply Thiele's method of computation to the four 
apparent series. 

In the year 1907, Professor H. Kayser called the attention of the 
senior author to the importance of repeating and extending Jung- 

1 Astrophysical Journal, 14, 323, 1901. 2 Ibid., 20, 237, 1904. 

3 H. Kayser and C. Runge, Abhandlungen der koniglichen Akademie der Wissen- 
schaften, Berlin, 1889, Anhang. 



STRUCTURE OF THIRD CYANOGEN BAND 437 

bluth's work, in the hope that new light might be thrown on Thiele's 
hypotheses and on the laws of band structure in general. The work 
was commenced as soon as possible, but its progress was interrupted 
to such an extent that it could not be completed before the present 
! year. 

APPARATUS AND SPECTROGRAMS 

The majority of the negatives of the 3590 and 3883 bands were 
taken at the Johns Hopkins University by H. S. Uhler. The third 
order of Rowland's original concave grating, which has a radius of 
curvature of 653 centimeters and 789 lines to the millimeter, was 
used exclusively. The best spectrograms of the more intense lines 
were obtained with fine-grained, lantern-slide plates manufactured 
to order by the M. A. Seed Dry Plate Co. With these plates the 
length of exposure varied from five minutes to two hours. The sen- 
sitive films had the peculiarity of developing more strongly near the 
edges than along the medial lines of the plates. This property was 
advantageous in picking out the spectral lines of different series. 
The region of the spectrum between X 3590 and X 3650 was so faint 
as to require four-hour exposures with "Seed 27 " plates. In order 
to minimize the effects of vibrations of the building all of the long 
exposures were made between 12 130 and 5 :oo a.m. The processes 
of development were carried out with great care and under the able 
guidance of L. E. Jewell. As source, a no-volt direct-current arc 
was used. To facilitate the identification of impurity lines, nega- 
tives were taken with regraphitized Acheson graphite rods as well 
as with ordinary commercial carbons. For obvious reasons, the 
electrodes were always maintained horizontal, so that only the image 
of the violet center of the arc fell on the slit proper. 

In addition to the spectrograms obtained in Baltimore, auxiliary 
ones were taken in this laboratory in the fourth order of one of 
Anderson's concave gratings. This grating has about the same 
radius of curvature as the one first mentioned, but three-fourths 
the number of lines per unit length. The individual rulings are 
unusually long, however, and the intensity of the spectra produced 
is correspondingly increased. All of the tails above X 3590 were 
photographed in the second order of the new grating and the strong- 
est ones were also recorded in the fourth order. 






438 H. S. UHLER AND R. A. PATTERSOX 

The wave-lengths have been calculated in the new international 
system, the secondary interferometer standards being employed 
directly whenever possible. In some instances the data given by 
Keivin Burns 1 were used and found to be very satisfactory. For 
sharp lines on clear background the wave-lengths are believed to 
be correct in absolute value to =•= 0.005 A, and in relative value to 
=t= o . 002 A. Other lines, including the edges of the heads and tails, 
are probably accurate to within = t o.oi A. 

EXPERIMENTAL RESULTS 

All the lines, between X 3590 and X 3883, except those too faint 
to be set upon even approximately, which are radiated by the carbon 
arc in air, have been measured and their intensities relative to 
neighboring lines estimated. Also many of the lines have been 
definitely assigned to certain series. These results are given in 
Table I. The first and second columns contain respectively the 
wave-lengths in dry air at 76 cm pressure, and the symbols indicat- 
ing the series and character of the lines. The key to the notation 
follows : 

Ai = belongs to singlet series from first head 

A 2 = belongs to doublet series from first head 

B r = belongs to singlet series from second head 

B 2 = belongs to doublet series from second head 

Ci = belongs to singlet series from third head 

T)i= corresponds to Jungbluth's IV series 

D, = corresponds to second branch of Jungbluth's IV series 

E = corresponds probably to Jungbluth's "fifth series" 

The subscripts on the foregoing letters designate different 
branches which are not definitely continuous. 

I = very intense F = very faint 

i = intense b = broad, diffuse 

m = medium d = probably double 

w = weak c = confused with 

f = faint s = superposed upon 

H I} H 2 , H 3 , H 4 = first four heads of 3883 band 
Hi, Hz, Hj = first three heads of 3590 band 
Ti, T 2 , T 3 .... =" tails" 

1 Lick Observatory Bulletin, No. 247. p. 27, 1913. 







STRUCTURE OF THIRD CYANOGEN BAND 




439 








TABLE I 








A 


Descr. A 




Descr. 


A 


Descr. / 


k 


Descr. 


883. 40- 1 


Hx '3876 


843 


Aiw 


3868.487 


B 2 f 3861 


711 


lb 




191 


Axi 


481 


A 2 i 




407 


AxmsB 2 


567 


AJbdsHj 




102 


Axi 


4i5 


A 2 i 




124 


Biw 


543 


f 


2 


990 


Axi 


3i5 


Axf 




°33 


B 2 f 


456 


f 




853 


Axi 5 


939 


A 2 i 


7 


963 


B 2 f 


3i7 


f 




75- 


A 2 f 


873 


A 2 i 




860 


A 2 f 


264 


Bif 




697 


Axi 


772 


AxF 




779 


A 2 msBi 


191 


B 2 w 




580 


A 2 w 


375 


A 2 i 




681 


B 2 F 


132 


B 2 w 




S2l 


Axi 


3 IQ 


A 2 i 




619 


AiisB 2 


026 


w 




38/ 


A 2 w 4 


79i 


A 2 i 




384 


Bxf 


992 


w 




321 


Axi 


727 


A 2 i 




302 


B 2 f 


916 


f 




171 


A 2 m 


602 


AxF 




234 


B 2 f 


829 


mb 




IOI 


Axi 


190 


A 2 i 




062 


A 2 f 


626 


AJsB, 


I 


938 


A,m 


123 


A 2 i 


6 


982 


A 2 msBi 


497 


B 2 m 




875 


Axi 


004 


Axf 




895 


B 2 f 


424 


B 2 m 




682 


A 2 i 3 


567 


A 2 i 




816 


AiisB 2 


276 


w 




616 


A 2 i 


5°i 


A 2 i 




555 


Bif 


221 


ms 




5S7 


Axi 


37i 


AxW 




47i 


B 2 w 


042 


f 




403 


A 2 i 2 


965 


A 2 m 




396 


B 2 w 59 


957 


Biis 




346 


A 2 i 


739 


Axi 




240 


A 2 w 


845 


B 2 w blurr 




305 


Axi 


252 


A 2 i 




168 


A 2 w 


783 


B 2 f 




106 


A 2 i 


180 


A 2 i 




108 


Bxf 


670 


Axld 




051 


A 2 i 


°57 


Aim 


5 


991 


AiisB 2 


5*7 


w 


O 


999 


Aii 1 


566 


A 2 i 




648 


Bif 


424 


\vb 




7Qi 


A 2 i 


501 


A 2 i 




563 


B 2 w 


277 


B x wc 




73i 


A 2 i 




sH 2 




492 


B 2 w 


204 


B 2 w 




670 


Axi 


44i 


H 2 




399 


A 2 w 


115 


B 2 w 




450 


A 2 i 


239 


Bim 




327 


A 2 w 8 


993 


\v 




392 


A 2 i 


133 


B t m 




151 


AxisBx 


918 


m 




327 


Axi 


010 


Bim 




085 


B 2 w 


836 


f 




092 


A 2 i 


876 


A 2 isB : 




010 


B 2 w 


789 


f 




033 


A 2 i 


808 


A 2 w 


4 


888 


F 


683 


Aiid 


79 


Ot>4 


Axi 


7i9 


Bim 




667 


Bxf 


59i 


Bxm 




712 


A 2 i 


665 


AimsB 2 




595 


A 2 mcB 2 


515 


B 2 w 




654 


A 2 i 


55o 


Bim 






blurr 


45° 


B 2 w 




578 


Axi 


481 


B 2 f 




458 


A 2 mcB 2 


256 


w 




311 


A 2 i 


358 


Bxm 




300 


Axi 


180 


w 




2 S3 


A 2 i 


283 


B 2 f 




123 


Bif 


098 


w 




183 


Axi 


146 


A 2 isBx 




062 


B 2 \v 7 


99 


w 


8 


891 


A 2 i 


069 


A 2 isB 2 


3 


993 


B 2 w 


896 


Bimc 




828 


A 2 i 69 


921 


AjibsBi 




661 


A 2 w 


814 


B 2 w 




740 


Axi 


831 


B 2 f 




593 


A 2 wsBx 


687 


Aiid 




5 77 


F* 


667 


Biw 




528 


B 2 w 


53° 


w 




448 


A 2 i 


580 


B 2 f 




390 


AxibcBa 


449 


w 




389 


A 2 i 


410 


A 2 isBi 


2 


976 


B 2 w 


334 


wb 




303 


Aim 


331 


A 2 isB 2 




900 


B 2 w 


158 


Bimc 


7 


989 


A 2 i 


180 


A x m 




768 


A 2 \v 


074 


B 2 f blurr 




025 


A 2 i .... 




Bi\v blurr 




694 


A 2 \v 6 


994 


B 2 f 




^2 


Aim 


066 


B 2 w 




489 


AiibsBx 


922 


m 




506 


A 2 i 


021 


B 2 w 




403 


B 2 w 


658 


Aiid 




446 


A 2 i 8 


829 


Bi\v 




324 


B 2 w 


5i6 


f 




35i 


A x w 


721 


B 2 w 




107 


F 


407 


Bimc 




005 


A 2 i 


645 


A 2 f 


1 


955 


f 


314 


B 2 f 


6.938 


A 2 i 


57i 


A 2 msBi 




854 


H 3 


234 


B 2 w 



L Foreign ? 



440 



H. S. UHLER AND R. A. PATTERSON 
TABLE I — Continued 



3856 
5 



49 



056 
964 
883 
791 
622 
■423 
•347 
123 

•932 
.851 
•744 
.662 
.566 

•3°5 

.252 

199 

144 

.062 

.909 

.812 

748 

.686 

• 57° 

• 487 

• 380 
.220 
.908 

•774 
706 

554 

■391 

190 

121 

.857 
.681 
■592 
•527 
285 
168 
.082 
937 
851 
739 
647 

525 
405 
302 
158 
056 
964 
876 

749 

646 



Descr. 



F 

f 

w 

m 

f 

A,IsB, 

B 2 w 

B 2 w 

w 

w 

Bjins 

H 4 

w 

AJbdsH 4 

w blurr 

f 

f 

f 

B,m 

w blurr 
w 

f 
f 

fc 

A.id 

mb 

B,mb 

w 

f 

m 

f 

AiIdsB, 



w 

m 

m 

B,m 

Axid 

w 

f 



Bjm 

mb 

w 

w 

A t id 

F 



B,mb 
F 



3849 



498 
423 
335 
260 
008 
844 
697 
612 
536 



194 

104 

052 

92 

839 



269 



965 
823 
677 
633 
537 
328 
266 



000 
919 
832 
797 
468 

427 
320 
214 
018 



846 
715 
643 
574 
497 
429 
352 
250 
206 
013 



Descr. 



f 
W 

m 

f 

A t id 

B.mb 

f 

w 

f 

F 

f 

f 

\v 

f 

f 

B I mbcA I 

A.idcBx 

F 

F 

F 

F 

F 

m 

f 

fcB, 

Bjmc 

fb 

Aa 

Aa 

f 
f 
f 

F 

F 

B,m 

w 

f 

f 

Aii 

Aii 

m 

f 

Bxis 

f 

f 

w 

f 

f 

f 

f 

f 

Axi 

A t i 

Bxm 



3843-831 
754 
691 
457 



39 



009 
973 
647 
464 
402 
252 
182 
953 

753 
710 



477 
392 
154 

994 

902 



479 
436 
105 



829 

739 
669 



497 
437 
346 
189 
141 

759 
719 



457 
349 



877 
825 
651 
614 
420 



083 



Descr. 



f 

f 

f 

mb 

f 

f 

AJsBj 

A,IsB, 

w 

f 

F 

f 

f 

Bxmd 

Aj 

Axi 

f 

vv 

w 

f 

CiWcB t 

Bimdc 

F 

F 

Aii 

Axi 

CiW 

F 

F 

B t md 

f 

f 

F 

F 

F 

f 

AiisCi 

Axic 

B x m 

B t m 

F 

f 

CiITlC 

F 
F 
Axi 

Axi 

Bxm 
B x m 

Ci\v 

F 

F 

f 
f 



3836.880 



.540 
•494 
,118 



839 
.772 



549 
■389 
•343 
.202 

147 



.897 
.824 



•635 
573 



,232 
.184 
.036 

• 05° 
842 

785 
.611 

160 
.062 
.016 

897 
■639 
.458 
.404 

173 

• 054 



753 
.644 

•356 
187 
.064 
.005 
.822 
.665 
.611 
•434 
.366 
295 
•073 



STRUCTURE OF THIRD CYANOGEN BAND 



441 











TABLE I— Cont 


i lined 








A 


Descr. > 




Descr. A 




Descr. > 




Descr. 


90I 


F 3823 


354 


F 3816 


547 


D,f 




F 


I 


796 


F 


267 


F 


278 


B x m 5810 


004 


W 




650 


Axi 


083 


Bxm 


201 


BimcAi | 09 


913 


Dxf 




588 


Axi 


024 


Bxm 


170 


A.icBx 


844 


Dxf 




494 


GF 2 


953 


Ci\v 


101 


Axi 


755 


Axi 




441 


BxmsDi 


879 


CiWsDi 5 


831 


CiW 


690 


Axi 




39° 


BimsDi 


839 


Dxf 


757 


CxW 


493 


CiW 




095 


F 




f 


525 


Dxf 


420 


CiW 


8 


967 


F 


645 


w 


462 


Dxf 


154 


B t m 




879 


F 


557 


F 


354 


F 


084 


Bxm 




811 


F 


481 


F 


236 


f 8 


997 


f 




673 


f 


322 


Axi 


079 


f 


747 


Dxf 




562 


f 


259 


Axi 4 


894 


Bxm 


674 


Dxf 




502 


Cxf 


089 


F blurr 


827 


Bxm 


637 


f 




454 


Dxf 


019 


F 


587 


AxIsCx 


421 


F 




399 


D x f 1 


812 


BxmcCiDx 


517 


AiIsCi 


337 


F 




211 


AjsBx 


728 


BxIcsC.Dx 


333 


Dxf 


150 


AxIbsCx 




155 


AxIsB, 


422 


F 


244 


i 7 


941 


Axi 


7 


976 


f 




F 


026 




774 


f 




723 


F 


190 


f 3 


939 




684 


B x m 




639 


D x f 


991 


f 


835 




602 


B t msDi 




577 


Dxf 


807 


AxisDx 


637 




496 


DxW 




372 


CxW 


746 


A.isDx 


558 




39° 


f 




206 


Fbd 


637 


CxW 


485 


Bxm 


298 


F 




103 


F 


567 


CiW 


43i 


Bxm 


154 


f 


6 


942 


BxITl 


421 


B : m 


33 1 


GmsDx 


068 


F 




886 


B,m 


378 


B t m 


258 


CimsDi 6 


861 


CxW 




770 


AxicDx 


159 


F 


119 


F 


786 


CxW 




708 


AxisDx 


086 


F 2 


984 


Axi 


643 


f 




58i 


F 19 


925 


\v 


923 


Axi 


440 


AxisDx 




490 


F 


783 


Dxf 


807 


f 


377 


AxisDx 




307 


CiW 


724 


Dxf 


655 


F 


191 


Bxm 




190 


CxW 


457 


CxW 


572 


f 


120 


Bxm 




073 


Fb 


384 


CiW 


441 


F 


035 


F 


S 


986 


F 


278 


Axi 


342 


F 5 


963 


F 




915 


F 


213 


Axi 


282 


F 


850 


f 




761 


D,F 


063 


Bxid 


193 


Dxf 


729 


f 




674 


BxmsDi 8 


739 


Dxf 


121 


Dxf 


524 


Cim 




616 


Bim 


670 


Dxw 


062 


BiisCi 


449 


Cim 




307 


Axi 


521 


F 1 


985 


BiisG 


191 


DiW 




239 


AxicCx 


45o 


F 


720 


F 


128 


DiW 




224 


CxWcAi 


373 


F 


650 


F 4 


932 


fd 




125 


Ci\v 


262 


CxW 


382 


Axi 


774 


Axi 




033 


F 


193 


CiW 


315 


Axis 


696 


AxIsBx 


4 


946 


F 


080 


fb 


180 


F 


619 


Bxm 




795 


D,f 7 


840 


B,m 


056 


Dxf 


552 


F 




739 


Dxf 


732 


AxisDx 


992 


Dxf 


462 


f 




38S 


B,m 


670 


AxisDx 


912 


F 


358 


F 




325 


Bxm 


384 


Bxm 


789 


CiW 


285 


F 




085 


Ci\v 


142 


f 


712 


CxW 


176 


CxW 




017 


Ci\v 


°55 


Ci\v 


615 


B t m 


098 


CiW 


3 


823 


A.isDx 6 


985 


G\v 


542 


Bxm 3 


992 


Dxf 




760 


AxisDx 


720 


F 


332 


F 


928 


Dxf 


•533 


f 


622 


Dxf 


248 


F 


680 


f 



442 


E. S. 


UHLER AND R. A. PATTERSON 












TABLE I — Continued 






A 


Descr. ) 


1 


Descr. 1 


1 


Descr. ) 


1 


Descr. 


3803.57O 


w 3797 


234 


CiW 3790 


535 


Bim 3783 


9°5 


BJsCiE 




460 


fb 


i54 


CiW 


465 


Bim 


819 


BxIsCxE \ 




174 


Bim 


057 


Ef 


310 


F 


54i 


Axi 




090 


AiIsB, 6 


962 


BimsE 


230 


F 


465 


Axi 




013 


AA 


890 


Bim 


132 


F 


°93 


Diw 


2 


808 


CimsDi 


730 


F 89 


985 


CiW 2 


998 


D{w 




727 


CimsDi 


658 


F 


916 


CxW 


870 


F 




577 


w 


589 


fc 


879 


Ew 


799 


F 




486 


w 


555 


fc 


780 


Ew 


670 


Ef 




333 


f 


306 


w 


590 


F 


582 


Ew 




214 


f 


184 


Axi 


5i5 


F 


395 


CxW 




060 


F 


104 


Axi 




F 


310 


CiW 


I 


900 

820 


f 




F 


273 
193 
040 


F 


213 


B t m 




fb 




F 


F 


134 


Bim 




740 


i 


805 


GmsE 


Axi . 1 


685 


AxisD,' 




643 


BiTTl 


722 


CiwbcE 8 


968 


Axi 


605 


AiisDx 




569 


B x mcDi 


377 


Bim 


892 


Bim 


438 


Ef 




5°3 


DiWcG 


300 


Bim 


816 


Bim 


292 


Fb 




444 


dwcDi 


085 


w 


696 


Ef 


175 


Fb 




375 


A.isC, 4 


991 


w 


610 


Ef 


063 


F 




308 


Ad 


844 


Fd 


526 


Cims 


005 


F 




146 


F 


621 


Ef 


456 


Cimcs 


862 


dw 




o4S 


F 


531 


Ef 


207 


F 


756 


CxW 


O 


932 


F 


4i7 


AxicCx 


058 


F 


5°9 


B!mc 




873 


F 


35i 


AiicCi 7 


959 


f 


434 


Bimc 




683 
580 


F 




me A 1 


823 
701 


f 


314 


DxfsE 




f 


117 


F 


F 


227 


DifsE 




500 


f 


049 


F 


489 


Ef 79 


806 


Axi 




3ii 


Em 3 


914 


F 


406 


Ef 


732 


Axi 




248 


F 


787 


Bxis 


228 


AJcsBi 


599 


F 




179 


F 


699 


Bxis 


155 


AxIcsBx 


492 


f 




098 


B t m 


447 


Ef 6 


906 


df 


394 


f 




032 


BiisCi 


358 


Ef 


777 


Cif 


314 


CiW 


799 


974 


Cim 


158 


F 


5io 


Fd 


219 


Cxwc 




663 


AJ 


088 


F 


283 


Ef 


085 


F 




587 


A z i 2 


922 


CiW 


202 


Ef 8 


916 


Diw 




2 *7 


Ew 


840 


CiW 5 


976 


F 


808 


BiisDi 




134 


Ew 


639 


Axi 


898 


F 


730 


Bxm 


8 


9 J 5 


f 


565 


Axicd 


832 


DxW 


467 






860 


f 


389 


w 


733 


Diw 


420 






761 


f 


272 


Ef 


574 


Bim 


345 






647 


dw 


164 


BxisE 


495 


B t m 


155 






552 


BJbsCi 


083 


Bxis 


39° 


AJsCi 


089 






459 


B t m 1 


904 


fb 


319 


AxIsCx 7 


919 


Axi 




326 


F 


805 


F 


248 


w 


S42 


Axi 




225 


F 


724 


F 


074 


Ew 


755 


CiW 




158 


F 


579 


fb 4 


993 


Ew 


664 


CiW 




083 


Ef 


473 


dw 


799 


f 


509 


Diw 


7 


986 


Efc 


386 


CiW 


678 


f 


403 


DimsE' 




926 


Aiic 


196 


w 


464 


Di'm 


272 


E'f 




852 


Axi 


085 


Ews 


37i 


Dim 


092 


Bxib 




676 


f 


996 


Ef 


221 


F 




F 




543 


fb 


846 


Axi 


129 


F 




F 




372 


f 


771 


Axi 


063 


F 6 


335 


F 

























STRUCTURE OF THIRD CYANOGEN BAND 




443 








TABLE I — ■Continued 








\ 


Descr. > 


1 


Descr. > 


i 


Descr. > 


Descr. 


3776 187 


CiWsE' 3768 


302 


Aii 3760 


363 


A 'i 375o 


808 


E"F 




098 


CimsDt'E' 


247 


AxIsBx 


290 


Axi 


~o 2 


E"F 




015 


A.isDx' 


166 


Biisd 59 


976 


dwdcD'x' 


206 


Axi 


5 


944 


Aii 


100 


CiW 


898 


CiWcD'x' 


134 


Axi 




515 


F 7 


949 


F 


727 


fbd 49 


891 


BimcsCi 




446 


F 


791 


F 


180 


Bxm 


788 


B x icCi 




287 


B t m 


649 


f 


103 


Bim 


587 


D'/fsE" 




204 


Bim 


540 


Dx'm 8 


546 


D'.'w 


502 


D'/fsE" 


4 


979 


E'f 


402 


E'f 


452 


D'/f 8 


838 


F 




812 


E'f 


301 


E'f 


348 


AiiscCi 


313 


E"F 




677 
596 
5i5 
279 


Dtf 




F 


287 


AiiscCi 


215 
141 
068 


E"F 




CimsDi .... 




F 


F 


AiisCxD'/ 




Ci\v .... 




F 




F 


AiisCxD'/ 




f 6 


799 


F 7 


503 


, f 7 


993 


B x m 




107 


Axi 


666 


F 


446 


f 


916 


Bxm 




030 


Axi 


558 


CiW 


337 


B t m 


072 


E"f 


3 


728 


E'f 


462 


BiisCi 


260 


Bxm 6 


987 


E"f 




SS6 


BimsE' 


378 


B,m 


064 


D'/f 


608 


D'/f 




475 


B r m 


322 


Axi 6 


968 


D'/f 


5i3 


D'/f 




244 


Dff 


247 


Axi 


657 


CxW 


437 


CiW 




156 


Dtf 


127 


E'f 


589 


CiW 


355 


C t w 




010 


Ci\v 


031 


E'f 


332 


Axi 


°75 


AxIcsBx 


2 


925 


Ciw 5 


790 


Fb 


26.3 


Axi 


004 


AxIcsBx 






F 


667 


Fb 


003 

878 
569 


! 


S45 
755 
098 


E"f 






F 


F 1; 


E"f 




472 


E'f 


299 



w 


D'i'ws 


Di'w 




358 


E'f 4 


923 


CxW 


484 


BxisD'/ 


028 


D'/w 




180 


Axi 


843 


CiWsE' 


406 


Bxm 4 


728 


Cim 




106 


Axi 


764 


E'F 


285 


CxW 


640 


CxmsE" 


1 


805 


B,isDx 


653 


Bxm 


149 


Cim 


544 


E"F 




724 


BxisD; 


57i 


Bim 4 


5ii 


E"f 


102 


B t m 




413 


CiW 


35° 


Axi 


394 


E"f 


041 


B im 




325 


Ciw 


277 


Axi 


300 


Axi 3 


980 


Axi 




208 


E'f 3 


789 


F 


227 


Axi 


910 


Axi 




097 


E'fb 


681 


F 


085 


D'/f 


624 


D'/fbd 





984 


F 


584 


E'f 3 


994 


D'/f 


426 


D 2 fsE" 




859 


F 


487 


E'f 


623 


B r m 


343 


D 2 fsE" 




729 


F 


283 


CiW 


544 


B im 


009 


d\v 




593 


fb 


196 


CiW 


372 


F 2 


929 


CiW 






F 2 


965 
845 


D'/f 


289 

199 


F 


9CC 


BimsE" 
B im sE" 




240 


AxicsDi 


BxicsD'x 


dwsE" 


z J 

181 




169 


AiicDi 


760 


Bxm 


109 


CiWsE" 1 


887 


AxisD 2 




029 


Bxm 


362 


AxisE' 2 


586 


D'/f 


817 


AxisD 2 


69 


947 


B z msE' 


290 


AiisE' 


498 


D'/f 


707 


f 




804 


CjWsE' .... 




F 


258 


Axi 


658 


f 




7i4 


CiW 1 


829 


F 


187 


Axi 


287 


CxW 






F 


734 
631 

547 
514 


F 


044 
937 
750 
675 


E"F 


209 

077 

485 
441 


CxW 

E"f 






F 


CiW 1 


E"F 






F 


CiWc 


Bim 
Bxm 


D 2 f 
D 2 fc 


8 


933 


Dx'f 


D'/fc 




883 


Dif 


352 


D'x'fb 


536 


CiW 


349 


B im 




793 


F 


016 


Bxm 


452 


CiW 


274 


Bxm 




670 


E'fb 


938 


B im 


089 


D'/f 39 


783 


Axi 


•57o 


E'f 


792 


F 


007 


D'/ws 


716 


Axi 



444 


H. S. 


UHLER AND R. A 


. PATTERSON 












TABLE I — Continued 








A. 


Descr. < 


K 


Descr. < 


^ 


Descr. - 


V 




Descr. 


3739 564 


Ciw 3730 


380 


F 3718 


690 


CiW 3707 


252 


Axi 




483 


Ci\v 


3°9 


F 


616 


CiW 


191 


Axi 




154 


f 


091 


D 2 w 


45S 


D 2 f 6 


944 


Btm 




014 


D 2 f 


Ol6 


D 2 w 


382 


D 2 f 


882 


Btm 


8 


926 


D 2 f 29 


875 


F 


273 


Axi 


588 


CiW 




52° 


F 


809 


F 


210 


Axi 


522 


CiW 




426 


Bims 


I30 


Axi 7 


65 


F 


255 


D^f 




347 


Btm 


064 


AxIsC, 


54 


F 


195 


DJf 


7 


832 


CiW 8 


994 


CiW 


32 


F 


034 




756 


CiW 


697 


B,m 


28 


F 


031 


Axi 




672 


Axi 


633 


BjisD, 


048 


D 2 f 4 


967 


AtlsBtDi 




604 


Axi 


540 


D 2 f 6 


960 


CiWsD 2 


888 


BtmsCtD : ' 




527 


D 2 f 7 


469 


f 


877 


BiisCt 


817 


Ctw 




424 


D 2 fbc 


384 


dws 


806 


B t m 3 


735 


D^f 




296 


f 


302 


CiW 


083 


Axi 


677 


D^f 


6 


915 


fb 


150 


D 2 f 


020 


Axi 


180 


CxW 




494 


Btm 


076 


D 2 f 5 


654 


D 2 f 


120 


C x w 




420 


B : m 6 


975 


Aj 


586 


D 2 f 2 


949 


B,m 






F 


906 


Axi 


217 


Ci\v 


899 


Btm 




103 


CiW 


747 


6,111 


149 


CiW 


805 


Axi 




029 


CimsD 2 


678 


Btm 4 


893 


Btm 


750 


Axi 


5 


947 


D 2 f 


55-' 


F 


828 


Btm 


470 


D 2 fb 




612 


Axi 


479 


F 


5i6 


Fb 1 


492 


CiW 




444 


Axi 5 


703 


D 2 fc 


2 73 


m 


429 


Ctw 




207 


f 


646 


C I mcD 2 


203 


D 2 f 


305 


D^f 




124 


f 


576 


Ci«x 


073 


Fb 


263 


Btm 


4 


553 


BtmsD 2 4 


908 


fc 3 


985 


F 


968 




47i 


BimsD 2 


S04 


AxIsB, 


884 


Axi 


915 


-Btm 




290 


Cim 


732 


AxIsBx 


823 


Axi 


575 


Axi 




006 


F 




F 


487 


CiW 


520 


Axi 


3 


933 


F 




F 


423 


CxW 


313 


f ' 




625 


f 3 


907 


CjW 2 


907 


BtmsD 2 699 


805 


CiW 




417 


Axi 


831 


Ci\v 


844 


B,msD 2 


752 


CiW 




344 


Axi 


656 


f 


661 


f 8 


986 


BtmsD'/ 






F 


!5 2 


f 1 


764 


Ctw 


933 


BtmsD" 




051 


D 2 f 2 


815 


Bim 


682 


AtlsCt 


342 


Axi 


2 


971 


D 2 f 


74i 


Bim 


618 


Axi 


287 


Axi 




902 


F 


639 


Axi 


5°5 


T>ii 


136 


CiW 




824 


F 


572 


Axi 


920 


Btm 


077 


CiW 




617 


BjisCi 


165 


Ci\v 


857 


Bim 7 


817 


D' 2 'f 




544 


BxisC, 


092 


CiW 


565 


f 


778 


D' 2 'f 




172 


F 1 


922 


fb 


275 


Djwb 6 


974 


Btm 




106 


F 


296 


D^f 09 


837 


fbd 


923 


B,m 


1 


809 


f 


219 


D£fc 


470 


Axi 


685 


D' 2 'fd 




73i 


f 


193 


Fc 


411 


Axi 


467 


CiW 




569 


D 2 f 


073 


F 8 


935 


Btm 


416 


Ctw 




484 


D 2 f 


843 


Bim 


867 


BtisD 2 


104 


Ati 




276 


Axi 


777 


Btm 


769 


D,'f 


053 


Axi 




208 


Axi 


457 


AxicsCi 


293 


CxW 5 


620 


D' 2 'fd 





922 


Ci\v 


399 


AiicsCi 


228 


CxW 


002 


Btm 




863 


Ci\v 19 


88 


D 2 fc 7 


910 


F 4 


95i 


Btm 




747 


f 


799 


D 2 f 


825 


F 


809 


Ctwd 




663 


B t m 


45i 


Fb 


54° 


B'd 


592 


D' 2 'fd 




59° 


B,m 8 


894 


Btib 


483 


Di*f 3 


863 


Axi 

1 





















STRUCTURE OF THIRD CYANOGEN BAND 
TABLE I — Continued 



445 



3693 

2 

I 

O 
89 

8 

7 

6 


813 
58i 
144 

°9S 
018 
968 

575 
622 
57o 
472 
038 
987 
763 
901 
858 
372 
327 
061 
009 
283 
122 
082 
039 
93i 
702 
669 










5 
4 


"5 
077 
872 
832 
339 






3 

2 

1 


792 
577 
544 
438 
148 

113 
622 
582 
172 
764 
192 

153 
083 





5ii 
470 
37o 
33i 



Descr. 



Axi 

D' 2 'w 

CiW 

CiW 

B,m 

Bim 

D' 2 'f 

A t i 

A,icDY 

Cifcd 

Bim 

B,m 

D'/f 

Ci\v 

CiW 

Aii 

Axi 

B x m 

B im 

Cfd 

Axi 

AJsBx 

Bxi 

f 

CiW 

CiW 

F 

F 

F 

BiicsCi 

B t icsCi 

Axi 

Axi 

fb 

F 

F 

fb 

Ci\v 

CiW 

f 

B z m 

Bxm 

Axi 

Axi 

Ci\v 

Ciwb 

Bxm 

B,m 

f 

F 

CiW 

CiW 

Axi 

Axi 



3679 



69 



327 
232 
191 
994 



116 

080 



628 

513 
291 

255 



074 
864 
830 
336 
636 
614 

577 
412 
242 

937 
602 
368 
829 
682 

493 
368 
335 
499 
605 



°99 



897 
690 



037 
852 
648 

533 

804 

599 
423 
615 
244 
942 



Descr. 



f 

Bxm 

Bxm 

Ci\vd 

F 

F 

F 

Aii 

Axi 

F 

F 

f 

Cfbd 

B im 

B.m 

F 

F 

F 

Cxfd 

A t m 

Aim 

B x wd 

Cxf 

Aim 
Axin 
Biwd 

Cxf 

f 

F 

Fb 

Cxfb 

f 

Biwd 

Aim 

Aim 

df 

Bimdc 

F 

AimdsCi 

F 

F 

f 

Biwd 

F 

f 

Aimd 

f 

f 

B,w 

f 

f 

Aimbd 

F 

BiW 



3663 



59 



791 



093 
909 
866 

375 
166 

073 
997 
911 



976 



365 
246 
140 



506 
317 



960 
732 
654 
4i3 
086 
910 



147 



916 
600 

39° 
308 
678 
549 
383 
187 
852 
835 
706 
310 

259 
179 
087 

455 
362 



Descr. 



075 
732 
659 



Fbd 

F 

Fbd 

F 

F 

A t md 

F 

Biw 

f 

F 

F 

F 

F 

f 

F 

F 

BiW 

A r m 

Fb 

Fb 

fbd 

f 

F 

fbd 

F 

F 

B,w 

T t fb 

A.mbd 

F 

f 

F 

fc 

B,w 

f 

f 

Aimbd 

f 

f 

f 

fc 

B t fc 

F 

F 

F 

f 

F 

A t mc 

f 

F 

F 

B.fcd 

F 

F 



3652 



49 



217 
090 
956 
474 
256 

113 

030 



690 
595 
275 
182 
036 

939 
720 
587 
506 
387 
290 

255 
055 



630 
404 
346 



843 
523 
468 
S56 
671 
601 
192 
826 
736 
303 
"3 
997 
904 
668 
56i 
181 
070 
376 
276 
192 
938 
582 
477 
in 
806 
691 
334 
039 



Descr. 



F 

fbd 

F 

f 

AimbcdBt 

F 

F 

Fbd 

F 

F 

F 

w 

F 

F 

F 

BxF 

BiF 

F 

fc 

fc 

AiW 

F 

fb 

f 

f 

F 

B X F 

f 

f 

AiW 

fb 

fb 

Biwb 

fb 

fb 

F 

F 

f 

F 

Aifb 

BiF 

fb 

fb 

F 

F 

F 

Bif 

F 

Ai\vb 

F 

f 

f 

BxF 

F 



446 



H. S. UHLER AND R. A. PATTERSON 



TABLE I — Continued 



K 


Descr. 1 


1 


Descr. ) 


I 


Descr. ) 


I 


Descr. 


364O.973 


F 3628 


457 


W 3617 


435 


w 3610 


008 


W 


,908 


F 


320 


w 


058 


w 09 


729 


W 


.296 


A x fb 7 


998 


w 6 


920 


W 


688 


W 


•141. 




746 


w 


871 


W 


569 


W 


39-532 




594 


BiW 


446 


W 


525 


f 


.383 




418 


wb 


35° 


f 


349 


w 


•215 




o39 


w 


318 


mc 


239 


w 


.076 


f 6 


846 


mb 5 


828 


w 


174 


w 


8.794 




563 


F 


760 


f 


072 


f 


.626 




332 


w 


701 


f 


019 


w 


.164 


BxF 


2 73 


w 


242 


ibd 8 


754 


w 


.070 


fb 


121 


BiW 


070 


w 


681 


m 


7.865 


1 5 


710 


w 4 


729 


w* 


567 


F 


.328 




632 


w 


674 


w 


529 


f 


.189 


F 


518 


F 


642 


w 


344 


w 


.097 


fb 


435 


F 


332 


w 


263 


w 


6-743 


F 


237 


w 


196 


w 


195 


w 


.609 


BxF 


160 


w 


i45 


w 


038 


m 


•304 


F 4 


869 


w 


000 


w 7 


789 


m 


.199 


wb 


757 


f 3 


916 


f 


717 


m 


.025 


F 


612 


w 


689 


wb 


578 


F 


5-872 


F 


436 


F 


607 


wb 


547 


F 


•314 


fb 


263 


F 


298 


w 


437 


F 


.086 


Bxf 


046 


ib 


256 


w 


313 


m blurr 


•045 


Bxf 3 


886 


w 


153 


w 


230 


mc 


4-965 


F 


53i 


w 


087 


m 6 


837 


mc 


•537 


F 


289 


W 2 


749 


F 


765 


f 


.488 


F 2 


984 


W 


621 


w 


675 


m 


.408 


F 


639 


f 


575 


m 


595 


fed 


.094 


F 


560 


f 


494 


f 


499 


F 


.013 


F 


484 


F 


426 


w 


38i 


m 


3-885 


f 


406 


w 


359 


F 


3°i 


w 


• 734 


f 


029 


f 


104 


w 


257 


f 


.667 


F 1 


978 


f 


051 


w 


114 


fbd 


.308 


f 


688 


W I 


959 


w 5 


919 


m 


2.941 


\vc 


576 


f 


878 


w 


838 


w 


.867 


\vc 


461 


w 


721 


f 


786 


f 


.672 


f 


020 


w 


680 


f 


636 


fb 


.489 


w 


877 


f 


586 


w 


459 


m 


•159 


f 


384 


w 


553 


w 


382 


w 


.069 


Bxf 


252 


f 


416 


f 


327 


f 


1.984 


B t f 


174 


f 


317 


w 


160 


Fb 


.764 


w 19 


963 


f 


271 


w 


013 


m 


.080 


wc 


776 


wb 


173 


F 4 


926 


w 


0.651 


w 


585 


f 


0S2 


f 


864 


f 


■ 54° 


BxW 


481 


w 


020 


w 


678 


fb 


•435 


w 


181 


wb 


765 


w 


559 


m 


29.796 


w 8 


593 


wb 


729 


w 


472 


w 


.680 


f 


295 


f 


577 


f 


388 


f 


. 190 


m 


191 


f 


525 


f 


325 


f 


•057 


BiW 


020 


wb 


436 


F 


106 


wc 


8-733 


wc 7 


670 


f 


239 


w 


015 


wc 


.689 


T 2 w 


558 


w 


198 


w 3 


665 


ic 


-589 


w 


469 


w 


067 


w 


575 


mb 



STRUCTURE OF THIRD CYANOGEN BAND 
TABLE I — Continued 



447 



A 


Descr. 


A 


Descr. 1 


1 


Descr. 


A 


Descr. 


3603.462 


f 


3600. I92 


f 3596 


503 


W 


3592.880 


w 




396 


f 


. Ill 


i 


411 


m 


.786 


m 




247 


mbd 


599.962 


w 


272 


w 


.667 


F 




no 


mb 


•839 


w 


168 


F 


■57° 


i 


2 


987 


m 


•7Si 


w 


067 


m 


.470 


f 




879 


m 


.687 


w 5 


991 


F 


.361 


f 




787 


T 3 m 


•477 


i 


906 


i 


•193 


ib 




674 


m 


•39 1 


f 


713 


f 


.085 


w 




485 


w 


•243 


w 


on 


ib 


1.985 


f 




451 


w 


.136 


f 


41/ 


f 


.878 


ibc 




333 


m 


.046 


i 


323 


ib 


■789 


F 




224 


m 


8.867 


f 


129 


m 


.696 


f 




103 


w 


.790 


m 


042 


m 


•595 


w 




026 


w 


.699 


f 4 


899 


wb 


•505 


ibc 


I 


892 


m 


•45° 


w 


787 


w 


•396 


f 




778 


m 


•35i 


w 


659 


w 


.308 


f 




676 


w 


.306 


m 


587 


m 


.187 


m 




611 


w 


.105 


m 


486 


w 


.117 


m 




458 


w 


.011 


f 


403 


m 


0.988 


m 




328 


w 


7-773 


wc 


107 


ib 


• 9°3 


f 




296 


w 


.722 


wc 3 


966 


w 


.818 


f 




222 


f 


.672 


wc 


927 


m 


.769 


w 




014 


w 


•434 


w 


759 


w 


.676 


w 


O 


899 


wbc 


.299 


mb 


674 


ic 


•4i5 


h; 




842 


wc 


.103 


i 


5io 


fb 


85.911 


h: 




562 


m 


6.967 


m 


294 


ibc 


3-935 


h^ 




467 


w 


•75° 


m 


074 


f 








432 


w 


.629 


w 2 


919 


ibc 







Since series A T is the longest one known and affords excellent 
material for testing formulae, certain useful data pertaining to it 
have been collected in Table II. In the hrst column may be found 
the ordinal numbers of the lines; in the second, the wave-lengths 
in air; in the third, the frequencies or number of wave-lengths per 
centimeter in vacuo; and in the fourth and fifth columns, the first 
and second differences of the frequencies respectively. (First dif- 
ferences are always calculated from the mean positions of the 
resolved doublets.) The last two columns show clearly that the 
lines do not follow a smooth curve exactly. 



DESCRIPTION OF SERIES 



All except three of the lines measured between the first and third 
heads have been assigned to different series. By this classification 
it is found that both the spectrum from the first head and that from 



44 8 


H. S. 


UHLER AND R. A. 


PATTERSON 












TABLE II 










No. of 


\ 


10 s 


First 


Second 


No. of 




IO 8 


First Sec 


ond 


Line 




A . 


Diff. 


Diff. 


Line 




*, 


Diff. D 


iff. 


O. . 




3883.402 


25743-46 






27... 


3875-772 


25794- 15 






I . . 












28. . . 


missing 
4.602 




















29... 


801.94 


















3-98 
















30... 


.004 


5-92 




23 . 














4. 21 


4 • 




3883.191 


25744 -86 


0-59 




31. . . 


3-371 


10.13 


4-23 


.02 


5- 




. 102 


5-45 


•75 


O. 16 


32... 


2-739 


4-36 


4-53 


■30 


6.. 




2.990 


6.20 


.88 


■13 


33- ■ • 


•057 


8.89 






7-- 




•853 


7.08 




•17 


34- • ■ 


concealed 












1 -°5 










8.. 




.697 


8.13 


1. 17 


. 12 


35- • • 


0.665 


28.19 


4.98 




9 • 




• 521 


9 30 


1.32 


■15 


36... 


69.921 


33- 17 


4.92 


06 


IO. . 




.321 


50.62 


1.46 


■14 


37- •• 


.180 


8.09 


5-17 


25 


ii . . 




. IOI 


2.08 


i-5° 


.04 


38... 


8.407 


43.26 


5-25 


08 • 


12. . 




1.875 


3-58 


1.92 


•42 


39- •• 


7.619 


8.51 


5-38 


13 


13- • 




.587 


5 -5° 


1.88 


- .04 


40... 


6.816 


53 89 


5-52 


14 


14. . 




• 305 


7.38 


2.02 


•14 


41. . . 


5-991 


9.41 


5.62 


IO 


IS-- 




0.999 


9.40 


2. 19 


•17 


42.. . 


■151 


65-°3 


5 69 


07 - 


16. . 




.670 


61.59 


2.28 


.09 


43- ■■ 


4.300 


70.72 


6.09 


40 


17 •• 




■ 327 


3-8 7 


2.41 


■13 


44. . . 


3-39° 


6.81 


6.03 


06 


18. . 




79.964 


6.28 


2.56 


■15 


45- •- 


2.489 


82.84 


6.18 


15 


19.. 




.578 


8.84 


2.63 


.07 


46... 


1-567 


9.02 


6.32 


14 ' 


20. . 




.183 


71-47 


2.86 


•23 


47... 


0.626 


95-34 


6.41 


09 


21. . 




8.749 


4-33 


2.97 


. II 


48... 


59.670 


901 -75 


6.62 


21 


22. . 




• 303 


7-3° 


315 


.18 


49... 


8.683 


8-37 


6.69 


07 


23 •■ 




7.832 


80.45 


3 19 


.04 


50... 


7.687 


15.06 


6.92 


23 


24 • 




• 351 


3- 64 


3-38 


.19 


Si... 


6.658 


21.98 


6-95 


03 


25- • 




6.843 


7.02 


3-51 


■13 


52... 


5.622 


8-93 


7. 12 


17 


26.. 




■ 315 


9° -53 




. II 


53 ••• 


4.566 


36.05 




14 








3.62 










7.26 


* 

























' 



STRUCTURE OF THIRD CYANOGEN BAND 
TABLE II— Continued 



449 



No. of 


\ 


10 8 


First 


Second 


No. of 


A 


IO 8 


First 


Second 


Line 




^ 


Diff. 


Diff. 


Line 




^ 


Diff. 


Diff. 


54- •■ 


3853 487 


2594331 




O. II 


74... 


3828.2II 


26114.59 




O.07 










7-37 






■155 


•97 






55- • ■ 


2.391 


50 


68 


7.46 


.09 


75- •• 


6.77O 


24.42 


9-85 


•17 


56.... 


1.285 


8 


14 


7.60 


14 




.708 


.84 


I0.02 




57 


0.158 


65 


74 


7.76 


.16 


76... 


5-307 
•239 


34-41 
.89 




. IO 


58.... 


49.008 


73 


5° 


7.91 


-15 


77... 


3-823 


44-56 


IO.I2 


•15 


59 ••■• 


7-839 


81 


4i 


7.98 


• 07* 




.760 


.98 


IO. 27 




60. . . . 


6.677 
•633 


9 


26 
53 


8.17 


.19 


78... 


2.322 
•259 


54-82 
5 27 


IO.37 


. IO 


61.... 


5.468 
.427 


97 


44 
69 


8.23 


.06 


79... 


O.807 
.746 


65.20 
.64 


IO.47 


.10 


62... 


4-250 

. 206 


6005 


65 
94 


8.37 


• 14 


80... 


I9.278 
•213 


75-67 
6. 12 


IO.60 


•13 


63... 


3.009 
2-973 


14 


04 
29 


8.54 


•17 


81... 


7-732 
.670 


86.28 
• 7i 


10.73 


•13 


64.... 


1-753 
.710 


22 


55 
87 


8.63 


.09 


82... 


6. 170 
. 101 


97.00 

•45 


IO.89 


.16 


Is 


0.479 
• 436 


3 1 


20 
48 


8.75 


. 12 


83... 


4-587 
•517 


207.87 
8.36 


IO.98 


.09 


66 ... . 


39.189 
.141 


39 
40 


93 
25 


8.92 


•17 


84... 


2984 
-923 


18.88 
9-32 


II .04 


.06 


67.... 


7.877 
-825 


48 
9 


84 
18 


9.06 


14 


85... 


1.382 
■315 


29.91 
30.37 


II . 20 


.16 


68.... 


6.540 
•494 


57 
8 


92 
22 


9.14 


.08 


86... 


09-755 
.690 


41 . 12 
56 


II.52 


■32 


69... 


5.202 
•147 


67 


04 
38 


9. 22 


.08 


87... 


8.150 
7-941 


52.16 
3-57 


II. 31 


— . 21 


70. . . . 


3.842 
.785 


76 


25 
62 


9.41 


.10 


88... 


6.440 
■377 


63.96 
4-39 


H-53 




71.... 


2.458 
.404 


85 
6 


66 
02 


9-51 


. IO 


89... 


4-774 
.696 


75-43 
-99 


11.65 


. 12 


72.... 


1 .064 
.005 


95 


15 
56 


9.64 


•13 


90... 


3.090 
.013 


87.09 
•63 


11.82 


•17 


73 • • ■ ■ 


29.650 

.588 


104 
5 


79 

20 




■14 


91... 


1-375 
.308 


98 -95 

9.42 




•05 








9.78 










11.87 





45° 



H. S. UHLER AND 
TABLE II 



R. A. PATTERSON 

—Continued 



Xo. of 


\ 


IO 8 


First 


Second 


No. of 


A 


IO 8 


First 




Second 


Line 




^ 


Dig. 


Diff. 


Line 




\ 


Diff. 


" 


92... 


3799.663 

087 


26310.79 
i-33 


12.03 


0. 16 


no. . 


3766.322 

•247 


26543 71 

4-23 


13.90 


-O.II 


93- ■■ 


7.926 

■ 852 


22.83 
3-35 


12. IO 


•07 


III. . 


4-350 

.277 


57.62 
8.13 


I4-03 


• 13 


94... 


6.184 
. 104 


34-92 

5-47 


12.21 


. II 


112. . 


2.362 
. 29O 


7165 
2. 16 


14. 12 


• 09 


95- •• 


4-417 
•35i 


47-i8 
.64 


I2.38 


•17 


113.. 


O.363 
.290 


85- 77 
6.29 


14.22 


. IO 


96... 


2.639 
•565 


59-53 
60 . 05 


I2.48 


. IO 


114. . 


58.348 

.287 


600 . 03 

•47 


I4-30 


.08 ! 


97... 


0.846 

•77i 


72 .00 
. -54 


12.54 


.06 


115.. 


6.332 
.263 


i4-3i 
•79 


14-43 


• x 3 ! 


98... 


89 . 040 
8.968 


84.56 
5.06 


12.63 


• 09 


Il6.. 


4.3OO 

.227 


28.72 
9.24 


14-47 


■04 I 


99- ■ • 


7.228 
•155 


97.19 
.70 


I2.8I 


.18 


117.. 


2.258 
.IS? 


43- 20 

•7o 


14-59 


.12 


100. . . 


5-39° 
•319 


410.01 
•5i 


12.93 


. 12 


Il8.. 


O. 206 
•134 


57-78 
8.30 


14.68 


■09 


101 . . . 


3-541 
-465 


22.91 
3-47 


I2.99 


.06 


119. . 


48.I4I 
.068 


72.46 
.98 


14.70 


.02 


102. . . 


1.685 
.605 


35-9° 
6.46 


I3.O9 


. IO 


I20. . 


6.O75 
.OO4 


87.17 
.68 


14-93 


•23 


103. . . 


79 . 806 
•732 


49.02 
•53 


13.22 


•13 


121 . . 


3.980 
.9IO 


702.11 
.61 


14-95 


.02 


104. . . 


7.919 
.842 


62. 23 

•77 


13-32 


.IO 


122. . 


I.887 
.817 


17.06 
•56 


15.00 


■ -05 


io 5 ■ ■ • 


6.015 

5-944 


75-57 
6.06 


I3-4I 


.09 


I23. . 


39-783 

.716 


32.07 
■56 


15.10 


.10 


106. . . 


4.107 
.030 


88.96 
9-5o 


13-52 


. II 


124. . 


7.672 
.604 


47.18 
.66 


15. 11 


.01 


107... 


2.180 
. 106 


5°2-49 
3.01 


I3.62 


. IO 


125.. 


5.6T2 

•444 


61 .92 
3 14 


15-39 


.28 


10S. . . 


0.240 


16. 12 




- 03 


126. . 


3-417 


77.66 




- -05 




.169 


.62 


13-59 






•344 


8.18 


15-34 




109. . . 


68.302 

•247 


29.76 
30.16 


I4.OI 


• 42 


I27. . 


1.276 
.208 


93.02 

■5i 


15-41 


•07 



STRUCTURE OF THIRD CYANOGEN BAND 
TABLE II — Continued 



451 



No. of 


A 


IO 8 


First 


Second 


No. of 


A 


IO 3 


First 


Second 


Line 




^ 


Diff. 


Diff. 


Line 




^ 


Diff. 


Diff. 


128. . . 


3729.130 


26808 . 44 




0. 10 


146. . 


3689.372 


27097.32 




O.04 




.064 


.91 


15-51 






•327 




64 


16.52 




129... 


6-975 
.906 


23-94 
4-43 


15.62 


. II 


147.. 


7.122 
.082 


113 

4 


86 
15 


16.57 


•05 




4.804 

•73 2 


39-55 
40.07 


15.61 


— .01 


148. . 


4.872 
.832 


30 


43 
73 


16.56 


— .01 


131. . . 


2.639 
■572 


55 18 
.67 


15-71 


.IO 


149. . 


2.622 
.582 


47 


00 
29 


16.60 


•04 


132. . . 


o.457 
•399 


70.94 
i-34 


15-79 


.08 


150.. 


O.37O 
•331 


63 


60 
89 


16.63 


•03 


*33-- 


18.273 
.210 


86.71 
7.16 


15-85 


.06 


151.. 


78.116 
.080 


80 


25 
5i 


16.63 


.00 


134 ■•• 


6.083 
.020 


902.56 
3.01 


I5-92 


•07 


152.. 


5.864 
.830 


96 

7 


88 
15 


16.65 


.02 


135- •■ 


3.884 
.823 


18.47 
■ 94 


15.98 


.06 


153- ■ 


3-6l4 

•577 


213 


54 
80 


16.65 


.OO 


136. . . 


1.682 
.618 


34 46 
.91 


16.04 


.06 


154- ■ 


1.368 
•335 


30 


20 
45 


16.70 


•05 


137- •■ 


09.470 
.411 


50.52 
•94 




.09 


155- • 


69 . 099 


47 


03 


16.71 


.OI 








16.13 




156.. 


6.852 


63 


74 




- .07 


138... 


7252 


66.64 




■05 










16.64 






.191 


7.08 


16.18 




157- • 


4615 


80 


38 


16.68 


•04 


139 -■• 


5-03I 

4.967 


82.81 
3-27 




.OI 


158-. 


2-375 


97 


06 


16.66 


— .02 








16.19 




159- • 


0. 140 


313 


72 




— .02 


140. . . 


2.805 


99 03 




•07 










16.64 






•75o 


•43 


16.26 




160. . 


57-9IO 


30 


36 


16.72 


.08 


141... 


°-575 

■520 


7°i5-3i 

.67 




•05 


161.. 


5.678 


47 


08 


16.63 


- .09 








16.31 




162. . 


3-455 


63 


7i 




- .16 


142.. . 


698.342 


31.60 




•04 










16.47 






.287 


2.01 


16.35 




163.. 


1.256 


So 


18 


16.52 


■05 


143- •• 


6. 104 
■053 


47-97 
8-34 




■04 


164. . 


49055 


96 


70 


16.51 


— .OI 








16.39 




165.. 


6.856 


413 


21 




- -05 


144 •• • 


3-863 


64.36 




.06 










16.46 






.813 


■73 


16.45 




166.. 


4.668 


29 


<>7 


16.50 


-04 


145- •• 


1 .622 
•57° 


80.80 
1. 19 




•03 


167.. 


2-477 


46 


17 


16.45 


- -05 








16.48 




168.. 


0.296 


62 


62 







452 H. S. UHLER AND R. A. PATTERSON 

the second consist of two series — one a singlet series, the other a 
doublet series. (The term " singlet" is here used, although trie 
series are, in all probability, really composed of unresolved doublets 
near the heads.) 

The A series. — The intense first head apparently consists chiefly 
of the series A t . On leaving this head and going toward shorter 
wave-lengths one acquires the impression that the A 2 series gradu- 
ally grows out of, and away from, A T . The first component of A 2 
appears as a close companion of the eighth line of A r . Line 12 of 
Ai seems to be slightly displaced, is more intense and less diffuse 
than any of the other preceding lines. The second component of 
A 2 first appears as a close companion to line 13 of A 1 . Series A t is 
relatively much stronger in intensity at first than A 2 , but its inten- 
sity decreases steadily until it vanishes completely for line 28. At 
X 3880 . 4 the intensities of A x and A 2 are equal. From here onward, 
the intensity of A 2 steadily decreases until at the third head it 
becomes so weak as to be lost in the increased complexity of the 
band structure. A most striking anomaly occurs at X 3872, where 
line 32 of the A x series is displaced from its expected position by 
about o . 02 A and is relatively very broad and intense. Here also 
the component lines of A 2 are replaced by a single narrow line of 
weaker intensity than its congeners and displaced by about 0.08 A 
from its predicted position. From the missing line (28) onward, 
the intensity of A t seems to increase slowly until at 39 it becomes 
the strongest series in intensity and maintains this rank throughout 
its length. Its absolute intensity from line 39 diminishes up to the 
third head where again it seems to increase steadily until line 67 is 
reached. Thence its intensity diminishes slowly but uniformly. It 
is difficult to follow the absolute intensity of a series on account of 
the many superpositions of other lines. From line 47 on, the ulti- 
mate doublet nature of A x is apparent. The first line actually 
resolved is 60. The separation of these components increases 
gradually up to line 76, whence it is fairly constant as far as line 87. 
Here we find a second anomaly similar to the first. The two com- 
ponents are widely separated — the wave-length interval having 
increased from about o . 07 A to 0.21 A — and both are relatively 
more intense. The first component is this time the broader, prob- 



STRUCTURE OF THIRD CYANOGEN BAND 453 

ably owing to the superposition of a line from the C series. In 
line 88 the former state of affairs is resumed, but from here onward 
the components seem to be more widely separated. At line 125 we 
again find an anomaly. The components are widely separated 
(about 0.17 A), whereas line 126 appears normal. The interval 
between the components now diminishes, at first slowly, then more 
rapidly, until at line 155 the components are unresolved, although 
the lines are apparently of doublet nature. Meanwhile at about 
line 1 50 the first differences of wave-length have reached a maximum 
and begin to decrease. The last lines of the series are relatively 
extremely faint, having been obtained only with exposures of 
four hours. Owing to the weak and uniform intensity of the 
lines from 168 onward and to their great number, it is impossible 
to trace this series farther. The superposition of lines from other 
series and the accompanying changes in intensity are noted in 
Table I. 

The B scries. — As in the case of the first head, the intensity of 
the second head seems to consist chiefly in that of the singlet series. 
But here the doublet series, apparently emerging from behind the 
singlet series and simultaneously increasing in intensity, seems to 
precede the singlet series. On account of the superposition of so 
many lines, nothing definite can be ascertained concerning the abso- 
lute intensity of these series. For the same reason no attempt has 
been made to trace series B 2 beyond the fourth head. A line of 
series B t is missing at X 3863.0, and another is concealed by the 
third head. This series first appears double at X 3838. 7. The 
interval between the components increases steadily up to X 3821 . 8. 
Here it suddenly decreases and the line at X 3819.0 is single, rela- 
tively more intense, and displaced slightly from its predicted posi- 
tion. The next line consists of two widely separated components 
with an interval of about 0.45 A. The mean position of the com- 
ponents, however, corresponds very nearly to the expected position. 
In the next line the components are once more near each other, 
although from here onward they are distinctly, on the whole, about 
o. 02 A farther apart than below X 3820. 4. A noteworthy anomaly 
occurs at X 3777.1, where instead of a doublet we find a single, 
diffuse, ' relatively more intense line displaced from its calculated 



454 H. S. UHLER AND R. A. PATTERSON 

position. Again the following doublets seem to be farther sepa- 
rated, but only slightly so. 

At X 3718.9 we have a precisely similar phenomenon. In all 
three anomalies the displacement of the single line from its pre- 
dicted position is toward longer wave-length. Also, the average 
interval between the single line and its adjacent neighbors is larger 
than one would expect, as if the series had been stretched out at 
this point. The interval between the components has already 
begun to decrease and, from here onward, it steadily diminishes 
until at X 3679. 2 the components are again unresolved. All the 
lines, and they are numerous, in the region immediately following 
are of almost equal intensity. Consequently, it is difficult to be 
certain that the lines actually do belong to the series to which they 
are ascribed. Lines at XX 3649. 5, 3635.0, and 3632.0 appear to 
be double, although only one of the apparent components may 
really belong to this series. Lines expected at XX 3639. 7 and 
3633 . 5 have not been found. 

The C series. — -Beginning with the third head the structure 
becomes so dense and complex that no attempt has been made to 
disentangle all the series beyond this point. Consequently the Ci 
series has not been traced back to its head, although, as will be 
seen later, there is reason to believe that it has its origin in the third 
head. Only the d series has been traced. Just as the Bj series is 
everywhere less intense than the A x series, so the d series appears 
distinctly weaker than the B t series. Its first anomaly occurs at 
X 3830. 6, where instead of a single line appear two widely separated 
lines, the interval being about o. 46 A and their mean position being 
displaced slightly from its expected position. The duality of this 
series appears suddenly at X 3826 . 2, where the components are sepa- 
rated by about 0.12 A. This interval, however, immediately 
shrinks to about 0.07 A. At X 3808. 1, the Ci series is apparently 
single and superposed upon the first component of line 87 of series A : . 
At X 3786.8 the two components appear rather faint and widely 
separated. There seems to be a discontinuity of some kind. It is 
here also that the second branch, Dj of the D series, appears. The 
components are again widely separated at X 3780.8. At X 3755.0 
no line appears for series d. However, there is a wide doublet at 



STRUCTURE OF THIRD CYANOGEN BAND 455 

3755. 2 that may really belong to d, as it has not been ascribed 
to any other series. If so, it is greatly displaced from its predicted 
I position. At X 3734.3 we have an anomaly similar to those found 
in series B x . At this point occurs a single line, relatively more 
intense, and displaced from its calculated position. At X3710, in 
which region series D 2 possesses an anomaly, no line appears to 
represent the d series. From here onward the interval between 
I the components decreases until at about X 3680 the lines are unre- 
solved. Another anomaly occurs at X 3682, where, instead of having 
a close doublet, two single lines appear, separated by an interval of 
about o . 41 A. No lines above X 3669 have been found for this series. 
The D series. — This series has not been traced back to its head, 
! but appears to belong to the fourth head, as Jungbluth has already 
j shown. The first few lines are faint and fuzzy. The double nature 
I of the lines appears at X 3829.4. The first section of D x ends at 
X 3800. 3. Here the series seems to be discontinued and the first 
section of E forces itself upon one's attention. The second section, 
Di, appears at X 3785.8 and continues for 14 lines. The compo- 
nents are distinctly farther apart than they were in the first branch. 
The 13th line, atX 3768.9, is a very close doublet; and the 14th, at 
X 5767 . 5, is a strong single line. There is some doubt as to whether 
these two lines should be ascribed to this series. Perhaps they 
should be replaced by XX 3768.883, 3768.793, and XX 3867.402, 
3867.301. Yet the latter doublet seems to go better with the 
second section of E. This series is again distinguishable at X 3762 . 9 
and continues to X 3743 .6. At the end of this section the compo- 
nents converge rapidly, the last line being unresolved and seemingly 
slightly displaced toward longer wave-length. Almost immedi- 
ately, at X 3743 .4, another section of apparently the same series (at 
least so far as one can tell by successive differences in wave-length) 
commences. This section is designated by D 2 . The first line, a 
doublet, has been assigned to two series, E" and D 2 , although its 
intensity is not sufficient to justify this procedure. There seem to 
be two lines missing at X 3724. 2 and X 3722.8. Yet a second 
branch, D 2 , puts in its appearance at X 3721 . 2. This section dis- 
plays an anomaly at X 3710. 2 where instead of a doublet there is 
a relatively more intense single line slightly displaced from its 



456 H. S. UHLER AND R. A. PATTERSON 

calculated position toward longer wave-length. From here onward, 
the components are scarcely resolved. At X 3702 . 5 the line appears 
to be actually single, although the next line is double. The follow- 1 
ing line is missing. The third branch, D", however, immediately 
appears and can be followed to X 3690.8. This line is apparently 
displaced toward longer wave-length. From here onward it is very 
difficult to extend this series, although at times it seems to reappear 
in single lines so situated relative to the A t , B x , and d series as to 
lead one to such an inference. 

The E series. — This series is first noticeable at X 3800.3 at the 
point where the first branch of D ends. Although most of its lines 
are confused with or superposed upon others, it can be traced to 
X 3780. 3, where it is lost. A second branch appears at X 377 7. 4. 
The components here are more widely separated than before. At 
X 3774 ■ 9 they are separated by o . 19 A which is more than twice their 
separation in the first branch. They converge, however, and at 
the end of this section, at X 3762 .3, they are not more than o. 10 A 
apart. It is in this region that D" is first found. The third branch 
of E first appears at X 3754. 5 and can be traced to X 3742 . 1, where 
it is confused with a titanium line. No effort has been made to 
trace this series farther, most of its sections having been found 
incidentally in the study of the other series. 

The series compared. — In order to show these series graphically 
Jungbluth's method of plotting the first differences in wave-length 
as ordinates against the wave-length of successive lines as abscissae 
has been adopted (see the diagram). To bring out the uncertainty 
with regard to the assignment of lines to series, due to the "pertur- 
bations" referred to by Deslandres, the successive points have been j 
connected by straight lines instead of smooth curves. The scale 
has been so chosen that practically every perturbation shown is 
real and cannot be due to errors in measurement. As would be 
expected, the graphs representing the series Ai, B x , C t , D I} and E 
are very similar, but not parallel throughout their entire lengths. 
They clearly supply another argument, besides that of relative 
intensity, for assigning the C x and D x series to the third and fourth 
heads respectively. The very existence of an E series suggests the 
possibility of a fifth head to the 3883 band. This graph also affords 



STRUCTURE OF THIRD CYANOGEN BAND 457 







458 H. S. UHLER AND R. A. PATTERSON 

the chief argument in favor of combining the different sections of 
series in the manner chosen. One very noticeable fact is that the 
perturbations within the series increase as one passes from A x to 
B x to Ci, etc. — that is, from series of the first head to series of the ' 
second head, and so on. A second noteworthy fact is that pertur- 
bations in the A x series seem to be represented also in the B x series, 
but at longer wave-lengths. For the A x series these particular 
regions are designated by the letter P; for the B x series, by Q; and 
so on. Corresponding perturbations on the different series are • 
designated by the same subscript. P marks the first anomaly of 
the Ax series. Its second anomaly is seen at P x . Corresponding to 
this are the regions Q T and Ri on B x and G respectively, both of 
which represent the first anomalies noted in these series. 5 X prob- 
ably does not correspond to Pi,Qi, and R 1} but is largely due to the 
fact that in this region the doublet nature of the lines of the D I series 
first appears. P 2 represents an apparent discontinuity in series A!. 
In this region all three series A t , B t , and G are confused with or 
superposed upon one another. Corresponding to P 2 we have Q 2 , I 
representing the second anomaly in series B t , and R 2 , implying a 
discontinuity in series d. At S 2 there is a gap in series D x and it A 
is in this region that E first appears distinctly. At P 3 , the third : 
anomaly of series A r is shown. Corresponding to it is the perturba- J 
tion at Q 3 where the B x and A t series are apparently exactly super- j 
posed. R 3 represents a change in the character of series G, and i 
also the region where one line is missing. At S 3 there is an anomaly 
in series D x as well as a gap. U 3 represents a region in E where \ 
apparently two lines are missing. It should be noted that this 
region is not wide enough for three missing lines nor small enough 
for two to fit the graph smoothly. We have the third anomaly of 
series B x at Q 4 . R 4 represents a similar phenomenon in series G 
followed immediately by the exact superposition of G and B x . S 4 
designates a change in character and very abrupt break in D x . In 
fact, owing to the sudden change in character at this point and the 
anomalous position of the first line of D 2 relative to the last line of 
D',', there is reason to believe that D" and D 2 are not actually 
sections of the same series. Yet this graph indicates that they are 
closely related in some way. U 4 simply represents the region where 



STRUCTURE OF THIRD CYANOGEN BAND 



459 



E" first appears. Q 5 designates an actual perturbation in B x . i? 5 isa 
region in d where a line is missing, and 5 5 represents two missing 
lines in D t while E has come to an end. Probably the members of 
this last group are not so intimately connected. The missing line 
in Ci is doubtless related to the anomaly in D z at that region, and 
the missing lines in D x to the anomaly in B r . R 6 represents irregu- 
larities in series G while 6*6 designates an anomaly in series Dj. 

THE TAILS 

In Table III are given both King's values and those obtained in 
this investigation for the wave-lengths in air of the so-called tails. 

King's grouping has been retained, but the separate tails have 
been denoted by subscripts which increase with increasing fre- 
quency. The intensity of group I is on the whole weaker than that 
of group II. Xo thing can be said with regard to the relative inten- 
sity of group III on account of its position between two bands. 
The relative intensity of the tails within each group has been indi- 
cated by the same notation as used in Table I. A detailed descrip- 
tion of the so-called tails follows. 

TABLE III 



Symbol 


King's A 


A in I.U. 


Description 


H 


Ti 

T* 

Tj 

x 

T 5 

T 6 

T 7 

T 8 

T 9 

T I0 

,T„ 

r T I2 

"T\, 


3658.34 
3629.06 
3603.12 

3465.69 
3433- 17 
3405 ■ 04 
3380.58 
3360.27 
3340.64 
3322.40 
3296.48 

3203.84 
3180.58 
3160.32 
3143.06 
3128.00 


3658.09 
3628.69 
3604. IO 


F 

f 
ib 




3432.99 
3404 ■ 85 


i 
I 


TT 


3360.OI 
3340.35 


m 
w 




3296.31 
3203.53 


f 
f 


l{Tx4 

T,s 

T,« 


3I59-94 
3142.60 


w 

w 











T t is extremely faint even on a negative obtained from a four- 
hour exposure. The head appears like a diffuse line, and there is 
a very faint blurr in the contiguous region on the side of longer 



460 



H. S. UHLER AND R. A. PATTERSON 



wave-length. The spectrum is too faint to tell definitely whether 
it is or is not a band structure. 

T 2 is also faint. In appearance it closely resembles T r but is 
stronger in intensity. Its band structure, if it possesses one, 
appears only as a smeared blurr. 

T 3 is not believed to be a band structure. It consists of a rela- 
tively intense, broad, diffuse line with a doublet close to it on the 
side of shorter wave-length and a single medium line close beside it 
on the side of longer wave-length. The lines in this region certainly 
do not form a series emanating from this so-called tail. This has 
already been noted by Ritz. 

T 4 under high dispersion exhibits no band structure. It con- 
sists of a medium, diffuse, broad line with a blurr on each side and 
also two or three fine lines. 

T s is one of the tails that is distinctly a band structure. Its 
head is relatively intense and sharp, shading off toward the red. A 
few of its lines have been measured and are given in Table IV. 

TABLE IV 



T s 


T« 


T s 


T« 


343 2 -99 


3404-85 


3433- 81 


3405 • 50 










.91 

4- °3 


.67 


3 


II 




95 


.86 




20 


5 


01 




6.06 




31 




09 




•30 




45 




17 




•56 




57 




26 




•85 




63 




37 




7.18 



T 6 , like T s , is truly a band spectrum. A number of its lines have 
been measured, and they seem to form a series. These wave- 
lengths are also given in the same table. The enormous number of 
fine lines which form the background in this region precluded the 
possibility of tracing the series to greater distances from the edges 
of T 5 and T 6 . For the same reason, the intention of reproducing the 
original negatives of all of the tails, by the half-tone process, had 
to be abandoned. 

T 7 exhibits no band structure under high dispersion. It seems 
to consist merely of two very close single lines superposed upon a 
foggy background. 



STRUCTURE OF THIRD CYANOGEN BAND 461 

Tg resembles a band only in so far as it has a clear background 
on the more refrangible side of its edge and shades off toward longer 
wave-lengths with the ordinary channeled gradation of intensity. 
This shaded region is very narrow and photographically continuous. 
Owing to the extremely large number of lines in this part of the 
spectrum it is impossible to state positively whether T 8 is a band 
or not. Certainly no line series can be traced from it. 

T 9 suggests band formation only in the very restricted sense of 
T 8 . It seems to have a second head very close to the first one. 

T I0 does not exist as a band structure. The region here consists 
of a foggy background upon which numerous lines are superposed, 
but there is no sign of a true tail. 

T n looks somewhat like a real band, although no series lines 
can be distinguished because of the general blurr. The head has 
the appearance of a diffuse doublet that is unresolved. 

T12 may be a band, but it does not possess channeled intensity. 
The region adjacent to the head on the side of longer wave-length 
apparently consists of about ten lines of equal intensity packed so 
closely as to be barely distinguishable. 

T I3 consists merely of a very close doublet in the midst of a 
cluster of fainter lines. High dispersion gives no evidence of any 
band structure whatever. 

T I4 and T I5 look a little like bands in the very restricted sense 
of T 8 . No series can be followed to the apparent edges. T I4 may 
be due simply to a collection of unrelated lines which suggest a 
band formation as a consequence of the relatively clear background 
on the more refrangible side of the group. T I5 is characterized by 
possessing a doublet at the edge. 

T l6 is not believed to be a true band. Its edge appears to con- 
sist of a broad diffuse line superposed upon a single line. Just to the 
side of longer wave-length of this composite line is a blurred region 
of uniform intensity in which several discrete lines are imbedded. 

DISCUSSION 

The deviation from Deslandres' law for band series is clearly 
illustrated by the diagram. In each series the first differences in 
wave-length attain a maximum and then diminish. The suggestion 



46: 



H. S. UHLER AND R. A. PATTERSON 



that each maximum is really the point of intersection of two inde- 
pendent series, running in opposite directions with approximately 
equal curvatures (as has been found to be the case in a number of 
other band spectra), merits consideration, but we have not been 
able to find any evidence in its favor in the series under investiga- 
tion. Deslandres has ascribed a fifth head, at'X 3852, to the 3883 
band. There seems to be a great deal of doubt as to the reality of 
this fifth edge. The existence of the E series certainly suggests the 
possibility of a corresponding head. Nevertheless, if one calculates 
the position of the hypothetical edge by extrapolation according 
to Deslandres' law, no positive indication of a real head can be 
found on our negatives. However, there are blurred areas in this 
region, one of which may either constitute a fifth head or, with 
equal probability, be due to the superposition of the many series. 
The fact that two series of lines have been traced from the first 
head and also two similar ones from the second head lends support 
to Deslandres' idea that each head gives rise to the same number of 
like series. Thus it would appear that the total structure of the 
3883 band consists of two series — one, a "singlet'' series; the other, 
a doublet series — -for each head. 

TABLE V 



Head 


Tail 


Ratio 


' Ratio 


3590-52 

3585-99 

3S84-IO 

3883.60 

387I-59 

3861. 9 1 


3203.84 
3180.58 
3160.32 

3465-69 
3433 17 

3405 ■ 04 


I . 1 2069 
I . 12746 
I-I3409 

I .12059 
I . 12770 
r-13417 


1 . 12077 

(I. 12755) 

I.13418 

( 1. 1 2063) 
I . 12772 
I. 13422 



King's conclusion that the so-called tails are actually the ends 
of series emanating from the heads was based largely upon the cor- 
relation of the heads and tails and the ratios of their wave-lengths 
given in Table V. The first three columns of the table contain 
King's data, 1 and the fourth column, the ratios calculated from the 
wave-lengths of the authors. The numbers in parentheses were 
obtained by using, in each instance, the wave-length of the strongest 

1 Aslrophysical Journal, 14, 326, 1901. 



STRUCTURE OF THIRD CYANOGEN BAND 463 

line in the region of the supposed tail. The concordance of the 
third and fourth columns seems to indicate that the present writers 
were measuring the same lines and edges as King. On the other 
hand, the brief description of the characteristics of the tails, given 
in an earlier section, shows conclusively that the tails (at least as 
we obtained them on several negatives) are far too unlike to justify 
any conclusions which may be drawn from the apparent agreement 
between the corresponding ratios in the two sections of Table V. 
Several of the tails may be due to the superposition of series of fine 
lines which form the background of the entire spectrum, and, if this 
be true, it would account for the apparent regularity in the spacing 
of the tails. By burning a carbon arc in oxygen and comparing the 
negatives with the spectra of the like arc in air, we found that the 
background was noticeably different in several places. As might be 
expected, the band groups at XX 3590 and 3883 were not eliminated 
by the oxygen atmosphere because it was impossible to remove all 
traces of nitrogen from the carbon rods. On the other hand, the 
spectrum of an arc between copper electrodes in carbon-free nitrogen 
brought out strongly the third and fourth cyanogen groups but not 
the tails. Unfortunately the experimental conditions did not admit 
of making exposures of several hours' duration and therefore the 
absence of the tails proves little or nothing. We desire, however, 
to lay special emphasis on the opinion that it would be quite useless 
for any of our successors to attempt to clear up the matter by again 
studying the ordinary carbon arc in air. The spectrum of the 
region of the tails must, if possible, be obtained in such a manner 
as to get rid of the background. Perhaps this can be accomplished 
either by the method used by Grotrian and Runge 1 or by using the 
"active modification" of nitrogen as Strutt and Fowler 2 have done. 
With regard to the first and second cyanogen groups King says : 
''Taking the successive heads of these two bands and locating their 
tails by means of the ratios, we find that the tails belonging to the 
first three heads of the 4216 band should be at XX 3762, 3722, and 
3684." Since these hypothetical tails belong to the three most 
intense heads of the 4216 band, we should expect them to be of 
greater intensity than either of the tails T T or T 2 , which King has 

1 Loc. cit. 2 Proc. Roy. Soc, A 86, 115, 1911. 



464 H. S. UHLER AXD R. A. PATTERSON 

ascribed to the fourth and fifth heads. They should therefore 
appear clearly on negatives which show the last two tails. A care- 
ful examination of such negatives (taken with high dispersion and 
resolving power) failed to reveal the slightest traces of tails in the 
first two regions. At X 3683.8 there is a structure which may be 
a tail but it is even weaker in intensity than T x . Taking all the 
evidence into consideration, we are forced to the conclusion that 
King's correlation of heads and tails is not valid. 

Let us now consider Jungbluth's combinations of the heads and 
tails. He was led, by a study of curves similar to those in the dia- 
gram, to the conclusion that the tail belonging to the A r series was 
at shorter wave-length than the tail pertaining to the B x series. 
For the series from the least refrangible head attained its maximum 
first difference and minimum terminal intensity later in its course 
than the series from the next head, and so on. Consequently, he 
joined the A t series to an assumed tail at X 3579, B x to T 3 , Ci to T 2 , 
and D x to T x . The tail of the shortest wave-length was purely 
hypothetical, its position being predicted by extrapolation based 
on certain relations found in the three other cases. As to the B x 
series, the present investigation has failed to verify the existence of 
a tail at X 3604. Furthermore, the diagram indicates (in our 
opinion) that the Bi graph does not bend around fast enough to 
meet the axis of abscissae at a point having as great a wave-length 
as T 3 . If these statements be admitted, then Jungbluth's correla- 
tion is destroyed, since they leave no data by means of which to 
calculate relations which might support his arrangement. More- 
over, although series Ci can be produced to meet T 2 in a fairly 
smooth curve, certainly the trend of the graph representing series 
D is not such as to lead to T x smoothly. As mentioned above, 
series D presents a definite discontinuity at X 3743. 5. Here, the 
position of the first line of branch D 2 with respect to the last line 
of branch Di suggests at once the possibility that D 2 may represent 
the sudden reappearance of the doublet series corresponding to Di. 
Indeed, it may well be that these series do not exist actually as 
continuous series but are really composed of discrete segments each 
of which is a true series in itself, usually beginning and ending with 
a discontinuity of some sort. 



STRUCTURE OF THIRD CYANOGEN BAND 



465 



P. Weiss 1 has already called attention to the fact that Jung- 
bluth's arithmetical progressions for both the lengths of the series and 
also the ratios of the wave-lengths of the heads to those of the tails 
have but slight significance as arguments in favor of any intimate 
connection between the heads and tails. The present work confirms 
and strengthens this adverse criticism. However, Jungbluth's cor- 
relation of heads and tails, as contrasted with King's arrangement, 
is probably correct if the series actually converge to tails. Jung- 
bluth was also the first to state that the maxima of the first differ- 
ences in wave-length of the series form an arithmetical progression. 
The degree of accuracy to which this holds is shown in Table VI. 
The first column gives the series; the second, the maximum first 
differences; and the third, the successive differences between the 
numbers in the middle column. The values of the maximum inter- 
vals were obtained from the diagram and are, therefore, only 
approximate. 

TABLE VI 



Series 

Ax 

Bx 

Cx 

Dx 

E 



Max. Interval 



Difference 



2.252 
I.992 
1 ■ 75^ 
1 ■ 5°4 
(1.264) 



o. 260 

. 240 

.248 

(o . 240) 



In conclusion, it seems appropriate to review very briefly all the 
salient points in the evidence bearing on Thiele's hypotheses. The 
heads and tails in the cyanogen spectrum have been correlated in 
two different ways by King and Jungbluth. The arrangement pro- 
posed by the former is destroyed by the facts that some of the tails 
certainly do not exist and that there are marked differences in char- 
acter among the remaining structures which may perhaps be looked 
upon as tails. The correlation suggested by the latter is practically 
without foundation for the following reasons: (a) the tail at X3604, 
which is necessary for the formation of the arithmetical progressions, 
has an extremely doubtful existence; (b) the tail at X 3579 is purely 

1 Aslrophysical Journal, 35i 79-83, 1912. 



466 H. S. VHLER AND R. A. PATTERSON 

hypothetical; (c) the more refrangible ends of the graphs for the 
series Ai, B x , d, and D cannot all be extended so as to meet the 
axis of wave-lengths at the points marking the tails ; and (d) Jung- 
bluth's arithmetical progression for the lengths of the series (if 
admitted) can be accounted for by elementary calculations based 
on the approximate laws of Deslandres. Two of the tails, T s and 
T6, possess a finite number of resolvable lines up to their edges and 
hence they must be looked upon either as ordinary bands shading 
off toward the red — in which case two more tails drop out of the 
list — or as tails which do not conform to Thiele's hypothesis con- 
cerning an infinite number of lines at the convergence wave-length. 
Furthermore, in the preceding paper 1 by the senior author it vas 
shown that Thiele's "phase," c, is not constant for the a and 8 
series of the X 5165 carbon band, and that the Ai and A 2 series of 
the third cyanogen group do not constitute the positive and negative 
branches of a complete Thiele series. It appears, therefore, that the 
properties of band spectra implied by the formula X=/[(«-f-c) 2 ], and 
stated very unambiguously in words by Thiele, are not realized in 
nature. 

On the other hand, the generalized conception of conjugate 
heads and tails is not invalidated by the preceding arguments. The 
experimental part of the investigations of King, of Strutt and 
Fowler, and of Geuter show conclusively that the same source may 
simultaneously radiate bands, or bandlike structures, which shade 
off in opposite directions. Also the occurrence of maxima in the 
first differences of wave-length in the cyanogen (or nitrogen) spec- 
trum, and in the arc spectrum of phosphorus, 2 is usually considered 
as constituting an additional argument in favor of some general 
connection between heads and tails. Nevertheless, the facts that 
such maxima have not been found in the majority of band spectra 
and that, when maxima are observed, the series apparently vanish 

1 After this paper appeared in print its author received letters from Professor 
J. A: Anderson in which it was stated that he had tested the new method of calculat- 
ing c on two bands, near XX 5327 and 5500 in the absorption spectrum of iodine 
vapor, and found that the phase was "very far from constant" for the region of the 
head of each band. The number of lines used was from 50 to 70 and the wave- 
lengths did not have errors as great as 0.002 A. 

2 P. Geuter, Zeitschrift fiir wissenschafUicke Photographie, 5, 1, 1907. 



STRUCTURE OF THIRD CYANOGEN BAND 467 

at a relatively short distance beyond the stationary points, may be 
interpreted as meaning that bands do not in general converge to 
tails, that the bands which fail to attain maxima constitute the 
normal mode of radiation, and that the few bands which do exhibit 
maxima are exceptional cases, the lines beyond the maxima corre- 
sponding perhaps to a condition of partial instability. Lastly, that 
line and band spectra may be intimately related in the general sense 
suggested by Thiele and others is borne out by the recent investiga- 
tions of the band spectrum of helium by Fowler 1 and by Nicholson. 2 

SUMMARY 

1. An exhaustive study of the 3883 band radiated by the ordi- 
nary carbon arc in air has been made. The wave-lengths of all the 
lines between X 3883 and X 3590 (about 1740), that could be meas- 
ured even approximately, have been calculated in international 
units. The dispersion and resolving power used were 4/3 times as 
great as Jungbluth employed in the same region. 

2. The intensity of each line relative to neighboring lines has 
been indicated. 

3. Segments of seven different series have been traced, and the 
anomalies within them described. 

4. The superposition of lines of different series has been noted. 

5. The perturbations and anomalies occurring within these 
series are shown graphically, and an apparent relation between 
anomalies in the different series has been suggested. 

6. All the tails of shorter wave-length than X 3883, given by King, 
have been measured under high dispersion and their structure 
described. 

7. A brief discussion of the present status of Thiele's hypothesis 
regarding tails has been given and the following conclusions drawn : 
(a) that there is no indication that any of the so-called tails are 
directly connected with the heads of the 3883 band; and (b) that, in 
agreement with the view of P. Weiss, the only experimental evidence 
in favor of Thiele's hypothesis is the occurrence of band structures 
shading off toward the red, and the existence of maximum intervals 
between the lines of the same series. 

1 Proc. Roy. Soc, A 91, 208, 1915. 2 Ibid., 432, 1915. 



4 68 



H. S. UHLER AND R. A. PATTERSON 



8. A band, hitherto unrecorded so far as we can learn, has been 
found and its series lines measured. (See Appendix.) 

In conclusion the authors desire to express their sincere thanks 
to Professor H. Kayser for suggesting the problem and for his 
counsel during the work, and to Professor J. S. Ames for placing 
at the disposal of the senior author all the facilities of the Johns 
Hopkins physical laboratory. 



APPENDIX 



A NEW BAND SPECTRUM 



In the course of the preceding investigation a carbon arc was burned in an 
atmosphere of nitrogen from which oxygen and carbon dioxide had been 
removed. On the negatives thus obtained appear two faint bands shading off 
toward the red, which, so far as we can find in the literature of the subject, 
have not been previously recorded. The exact source of these bands has not 
yet been investigated by us. The one at shorter wave-length could not be 
traced to its head on the negatives obtained. The other seems to possess a 
head at A 3280. 85. This head is blurred and confused and certainly does not 
consist of many lines — probably only one. The first few lines are double but 
soon close up and appear single. These singlets then break up into doublets 
of which the components of longer wave-length later develop into doublets 
also, thus forming a triplet series. The first band similarly seems to consist 
of a triplet series. A table giving the wave-lengths of the lines belonging to 
the second band follows. 

TABLE 



A 


A 




A. 


A 






\ 


; 




head^ 


329O.5O 


3302-3 1 


33I3-9 1 


3326.42 


3336.49 


3280.85/ 


2 


5i 


•43 


4 


20 




88 


7 


OS 


.98 




59 


4.88 


6 


74 


7 


42 




20 


1. 22 


4 


7i 


505 


7 


°5 


9 


75 


8 


12 


•34 




83 


.21 




38 


30 


28 


9 


46 


•97 


7 


06 


7.72 


9 


90 




93 




78 


2.78 




18 


.92 


20 


26 


3 


02 




86 


.86 




23 


8. 11 




64 




11 


40 


09 


3-97 


9 


55 


10.62 




73 




72 




5-30 




67 


.87 


3 


13 




81 




6.84 




77 


1 .10 




54 


4 


48 




8.58 


302 


16 


3-64 




99 


6 


31 







Sloan e Physical Laboratory 

Yale University 

June 1915 



ON THE WAVE-LENGTHS OF IRON ARC LINES IN THE 
NEIGHBORHOOD OF THE CALCIUM H AND K LINES 

By E. G. BILHAM 

The question as to whether the wave-length of a given spectrum 
line is susceptible to slight changes depending upon the nature of 
the source producing it is of fundamental importance in spectro- 
scopic measurements of precision, and has received considerable 
attention in recent years. A number of different aspects of the 
problem present themselves. Slight differences have been detected 
between the wave-lengths of certain lines in arc and spark spectra 
of the same element under normal atmospheric pressure. 1 Thus it 
seems reasonable to suppose that in some cases the wave-length of 
the radiation is a function of the electrical stress prevailing in the 
exciting mechanism. Since a large amount of the information 
derived from the astronomical applications of spectroscopy is 
dependent upon measurements of displacements of spectrum lines 
derived from sources whose electrical and temperature conditions 
we can, in most cases, only surmise, the importance of increasing 
our knowledge in this direction can scarcely be overemphasized. 

Another interesting aspect of the question has to do with the 
effect on the lines in, say, the arc spectrum of a given pure element, 
of mixing with it a large or small amount of a foreign substance. 
As an example of an effect of this kind, attention may be drawn to 
the work of Dr. K. Burns, 2 who found that, in certain cases, the 
wave-lengths of lines due to substances occurring as impurities in 
the iron arc were not the same as those obtained from the carbon 
arc containing a salt of the metal under consideration. Thus, in 
the case of manganese, the wave-length of each line in the triplet 
6013, 6016, 6021 was found to be about 0.030 A greater when 
determined from the impurity lines in the iron arc than that 
obtained by Kilby, using a manganese salt in the carbon arc. 
Similar displacements, but in the opposite sense, were also detected 

1 Bilham, Phil. Trans., A 214, 368, 1914. 

2 Comptes raidus, 156, 1976, 1913. 

469 



470 E. G. BILHAM 

in lines due to barium. Whatever may be the cause of the shifts, 
there can be no question of the importance of recognizing their 
existence. The practical interpretation of the phenomenon is well 
expressed by Burns: "Ennn, l'existence de cet effet montre qu'il 
n'est pas prudent de prendre comme etalons des lignes d'impuretes, 
en leur attribuant les longueurs d'onde trouvees dans les mesures 
faites dans d'autres conditions." Published results seem to indi- 
cate that shifts of this character are only met with in isolated, and 
apparently fortuitous, instances. In many cases careful measure- 
ments have failed to detect any evidences of displacements. Mr. 
W. J. Hall, of this College, has investigated the case of an iron 
alloy containing a known percentage (25 per cent) of nickel. 
Repeated measurements of the nickel lines in the spectrum, obtained 
from the arc between poles of the alloy, gave results agreeing with 
the wave-lengths obtained from pure nickel, within the limits of 
experimental error. The lines measured were for the most part 
comprised within the limits X 3700 and X 4200. 

Professor Fowler has suggested to me the desirability of inves- 
tigating what may be described as the inverse of the effect dis- 
cussed above. The possibility presents itself that a very strong 
line due to an impurity may be capable of producing displacements 
of lines of the predominating substance in the immediate neighbor- 
hood. In order to test this point in a typical instance, a number 
of photographs were taken over the region X 3700-4000, with a 
10-ft. Rowland concave grating, using the third order. The car- 
bon arc containing iron filings was used as the source of light. A 
second set of exposures was then made, in which the carbon arc 
was charged with a mixture of iron filings and calcium chloride, the 
other conditions remaining the same. By this means the lines H 
and K were obtained very strong and reversed, superimposed on 
the iron spectrum. A number of iron lines in the immediate neigh- 
borhood of H and K were then measured on all the plates, with 
reference to selected standards (indicated by a letter s), whose 
wave-lengths were assumed to be those obtained by Burns. 1 The 
lines measured were in most cases very suitable for accurate 
measurement. The dispersion in this region is approximately 

1 Lick Obs. Bull., Xo. 247, 8, 27, 1913. 



LIXES IN IROX ARC XEAR H AXD K 



471 



1 . S5 A per millimeter, so that it could be considered possible to 
obtain an accuracy of 0.001 A. Each plate was measured in 
both directions, using a Hilger measuring machine provided with 
a parallel-wire eyepiece. 

The results of the measurements are given in Table I. The 
first two columns contain the wave-length, intensity, and quality 
of each line as given by Burns. The mean wave-lengths calculated 
from the two sets of plates are given in columns 3 and 7. In each 
case the probable error was calculated from the formula 



probable error = o . 6745 

and the values are given in columns 6 and 10. Columns 4 and 8 
contain the intensities estimated from the plates. 

TABLE I 



Wave- 
Length 
(Bums) 



z 
< 



Fe Filings ox Carbon 



Fe Filings +CaClj on Carbon 



Wave-Length 
A 



39 2 5 945 
393 2 -635 



3935 
3937 
3942 

3956 
3961 
3966 
3966 
3967 



3969 

307^ 
397i 
3977 



817 
334 
446 

461 

534 
069 
626 
426 



3B 
3A 



263 
394 
328 

747 



4-i 
2A 
3A 

4A 
iD 
5A 

5 bB 
4A 



7+B 
2A 

4 A 

5+i 



No. of 
Plates 



[3925 
3932 
3933 
3935 
3937 
[3942 

[3956 
3961 
3966 
3966 

3967 
3968 

3969 
397° 
397i 
[3977 



945] 
631 
658 
817 
333 
446] 

461] 

53i 
068 
624 
427 
474 
257 
393 
327 
747] 



Prob. 
Error 



OOI 
OOI 
OOI 
OOI 



OOI 
OOI 
OOI 
OOI 
OOI 
OOI 
OOI 
OOI 



Wave-Length 
B 



[3925 
3932 
3933 
3935 
3937 

[3942 

[3956 
3961 
3966 
3966 

3967 
3968 

3969 
397° 
3971 

[3977 



945J 
634 
666 
816 

33i 
446] 

461] 

535 
069 
616 
429 

475 
258 
387 
327 
747] 



40R 



3 
9 
3 

2b 

2 
30R 

9 

1 

3 

4 



No. of 
Plates 



Prob. 
Error 



002 
002 
OOI 
OOI 



OOI 
OOI 

002 
002 
002 
002 

OOI 

002 



A-B 



- 



- 



003 
008 

OOI 

002 



004 

OOI 

008 

002 

OOI 
OOI 

006 
000 



The H and K lines were obtained on the first set of plates as 
impurity fines of moderate strength, being probably derived from 
the carbon poles. They were measured in a number of cases and 
their wave-lengths computed in order to compare them with the 
values obtained by measuring the reversals on the second set of 



472 E. G. BILE AM 

plates. The agreement may be considered satisfactory in the case 
of H, the values obtained being also concordant with that found 
by St. John, 1 viz., 3968.476. The K line, on the other hand, 
exhibits a displacement of o . 008 A toward the violet in the case 
where it occurs as impurity, as the term is usually understood. 
This result was somewhat unexpected in view of the close concord- 
ance of the wave-lengths obtained by St. John under a great 
variety of different conditions. His mean value for the wave- 
length of K is 3933.667. It appears, then, that the K line is sus- 
ceptible to a shift of the kind described by Burns, whereas H is 
stable. 

With regard to the iron lines, only two exhibit any marked 
tendency to undergo displacements. Of these, the line 3966.6, 
which shows a violet shift of o. 008 A, is very unsymmetrical, being 
shaded toward the blue. On this account the measurements are 
subject to a personal error in estimating the position of the maxi- 
mum. The uncertainty would not be the same in both sets of 
measurements because in set B the line is buried in the wing of the 
H line, so that its lack of symmetry is obscured. The shift of 
0.006 A in the case of the line 3970.4 affords some evidence that 
an adjacent heavy impurity line may be capable of affecting wave- 
lengths of other lines, and indicates the desirability of further work 
on this question. 

The possibility of a purely photographic displacement must not 
be lost sight of. The presence of a violent perturbation in the film 
at a given point might conceivably have some effect at a short 
distance. Judging, however, from the fact that the iron lines near- 
est on either side to H and K exhibit no change of wave-length 
beyond the limits of experimental error, it would seem that such an 
effect is negligibly small, if it exists at all. 

Imperial College of Science and Technology 

South Kensington, London 

July 1915 

1 Astrophyskal Journal, 31, 143, 1910. 



THE SPECTRA OF CATHODE METALS 

By PHILIP ELY ROBINSON 

Many workers with vacuum tubes have observed lines of the 
metals composing the electrodes in the spectra of the gases in the 
tubes. These lines are strongest near the cathode, though in work- 
ing with an induction coil they may also appear near the anode, 
especially if the inverse current is marked. A systematic investi- 
gation of this phenomenon was undertaken by Goldstein. 1 He 
found that the lines of many metals, fifteen in all, used as cathodes, 
appeared, but only if the gas in the tube was nitrogen, and that 
the brilliancy of the metallic spectrum was greatly enhanced by 
immersing the vacuum tube in liquid air. It seems worth while 
to record the preliminary results of some work along the same line. 

The tubes first used were straight, having an internal diameter 
of 2 cm. The electrodes were from 15 cm to 20 cm apart. A 
quartz window on the side of the tube permitted a view of the 
cathode and its immediate neighborhood. It was quickly found 
that this window must be removed to the end of a side tube some 
6 cm or more long to avoid its being obscured by the sputtering 
of the cathode. The final tube used, 1 . 2 cm in internal diameter, 
was H-shaped, with four electrodes of different metals, one in each 
branch. This made possible the investigation of four different 
metals under similar conditions. The cross bar of the H afforded 
an end-on discharge of the gas in the tube free from the cathode 
spectrum. The cathodes throughout were disks of metal nearly 
filling the cross-section of the tube. At first these disks had one 
large central hole. Later they were pierced by numerous small 
holes. 

The source of current was an induction coil capable of giving 
a 15 cm spark. The voltage in the primary circuit was generally 
18 volts, occasionally 24 volts. Variations in the voltage did not 
seem to affect greatly the production of the spectrum of the cathode. 
On the other hand, a condensed discharge was usually more effective 

1 Physikalische Zeitschrift, 6, 14, 1905. 

473 



474 PHILIP ELY ROBINSON 

in securing a brilliant cathode spectrum than a discharge where 
no condenser was used. 

Early experiments indicated that the cathode should be thin. 
No evidence of metallic lines was obtained with cathodes 1-2 mm 
thick. From later experiments I believe a thick electrode might 
be used successfully if pierced by numerous small holes, as used in 
obtaining positive rays. It was first thought that the cathode 
should be thin, so that it might become hot. But though increased 
temperature appears to strengthen the cathode spectrum, it does 
not seem necessary for its production. 

While the cathode spectrum is obtained with most ease in 
nitrogen, it can be produced in other gases as well. For obtaining 
the cathode spectrum there is a most favorable pressure which 
varies with the gas in the tube and with the material of the cathode. 
The range of pressure over which the cathode spectrum is easily 
excited is large for nitrogen. This probably explains in part why 
Goldstein should have found the cathode spectrum in nitrogen 
only. The cathode spectrum has been obtained in hydrogen, 
contrary to Goldstein's direct statement, in carbonic oxide, and 
with especial brilliance in oxygen. 

The spectra have been photographed with a small quartz spectro- 
graph made by Hilger, and the wave-lengths determined. The 
spectra were found to be the spark, rather than the arc, spectra. 
But it is particularly suggestive to note the selection of lines which 
appear and their relative intensities. A comparison of Table I 
with the tables in Kayser's Handbuch, 5, will show that while 
in general only the stronger lines there given have appeared in 
these experiments, yet many strong lines have not, and many faint 
ones have been recorded. Furthermore, the selection of lines and 
their relative intensities depend upon the gas in the tube. Com- 
pare, for example, the intensities of the copper lines XX 2770 and 
2766 in oxygen and in carbonic oxide or in air. Note also the 
great intensity of X 2370 in oxygen, while it was found to be want- 
ing in both carbonic oxide and in air. It has not been definitely 
settled whether the converse case exists of lines that appear in 
carbonic oxide or in air, but yet are not to be found in oxygen. 
Lines are to be seen in the photographs of the cathode spectra in 



THE SPECTRA OF CATHODE METALS 475 

air and in carbonic oxide that apparently fulfil this condition. 
For example, in the case of air there is a fairly strong line, inten- 
sity 3, which appears to coincide with the copper arc comparison 
line at X 2260. 6. This line is not to be found on the oxygen plate. 
But four metals have so far been used as cathodes. Of these 
only copper was examined at all thoroughly. The results are 
summarized under the head of each metal and the gas in the tube. 

COPPER 

Hydrogen. — The cathode spectrum of copper was obtained in 
hydrogen, usually close to the cathode. Occasionally, when a 
condensed discharge was used, brilliant green flashes, showing 
copper lines vividly, occurred in the neighborhood of the cathode. 
On one occasion, after the tube had become well coated with 
copper, a fairly brilliant cloud, pale green in color, appeared about 
a centimeter or more in front of the cathode, i.e., toward the anode. 
Visually examined this showed the copper lines at XX 5218, 5153, 
and 5106 with great brilliance. Photographed with a two-hour 
exposure, it showed a number of copper lines, while the hydrogen 
spectrum was strong. These copper lines are given in the table 
under H. The hydrogen was not quite free from CO and water- 
vapor, but nearly so. 

Air. — In air the copper lines appeared easily, and much more 
brilliantly than in hydrogen. In the photograph the nitrogen 
bands obscured some of the copper lines, making it uncertain just 
which copper lines were present. Exposures of equal length 
yielded more copper lines than appeared in hydrogen, corresponding 
to the greater intensity of the cathode spectrum. In the table 
under N only such copper lines are noted as were definitely identi- 
fied. With three exceptions these comprise all the lines of wave- 
length shorter than 235 ;u/z that appear on the plate. These three 
exceptions apparently coincide with lines in the adjacent copper 
arc comparison spectrum. 

Carbon compounds. — -Occasionally through accidental heating 
of the sealing-wax used to seal in the electrodes, carbon spectra 
became predominant in the tube. The copper lines were readily 
obtainable therein. As with nitrogen, the carbon bands greatly 



476 



PHILIP ELY ROBINSON 



interfered with identification of the copper lines present. Only 
such as were certainly present are given under C in the table. 
Nitrogen bands are not apparent in the photograph, though they 
are to be expected from this source. 

TABLE I 

Lines of Copper Cathode in Various Gases 

(Only lines of wave-length less than 331 fj.fi are given) 



Intensity 



a s O N C H 



Intensity 



a s O N C H 



Intensity 



3308 . 1 
3279.9 

74- 1 

47-7 

08.3 

3*94- 2 

3°94- 1 
10.9 

2961 . 2 
2824.5 
2769.9 

66.5 
22.0 
19.0 
138 

°3 -5 

01.3 

2689.6 

66.6 

18.5 
00.5 

2599- 1 
90.8 

53-3 
45- 1 
29.6 
26.8 
23.2 
18.5 
16.5 
13.2 

«-S 

08.7 

06.5 

2492 . 2 



3 • 
3 3 

10 10 
io|io 

4 

5 

6 

7 3 
4 



86 


/ • • 
6.. 


86 


0. . 


82 


4- • 


78 


4- • 


73 


5 • ■ 


68 


6.. 


58 


9- • 


5i 


9- 


44 


5 • ■ 


4i 


7 ■ ■ 


36 


0. . 


33 


7-- 


3° 


6.. 


28 


4- • 


24 


7- • 


12 


5-- 


03 


6.. 


00 


2. . 


2392 


7- 


76 


5- 


70 


0. . 


56 


7 ■ ■ 


55 


2. . . 


45 


6... 


36 


3-- 


°3 


2. . . 


2299 


7... 


96 


9... 


94 


4. .. 


Q2 


0. . . 


86 


8... 


78 


5- • • 


76 


3- ■ • 


65 


S-- 



. . 2263 


9 




55 


1 




49 


1 




47 


1 




44 


3 




42 


7 




30 


2 




28 


9 




27 


8 




25 


8 




24 


9 




18 


2 




■ ■ 15 


4 




14 


8 




12 


9 




10 


4 




. . 2199 


8 




95 


9 




92 


4 




.. 89 


7 




81 


8 




79 


4 




75 


1 




.. 65 


1 




61 


4 




5i 


9 




49 







• • 36 







34 


5 




2 26 


i 




23 


1 




17 


4 




12 


2 




04 


9 





a = arc spectrum of copper. 
s=spark spectrum of copper. 
0=oxygen. X =air from leak. 



P = present on lines of gas. 
— = definitely not present. 
C =carbon compounds. H = hydrogen. 



Oxygen. — The copper spectrum was obtained with great bril- 
liance in oxygen to the practical exclusion of all lines of oxygen. 



THE SPECTRA OF CATHODE METALS 477 

In the table under O is given every line shorter than X 3310 that 
showed on the plate, with three exceptions. The first exception, 
at X3135, intensity 2, was probably due to carbon as impurity. 
The second, at X 2883, intensity 2, was due to CO. The third, at 
X 2600, has not been indentified. The time of exposure was i h 
5o m . The immediate neighborhood of the cathode was filled with 
a greenish-white vapor. On one occasion with a condensed dis- 
charge a brilliant green cone of vapor showing the copper spectrum 
vividly shot out to the rear of the large hole in the cathode, i.e, 
away from the anode, for a distance of 2 cm or more. It was not 
found possible to maintain this green cone for more than a few 
seconds at a time. 

The results for copper are summarized in Table I. The wave- 
lengths are given under X. Under a and 5 are stated the intensities 
of these lines in the copper arc and spark, respectively, as given 
in Kayser's Handbuch, 5. Under O, N, C, and H are given the 
intensities as they appeared in the cathode spectrum in oxygen, 
air, carbonic oxide, and hydrogen respectively, 1 denoting a line 
so faint as to be barely recognizable, and 10 maximum intensity. 

ALUMINIUM 

The aluminium cathode spectrum was only observed visually. 
The electrode was a wire about 2 mm in diameter ordinarily used 
as the anode in the tube in which copper was investigated. Alu- 
minium lines were observed in the same gases as copper and with 
the same relative ease in production. The most favorable pressure 
for aluminium was less than that for copper. In oxygen there 
appeared on the rear of the electrode a small yellowish-green tuft, 
which showed the aluminium spark lines brilliantly. At the same 
time two other workers in the laboratory, who were investigating 
gaseous spectra, found aluminium spark lines from their electrodes 
in their photographs, Mr. Matthews in hydrogen, and Mr. Brooks- 
bank in CO. 

IRON 

The iron cathode spectrum was observed first when the tube 
was filled with a mixture of air and carbon compounds coming from 
a leak caused by the melting of the sealing-wax. The addition 



478 PHILIP ELY ROBINSON 

of oxygen greatly increased the intensity of the iron spectrum. 
In fairly pure oxygen and with a condensed discharge, a bluish 
vapor extended for several millimeters on both sides of the cathode. 
The spectrum of this vapor showed a great many strong iron lines 
with relative intensities indicating the spark spectrum. Lines of 
the gas in the tube were also present. An exposure of twenty 
minutes was sufficient for a strong photograph. 

Oxygen is a gas which disappears rapidly in a vacuum tube. 
A constant supply of it is necessary to keep the tube running con- 
tinuously. Yet with both copper and iron, when the cathode 
spectrum had been established, a much smaller supply of oxygen 
was necessary. 

SILVER 

Very little was done with silver. What were apparently 
spark lines were observed visually in air. 

The results may be roughly summarized by saying that condi- 
tions favorable to the sputtering of the cathode were found to 
favor excitation of the spectrum of the metal of the cathode. 

In closing it is a pleasure to thank Professor A. Fowler, at 
whose suggestion and in whose laboratory these experiments were 
carried out, for granting me the facilities of his laboratory. 

Royal College of Science, London 
July 191 5 



INDEX TO VOLUME XLII 



SUBJECTS 

PAGE 

Absorption, Fluorescence, and Phosphorescence, Theory of. E. C. C. 

Baly 4 

Andromedae, Orbital Elements of Eclipsing Variable TW. John Q. 

Stewart 315 

Aqueous Vapor, Transparency of. F. E. Fowle 394 

Arc Lines in Neighborhood of Calcium H and K Lines, Wave- 
Lengths of. E. G. Bilham 469 

Arc, Study of Pole-Effect in Iron. Charles E. St. John and Harold D. 

Babcock 231 

Band, and Associated Tails, Structure of Third Cyanogen. H. S. 

Zlder and R. A. Patterson 434 

Band Spectra, On Thiele's Phase in. H. S. Uhler .... 72 
Barium, Infra-Red Arc Spectrum of. H. M. Randall .... 195 
Calcium H and K Lines, Wave-Lengths of Iron Arc Lines in Neigh- 
borhood of. E. G. Bilham 469 

Cassiopeiae, Elements of Eclipsing Systems TV, TW, TX. R. J. 

McDiarmid 412 

Cathode Metals, Spectra of. I. Philip Ely Robinson .... 473 

Cluster N.G.C. 1647, Color-Indices in. F.H.Seares .... 120 

Cluster N.G.C. 1647, Effective Wave-Lengths of 184 Stars in. 

E. Hcrtzsprung 92 

Cobalt, Variation of Temperature of Electric Furnace Spectra of. 

Arthur S. King 344 

Color-Indices in the Cluster N.G.C. 1647. F.H.Seares . . . 120 

Cyanogen Band and Associated Tails, Structure of Third. H. S. 

Uhler and R. A. Patterson 434 

XX Cygni, Light-Curve of. Harlow Shapley and Martha Betz 

Shapley 148 

Densities of Second-Type Stars. Harlow Shapley .... 271 

SX Draconis, Orbital Elements of Eclipsing Variable. W. Van B. 

Roberts 312 

Eclipsing Variables, TV, TW, TX Cassiopeiae and T Leonis Minoris, 

Elements of. R. J. McDiarmid 412 

Editorial Note 372 

Electric Furnace Spectra of Cobalt and Nickel, Variation of Tempera- 
ture of. Arthur S. King 344 

479 



4S0 INDEX TO SUBJECTS 



PAGE 



Electric Spark. W. 0. Sawtelle 163 

Fluorescence, Phosphorescence, and Absorption, Theory of. E. C. C. 

Baly 4 

Herculis, Orbital Elements of Eclipsing Variable TU. John Q. 

Stewart . 315 

Huggins, Lady. Sarah F. Whiting 1 

Images, Adaptation of Koch Registering Microphotometer to Meas- 
urement of Sharpness of Photographic. Orin Tugman . 321 
Iron Arc, Pole-Effect in. Charles E. St. John and Harold D.Babcock 231 
Iron Arc Lines in Neighborhood of Calcium H and K Lines, Wave- 
Lengths of. E. G. Bilham 469 

T Leonis Minoris, Elements of Eclipsing System. R. J. McDiarmid 412 

Light-Curve of XX Cygni. Harlow Shapley and Martha Betz Shapley 148 

McCormick Observatory, Stellar Parallax Work at. S. A. Mitchell 263 

Metals in Ultra-Violet Region of Spectrum, Reflecting Power of. 

E. 0. Hulburt 205 

Metals, Spectra of Cathode. Philip Ely Robinson .... 473 

Microphotometer, Adaptation of Koch Registering, to Measurement 

of Sharpness of Photographic Images. Orin Tugman . . 321 

Mirrors for Ultra-Violet Photography, Nickel Deposits on Glass. 

R. W. Wood 365 

Nickel, Variation of Temperature of Electric Furnace Spectra of. 

Arthur S. King 344 

8 Orionis, Eclipsing Variable Star. Joel Stebbins 133 

Ottawa, Spectroscopic Determination of Solar Rotation at. J. S. 

Plaskett 373 

Parallax Work at McCormick Observatory, Stellar. S.A.Mitchell 263 

Phosphorescence, Theory of Absorption, Fluorescence, and. E. C. C. 

Baly 4 

Photographic Images, Adaptation of Koch Registering Micropho- 
tometer to Measurement of Sharpness of. Orin Tugman . 321 
Photographic Plates, Resolving Power of. Orin Tugman . . . 331 
Photography, Nickel Deposits on Glass Mirrors for Ultra-Violet. 

R. W. Wood 365 

Pole-Effect in Iron Arc, Study of. Charles E. St. John and Harold 

D. Babcock 231 

Pyrometry, Effective Wave-Length of Transmission of Red Pyrome- 
ter Glasses and Other Notes on. Edward P. Hyde, F. E. Cady, 

and W. E. Forsythe 294 

Radial Velocities of Five Hundred Stars. Walter S. Adams . . 172 

Radial Velocities of Stars of Different Spectral Classes and Their 
Relation to Solar Motion, Some Peculiarities of Residual. 
C. D. Perrine 305 



INDEX TO SUBJECTS 481 

PAGE 

Reflecting Power of Metals in Ultra-Violet Region of Spectrum. 

E. 0. Hulburt 205 

Resolving Power of Photographic Plates. Or in Tugman . . . 331 

Reviews : 

Henry Crew and Alfonso de Salvio. Dialogues concerning Two 

New Sciences by Galileo Galilei (E. P. Hubble) .... 283 

Marcel Moye. V Astronomic (Philip Fox) 204 

Alfonso de Salvio and Henry Crew, Dialogues concerning Two 

New Sciences by Galileo Galilei (E. P. Hubble) .... 283 

R. A. Sampson. The Sun (Philip Fox) 203 

H. H. Turner. Tables for Facilitating the Use of Harmonic 

Analysis (Oliver J. Lee) 203 

Solar Motion, Some Peculiarities of Residual Radial Velocities of 

Stars of Different Spectral Classes and Their Relation to. 

C. D. Perrine 305 

Solar Rotation at Ottawa, Spectroscopic Determination of. /. 5. 

Plaskett 373 

Spark, Electric. W. 0. Sawtelle 163 

Spectra of Cathode Metals. Philip Ely Robinson .... 473 

Spectra of Cobalt and Nickel, Variation of Temperature of Electric 

Furnace. Arthur S. King 344 

Spectra, On Thiele's Phase in Band. H. S. Uhler .... 72 

Spectral Classes and Their Relation to Solar Motion, Some Pecu- 
liarities of Residual Radial Velocities of Stars of Different. 

C. D. Perrine 305 

Spectroscopic Binaries of Class M, Distribution and Some Possible 

Characteristics of. C. D. Perrine 37c 

Spectrum of Barium, Infra-Red Arc. H. M. Randall .... 195 

Spectrum, Reflecting Power of Metals in Ultra-Violet Region of. 

E. 0. Hulburt 205 

Spectrum, Visibility of Radiation in Red End of Visible. Edward 

P. Hyde and W. E. Forsythe 285 

Stars, Effective Wave-Lengths of Absolutely Faint. E. Hertzsprung 11 1 

Stars in Cluster X.G.C. 1647, Effective Wave-Lengths of 184. 

E. Hertzsprung 92 

Stars, Note on Densities of Second-Type. Harlow Shapley . . 271 

Stars of Different Spectral Classes and Their Relation to Solar 

Motion, Some Peculiarities of Residual Radial Velocities of. 

C. D. Perrine 305 

Stars, Radial Velocities of Five Hundred. Walter S. Adams . \-]2 

Structure of Third Cyanogen Band and Associated Tails. H. S. 

Uhler and R. A. Patterson 434 



482 INDEX TO SUBJECTS 

PAGE 

Temperature of Electric Furnace Spectra of Cobalt and Nickel, 

Variation of. Arthur S. King 344 

Thiele's Phase in Band Spectra. H. S. Uhler 72 

Ultra-Violet Photography, Nickel Deposits on Glass Mirrors for. 

R. W. Wood 365 

Vapor, Transparency of Aqueous. F. E. Fowle 394 

Variable Star 8 Orionis, Eclipsing. Joel Stebbins 133 

Variable SX Draconis, Orbital Elements of Eclipsing. W. Van B. 

Roberts 312 

Variables TV, T\V, TX Cassiopeiae and T Leonis Minoris, Elements 

of Eclipsing. R. J. McDiarmid 412 

Variables T\V Andromedae, TU Herculis, and RS Vulpeculae, Orbital 

Elements of Eclipsing. John Q. Stewart 315 

RS Vulpeculae, Orbital Elements of Eclipsing Variable. John Q. 

Stewart 315 

Wave-Length of Transmission of Red Pyrometer Glasses and Other 

Notes on Pyrometry, Effective. Edward P. Hyde, F. E. Cady, 

and W. E. Forsythe 294 

Wave-Lengths of Absolutely Faint Stars, Effective. E. Hertzsprung in 

Wave-Lengths of Iron Arc Lines in Neighborhood of Calcium H 

and K Lines. E. G. Bilham 469 

Wave-Lengths of 184 Stars in Cluster N.G.C. 1647, Effective. 

E. Hertzsprung 92 



INDEX TO VOLUME XLII 



AUTHORS 



Adams, Walter S. The Radial Velocities of Five Hundred Stars . 172 

Baly, E. C. C. A Theory of Absorption, Fluorescence, and Phos- 
phorescence 4 

Bilham, E. G. On the Wave-Lengths of Iron Arc Lines in the 

Neighborhood of the Calcium H and K Lines .... 469 

Cady, F. E., W. E. Forsythe, and Edward P. Hyde. The Effective 
Wave-Length of Transmission of Red Pyrometer Glasses and 
Other Xotes on Pyrometry 294 

Forsythe, W. E., and Edward P. Hyde. The Visibility of Radia- 
tion in the Red End of the Visible Spectrum .... 285 

Forsythe, W. E., Edward P. Hyde, and F. E. Cady. The Effective 
Wave-Length of Transmission of Red Pyrometer Glasses and 
Other Xotes on Pyrometry 294 

Fowle, F. E. The Transparency of Aqueous Vapor .... 394 

Fox, Philip. Review of: The Sun, R. A. Sampson .... 203 

Review of: UAstronomie, Marcel Moye 204 

Hertzspruxg, E. Effective Wave-Lengths of 184 Stars in the 

Cluster N.G.C. 1647 92 

Effective Wave-Lengths of Absolutely Faint Stars . . . 1 1 1 

Hubble, E. P. Review of: Dialogues concerning Two New Sciences 

by Galileo Galilei, Henry Crew and Alfonso de Salvio (Tr.) . 283 

Hulburt, E. O. The Reflecting Power of Metals in the Ultra- 
Volet Region of the Spectrum 205 

Hyde, Edward P., and W. E. Forsythe. The Visibility of Radia- 
tion in the Red End of the Visible Spectrum .... 285 

Hyde, Edward P., F. E. Cady, and W. E. Forsythe. The Effective 
Wave-Length of Transmission of Red Pyrometer Glasses and 
Other Notes on Pyrometry 294 

King, Arthur S. The Variation of Temperature of the Electric 

Furnace Spectra of Cobalt and Nickel 344 

Lee, Oliver J. Review of: Tables for Facilitating the Use of Har- 
monic Afialysis, H. H. Turner 203 

McDlarihd, R. J. The Elements of the Eclipsing Systems TV, 

TW, TX Cassiopeiae and T Leonis Minoris .... 412 

Mitchell, S. A. Stellar Parallax Work at the McCormick Observ- 
atory 263 

483 



484 INDEX TO AUTHORS 

Patterson, R. A., and H. S. Uhler. The Structure of the Third 
Cyanogen Band and the Associated Tails 

Perrine, CD. On Some Peculiarities of the Residual Radial 
Velocities of Stars of Different Spectral Classes and Their 

Relation to the Solar Motion 

The Distribution and Some Possible Characteristics of the 
Spectroscopic Binaries of Class M 

Plaskett, J. S. The Spectroscopic Determination of the Solar 
Rotation at Ottawa 

Randall, H. M. The Infra-Red Arc Spectrum of Barium 

Roberts, W. Van B. The Orbital Elements of the Eclipsing Variable 
SX Draconis 

Robinson, Philip Ely. The Spectra of Cathode Metals . 

St. John, Charles E., and Harold B. Babcock. A Study of the 
Pole-Effect in the Iron Arc 

Sawtelle, W. O. The Electric Spark 

Seares, F. H. Color-Indices in the Cluster N.G.C. 1647 . 

Shapley, Harlow. Note on the Densities of the Second-Type Stars 

Shapley, Harlow, and Martha Betz Shapley. A Stud} 7 of the 

Light-Curve of XX Cygni 14J 

Shapley, Martha. Betz, and Harlow Shapley. A Study of the 

Light-Curve of XX Cygni 145 

Stebbins, Joel. The Eclipsing Variable Star 8 Ononis ... 13^ 

Stewart, John Q. Orbital Elements of the Eclipsing Variables 

TW Andromedae, TU Herculis, and RS Vulpeculae . 31 « 

Tugman, Orin. An Adaptation of the Koch Registering Micro- 
photometer to the Measurement of the Sharpness of Photo- 
graphic Images 32] 

The Resolving Power of Photographic Plates .... 33 ] 

Uhler, H. S. On Thiele's Phase in Band Spectra .... 7: 

Uhler, H. S., and R. A. Patterson. The Structure of the Third 

Cyanogen Band and the Associated Tails 434 

Whiting, Sarah F. Lady Huggins ] 

Wood, R. W. Xickel Deposits on Glass Mirrors for Ultra-Violet 

Photography 36; 



b i 



— v<} 10 




\2>S0 



JfGCI^/ 



PLATE I 




l^'oo' 



PLATE II 




Rotating Mirror System 




(l) (2) ( 3 ) 

b. Spectrograms of the Oscillatory Spark 

One hundred spark images superposed upon the slit. 

(1) Slit on initially negative terminal. 

(2) Slit in middle of the gap. 

(3) Slit on initially positive terminal. 



PLATE III 




tory Spark Discharge Controlled by Means of Ultra-Violet "Triggering" Action. Cadmium 
Electrodes. Linear Distance Traveled by Spark Images about 500,000 mm per Second. 
Variation in Time between Discharges Less than 2X10-7 Seconds. 



PLATE IV 




IN.K 



a. The Arc as Projected upon the Slit 




b. Sector and Prisms in Position 



Violet 



r i^rv. x r, \ 



Red 



Pole 



\5424 a X "^ co 

a. Displacements at pole toward violet for X 5424, toward 
red for X6400. Artificial lines ruled through centers of com- 
parison spectra. Enlarged 28 times. 



/). Iodine absorption line superposed upon iron line ^54-4- 
showing displacement of the latter at the negative pole. 
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Physical & 
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The Astrophysical journal 



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