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STAR CLUSTERS
Thirty-four Globular Cliutterv in ike Southern Milky Way.
HARVARD OBSERVATORY MONOGRAPHS
No. 2
STAR CLUSTERS
BY
HARLOW SHAPLEY
Published for the Observatory
by the
McGRAW-HILL BOOK COMPANY, INC.
NEW YORK: 370 SEVENTH AVENUE
LONDON: 6 & 8 BOUVERIE ST , E. C. 4
1930
COPYRIGHT, 1930,
BY HARVARD OBSERVATORY
PRINTED IN THE UNITED STATES OF AMERICA
All rights reserved. This book, or
parts thereof^ may not be reproduced
in any form without permission of
the publishers.
THE MAPLE PRESS COMPANY, YORK, PA,
PREFACE
FOR more than five years the writing of this second monograph
of the Harvard Observatory series has been in progress.
Several factors have contributed to the postponement of its
publication, but the chief cause of delay has been the desire to
provide a revised system of parallaxes for globular clusters.
All considerations of the dimensions, star densities, and lumin-
osities of clusters, and most of the conclusions concerning the
dimensions of the Galaxy and the distance to external systems,
depend at the present time on the period-luminosity relation of
Cepheid variable stars. In the preparation of a monographic
treatment of star clusters much preliminary work on Cepheids
has therefore been necessary. , At the McCormick and Mount
Wilson observatories investigations of proper motions have
been undertaken in order to fix the zero point of the period-
luminosity curve. At Harvard we have determined periods
and magnitudes of many variable stars in the Large and Small
Clouds of Magellan to provide a firmer photographic connection
between period and luminosity.
The revision of the parallaxes of globular clusters has also
depended largely on the study of individual systems. In my
determination in 1917 of the parallaxes of sixty-eight globular
clusters, there were only five systems for which the variables
had been sufficiently studied to enter directly into the measure-
ment of cluster distances. We now have nineteen clusters in
which variable stars have been adequately studied; the periods
and median magnitudes of more than five hundred individual
variables have been derived. In 1917 the magnitudes of the
high luminosity stars had been measured for twenty-eight
globular clusters; the number is now increased to forty-eight.
viii PREFACE
Much of the recent investigation of magnitudes in clusters is
the work of Miss Helen Sawyer at the Harvard Observatory;
my earlier photometric studies preliminary to the revision of
cluster distances were carried on at Mount Wilson and Harvard
with the aid of several assistants.
Probably one of the most satisfactory features of the present
volume is the bibliography in Appendix C. It is essentially
complete for all papers bearing directly on star clusters pub-
lished during the past fifty or sixty years. Particular attention
should be directed to the treatises by ten Bruggencate and
Parvulesco, who handle some special subjects in the field of
clusters more fully than they are treated here.
I am indebted to Dr. Cecilia Payne for extensive assistance
in the preparation of manuscript and bibliography and in other
details. In the interest of this study of clusters Dr. Walter S.
Adams has generously transferred to the Harvard Observatory
the photographs I made with the 6o-inch and loo-inch reflectors
at Mount Wilson. Miss Jenka Mohr has assisted in the prep-
aration of the manuscript and in editorial matters. To
several members of the Observatory staff I am indebted for
incidental or particular assistance with illustrations, com-
putations, and routine work on manuscript and proof. My
greatest debt is to the star clusters themselves, which have
provided persistent excitement and inspiration.
H. S.
CAMBRIDGE, MASS.,
June, 1930.
CONTENTS
PAOE
PREFACE . .... vu
CHAPTER
I INTRODUCTORY SURVFY i
1. The Significance of Clusters . . i
2. Historical Notes on Clusters . . . . 3
II. CLASSIFICATION, NUMBER, AND DISTRIBUTION 6
Q A Comparison of Galactic and Globular Clusters .... 6
tAA Classification of Galactic Clusters ... 8
j Classification of Globular Clusters. n
o! The Number of Clusters . . 14
fy The Apparent Distuibution of Galactic Clusters 1 7
18 NGC 5053 and NGC 2477 18
^ The Apparent Distribution of Globular Clusters . . 20
10. Clusters in or near Obstructing Nebulosity 22
* III. ON THE SPECTRAL COMPOSITION OF CLUSTERS . . 23
11. Integrated Spectra of Globular Clusters . . .23
12. Stellar Types in Globular Clusters 25
13. Distribution of Colors throughout Globular Clusters . . 30
14. Types of Stars m Galactic Clusters . . 32
15 Spectra in Individual Galactic Clusters 33
IV. VARIABLE STARS . ... 43
1 6 A Summary of Known Variables ... 43
17. The Frequency of Variable Stars 46
1 8 General Properties of Variables in Clusters ... 47
19. Notes on Some Individual Variable Stars . 50
20. Variable Stars in Galactic Clusters 53
2 1 . The Relation of Magnitude to Period for Cluster-type Variables 53
22. A Test for Hypotheses of Cepheid Variability . 55
23. Concerning Vestigial or Incipient Variation 60
24. A Composite Light and Color Curve for Cluster-type Variables 63
V. THE DISTRIBUTION OF STARS IN GLOBULAR CLUSTERS ... 65
25. Are Cluster Stars Arranged Spirally? 65
26. On the Laws of Distribution .... 67
27. Luminosity Curves for Clusters 72
X CONTENTS
CHAPTER PAGE
VI. THE FORMS OP GLOBULAR CLUSTERS 78
28. Definitions and Difficulties . . 78
29. The Elongation of Messier 13 . 81
30. Elhpticity of Globular Clusters 84
31. The Relation of Elongation to the Galactic Circle 88
32. Seven Peculiar Clusters . 89
VII. THE STRUCTURE OF GALACTIC GROUPS 95
33. Elongation of Galactic Clusters 95
34. The "Shoulder" Effect in Messier 67 and Elsewhere 99
35. Additional Remarks on Galactic Clusters 101
VIII. ON THE VELOCITY OF LIGHT. . 105
36. Stellar Eclipses in Light of Different Wave Lengths 106
37. Messier 5 and the Relative Speed of Blue and Yellow Light 108
IX. THE TRANSPARENCY OF SPACE. . . 113
38. Early Investigations of Light Scattering 114
39. Blue Stars in Messier 13 ... 116
40. Faint Blue Stars in the Milky Way 118
41. N G C. 7006 and the Scattering of Light 119
42. The Coma- Virgo Group of Nebulae 120
43. The Obstruction of Light in Space 121
X. THE PERIOD-LUMINOSITY CURVE ... 125
44. Historical Notes 125
45. Miss Leavitt's Work on the Periods of Cepheids 126
46. The Visual Period-luminosity Curve 128
47. The Periods of 106 Variables in the Small Magellanic Cloud 130
48. The Photographic Period-luminobity Curve 132
49. The Period-spectrum Relation 136
50. The Period-luminosity Relation for Galactic Cepheids 138
51. A Theoretical Period-luminosity Relation for Galactic Cepheids 142
52. The Zero Point 149
53. The Period-luminosity Relation in Clusters and External
Galaxies 151
54. Long-period Variables and the Pulsation Hypothesis . 153
XI. THE DISTANCES OF CLUSTERS 155
55. Distances of Globular Clusters Obtained from Cepheids and
Bright Stars . 155
56. Distances of Globular Clusters Obtained from Diameters and
Integrated Magnitudes . 16 r
57. A Working Catalogue ot Galactic Clusters (Appendix B). . 167
58. Parallaxes of Galactic Clusters . . 168
XII. DIMENSIONS OF THE GALAXY .... . . 171
59 Membership in the Galaxy ... .... 171
60. The Higher System of Globular Clusters 172
CONTENTS xi
CHAPTER . P AGE
61. The Distance to the Galactic Center 176
62 Galactic Dimensions. 178
63. The System of Galactic Clusters 179
XIII STAR CLUSTERS IN THE MAGELLANIC CLOUDS 183
64 A Summary of Clusters and Nebulae . 183
65. The Globular Star Clusters . 185
66. Distances of the Clouds Derived from Variables and Globular
Clusters 188
67. On the Relation of the Clusters to the Magellanic Clouds 190
XIV DATA BEARING ON THE ORIGIN OF THE GALAXY . 193
68. The Earlier Interpretation .... 193
69. The Research on Milky Way Variable Stars 190
70. Peculiarities in the Distribution of Galaccic Clusters 197
71. Rddial Velocities of Globular Clusters 199
72. Dimensions and Star Densities of Clusters 200
73. On the Masses of Giant Stars 203
74. On the Evolution of Globular and Galactic Groups . 207
75 The Galactic System as a Super-galaxy 209
XV A PARTIAL SUMMARY 213
APPENDIX A CAI \LOGUE OF GLOBULXR CLUSTERS . 223
APPENDIX B CATALOGUE OF GALACTIC CLUSTERS 228
APPENDDC C BIBLIOGRAPHY . . ... 235
APPENDIX D SPECIAL BIBLIOGRAPHIES 268
INDEX 269
SPECIAL INDEX TO INDIVIDUAL CLUSTEHS . . . 277
STAR CLUSTERS
CHAPTER I
INTRODUCTORY SURVEY
FROM a place deeply involved in stellar organizations we look
out at the sidereal universe. Immediately around our minute
association of sun and planets are the bright white stars of the
Ursa Major cluster, with one of its members, Sirius, but a few
light years distant. Much greater than such near-by groups
is the local system, a star cloud that includes thousands of the
surrounding bright stars and a million or so of the fainter.
Still more inclusive is the Galaxy, which holds sun, clusters, and
star clouds, and which, in turn, may be but one unit in a higher
example of the gravitational clustering of sidereal bodies.
i. The Significance of Clusters. In time as well as in space
we are involved in clustering tendencies we witness the
sidereal universe undergoing formative and disruptive proc-
esses. The evidence of our situation in the mid-course of the
transformation of stellar systems, rather than at the beginning
or end, is well illustrated in the mixture of stars, nebulae, and
sidereal groups that go to make up the Clouds of Magellan or
any large section of the Galaxy. In such places we find star
clusters in nearly all degrees of richness and condensation; we
find nebulosity associated with stars and groups of stars,
and everywhere there are large irregularities in the general
stellar distribution. The contrast is striking between the
smoothness of a typical globular cluster, where an obvious
state of equilibrium prevails, and the heterogeneity of content
and irregularity of form in the galactic system. The globular
2 INTRODUCTORY SURVEY
cluster, when undisturbed from without, apparently attains a
steady stage, but the star clouds and the Galaxy, with their
clusters, star streams, and secondary organizations, are far
from that condition.
By star clusters we ordinarily mean both_the_typical globular
.systems and the mon^numerous and less well-defined open
clusters which range, for instance^Jirom the Hyades to the
fairly compact system of Messier n. Such clusters are com-
posed of stars which are. known to be physically connected or
may be assumed from their apparent positions to constitute
distinct physical organizations. But also, in all parts of the
sky, among the faint stars there are thousands of less obvious
groupings. The studies of star distribution on the astrographic
charts by Turner, 1 and by Opik and Lukk, 2 indicate that the
distribution is not at random. Working on this problem with
Harvard plates, 3 1 have shown that the clustering and vacancies
are real and are not to be attributed to occultation by nebu-
losity. Random distribution among galactic stars, it seems,
does not exist. The observed irregularities in the star counts,
beyond those allowed by the law of chance, are to be attrib-
uted, in general, to the very prevalent stellar associations,
which are not commonly recognized by casual inspection and
cannot be separated from surrounding stars except through
laborious investigation.
(pie typical star clusters, however, are in themselves numer-
ous and widely distributed, and their problems are intimately
interwoven with some of the most significant questions of
stellar organization and galactic evolutioiD The general study
of clusters deals with a wide variety of subjects. It involves,
for instance, the problems of supergiant stars, stellar luminosity
curves, irregularities in stellar distribution, star streaming,
island universes, and the genesis of galactic systems; it con-
siders primarily, however, the composition, structure, distribu-
'Obs^S, 173, 1925.
2 Publ. de TObs. Astr. de 1'Univ. de Tartu (Dorpat), 26, No. 2, 1924.
8 H. C. 281, 1925.
HISTORICAL NOTES ON CLUSTERS 3
tion, and cosmic position of the easily recognizable galactic
and globular clusters, and in the following chapters these groups
will receive almost exclusive attention.
2. Historical Notes on Clusters. The history of the scientific
study of star clusters fs neither extensive nor very significant.
Several clusters of naked-eye stars for example, the Pleiades,
Praesepe, Coma Berenices have, of course, always been known,
though their definite assignment to the cluster category came
with the work on proper motions in the last 50 years. For a
few constellations, the majority of the bright stars are now known
to lie near together in space and to form physical systems.
Such constellation groups are Taurus, Orion, Ursa Major,
Perseus, Scorpio, Sagittarius, and Vela. But no close physical
connection exists for the bright stars of Cassiopeia, Lyra,
Aquila, Canis Major, and many others.
A score of the brighter galactic clusters and half a dozen of the
globular clusters can be seen with the naked eye under good
conditions. These were probably all known, therefore, to
the ancients, but only a few appeared in our permanent records
before the latter half of the eighteenth century.
The records of Hipparchus contain references to the double
cluster in Perseus and to Praesepe, although neither was recog-
nized as a group of distinct stars until the invention of the
telescope. Both were first resolved by Galileo, who described
"the nebula called Praesepe" as "not one star, only, but a
mass of more than forty small stars. " 4
Messier 22, the first globular cluster to be recorded as such,
was discovered by Ihle 5 in 1665; w Centauri was noted as a
lucid spot in the sky by Halley in 1677 and had previously
been known to Bayer as a hazy star and to Ptolemy as a star
in the cloud on the Horse's back; in 1702 Kirch discovered
Messier 5, and the famous Messier 13 (the Hercules cluster),
4 Galileo, Nuncius Siclereus, 1610; Allen, Star Names and Their Meanings,
113, 1899.
6 Wolf, R , Geschichte der Astronomic, 420, 1877.
4 INTRODUCTORY SURVEY
the brightest in the northern sky, was accidentally found by
Halley in 1714.
The open cluster Messier n had already been recorded by
Kirch in 1681; but the majority of bright galactic clusters,
except the Pleiades and the Hyades, were first recorded as
such by Messier 6 in 1771. The conspicuous groups of stars
around t\ Carinae and the cluster near K Crucis were discovered
by Sir John Herschel.
For both open and globular clusters, as well as for bright
nebulae of all kinds, the systematic listing by Messier in 1784
marked an epoch in the recording of observations. The
Herschels advanced the work materially. Especially significant
were the General Catalogue published by Sir John Herschel
in i864 7 and its important sequels by Dreyer in the New
General Catalogue and the Index Catalogues.
Schultz and Barnard were among the pioneers in determining
visually the positions of the individual stars in globular clusters.
The superior photographic method of charting positions was
first used by the Henrys and Gould for galactic clusters and by
Scheiner, Ludendorff , and von Zeipel for globular systems.
The Pleiades, the Hyades, Praesepe, h and x Persei, and some
of the other bright galactic groups have, for the past 50 years
or more, been the subject of frequent investigations of positions
and proper motions. It is not unfair to say, however, that,
except for studies of these nearby objects, the work done on
individual clusters before the present century is now of little
value. The development of photographic methods, the modern
large telescopes with their rapid spectroscopes, and the stand-
ardizing of magnitude sequences have all tended to make the
earlier work obsolete. The present views of the nature, dimen-
sions, and significance of the globular dusters are less than 15
years old.
In striking contrast to the present conception of a hundred
globular clusters and hundreds of thousands of extra-galactic
Hist, de 1'Acad. R. des Sci., Paris, 435, 1771.
7 Phil. Trans , 154, i, 1864.
HISTORICAL NOTES ON CLUSTERS 5
nebulae spread throughout measured millions of light years,
with diameters of hundreds of light years for the clusters and
thousands of light years for the star clouds and nebulae, is
the picture suggested by Halley's comment on his discovery of
the Hercules cluster:
But a little patch and similar to the lucid spot around Theta Orionis
[Orion Nebula] Andromeda [Andromeda Nebula], and in the Centaur
[w Centauri] most of them but a few minutes in diameter; yet since they
are among the fixed stars . . . they cannot fail to occupy spaces
immensely great, and perhaps not less than our whole solar system.
CHAPTER II
CLASSIFICATION, NUMBER, AND DISTRIBUTION
CLUSTERS have been described and classified as loose, irregu-
lar, ragged, coarse, open, furrowed, poor, galactic, globular,
open globular, rich, condensed, nebulous, with various qualify-
ing adjectives for each class. All of these descriptions are
necessarily based on superficial appearances and, because of the
imperceptible gradation from one form to another, are little
more than working conveniences. Recently, however, the
globular clusters shown on Harvard plates have been classified
according to central concentration, 1 and both Trumpler 2 and
I have proposed simple classifications of the brighter galactic
clusters in terms of the spectral characteristics of their stars.
3. A Comparison of Galactic and Globular Clusters. It is
proposed to adopt in the present treatment only two main
divisions globular clusters and galactic clusters. 3 Globular
clusters may be "typical," likejMe_ssier j^open, like Messier
4 and N. G. C. 3201, or elongated, like Messier 19. Their
principal characteristics are strong central concentration and
richness in faint. .stars. The galactic clusters are extremely
varied; for example, Messier n is relatively rich, Messier 35
is irregular, the Pleiades and Messier 16 are nebulous, and
Messier 103 and N. G. C. 1981 may be but accidental groupings.
The so-called moving clusters are merely the brighter and
nearer of the galactic types in which radial or transverse motions
1 Shapley and Sawyer, H. B. 849, 1927.
* P. A. S. P., 37, 307, 1925-
3 The term "galactic cluster," suggested by Trumpler (P. A. S. P., 37, 307,
1925) and others, is a natural name for the non-globular cluster, which is almost
without exception near the galactic plane. It replaces the term "open cluster,"
which has caused some confusion because of the open type of globular cluster.
6
GALACTIC AND GLOBULAR CLUSTERS 7
have been measured. The broad category of moving clusters
includes Praesepe and the Pleiades as well as Ursa Major,
Scorpio-Centaurus, and similar systems (see Chapter VII,
Section 35).
Some of the irregular galactic clusters resemble the small
galactic star clouds; and such star clouds near the galactic
circle are similar in many features to star clouds outside the
Galaxy that is, to stellar organizations like N. G. C. 6822
and the Magellanic Clouds, which lie well beyond the main
body of galactic stars. These clouds, in turn, are typical of a
considerable class of extra-galactic systems and apparently
grade directly into the spiral nebulae and affiliated forms.
In future studies, especially of the Magellanic Clouds, we
may find further examples of clusters in a transitional stage,
between the richer galactic groups and the most open globular
clusters. At present, however, there seems to be a rather sharp
division which distinguishes the globular clusters as a special
group of sidereal organization a group limited to about 100
objects 4 while the galactic clusters grade indefinitely into
multiple stars in one direction and, in another, as indicated
above, into small irregular star clouds.
Clear discrimination between galactic and globular clusters
is also possible on the basis of distribution in the sky. The
subject had been considered 3 with more or less care by Bailey,
Bohlin, Hinks and Hardcastle, Melotte, and Perrine before
it was taken up by the writer as a part of the systematic work
on clusters. UThe most conspicuous feature of the distribution
is that galactic (open) clusters are almost exclusively in the
Milky Way and distributed irregularly throughout all galactic
longitudes, while the globular clusters are rather widely scat-
tered in latitude but quite restricted in longitude} (The globu-
4 The future resolution of external star clouds will prolDaoly disclose many
apparently globular clusters, but because of their great distance it may never be
possible to say definitely that these remote groups are not merely rich clusters of
the galactic type or even poor clusters involved in strong nebulosity.
8 See the general bibliography in Appendix C.
8 CLASSIFICATION, NUMBER, AND DISTRIBUTION
lar clusters are, in fact, mostly in one half of the sky, as will
be shown in subsequent diagrams.^
The considerations outlined above justify the division of
clusters into the two main groups. The subdivisions de-
scribed below have been found of practical use in the study of
clusters and are perhaps indicative also of the various stages of
development or decay, though they are essentially descriptive
and do not directly imply an evolutionary theory.
4. Classification of Galactic Clusters. In the studies
of galactic clusters at Harvard we have for some time followed
a two-dimensional classification, (pne parameter is related to
the apparent number and concentration of the stars and may be
called "compactness"; the other depends on the distribution
of spectral classes among the cluster members. '
The classification based on appearance is intended to cover
the whole range of galactic clusterings, from multiple stars
to globular clusters. The subdivisions are as follows:
a. Field Irregularities. That there are many deviations
from random stellar distribution is obvious from star counts,
or even from a casual inspection of photographic plates in
nearly any region of the sky. Such "excess irregularities"
have been referred to in Chapter I, where it is pointed out that
neither dark nebulosity nor random distribution can account
for the many faintly outlined non-uniformities in stellar fields.
These incipient or vestigial star clouds vary in population
from a few scattered members to vast indefinitely limited con-
gregations of stars. There seems to be no immediate need of
attempting to unravel or catalogue them; but the assignment of
a classification letter to the field irregularity is recognition of its
significance in stellar distribution.
b. Star Associations. In this category fall wide-spread mov-
ing clusters, such as the Ursa Major group, and the peculiar
stars of high and parallel velocities. The class will be recruited
largely through studies of proper motion and radial velocity.
It grades imperceptibly into the next class.
CLASSIFICATION OF GALACTIC CLUSTERS 9
c. Very loose and irregular clusters, typified by the Hyades
and Pleiades. The large cluster of bright stars around a Persei
might be placed in this class or, better, perhaps, placed with the
Orion nebula cluster in Class b. Class c corresponds, in general,
with Bailey's D3 and with Melotte's IV. 6
d. Loose Clusters. Messier 21 and Messier 34 are examples
of a class equivalent to Bailey's D2 and Melotte's III.
e. /, g. Compact Clusters. These groups are equivalent
to Bailey's Di and Melotte's II. The division into three
types is made on the basis of richness and concentration ; examples
are Messier 38, Messier 37, N. G. C. 2477. ^ n the classification
of clusters, the globular systems follow immediately after
Class g. In fact, several of the most compact Class g galactic
clusters appear more nearly like globular clusters than do the
loosest globular clusters classified as such by criteria other than
appearance.
In practice, the galactic clusters are generally taken to com-
prise only classes c to g. A number of the classes are illustrated
in Plate II. A further consideration of the size and structure
of the various systems is deferred to Chapter VII. The dis-
tribution among the classes of the 249 clusters listed in Appendix
B is as follows:
Class Number
C 20
d 85
e 67
f 47
g 30
The preceding classification is based on appearance and
depends mainly on the population and distance of a group;
it is independent of the spectra of the stars involved or of the
stage of development of the cluster. I have found it convenient
to divide galactic clusters also into two principal groups on the
basis of the spectra or colors of the component stars (i) the
Pleiades type and (2) the Hyades type. Each includes mem-
bers of classes c to g. In the Pleiades type, the stars, almost
B Bailey, II. A., 60, 200, 1908; Melotte, Mem. R. A. S., 60, 175, 1915.
10 CLASSIFICATION, NUMBER, AND DISTRIBUTION
without exception, lie along the "main branch" of a Russell
diagram, with the earliest classes B or A; and in the Hyades
type, yellow spectral classes occur with the same apparent
brightness as the predominant A stars.
The tabulation of the brighter stars in the Pleiades and the
Hyades on page 32 fully illustrates the difference between
the two major types. More than 95 per cent of the galactic
clusters for which spectral classes or colors have been determined
fall in one or the other of these two types, which are about
equally numerous. There are a few aberrant clusters. Messier
67, for instance, appears to be a variant of the Hyades type,
in that blue giant stars are absent. Prominent examples of
the Pleiades type are the double cluster in Perseus, Messier 36,
and Messier 34; the Hyades type includes Messier n, Messier
37, Praesepe, and the scattered cluster in Coma Berenices.
Trumpler has also proposed and used a classification of
galactic clusters based on spectral composition. 7 For clusters
that he has so far observed, he uses types la, ib, 2a, and 2f,
with provision for other types if found. Figure III, 9 shows
the distribution of spectral classes among the four types. In
Type i he includes clusters from which the giant branch (yellow
and red stars) is entirely missing or in which there are so few
scattered stars falling within their limits that it is uncertain
whether they are physical members or background stars. This
is the equivalent of my Pleiades type, where all the stars fall
along the main sequence. Type 2, corresponding to my Hyades
type, comprises "the clusters which show a marked crowding
of stars along the giant branch although their number may
still be small compared with that of the dwarf stars." 8
Remarks on the possible significance of the two main types
of galactic clusters will appear in a later chapter.
7 P. A. S. P., 37, 307, 1925. A more recent study of galactic clusters is
presented by Trumpler (L. O B. 14, No. 420, 1930), where he gives a three-
dimensional classification. The investigation includes statistical material on
distances, magnitudes, dimensions, and spectra.
8 Ibid.
K. G. T, 7006, Class I.
x, (i. c, KM, class in.
Messier t<>, Class VIIL
PLATK I. -GLOBI*LAR STVK
Messier 4, Class IX.
CLASSIFICATION OF GLOBULAR CLUSTERS n
5. Classification of Globular Clusters. Notwithstanding
the general similarity of globular clusters in size, form, content,
and absolute brightness, there are many deviations from the
average. Clusters such as Messier 19 and w Centauri are
conspicuously elongated; Messier 62 is strikingly non-symmetri-
cal; N. G. C. 4147 is deficient in giant stars; and, as intimated
above, nearly one third of the globular systems are so loosely
organized that from a casual examination, photographic or
visual, we might place them with the galactic clusters and
exclude them from their true affiliation. That such loosely
built systems are of the globular class is made certain by long-
exposure photographs which bring out thousands of faint stars
such as have never been observed in even the richest of galactic
clusters; and their attribution to the globular class is also often
indicated by high galactic latitude and by the presence (as in
Messier 4, Messier 72, N. G. C. 3201, N. G. C. 5053) of many
cluster-type Cepheid variables.
Until recently, however, no systematic attempt has been
made to classify the globular clusters beyond noting that some
were variable-rich, some variable-poor; some open, some com-
pact. I proposed a few years ago 9 that N. G. C. 7492 might be
taken as a type of a rather distinct subdivision, called the "loose
globular cluster," which would include those parenthetically
mentioned in the preceding paragraph and N. G. C. 288, I. C.
4499, an d N. G. C. 5466.
A detailed examination by Miss Sawyer and the writer of
the globular clusters on good Bruce photographs, which are
available in the Harvard collection for practically all the 103
systems now listed as globular, shows that many intermediate
forms exist between the loosest and most concentrated clusters.
Instead of classing the clusters, therefore, in the two or three
broad and obvious categories, such as compact, medium, loose,
we arrange them in finer subdivisions, in a series of grades on the
basis of central concentration. In Table II, I is given a list
of globular clusters chosen as typical of the 12 subdivisions.
Mt. W. Contr. 161, 1918.
12
CLASSIFICATION, NUMBER, AND DISTRIBUTION
Photographs of six of the representative types are reproduced
in Plate I. For the classification of individual clusters,
reference may be made to Appendix A.
TABLE II, I. TYPICAL GLOBULAR CLUSTERS OF THE TWELVE CLASSES
Class
N. G. C.
R A
(1900)
Dec
(1900)
Pg
Mag.
Class
N. G. C.
R. A.
(1900)
Dec.
(1900)
Pg
Mag.
h m
'
h m
I
2808
9 10 o
-64 27
5 7
VII
6656
18 30 3
-23 59
3 6
II
7089
21 28 3
- I 16
5 o
VIII
6402
17 32 4
- 3 II
7 4
III
104
o 19 6
-72 38
3
IX
6218
16 42 o
- I 46
6 o
IV
1866
5 13 3
-65 35
8 o
X
288
o 47 8
-27 8
7 2
V
7099
21 34 7
-23 38
6 4
XI
6809
19 33 7
31 10
4 4
VI
6752
19 20
-60 8
4 6
XII
7492
23 3 i
-16 10
10 8
It is not likely that detailed counts of stars will always arrange
the clusters in the order shown by the concentration class. The
numerical concentration, determined from counts, certainly
varies with stars of different magnitudes, and because of crowd-
ing and Eberhard effect it will always be of doubtful value
except for the brighter stars. Our estimated concentrations
are also slightly influenced by the quality of the plates and the
total brightness and angular diameters of the clusters; but we
believe that these factors are not of such consequence that they
detract appreciably from the value of the classification. Class
I represents the highest concentration toward the center, and
Class XII the least. The distribution among the various classes
and the mean photographic magnitude for each class are as
follows:
Class
Magnitude
Number
I
8 85
4
II
7 80
7
III
6 76
7
IV
9 01
12
V
7 88
12
VI
8.91
11
Class
Magnitude
Number
VII
7 90
8
VIII
7 8 5
10
IX
8.84
10
X
8 88
9
XI
9-54
9
XII
9 58
4
The present classification of globular clusters is essentially
a description of apparent central concentration. It is interest-
ing, therefore, to note that there is no correlation of class with
CLASSIFICATION OF GLOBULAR CLUSTERS
integrated photograpliic magnitude as determined from Har-
vard plates of small scale. The distribution of magnitude
among the various classes is shown in the scatter diagram in
Figure II, i, where also the mean magnitude for a given class
is plotted as a cross, and the average class for each interval of
one magnitude is plotted as a circle.
IV
VIII
XII
x *&
\ M
<W*
30
50 7.0 90 110 130
FIGURE II, i.
The scatter diagram of classes of globu-
ular clusters (ordmates) and integrated
photographic magnitudes. Circles and
crosses indicate means
The galactic distribution of the most concentrated clusters
does not differ measurably from that for the least concentrated.
We have, for example:
Classes I to VI Mean longitude 265 Mean latitude 23
Classes VII to XII Mean longitude 263 Mean latitude 21
For these computations the globular clusters in the Magellanic
Clouds are excluded.
To maintain homogeneity, the classifications of globular
clusters were all made on plates with the scale of i mm = i'.
Superposed stars have occasionally interfered somewhat with
the assignment of the class, especially for N. G. C. 4147, 6284,
6453, 6553, 6569, 6624. A few peculiarities were noted that
are not completely taken care of by our classification based on
central condensation alone. For instance, the bright cluster
w Centauri is peculiar in what appears to be a remarkable
uniformity in the magnitudes of the brighter stars. Clusters
somewhat similar to w Centauri in this respect are N. G. C.
14 CLASSIFICATION, NUMBER, AND DISTRIBUTION
5272 (Messier 3), 5927, 6273, 6656 (Messier 22). These clusters
also resemble each other in their moderate concentration (classes
VI to VIII), and two of them, w Centauri and Messier 3, are
the richest of all in variable stars. It should be noted, however,
that the clusters with many variable stars are scattered through-
out all classes.
In conclusion, we observe that the classes of globular clusters
are probably indicators of developmental age. They should
prove increasingly useful in studies of linear diameters, motions,
luminosity curves, and the deeper problems of the origin and
life history of stellar clusters.
6. The Number of Clusters. Since the time of the Her-
schels, very few globular clusters have been discovered, not-
withstanding the considerable increase in telescopic power and
the great increase in the known number of stars and nebulae.
Every recognized globular cluster except one bears a number
from the New General Catalogue of Dreyer, an indication that
in spite of great distance and the faintness of the individual
stars, all of these objects were known prior to 1880. They
were known, indeed, before 1864, the date of Sir John HerscheFs
General Catalogue, and all but a few were catalogued more
than 90 years ago in the earlier Herschelian lists. This early
completion of the discovery of the globular clusters led Bailey 10
to suggest that the limit of the region occupied by these systems
had been reached, a suggestion that appears to be supported
by subsequent work. Thousands of new nebulae and millions
of stars have been added by modern telescopes and photo-
graphic plates, but the essentially complete listing of globular
clusters antedated photography.
There is, however, a vast difference between cataloguing
an object and recognizing its true character. Many of the
entries given in the N. G. C. as globular clusters have proved
to be something else, generally galactic groups or extra-galactic
nebulae; and 34 of the globular clusters now recognized were
H. A., 76,43, 1915-
N. G. C. 247?
Messier 16 Messier 7
PLAIB H.GAMCTK STAR CLUSTKRS.
THE NUMBER OF CLUSTERS 15
not described as such in the New General Catalogue. The
large photographic telescopes have been of service in recent
years in examining many faint and doubtful N. G. C. objects,
and an occasional addition to the list of globular clusters has
resulted. A number of remote groups remain doubtful, how-
ever, even after some of them have been tested with large reflec-
tors. Chief among the doubtful objects are the following: 11
N. G. C. Radec* Galactic Distancef Note
1651 0438 - 71 249 - 36 Rejected, see H. C. 271, 1925
5946 1528-50 295+04 322 A small, poor, loose cluster in a rich
region
6352 1718 48 308 07 19.7 A comparatively large cluster of very
famt stars, on the edge of the Milky
Way
6426 1740 + 03 356 + 15 371 Very faint and poor; suggestion of a back-
ground on Mount Wilson plates
6535 1759 00 354 + 10 26.7 A small cluster, on the edge of a nch
region, with few stars
6539 1759 "" 08 348 +06 38 7 A very faint cluster in a large obscured
area
6712 1848 09 353 06 26 2 A little, irregular knot of stars in a nch
cloud
6760 1906 + Ol 003 05 28.6 A faint, sparse, loose cluster in a rich
region
*The approximate positions for 1900 m equatonal coordinates are conveniently con-
tracted for tabulation into the form here given, the first four figures give the hours and
minutes of nght ascension, and the sign and subsequent figures indicate the declination in
degrees (and may be extended to minutes, if desired).
f The distance in kiloparsecs is estimated on the assumption that the clusters are globular.
Sixty-six globular clusters were included in the catalogue
of bright clusters and nebulae compiled in 1908 by Bailey. 12
To this number Hinks 13 added 41 from Dreyer's catalogue,
though several of the additions are not now accepted. Bohlin 14
considered about 75 objects truly globular. Miss Clerke 15
stated that approximately 500 clusters of all kinds were known,
1 20 having globular forms. In later publications, Bailey 16
placed the total number of globular clusters at 76, and the total
11 Sawyer and Shapley, H. B. 848, 1927.
12 H. A., 60, 199, 1908.
18 M. N. R. A. S., 71, 697, XQII.
14 Swedish Acad., 43, No. 10, 1909.
16 System of the Stars, 227, 1905.
"H. A., 76, 43, 1915-
16 CLASSIFICATION, NUMBER, AND DISTRIBUTION
of all kinds at nearly 700. This high total includes many chance
aggregations and a number of minor condensations in the Milky
Way.
The data on which the above estimates are based lack homo-
geneity. Melotte's catalogue, 17 however, which was made from
the Franklin Adams plates and contains 83 globular and 162
open clusters, constitutes a fairly homogeneous list of all clusters
with diameters greater than one minute of arc and brighter
than the sixteenth or seventeenth photographic magnitude.
His list of galactic clusters is revised and extended in Appendix
B, which contains 249 entries. From his list of globular clusters
a few objects have been dropped; others have been added,
mainly as a result of my work and Bubble's with the 60- and
loo-inch reflectors at Mount Wilson. As stated above, the
total number, those accepted for the tables in Appendix A
and 10 globular clusters in the Magellanic Clouds, is 103. Fur-
ther additions will probably be slow and will come through the
closer analysis of small groups in and near the Milky Way
star clouds and the detailed examination of small nebulous
objects that are now assumed, without very good reason, to be
elliptical extra-galactic nebulae.
An example of a recent addition is the observation at the
Lowell Observatory, verified at Mount Wilson, that the object
N. G. C. 2419, described in the New General Catalogue as
"pB, pL, IE 90, vgbM, *7.8 267, 4' dist," and not listed by
Melotte, is, in fact, a remote globular cluster in the part of the
sky that is otherwise devoid of these systems. 18
It may be well to recognize at this point that if the spheroidal
extra-galactic nebulae are actually stellar throughout, perhaps
many of them are essentially globular star clusters, probably
at much greater distances than the objects here studied
and of a greatly different order of dimensions. In the list of
faint nebulae, shown on Bruce plates made at Arequipa and on
similar photographs, there are large numbers of very small
17 Mem. R. A. S., 60, 175, 1915.
18 Shapley, II B. 776, 1922.
DISTRIBUTION OF GALACTIC CLUSTERS 17
unresolved circular images that are listed hopelessly as nebulae
of the spiral family. Occasionally, one of these may be a very
remote (but ordinary) globular cluster. A comparative study
of the distribution of light throughout the images can, however,
give us some indication of their nature; their distribution with
respect to other extra-galactic objects will probably show most
of them to be sidereal systems of a higher order than globular
clusters.
7. The Apparent Distribution of Galactic Clusters. The
new catalogue of galactic clusters has been prepared on the
FIGURE II, 2.
Distribution of galactic clusters in galactic coordinates. Cluster classes are
indicated as follows c, O; d, , e, 3; f, O; g, .
basis of a fairly uniform series of Harvard photographs (Appen-
dix B). The plates studied were made with the 8-inch Bache
and Draper and the 10- and 1 6-inch Metcalf telescopes. Scores
of loose groups of a few stars, which appear in the N. G. C.
and in other lists, are omitted from the new catalogue. At the
same time, 21 new clusters, never before listed, are now included.
The total number for which we consider the distribution is 249.
Figure II, 2 shows the distribution of galactic clusters in
galactic coordinates. The high concentration in low latitudes
is immediately evident. The galactic clusters with latitudes
greater than 15 are given in Table II, II.
l8 CLASSIFICATION, NUMBER, AND DISTRIBUTION
TABLE II, II. GALACTIC CLUSTERS WITH LATITUDE GREATER THAN 15
N. G. C.
Galactic
Remarks
Longitude
Latitude
o
188
90
+ 23
752
105
-23
Melotte 22
134
22
Pleiades
Melotte 25
147
-23
Hyades
2243
206
-16
2281
142
+ 18
2420
1 66
+ 21
2548
196
+17
2632
174
+34
Praesepe
2682
184
+33
Messier 67
Melotte in
200
+85
Coma Berenices
14665
358
+ 16
The high latitudes for Coma, Praesepe, the Pleiades, the Hyades
are not remarkable, because the parallaxes are relatively large
and the linear distances from the galactic plane accordingly are
relatively small. A further discussion of the distribution of
galactic clusters is to be found in Section 70 below.
An interesting and significant result of the special surveys
that have been made of objects of doubtful class is the evidence
that every faint little-condensed cluster in galactic latitude
higher than 15 or 20 is really globular, although for many of
them short exposures and visual observations had originally
recorded few stars. Long exposures, however, invariably bring
out the globular nature of the objects, with the possible excep-
tion of N. G. C. 5053, noted below. All the similar faint objects
along the galactic equator remain open groups, with no con-
densed background of faint stars appearing on long exposures.
8. N. G. C. 5053 and N. G. C. 2477. The most conspicuous
apparent deviation from the rule of low latitudes for galactic
clusters is for the faint object N. G. C. 5053. Its latitude is
+77. Baade 19 first noticed that this object, described as
19 Baade, Hamb. Mitt , 5, No. 16, 1922.
N. G. C. 5053 AND N. G. C. 2477 19
"Cl, vF, pL, iR, vgbM, st 15" in the N. G. C., appears to be
an open cluster of faint stars. His longest exposures with the
Bergedorf reflector, however, left the matter indeterminate.
At my request Dr. Hubble made an exposure of 90 minutes
with the loo-inch reflector. From this plate the cluster does
not seem to be globular; that is, no concentrated background
of faint stars appears at the center the total number of
the stars appears to be a few hundred.
More recently Baade 20 has found in N. G. C. 5053 eight
variables of the cluster type, which certainly cannot be con-
sidered random members of the foreground. No galactic
cluster has variables of this sort; they are common in globular
systems. Baade also finds the general luminosity curve of
N. G. C. 5053 similar to those I have obtained for globular
clusters. Its population, however, is only a fourth that of a
typical globular system such as Messier 3. On three counts,
therefore, we call N. G. C. 5053 a globular cluster its position,
its variables, and the frequency of absolute magnitudes.
In superficial appearance N. G. C. 2477, galactic latitude
5, is the richest of galactic clusters; or perhaps it is the loosest
of globular clusters. No variables have been found within it,
but the examination has not been exhaustive. Miss Sawyer
has determined the general luminosity curve to magnitude 16.8
for a circle with radius i4'.o. The correction for the foreground
and background stars (232 in all) was made on the basis of star
counts in adjacent fields. The results are as follows:
Limiting Cluster Total Limiting Cluster Total
Magnitudes Stars Stars Magnitudes Stars Stars
]io o o o 13 5-14 o 134 162
10 o-io 50 3 14 0-14 5 121 153
10 5-11 02 4 14 5-15 o 115 158
11 o-ii S3 4 IS 0-15 5 74 109
11 5-12 03 10 15 5-16 o 51 76
12 0-12 5 17 30 l6.0-l6.S S8 76
12 5-13 o 79 89 [16.5 30 35
13 0-13 5 H7 126
Total 804 1,036
20 Ibid , 6, No 29, 1927
20
CLASSIFICATION, NUMBER, AND DISTRIBUTION
For the present we leave N. G. C. 2477 in the list of galactic
clusters, awaiting further photometric and spectroscopic analy-
sis with larger telescopes.
9. The Apparent Distribution of Globular Clusters.
In a form comparable to that of the preceding diagram, the
FIGURE II, 3
Distribution of globular clusters in equatorial coordinates. Small dots indicate
more distant clusters. The galactic circle is shown by a heavy line. The
clusters in the Magellamc Clouds have been omitted.
FIGURE II, 4.
Distribution of globular clusters in galactic coordinates.
distribution of globular clusters is shown in Figures II, 3 and
II, 4. The equatorial and galactic coordinates of each cluster
DISTRIBUTION OF GLOBULAR CLUSTERS
21
are given in Appendix A, and a discussion of their distribution
in space appears in later chapters. The remarkable contrast
in the galactic affiliation of the galactic and globular clusters
-40
-20
+20 +40
+40 -40
Degrees
FIGURE II, 5.
Numbers of galactic clusters (circles) and globular clusters (dots) for two-
degree intervals in galactic latitude Left, hemispheres separately; right,
means.
20
15
10
100
200
Degrees
300
40
FIGURE II, 6.
The frequency distribution of globular clusters in galactic
longitude Ordmates are numbers of clusters; abscissae,
degrees of longitude.
is evident from the diagrams and is further illustrated in Figure
II, 5. The remoteness of the globular clusters suggests that
obstruction by dark nebulosity in the Milky Way can easily
22 CLASSIFICATION, NUMBER, AND DISTRIBUTION
influence their observed scarcity near the galactic equator
without affecting at the same time the distribution of the
galactic clusters.
In Figure II, 6 is shown the distribution of globular clusters
in galactic longitude. From this diagram and the preceding
figure we find that the center of the system of globular clusters
lies in the direction of galactic longitude 327, galactic latitude
o. The probable error of this determination is about i. The
corresponding equatorial coordinates are right ascension 17*
28**, declination 29.
10. Clusters in or near Obstructing Nebulosity. The
large groups of bright B stars in Orion, Scorpio, and elsewhere
are associated with important bright and dark nebulosity.
The Pleiades nebulosity is well known. A number of nebulous
galactic clusters, such as Messier 8, are on record, and clusters
of this sort also appear in the Magellanic Clouds. It is doubt-
ful, however, if much would be known of the nebulosity in
these galactic clusters if their distances were ten times as great.
By implication, therefore, nebulosity in galactic clusters may
be more common than appears from general inspection.
There are a few individual globular clusters, N. G. C. 4372,
N. G. C. 6144, and N. G. C. 6569, that are in or near recognized
dark or luminous nebulae. Of these, the first appears to be
dimmed by one of the long dark streamers from the Coal Sack;
the second is at the edge of the heavy p Ophiuchi nebulosity.
N. G. C. 6569 is in a rich star field in Sagittarius but may also
be involved in wisps of obscuring nebulosity.
To what extent the magnitudes and colors in galactic and
globular clusters are directly affected by associated nebulosity
is not as yet determined. For individual nebulous stars, Scares
and Hubble have found a color effect and presumably a corre-
sponding deficiency in apparent brightness.
CHAPTER III
ON THE SPECTRAL COMPOSITION OF CLUSTERS
THE variety of spectral classes in galactic clusters and the
differences in composition from system to system have long
been known; the Pleiades and the Hyades, for example, exhibit
wide diversity and contrast. Also, among globular clusters
some have been noted as relatively yellow, others white; but
their contrasts are less marked. The first definite observation
of color in a globular cluster was made by Barnard, 1 who com-
pared photographic magnitudes with visual and photovisual
magnitudes for a number of stars in Messier 13, the Hercules
cluster. Further determinations of colors and spectra in globu-
lar clusters 2 have been based primarily on work with the Mount
Wilson photographs, which will be described in Section 12.
ii. Integrated Spectra of Globular Clusters. Inte-
grated spectra were determined for several clusters many years
ago at the Lick, Mount Wilson, and Lowell observatories,
mainly by Fath 3 and Slipher, 4 who found spectra of composite
character, principally classes F and G. The Henry Draper
Catalogue records without close classification the integrated
spectra of numerous clusters. At my request Miss Cannon has
recently examined closely all available Harvard photographs
showing spectra of globular clusters. 5 In classifying more than
40 integrated spectra she has greatly increased our knowledge
of the average effective composition of such systems.
1 Ap. J., 12, 176, 1900; 29, 72, 1909; 40, 173, 1914.
2 See Appendix D for special bibliography on spectra.
3 L. O. B., 5, 74, 1908; Mt. W. Contr. 49, iQ"-
* Pop. Astr., 25, 36, 1917; 26, 8, 1918.
H. B. 868, 1929.
23
24 ON THE SPECTRAL COMPOSITION OF CLUSTERS
The results are briefly summarized in Table III, I, which
gives the N. G. C. designation, the cluster class, and the spec-
trum. For some clusters, such as N. G. C. 4147 and N. G. C.
6624, the observed spectrum may be largely due to one or two
stars, and they, of course, may be foreground objects. A
frequency diagram of the classes is given in Figure III, i ; classes
F, G, and K of Table III, I are taken as Fo, Go, and Ko. The
class of spectrum does not appear to be closely related to cluster
TABLE III, I. SPECTRA OP GLOBULAR CLUSTERS
N. G. C.
Cluster
Class
Spectral
Class
N. G. C.
Cluster
Class
Spectral
Class
104
III
G 5
6293
IV
G S
362
III
GS
6304
VI
K:
1261
II
G
6316
III
GS
1851
II
Go
6333
VIII
K:
1866
IV
F8
6341
IV
G S :
1904
V
F8
6356
II
Ko
2808
I
Ko
6388
III
K
4M7
IX
A 7 :
6397
IX
G:
4590
X
Note
6441
III
Ko
5024
V
Note
6541
III
G
5272
VI
G
6624
VI
Mo
5286
V
Go
6626
IV
GS
5824
I
F8
6637
V
K2
5904
V
G:
6652
VI
KS
5986
VII
F8
6715
III
F8
6093
II
Ko
6723
VII
G 5 :
6121
IX
F
6752
VI
Go
6205
V
Go
6864
I
Go
6229
VII
Note
6934
VIII
Go
6254
VII
Note
7078
IV
F
6266
IV
Ko
7089
II
FS
6273
VIII
G 5 :
7099
V
F8
6284
IX
F:
NOTES TO TABLE III, I
N. G. C. 4590. Dark lines are seen in the violet.
5024. Dark lines H5, H, and K faintly seen.
6229. Several dark lines are seen, apparently including H and K.
6254. Dark lines in the violet appear to be H, K, and Hf.
STELLAR TYPES IN GLOBULAR CLUSTERS
class, apparent magnitude, or any other significant property
of the clusters. We have here only an indication of the probable
diversity in predominant type of the stars that are effective in
producing the integrated spectrum.
A
AO AS FO F5 F8 GO OS KO K2 K5 MO
FIGURE III, i.
Integrated spectra of globular clusters.
Coordinates are numbers of clusters
and spectral classes.
^12. Stellar Types in Globular Clusters. From inte-
grated spectra and colors we pass to the types of individual
stars in globular clusters, noting some similarities to the distri-
bution in the Galaxy but also some important differences. The
discussion of variable stars and their problems is left to the
next chapter.
a. Common Spectral Classes. The color indices in various
globular clusters, especially Messier 13 6 and Messier 3 7 , show aJ
normal range from about 0.3 to +i.6. 8 This indicates, no(
doubt, the presence of all spectral classes from B to M; and nor-
mal spectra from A to G have, in fact, been directly observed.
The spectra of about 50 individual stars in Messier 13 and
other bright globular clusters have been classified by Pease and
Shapley, Mt. W. Contr. 116, 1915.
'Ibid., Mt. W. Contr. 176, 1919.
9 Ibid., Mt. W. Comm. 44, 1917.
26 ON THE SPECTRAL COMPOSITION OF CLUSTERS
Sanford 9 on plates made at Mount Wilson, but the details of the
work have never been published. In Messier 13 Pease finds
the classes of 39 stars distributed as follows (classifications by
Adams) :
Class Number
Ao 3
AS ii
Fo ii
FS ii
Go 3
The relative frequency of the various classes probably differs
somewhat from one cluster to the next, as indicated by the
diversity of the integrated spectra, but sufficient observations
are not yet available to decide this rather important matter.
The most frequent color index in Messier 13 (outside the
unresolved center where the heavy stellar concentration and the
Eberhard effect have prevented satisfactory work) is about
+0.70, and the average color index is +0.55, corresponding
to the spectrum gF-4. Seventeen per cent of the stars brighter
than the working limit (photo visual magnitude 15.5) have nega-
tive color indices, indicating spectral classes earlier than A. In
Messier 3, on the other hand, there is a smaller proportion of
negative color indices (4.7 per cent down to photovisual magni-
tude 17.00) but an excess of Class A stars of about the magni-
tude and color of the cluster-type variables. It should be
noted, however, that an error in the zero point of either photo-
visual or photographic magnitudes would shift the spectral
frequency curve bodily. Such error may exist and may not be
inappreciable.
" / b. The Color 'magnitude Arrays. The distributions of color
indices and photovisual magnitudes are shown in Tables III,
II and III, III for Messier 13 and Messier 3, respectively. 10
Pease, Mt. W. Ann. Rep., 9, 219, 1913; 10, 268, 1914. Sanford, ibid., 14,
212, 1918; Pop. Astr., 27, 99, 1919.
10 Ten Bruggencate has plotted the coordinates (my magnitudes and colors)
for the individual stars used in making these color-magnitude summaries, and has
sought particular significance in the details of the resulting " Farbenhelligkeits-
diagramme" (Sternhaufen, Berlin, 1927). I think that there is little gain and
STELLAR TYPES IN GLOBULAR CLUSTERS 27
TABLE III, II. COLOR-MAGNITUDE ARRAY FOR MESSIER 13
Limits of
Photovisual
Magnitude
Color Class
All
Colors
bo to
bs
bsto
ao
aoto
as
as to
fo
foto
fs
fS to
go
goto
gs
"&
ko to
ks
ksto
mo
12 00-12 19
I
3
2
6
12 20-12 39
I
i
2
12 40-12 59
3
2
5
12 60-12 79
i
i
I
2
5
12 80-12 99
4
2
6
13 00-13 19
I
I
8
3
13
13 20-13 39
I
4
2
I
8
13 40-13 59
I
6
I
8
13 60-13 79
2
3
I
i
7
13 80-13 99
3
2
6
M
6
2
33
14 00-14 19
i
9
3
2
IS
14 20-14 39
r
IO
IJ
4
28
14 40-14 59
i
i
7
3
24
16
4
56
14 60-14 79
6
2
I
6
12
I
I
29
14 80-14 99
5
3
2
5
8
2
25
15 00-15 19
24
9
3
3
19
IO
2
70
15 20-15 39
10
21
7
5
12
28
IS
98
IS 40-15 59
4
It
6
4
II
II
5
I
I
54
15 60-15 79
i
5
3
3
10
4
i
27
Total
16
70
36
27
50
135
IIS
33
9
4
495
The tabulated quantities are numbers of stars. For Messier
13, no stars within 2' of arc of the center are included; for
Messier 3, the limits are a'.o to n'.3. The perils arising from
the Eberhard effect are thus largely avoided.
Similar arrays are given in greater detail for these two clus-
ters, for Messier 68, and for the galactic clusters Messier 67
and Messier n in my special discussions of the individual
systems (see Appendix C). In all arrays the last tabulated line
or two are near the practical fainter limit for magnitude work and
may be deficient in numbers and inaccurate. The color classes^
b, a, f, . . . , corresponding to the color index intervals 11
-0.4 to o.o, o.o to +0.4, +0.4 to +0.8 . . . , are nearly
some danger in detailed subdividing of the observational material. Actual
experience with the photometric measures in globular clusters leads to a belief
that the group values presented in my color-magnitude arrays go as far as is
justifiable in subdivision.
11 Scares, Mt. W. Comm. 16, 1915.
28 ON THE SPECTRAL COMPOSITION OF CLUSTERS
TABLE III, III. COLOR-MAGNITUDE ARRAY TOR MESSIER 3
Color Class
Limits of
Photo visual
Magnitude
All
Colors
bo to
b5
bsto
ao
ao to
&5
a to
fo
foto
fs
fSto
go
goto
85
85 to
ko
Icoto
ks
>ks
]I2 00
i
I
I
3
xa.oo-i2 19
12.20-12 39
I
I
12.4012 59
I
i
2
12.60-12 79
i
I
2
4
12.80-12 99
i
4
5
13.00-13 19
5
2
7
13.20-13 39
i
2
3
13.40-13 59
i
4
I
6
13.60-13 79
4
3
7
13-80-13 99
i
7
6
14
14.00-14 19
i
2
2
5
I
ii
14.20-14 39
I
3
3
7
14 40-14 59
I
i
3
16
6
27
14.6014.79
14.80-14 99
i
I
3
7
4
27
16
IS 00-15 19
i
2
7
i?
3
30
IS 20-15 39
i
4
4
IS
19
U
I
57
IS.40-I5 59
9
23
12
IS
26
I
86
IS.60-IS 79
8
6
4
2
28
8
2
58
IS.80-I5.99
2
6
7
17
5
37
16 O0-i6 19
2
2
2
12
14
6
38
16 2O-I6 39
I
I
4
16
13
i
I
37
16.40-16 59
I
9
21
19
SO
16 60-16 79
2
20
26
II
I
60
16.80-16.99
2
4
24
38
I
69
Total
4
27
49
83
158
191
92
42
12
4
662
analogous to the spectral classes B, A, F, . . . This analogy
is close because the cluster stars under study are all giants.
The agreement would not be so satisfactory for dwarfs.
The general similarity of globular clusters, especially in the
color-magnitude relation for giant and supergiant stars, is
nicely illustrated in Table III, IV, where the brightest stars
in two of the nearby globular clusters are compared with the
brightest stars in the faintest and most remote globular cluster
known. N. G. C. 7006 is five times as distant as Messier 3
and Messier 13. The tabulation shows that the brighter
stars in all three systems have about the same average color
STELLAR TYPES IN GLOBULAR CLUSTERS 29
TABLE III, IV. COMPARISON OP N. G C. 7006 WITH MESSIER 3 AND MESSIER 13
N. G. C. 7006
Messier 3
Messier 13
Mean
Pv Mag
Num-
ber of
Stars
Mean
Color
Index
Mean
Pv
Mag.
Num-
ber of
Stars
Mean
Color
Index
Mean
Pv
Mag
Num-
ber of
Stars
Mean
Color
Index
IS 56
5
+ i 37
12 59
7
+ i 30
12 II
6
-f I 31
16 02
6
+ 1 14
12 90
5
+ 1 18
12 47
7
+ i 14
16 41
7
+ 1.04
13 10
7
-f i 61
12 72
5
-f 94
16 55
6
+ 1 16
13 43
9
+ 1 12
12 87
6
-fo 82
16 82
7
-HO 06
13 70
7
+o 99
13 05
6
-fo 92
17 08
7
+0 95
(13 90)
(13)
( + o 96)
13 14
6
+ 93
Mean 16 46
38
+ i 09
13 17
35
-hi IS
12 72
36
-f-i 02
TABLE III, V.* COLOR-MAGNITUDE ARRAY FOR MESSIER 22
T irrM+o of
Color Class
iwirnits 01
Photovisual
Magnitude
<bo
bo
to
bS
to
ao
to
as
to
fo
to
fs
to
go
to
gS
to
ko
to
k5
to
mo
to
>ms
All
Colors
bS
ao
as
fo
fs
go
85
ko
ks
mo
ms
10.20-10.39
i
i
ro 40-10.59
10 60-10.79
I
i
10.80-10.09
i
3
4
I I. 00-11. 19
i
3
3
7
ii 20-11.39
3
6
9
ii 40-11 59
2
2
i
5
II.6O-II 79
i
2
I
I
5
II 80-11.99
i
2
5
I
9
12 00-12 19
3
I
i
5
12 20-12 39
2
2
8
2
14
12.40-12 59
I
3
5
2
2
13
12 60-12 79
i
I
6
IS
2
25
12 80-12 99
i
3
4
3
ii
13 00-13 19
i
I
4
3
I
10
13 20-13 39
I
6
9
3
I
20
13 40-13.59
I
i
8
6
6
i
23
13 60-13 79
i
12
28
16
57
13 80-13 09
i
I
4
34
59
7
106
14 00-14 19
2
i
17
39
12
71
14 20-14.39
i
I
II
40
61
39
3
156
u 40-14.59
I
19
26
20
2
68
14 60-14 79
3
3
Totals
I
3
36
68
105
138
123
57
45
17
10
12
8
623
*See Harvard Bulletin 874, 1930, and Chapter XIV below.
30 ON THE SPECTRAL COMPOSITION OF CLUSTERS
and the same progression of color with magnitude. A similar
result is found in all globular clusters tested, though some, such
as N. G. C. 4147 and N. G. C. 5053, are less populous in giant
stars. Occasionally, there are abnormally bright blue stars,
as in Messier 13, but even these are faint absolutely, compared
with some of the galactic B stars.
In the array for Messier 22 in Table III, V the small disper-
sion of magnitude within one color class is conspicuous.
The color-magnitude arrays establish the fact that in the
condensed clusters, as well as in some loose galactic groups, the
average color is redder the higher the visual brightness.
The result naturally bears on current consideration of the evolu-
tion of stars. The arrays call particular attention to the frequency
of the high-luminosity red stars, similar to Antares and Betel-
geuse, presumably of great mass. The apparently universal
occurrence of red and yellow supergiants in globular clusters
argues for exceedingly slow development and consequently for
subatomic sources of stellar energy. The presence of a single
supergiant, such as Antares, in a cluster might be ignored in
theoretical work it might be treated as an abnormal occur-
rence. But we find that in nearly every large assemblage of
stars there are reddish low-density objects which contraction
would have transformed in a few thousand years, but which
appear nevertheless to be untouched by age. The question is
again taken up in Chapter XIV.
13. Distribution of Colors throughout Globular Clusters.
The relation of the colors of the brighter stars to their
positions in the clusters, although very important, is difficult
to determine satisfactorily, because the Eberhard effect is
certain to produce a spurious reddening in the crowded central
regions. 12 Nevertheless, the conspicuous centralization of
red stars in the galactic cluster M 67, discussed later in Section
34, encourages an examination of the phenomenon in clusters
of the globular type.
"Shapley, Mt. W. Contr. 116, 58, 1915.
DISTRIBUTION OF COLORS
Observations that bear on the matter are contained in Figures
III, 2, III, 3, and III, 4. The first two show the mean color
indices (stars of all magnitudes) plotted against distance from
V <
06
0.5
04
V
*%
X
**--^
_.-^
~~~~
^r^
) 2' 4' 6' 8' 10' 12
FIGURE III, 2.
Change in Messier 3 of color index (ordinates) with
distance from the center.
the center for Messier 3 and Messier 13. The plots are based
on my observations contained in Mount Wilson Contributions
+ 1UU
090
*080
+070
'0.60
0.50
N
\
V
V
^ =-_
^*>. ,
.-M..
)' I 1 2' 3' 4' 5' 6*
FIGURE III, 3.
Change in Messier 13 of color index (ordinates)
with distance from the center.
116 and 176. The high point in Figure III, 3, connected with
the next highest point by a broken line, is undoubtedly raised
-05
FIGURE III, 4.
Change in Messier 13 of color
index (ordinates, with arbi-
trary zero) with distance from
the center.
by the Eberhard effect. Neither cluster shows any very definite
change in mean color with distance from the center, but stars
ON THE SPECTRAL COMPOSITION OF CLUSTERS
fainter than absolute magnitude +i are only slight factors in
producing these results.
Figure III, 4 shows results derived by Hogg 18 from an investi-
gation of the integrated light of Messier 13. The changes in
color from the center to the edge are seen to be negligible. It
appears, therefore, as far as the present data go, that the colors
of the giant stars in globular clusters are not related to the
radial distance from the center of the cluster.
J 14. Types of Stars in Galactic Clusters. In the early
work on stellar spectra it was found that the Pleiades are devoid
of bright yellow stars, the most luminous members being of
Class B. From the neighboring Hyades cluster, on the other
hand, the B stars are completely absent; the bluest stars are
of Class A, and intermingled with them are a few equally bright
K stars. The visual magnitudes and the spectral classes of the
ten brightest stars in each system are as follows:
Pleiades
Alcyone
2
06 Bse
Atlas
3
80 B8
Electra
3
81 B 5
Maia
4
02 85
Merope
4
25 B S e
Taygeta
4
37 B S
Boss 879
5
18 BSe
Boss 851
5
43 B 5
Boss 872
5
Si B8
Boss 861
5
85 B8
Hyades
62 Tau
cTau
7 Tau
a Tau
0i Tau
Br 601
61639
KI Tau
uTau
Br 605
3 62 AS
Ko
Go
Ko
Ko
Ao
AS
A3
AS
Ao
3 63
3 86
3 93
4 04
4 24
4 30
4 3 6
4 40
4 60
As long ago as 1897, Mrs. Fleming examined the spectra of
individual stars in a number of loose galactic clusters, mainly
southern. She noted not only that each cluster contains more
than one spectral class but also that some clusters show a
preponderance of blue stars, others of yellow or red stars, 14
thus foreshadowing the present general subdivision into Pleiades
and Hyades types.
13 H. B. 870, 1929.
14 Pickering, H. A., 26, 1891; see Table III, VI.
SPECTRA IN INDIVIDUAL GALACTIC CLUSTERS 33
Adams and van Maanen in 1913 noted the commonness of
early B stars in the double cluster in Perseus, 15 and some unpub-
lished colors and spectra that I obtained at Mount Wilson in
1919 showed that this system follows the Pleiades model in
spectral distribution.
13. Spectra in Individual Galactic Clusters. For a
number of the largest galactic clusters there are fragmentary
data in the Henry Draper Catalogue, the spectra of a few
of the brighter stars having been classified in the routine course
of the general program. To the extent of their value, these
data have been used by various investigators, especially Doig 16
and Raab. 17
The numerous investigations of the colors and magnitudes of
galactic clusters are listed in Appendix C and separately tabu-
lated in the special bibliography in Appendix D. Representa-
tive papers, giving the colors of individual stars, are those by
Hertzsprung 18 and by Scares 19 for N. G. C. 1647, by von Zeipel
and Lindgren 20 for Messier 37, by the writer and Miss Rich-
mond 21 and by Graff 22 for faint stars in the Pleiades. All these
studies emphasize the diverse spectral structure of galactic
clusters. The spectral composition of the individual clusters
has been discussed by Doig, 23 ten Bruggencate, 24 and Raab 25
and is in the process of exhaustive analysis by Trumpler 26
at the Lick Observatory. Some of these systems are described
in Subsection 5, and Trumpler's results are discussed in Sub-
section c. The Harvard material is taken up first.
15 A. J., 27, 187, 1913-
" J. B. A. A., 35, 201, 1925.
17 Lund Medd., Ser. 2, 28, 1932.
18 Mt. W. Contr. 100, 1915,
19 Ibid., 102, 1915.
20 Proc. Swedish Acad., 21, No. 16, 1921.
21 Mt. W. Contr. 218, 1921.
22 Hamburg Abh., 2, 3, 1920.
28 J. B. A. A., 35, 201, 1925.
24 Seeliger Festschrift, p. 50, 1924.
25 Lund Medd., Ser. 2, 28, 1922.
29 P. A. S. P., 37, 307, 1925.
34
ON THE SPECTRAL COMPOSITION OF CLUSTERS
a. Harvard Studies. Mrs. Fleming 14 tabulated the spectra for
seven galactic clusters: the Pleiades, Praesepe, Coma Berenices,
I. C. 2602, N. G. C. 3532, Messier 6, and Messier 7. The stars
for which spectra are classified are distributed over a larger
area than that actually covered by the clusters, and foreground
stars, of course, cannot generally be differentiated and excluded;
very faint stars, barely distinguishable on the plates, are
included. Some results are summarized for Class A in Table
III, VI.
TABLE III, VI. PERCENTAGE OP CLASS A STARS IN SEVEN GALACTIC CLUSTERS
Cluster
Stars Classified
Stars in H. D. C.
Per cent Class A
Pleiades
91
*
65
Praesepe
QO
*
31
7. C. 2602
64
58
77
N. G C. 3532
204
135
93
Coma
117
*
IS
Messier 6
91
75
75
Messier 7
346
177
78
* Limits indefinite.
Although the classification was crude, and for some stars quite
uncertain, the existence is clearly shown of a spectral distribu-
tion in Praesepe and Coma different from that in the other
five clusters. It is the same distinction that is now recognized
in the Pleiades and Hyades types or in Trumpler's types i
and 2. 27
The Henry Draper stars in I. C. 2602, N. G. C. 3532, Messier
6, and Messier 7 (third column of Table III, VI), are arranged
in order of spectrum and magnitude in Table III, VII. The
large percentage of A stars in the Pleiades type of cluster is here
seen in detail. It is to the frequency of the A stars in galactic
clusters that we owe the attempts to determine spectral paral-
laxes for these systems on the basis of the material of the Henry
17 Ibid. See footnote 7, Chapter II, on his later work.
SPECTRA IN INDIVIDUAL GALACTIC CLUSTERS
35
Draper Catalogue. 28 The wide dispersion in magnitude also
shows why the attempts are not always happy.
TABLE III, VII. SPECTRA AND MAGNITUDES FOR SOUTHERN CLUSTERS
Cluster
Pg
Mag
O
Bo-2
B3-5
B8-9
Ao-2
A 3 -S
F
G
K
M
All
I. C 2602
2
I
i
3
i
i
4
i
i
5
3
I
I
5
6
3
5
I
9
7
I
2
3
6
2
X
IS
8
6
5
i
2
14
9
7
i
I
3
12
All
2
10
IS
20
2
2
i
6
58
N G C 3532
5
(0
(O
6
7
3
2
5
8
I
13
25
1
3
5
2
SO
9
7
43
I
2
2
55
10
21
4
25
All
o
O
I
23
91
2
3
7
8
I3S
Messier 6
6
I
I
7
I
I
6
I
I
10
8
7
II
I
I
20
9
4
20
I
4
S
34
10
10
10
All
o
I
I
18
32
I
2
5
rS
o
75
Messier 7
6
3
I
I
5
7
i
14
18
I
3
37
8
3
19
SO
7
5
8
7
I
zoo
9
2
IS
2
2
2
6
I
30
10
3
2
5
All 1 i
o
3 1 38 | 87
9
8
12
17
2
177
b. Spectra in the Brighter Clusters. The Pleiades, 29 the
Hyades, 30 and Coma 31 fall under the head of "very loose and
irregular clusters" (division c in the classification of galactic
clusters in Chapter II). References to discussions of their
spectra and colors will be found in the special bibliographies
88 Doig, J. B. A. A., 35, 201, 1925; Raab, Lund Medd., Ser. 2, 28, 1922.
89 See special bibliography in Appendix D and, for a detailed summary,
Hertzsprung, M. N. R. A. S., 89, 660, 1929.
30 See Appendix D.
Ibid.
36 ON THE SPECTRAL COMPOSITION OF CLUSTERS
devoted to them. Figures III, 5 and III, 6 show, for the
Pleiades, the spectrum-magnitude and color-magnitude rela-
tions, the former compiled from the Henry Draper Catalogue
and Harvard Bulletin 764, and the latter taken from Hertz-
sprung's recent discussion. 32 The spectral data on h and
10
B5
AO
F5
GO
A5 FO
FIGURE III, 5.
Relation of spectrum to luminosity in the Pleiades. Ordinates,
photographic magnitudes, abscissae, spectral classes.
X Persei, Messier 34, Messier n, and two southern clusters are
summarized below.
i. The Double Cluster in Perseus. The table of spectra
and magnitudes for the (combined) Perseus clusters has been
M. N. R. A, S., 89, 660, 1929.
SPECTRA IN INDIVIDUAL GALACTIC CLUSTERS
37
compiled from the data given by Trumpler, 33 but also includes
some stars not given by him, which appear to belong to the
systems, on the basis of proper motion, radial velocity, 34 or
spectrum, 85 or more than one of these factors. The data are
plotted in Figure III, 7, which shows also a number of the
fainter stars that are plotted, but not individually listed, by
Trumpler. Two matters of exceptional interest in this cluster
are the fact that a large number of the brighter stars show the
c-character and that the numerous bright-line stars are by no
means the brightest members of the cluster.
+ 0.4
408
* Y.
*,.
3
11
13
15
7 9
FIGURE III, 6.
Color-magnitude curve for the Pleiades. Color index (ordmate) is
plotted against apparent photographic magnitude.
2. Messier 34. The magnitude-spectrum relation for
Messier 34 is illustrated in Figure III, 8, which is taken from
Trumpler's discussion of the classification of open clusters. 36
3. Messier n. In supplementing my earlier work on the
colors in Messier n, I found from plates made with the 100-
83 P. A. S. P., 38, 350, 1926.
34 van Maanen, Dissertation, Utrecht, 1911; Pop. Astr., 25, 108, 1917; Mt. W.
Contr. 205, 1920; Adams and van Maanen, A. J., 27, 137, 1913.
M Hertzsprung, B. A. N., I, 151, 1922; I, 218, 1923.
86 Trumpler, P. A. S. P., 37, 310, 1925.
ON THE SPECTRAL COMPOSITION OF CLUSTERS
10
11
A
A
A
13
BO
B2
B8
AO
A2
B4 B6
FIGURE III, 7.
The magnitude-spectrum relation for stars in h and x Persei.
Sources are as follows: -K Hertzsprung; X , van Maanen; A.
Trumpler; , Payne. A circle enclosing the symbol indicates
a c-star.
80
100
120
140
AO
FO
GO
KO
FIGURE III, 8.
Magnitude- spectrum curve for Messier 34. Or-
dinates are apparent visual magnitudes, abscissae
are spectral classes. The broken line represents
the dwarf branch. (After Trumpler.)
SPECTRA IN INDIVIDUAL GALACTIC CLUSTERS
39
TABLE III, VIII. MAGNITUDES AND SPECTRA FOR THE DOUBLE CLUSTER IN
PERSEUS
B.D.
H.D
Spec-
trum
Magni-
tude
Note
B.D.
H.D.
Spec-
trum
Magni-
tude
Note
+6 3 274
12301
cB S
S 50
i
+55S6 4
13970
B 3
8 4
2
-h57494
12953
CA2
5 96
2
+ 56soo
14052
BS
8 S
2
+ 556i2
14818
B2
6 05
2
+ S6498
I40S3
B2
8 S
2
+ 564 3 8
13267
cB3
6 19
2
+ S6545
14250
BS
8 S
3
+ 5647i
I38S4
cBi
6 20
2
+ 56485
13969
B2
8 6
3
+ 56530
I4I43
Bo
6 42
2
-fs6574
B 4
8 7
4
+ 56522
I4I34
Bo
6 42
2
+ 565S5
14357
B3
8 7
2
+ 57SI9
13476
cAo
6 50
I
+ 56577
14476
Boe
8 8
3
+ 56568
14433
CA2
6 60
2
+ 56527
B6
8 4*
2, S
+ S5588
14322
cBp
6 82
2
+ 56478
13890
cB8
8 9
3
-fs6593
14542
cB8
6 90
2
+ 56479
13900
BS
8 9
3
+633iS
14010
cB S
6 93
I
+ 55547
13561
B8
9 o
2
+ 56470
13841
c Bi
6 99
2
-f56565
14422
Bpe
9 2
3
+ 57582
15497
B 3
7 03
I
-f56535
14162
B
9 2
3
+ S7S68
14956
cBi
7 10
2
-f56588
14520
B 9
9 2
3
+ 57576
I53I6
CA2
7 36
I
+ 56575
CB2
9 3
4
-f S662I
14899
acAo
7 42
2
+ 56578
C B2
9 3
4
+5659i
14535
c Ao
7 46
2
+ 55596
14453
Ao
9 4
3
+ 54539
14827
B9
7 49
I
+ 56550
M32I
BS
9 4
3
+ 56475
13866
CB2
7 5
2
+ 56445
13370
Ao
9 4
2
-fS7$22
13633
Bp
7 63
I
+56576
C B2
9 5
4
-f59S3S
16778
cBp
7 69
I
+ 56507
14092
B8
9 S
3
+55S54
13745
B2
7 77
2
+ 5657i
B3
9 S
4
+ 57634
I7I45
cB
7 8
I
+ 56563
B 3 c
9 6
4
+ 57S26
U744
cAo
7 8
2
+ 56573
B 3 e
9 9
4
+633io
13590
cBs
7 9
I
+ 56572
B 4
I
4
+ 57594
15963
acAo
7 98
I
(van M 380)
B 3 e
O I
4
+ 56543
14210
Ao
8
2
(van M 374)
640
6
4
+ 58397
I34I2
acA2
8 3
I
+ 56s8o
BS
o 7
4
+ 56567
14434
Ba
8 3
3
(van M 385)
B6
o 8
4
-fS7S2S
13716
Bi
8 3
2
(van M 384)
B6
o 8
4
+ 56S70
14443
CB2
8 4
4
(van M 510)
BS
10 8
4
+ 56 4 69
13831
Bo
8 4
2
(van M 413)
B6
10 9
4
NOTES TO TABLE III, VIII
1. Hertzsprung (B A N. 35 and 37) suspects that these stars are members.
2. Included on the basis of the radial velocity given by van Maanen m Mount Wilson
Contribution 205 Two stars of Class O are excluded.
3. Nearby stars suspected of membership from their spectra and magnitudes
4. Members of * Persei enumerated by Trumpler (P A. S P , 38, 350, 1926). Twenty-
five stars that he plots but does not tabulate are omitted from this table.
5. Magnitude from the B. D.
ON THE SPECTRAL COMPOSITION OF CLUSTERS
inch reflector that the brighter spectra are chiefly of Class A. 37
This observation was later verified by Lindblad 88 on other
TABLE III, IX. SPECTRAL TYPES IN AND NEAR MESSIER n
Stratonoff
Spectrum
Photographic
Magnitude
Stratonoff
Spectrum
Photographic
Magnitude
545
B 7
8 29
523
A2
12 22
687
F 3
9 50
631
A3
12 26
694
Ko
9 85
452
Ao
12 29
437
B8 5
10 36
662
Ao
12 29
172
B?
11.40
356
Ao
12 3 2
237
B 9
ii Si
381
Ao
12 33
336
Ao.s
ii 55
158
B 9
12 36
227
Ai
ii 56
493
B 9
12 36
395
B8
ii 58
143
B 9
12 40
SGI
B 9
ii 60
462
A
12 40
5i6
B9 5
ii 62
647
Ai
12 47
58i
B7
ii 79
159
Ao
12 47
33i
Ao
ii 80
571
Ao
12 47
345
B 9
ii 89
664
B8
12 47
577
AS
ii 89
415
A2
12 54
235
A2
ii 94
385
B S
12 6l
663
A 5 :
ii 98
568
Ao
12 62
686
Ao
ii 99
273
Ao
12 66
232
Ao
12 OO
294
B 9
12 66
407
Ai
12 IO
563
A 4 .
12 66
211
Ai
12 14
193
A 3
12 73
245
B 9
12 14
1 88
A 4
12 80
456
Ao
12 14
267
Fo
12 80
566
A 4
12 14
698
K
12 83
544
AS
12 l8
221
B6
12 84
375
Ai
12 21
710
A2
12 98
70S
A3
12 21
620
A2
13 05
197
A 3
12 22
423
K2
13 31
740
B 9
12 22
* 7 The magnitudes determined for this cluster are apparently in error, probably
by a constant amount, notwithstanding the consistency of the Mount Wilson
photometric plates (Mt. W. Contr. 126, 1917). The color indices are system-
atically too great, as shown by my own spectrum plates (unpublished) and sub-
sequently by the similar work of Lindblad and Trumpler. A correction of 0.4
to the photographic magnitudes is indicated by an unpublished Harvard plate,
but still the colors and spectra are inconsistent. There is a possibility of differ-
ential light absorption within the cluster.
38 Mt. W. Contr. 211, 1918.
SPECTRA IN INDIVIDUAL GALACTIC CLUSTERS
Mount Wilson spectrograms. The spectral classes of 59 stars
in and around the cluster are given by Trumpler, 39 and his
data are shown in condensed form in Table III, IX. Successive
columns contain the number from StratonofTs catalogue, 40
Trumpler's spectral class, and my photographic magnitude.
4. N. G. C. 3532 and N. G. C. 3766. The distribution of
spectra in two southern galactic clusters has been derived by
AO FO GO KO M
Typelb
BO AO FO GO KO M Spectral
"T i i i i r class
v
TypeU
Type2a
TypeSf
+3
+4
+6
Absolute
visual
magnitude
FIGURE III. 9
Trumpler' s classification of galactic clusters.
Becker from his own photographs made at La Paz. 41 He
finds percentages as follows:
Bo-B? B8-A4 A5-A8 Ko K4 of Stars
N. G. 3532 38 86.3 1.5 8.4 o 131
N. G. C. 3766 442 39-5 4-7 o ii. 6 43
For N. G. C. 3532, Mrs. Fleming recorded 93 per cent of the 204
stars as Class A. 42
39 L. O. B., 12, 10, 1924.
40 Tashkent Publ., I, i, 1899.
A. N., 236, 327, 1929.
42 See Table III, VI.
42 ON THE SPECTRAL COMPOSITION OF CLUSTERS
c. Trumpler's Investigations. The kinds of spectral distribu-
tion among the stars of a galactic cluster, first recognized in the
early Harvard work, and amplified by all subsequent studies,
are defined in some detail in Trumpler's scheme of classification
(Section 4 in Chapter II), and a number of galactic clusters
are now assigned to the classes and their subdivisions. The
essentials of the classification are shown by Figure III, 9,
which is reproduced from Trumpler's paper.
The Lick studies, published and unpublished, have provided
for the classification of 52 galactic clusters by means of their
spectra, and the relative numbers in the various classes are
as follows:
Type Number
ib 24
ia 6
2a 20
2f I
Others I
It will be seen that the Pleiades type preponderates among the
systems bright enough to classify. This may, however, be an
effect of selection, as Type ib contains far brighter stars than
any of the others. The bearing of this selection on estimates
of distance is considered later (Section 58, last footnote).
CHAPTER IV
VARIABLE STARS
THE most inviting and productive field in the study of globu-
lar clusters is the discovery and analysis of light variability.
Fortunately, the field is rich. Almost a thousand variable
stars are enumerated in the census contained in the present
chapter. The first four sections refer to the many variables in
globular clusters, the next one to their scanty appearance in
galactic clusters, and the following sections deal with observa-
tional considerations of the nature of Cepheid variability.
16. A Summary of Known Variables. Examining some of
his earlier photographs of globular clusters, Dr. Common 1
noted the probable variability of some stars in Messier 5. Pro-
fessor E. C. Pickering 2 in 1889 and Mr. David Packer 3 in 1890
also made some early observations of the variables in globular
clusters, which were independently confirmed by Barnard a
few years later. 4 But the whole development of this special
branch of variable star astronomy is essentially due to Pro-
fessor Bailey, whose extensive research on globular clusters,
begun about 30 years ago, is the basis of much of our knowledge
concerning cluster variable stars. Employing mainly the
photographs made at Arequipa with various telescopes, Bailey
has found the majority of cluster variables now known and has
made by far the most important investigations of light curves
and periods. Aside from Bailey's work, the discovery and
1 M. N. R. A. S,. 50, 517, 1890; 51, 226, 1891.
* A. N., 123, 207, 1889; H. C. 2, 1895.
3 Sid. Mess., 9, 381, 1890; 10, 107, 1890; Engl. Mech., 51, 378, 1890.
4 A. N., 147, 243, 1898.
43
44 VARIABLE STARS
study of the variables has been almost exclusively the work of
Miss Woods at Harvard, Baade and Larink at Bergedorf, and
the writer and his collaborators at Mount Wilson and Harvard
(see references in Appendix C). Larink has made an extensive
check of Bailey's periods for cluster-type variable stars in
Messier 3, finding that, after a 2o-year interval, 82 periods
were unchanged and 29 probably had varied. My similar
check on 54 of Bailey's variables in Messier 5 results in
periods accurate to within a tenth of a second; in this cluster
the periods are nearly all constant throughout an interval of 30
years.
The data at present available concerning the variable stars
in globular clusters are summarized in Table IV, I. Clusters
examined with care but without discovery of variable stars
are also included in the table. Some stars suspected of vari-
ability are omitted in the absence of numerous or decisive
observations. Three of these, for instance, are in the Hercules
cluster, 5 where my measures on a few plates cannot be con-
sidered to furnish sufficient evidence of variability. In crowded
regions and for close doubles, the photographic development
(Eberhard) effect 6 may produce spurious variability, for it
varies from plate to plate under ordinary working conditions.
Aside from this and similar uncertainties, which lead to the
inclusion and exclusion of suspected variables, there is an ele-
ment of incompleteness in these tabulated results because of the
difficulty of thoroughly examining the centers of clusters, and
also because of the small number of plates sometimes involved
in the surveys. In general, also, it may be said that scarcely a
cluster has been examined with the accuracy and thoroughness
necessary to detect ordinary eclipsing stars of short range or
narrow minimum and to exhaust the possibility of Cepheids
of small range.
8 Shapley, Mt. W. Contr. 116, 79, 1915.
Eberhard, Phys. Zeitschr., 13, 288, 1912; Pots. Pub. No. 84, 26, i, 1926.
A SUMMARY OF KNOWN VARIABLES
TABLE IV, I. SUMMARY OF VARIABLES IN CLUSTERS
45
N. G. C.
X
ft
Class
Ellipticity
Variables
Period
Suspected
References
<i<
>i'
104
o
272
o
-44
III
8
7
3
I, 2
288
2I 4
-88
X
9
2
3
362
268
-46
III
8
14
I
1851
211
-34
II
9
3
4, 5
1904
195
-28
V
9
5
i
3201
244
+ 10
X
9
61
6,7
4H7
227
+78
IX
5
8
8
4590
268
+37
X
9
28
27
i
9, 10
4833
271
-8
VIII
8
5
5
5024
307
+79
V
9
40
II, 12
SOS3
310
+ 77
XI
8
9
8
13
5139
277
+ 16
VIII
8
132
95
5
I, I 4
5272
8
+ 77
VI
8
1 66
no
i
79
i, 15, 16,
17, 18 19
5286
280
+ 10
V
9 5
o
20
5466
8
+ 70
XII
9
14
12
12
5904
333
+45
V
9
84
6 9
3
8
I, 21
5986
305
+ 13
VII
i
I
6093
320
+ 18
II
10
4
i,39
6121
319
+ 15
IX
9
33
5
22
6205
26
+40
V
9 5
7
I
2
3
I, 17, 23,
24
6229
41
+39
VII:
i
8
6266
320
+ 7
IV
8
26
I
6293
325
+ 8
IV
9
3
25
6333
333
+ 10
VIII
9
i
3
6341
35
+34
IV
8
J4
17, 26
6362
293
-17
X
8
17
27,28
6397
3>4
12
IX
9
2
i
6539
348
+ 6
X
9
I
29
6541
317
12
III
9
I
30
6553
333
- 4
XI
9
O
2
25
6584
310
-18
VIII
9
O
20
6626
336
- 7
IV
9
9
I
6656
338
- 9
VII
8
21
9
2
4
I, 31, 32,
33
6712
353
- 6
IX:
I
8
4 6
VARIABLE STARS
TABLE IV, I.~(Continued)
N. G. C.
X
ft
Class
Elhpticity
Variables
Period
Suspected
References
<i*
>!*
6723
o
327
o
-18
VII
9 5
17
16
O
1,34
6752
303
-26
VI
I
i
6779
3>
+ 7
X
8
I
2
25,35
6809
335
-24
XI
9
2
I
6864
348
-28
I
9
II
5
25,36
6981
3
~34
IX
29
29
5
8, 25, 36
7006
32
20
I
II
ii
O
25,37
7078
33
-29
IV
8
74
60
I
I, 21
7089
22
~37
II
9
ir
I
i,38
7099
356
-48
V
9
3
i
7492
23
-65
XII
9
9
5
3
Bailey, H. A.. 38, 2, 1902.
Bailey, H. B. 783, 1923.
Mt W. Obs , unpublished.
< Bailey. H. B. 802, 1924.
Miss Swope, unpublished.
Miss Woods, H. C. 216, 1919.
7 Bailey, H. C. 234, 1922.
Miss Davis, P. A. S. P., 29, 260, 1917.
Shapley, Mt. W. Contr. 175, 1920. ,
Shapley, P. A. S. P., 3it 226, 1919
1 Baade, Hamburg Mitt , 5, No. 16, 1922.
' Baade, Hamburg Mitt., 6, No. 27, 1928.
Baade, Hamburg Mitt., 6, No. 29, 1928.
Innes, U. C. 59, 201, 1923.
Shapley. Mt. W. Contr. 91, 1914.
Shapley, Mt. W. Contr. 176, 1920.
1 Guthnick and Prager, Sitz d. Preuss.
Akad d. Wiss., 27, So8, 1925.
" Larink, Bergedorf Abhandlungen, a, No. 6,
1922.
19 Barnard, A. N., 172, 345, 1906.
" Bailey, H. B. Sot, 1924.
Bailey, H A., 78, 1917.
Miss Leavitt, H. C. 90, 1904.
Russ. Astr. Journ., i, 16, 1924.
Shapley, Mt. W. Contr. 116, 1917.
Ibid , Mt. W. Contr. 190, 1920.
Mis9 Woods, H. B. 773, 1922.
Miss Woods, H. C. 217, 1919.
Miss Woods, unpublished.
Hubble, letter.
Miss Woods, H. B. 764, 1922, see also
A. N., 2x5* 39i, 1922.
H. B. 848, 1927.
Z6-S6 Annals, xo, 1918.
Bailey, Pop. Astr., 28, 518, 1920.
Bailey, H. C. 266, 1924.
Miss Davis, P. A. S. P . 29, 210, 1917.
Mt. W. Contr. 195, 1920.
> 7 P. N. A. S., 7, 152, 1921.
Chevremont, Bui. Soc. Astr. de France,
12, 1 6, 90, 1898.
Bailey, H. B. 798, 1924.
17. The Frequency of Variable Stars. Although only
45 of the clusters enumerated in Appendix A have been
thoroughly examined for variables, we may profitable indicate
some preliminary results of the search.
a. Nearly 900 variable stars have been discovered in globu-
lar clusters, as enumerated in Table IV, I. The great majority
of those for which periods have been derived are cluster-type
THE FREQUENCY OF VARIABLE STARS 47
variables with periods less than a day. Nineteen have been
found, however, with periods greater than a day; reference is
made to some of them in Sections 19 and 53.
b. Ten clusters are known to contain more than 25 variable
stars each and may be considered rich in variables. The
"poor" clusters, with less than 5 known variables, are 18 in
number (excluding, of course, those that have been inadequately
examined).
c. Richness is slightly correlated with galactic latitude; the
mean latitudes for the 10 rich and the 18 poor clusters are
32 and 21, respectively. The mean distances of the rich and
the poor clusters from the galactic plane are 7,320 and 5,550
parsecs. Both these results, of which the latter is probably
the more significant, suggest a correlation between poverty
in variables and proximity to the galactic plane.
d. Figure IV, i illustrates the relation between the number
of variables and the class of cluster. Rich clusters are confined
to the intermediate classes; poor clusters are distributed equally
throughout all classes. It seems unlikely that observational
selection is responsible for this result, although possibly some
part of the effect may be attributed to the decreased discovery
chance in a very condensed cluster.
18. General Properties of Variables in Clusters. A few
somewhat disconnected points appear worth recording before
the special characteristics of cluster-type variables are dis-
cussed. Much work remains to be done in discovery, in deriv-
ing colors, periods, and light curves, and especially in checking
the earlier determinations of period (most of which are based
on scanty material) for the study of the highly significant
changes in periods and light curves.
a. The great majority of cluster variables are, on the average,
1.5 to 2.0 magnitudes fainter than the brightest stars in the
cluster. The difference is evaluated numerically in Chapter
XI for several clusters in which the variables have been studied.
For others, where they have been found but not analyzed in
4 8
VARIABLE STARS
detail, an inspection of the photographic plates and prints,
such as those in Harvard Annals, 38, supports this generaliza-
tion concerning the relative brightness of the variable stars
and the most luminous objects in the clusters.
b. In Miss Leavitt's survey of the Magellanic Clouds 7 no
variables were found fainter than photographic magnitude
150
100
60
II
VIII
XI
FIGURE IV, i.
Numbers of variable stars in clusters of various
classes. Circles represent smoothed means.
17.5 (revised scale). The plates, made with the 24-inch Bruce
telescope with exposures of from two to five hours, are sufficient
to test this matter. A similarly definite fainter limit to the
magnitude of Cepheids has been observed in globular clusters,
particularly in Centauri, Messier 3, Messier 5, and Messier
13. No dwarf Cepheids are on record in clusters or the Galaxy.
7 H. C. 173, 1912.
GENERAL PROPERTIES OF VARIABLES IN CLUSTERS 49
The negative results of the searches for faint variables and
the form of the period-luminosity curve, which flattens con-
spicuously for periods less than a day, suggest that dwarf
Cepheids do not occur.
c. There is as yet no convincing evidence of eclipsing binaries
in any cluster. 8 This is not very surprising, since in the Galaxy
the great majority of eclipsing stars that show appreciable
range are of Class A, with an average absolute magnitude of
about +i. They would therefore naturally be too faint for
any studies so far made, except perhaps those of Messier 13
(where I made a special search on a few plates for faint vari-
ables), Messier 3, Messier 22, and w Centauri.
d. The absolute magnitude of the variable stars, the period-
luminosity curve, and the relation of the ordinary Cepheid to
the cluster-type variable will all be further considered in Chap-
ter X. It may be remarked in passing that there is no evidence
that the Cepheid variables in clusters, whether of short or long
period, are different in their various characteristics from those
in the Galaxy at large. The color changes in cluster variables
are found to be of the usual sort. The light curves are of the
uniform pattern. 9 The long-period variables in 47 Tucanae
are also normal 10 their periods, ranges, probably their light
curves are exactly duplicated by well-known galactic variables
of the long-period class.
It is only in the relative numbers of different types and sub-
types of variables that we find peculiarities in the globular
clusters when contrasted with the galactic system, galactic
star clouds, or the Clouds of Magellan. These differences of
content and frequency have not been explained satisfactorily.
There are some indications that the Cepheids in the galactic
system have properties that depend on environment, which are
possibly the marks of differences in age and history. It is to
be noted, however, that very serious factors of incompleteness
8 But see Appendix C, Ref. 202.
See Figure IV, 2.
10 Shapley, H. B 783, 1923.
50 VARIABLE STARS
and selection affect the comparison of clusters with the Galaxy,
and also that there appear to be just as great differences in
variable star content between clusters as there is, say, between
cj Centauri or 47 Tucanae and the solar neighborhood.
19. Notes on Some Individual Variable Stars. It is the
less common variable with period greater than a day, rather
than the cluster-type variable, that is bright enough to be
studied in detail. The present section summarizes observation
on such variables in five clusters.
a. Messier 3; Variable Bailey No. 95. Bailey 11 found more
than 100 variables in Messier 3, of which No. 95 is one of the
brightest. It has a photographic magnitude of 13, 9, 12 brighter
than the value 13 (13.92) for the sixth star in the cluster. Our
final modulus 14 of 15.43 for Messier 3 gives the photographic
absolute magnitude of No. 95 as 1.5. The star has a large
positive color index. Bailey was not able to derive a period
from his observations.
Sanford 15 has obtained evidence of spectral variability for
the star. When at maximum, it showed an apparently late-
type spectrum with H 7 and H 5 bright; a month later, the star
seemed to be fainter and the bright lines did not appear. A
radial velocity of 300 kilometers per second was derived from
the emission spectrum; Slipher's value of the velocity of the
whole cluster is 125 kilometers per second.
Possibly the star is an irregular variable of the a Orionis
type. Although emission lines are uncommon in the spectra of
non-periodic red variables, they are sometimes found for
instance, in the spectrum of T Microscopii. It seems probable
from the brightness of the variable that it is actually a member
of the cluster and not a field star.
b. Bailey 9 s Long-period Variable in Messier 22. Among the
H. A., 78, i, 1913-
12 Shapley and Davis, Mt. W. Contr. 176, 1920.
13 Shapley and Sawyer, H. B. 869, 1929.
14 Shapley and Davis, Mt. W. Contr. 176, 1920.
18 Pop. Astr., 27, 99, 1919
INDIVIDUAL VARIABLE STARS 51
cluster-type variables in Messier 22 Bailey 16 found a star with a
period of 199^.5. It has a large range, but the form of the light
curve inclined the discoverer to regard it as a Cepheid rather
than a typical long-period variable. The star is remarkable as
being about a magnitude fainter than the other variables in
the cluster absolute magnitude about +1.0. This brightness
places it with the long-period variables rather than with the
brighter Cepheids (if, indeed, it is a member of the cluster),
and even for that class it would seem to be rather faint. If not
a cluster star, the variable must be in the background and very
remote; the distance of Messier 22 itself is 6.8 kiloparsecs. 17
c. Chevremont's Variable in Messier 2. One of the brightest
stars in Messier 2 was noted as variable by Chevremont in
1897. 18 The star does not seem to have had further attention.
The discoverer suspected a period of about 30 days, but the
published observations suggest irregularity, which is borne
out by estimates on 36 plates taken at Harvard and Mount Wil-
son. Throughout several years, a period of about n days is
indicated. The range is rather more than a magnitude. With
a photographic magnitude of about 12.5 at maximum, the star
is two magnitudes brighter than the sixth star and, on the basis
of the modulus 19 of 15.71, has an absolute magnitude of about
3. No data are available on color or spectrum. The star
is within the recognized bounds of the cluster but may possibly
not be a member.
d. Long-period Variables in 47 Tucanae. Of the seven known
variables in 47 Tucanae, the three brightest are of long period: 20
Period
d Maximum Minimum
2H.3 II O 14.4
203 II O 14 2
IQ2 II O 14.3
18 Ibid , 28, 90, 1920.
17 Shapley and Sawyer, H. B. 869, 1929.
18 Bui. Soc. Astr de France, 12, 16, 90, 1898.
19 H. B. 869, 1929.
20 Shapley, H. B 783, 1923-
VARIABLE STARS
They are between one and two magnitudes brighter than the
other four variables, for which no periods have been determined.
From the adopted modulus for 47 Tucanae 21 (obtained without
reference to the magnitudes of the variables) these long-period
variables have an absolute photographic magnitude at maxi-
mum of 3.
e. The Nova in Messier 80. Nova T Scorpii was discovered
nearly in the center of Messier 80 (N. G. C. 6093) in 1860 by
8
20
24
12 16
FIGURE IV, 2.
Light curve of variable No. 42, in Messier 5 Points with
less than six observations are indicated by circles. Coor-
dinates are photographic magnitudes and days.
Auwers (see Appendix C). If it is an actual member of the
cluster, its absolute magnitude at maximum, when the apparent
visual magnitude was 7.0, was 9.2, three magnitudes brighter
than the average galactic nova.
/. Messier 5; Variable 42. Illustrating the fact that the
classical Cepheids in globular clusters are comparable with
those of the Galaxy, a light curve of one of the variables in
Messier 5 is given in Figure IV, 2.
" H. B. 869, 1929.
RELATION OF MAGNITUDE TO PERIOD 53
20. Variable Stars in Galactic Clusters. Notwithstand-
ing a careful search, no variable stars of recognized type are yet
available for the estimation of the distances of galactic clusters.
Variables have been found in the vicinity of Messier n, 22
but probably they are members of the surrounding rich star
field. The double cluster in Perseus was found by Lindemann 23
to contain variables, and others were suspected by Waterfield 24
in a special search of Harvard plates; but for none have periods
been derived; all are probably irregular and may belong to
the surrounding star field.
The only definite attribution of a regular variable to a galactic
cluster is that by Doig; 25 he places T Serpentis, of maximum
visual magnitude 9.0 and period 341^.1, in the cluster N. G. C.
6633. The star is probably about two magnitudes brighter
absolutely than he assumed, and accordingly it is probably
more distant than the cluster. Doig's spectral parallax of
o".oo25 is nearly in accordance with the distance given in
Appendix B.
21. The Relation of Magnitude to Period for Cluster-
type Variables. It is well known from the investigations
of star clusters by Bailey and by the writer that the
absolute median magnitudes for the short-period Cepheid
variables in star clusters show very little dispersion. Further-
more, there is no dependence of median magnitude on length
of period.
In the southern cluster co Centauri, the subclasses a, b, and
c of the cluster-type variables, with mean periods of 0^.586,
0^.752, and 0^.395, have median apparent photographic magni-
tudes of 13.55, I 3-S4> an d I 3-6i, respectively, with an average
deviation for a single star of one-tenth of a magnitude. The
M Barnard, A. J , 32, 102, 1919; Pop. Astr., 27, 485, 1919; Ritchie, P. A. S. P.,
32, 61, 1920; Walton, Pop. Astr., 35, 25, 1927.
23 Bui. St. Petersburg Acad. Sci , Ser. 5, 2, 55, 1895.
Waterfield, W. F. H., unpublished,
wj. B. A. A., 35, 202, 1925.
54
VARIABLE STARS
mean of all (76 stars) is 13.57 o.oi. It appears that although
the ranges and light curves differ conspicuously, as shown in
Figure IV, 3, and the periods are in the approximate ratio of
3:4:2, the median magnitudes are, on the average, practically
identical. Stars of different subclasses evidently are equal in
total radiation. Whatever may cause the differences in period,
amplitude, and light curve, it seems not to affect the average
luminosity of the short-period Cepheids in this globular cluster,
in sharp contrast to the conspicuous change of absolute magni-
tude with period for classical Cepheids.
130
135
140
130
13.5
14.0
13.0
14.0
02
04
10
FIGURE IV, 3.
The three subclasses of cluster-type variables in to Centauri. The
coordinates are fractions of a day and photographic magnitudes.
Observations for 5, 5, and 4 stars are used for subclasses a, b, and c,
respectively.
Similarly, for Messier 3, Messier 5, and Messier 15, clusters
for which there is material suitable for a quantitative test
of the dependence of magnitude on period, the following means
have been derived from Bailey's original observations. The
data for w Centauri are also included.
HYPOTHESES OF CEPHEID VARIABILITY 55
TABLE IV, II. PERIOD AND MAGNITUDE FOR CLUSTER VARIABLES
Cluster
Number of Variables
Mean Period
Median Apparent
Magnitude
d
[ i
32
15 53
Messier 3
18
18
50
o 54
15.42
IS 53
1-8
o 60
IS 53
8
o 27
14 98
Messier 5
10
10
o 48
o 54
14 98
14 98
IO
o 63
14.96
Messier 15
I 29
131
o 36
o 64
15 66
15-72
[C34
0-39
13.61
a) Centauri
\ * 37
0-59
13.55
[big
o.7S
13.54
The magnitudes of the variables in Messier 2, Messier 68,
Messier 72, and other globular clusters yield results similar
to the foregoing. In each cluster, apparently, the total light
variation of the cluster-type variables is confined to a narrow
interval of brightness, and the deviations of the median photo-
graphic magnitudes from their mean value are well within the
errors of observation. 26 The median value is apparently an
astronomical constant and, for this type of variable, a funda-
mental property. Its constancy throughout a considerable
range of period length is a factor of some significance in the
interpretation of the nature of the variation and, indeed, pro-
vides a crucial test for theory.
22. A Test for Hypotheses of Cepheid Variability.
In all hypotheses of the cause of Cepheid variation that have
M There may be one known exception, No. 49 in Messier 15, which is six-tenths
of a magnitude brighter than the 60 other cluster variables in the system for
which periods are determined. But the star may be a component of an unre-
solved double, and therefore erroneously measured too bright, or possibly it is a
foreground variable of normal brightness.
56 VARIABLE STARS
attained even partial success, the fundamental gravitational
relation between the period and the mean density, P p-*,
is generally accepted as applicable. 27 Variables of subclass
c in a? Centauri should, therefore, as a group have nearly four
times the density of those of subclass b. The extreme periods
in the cluster are 0^.30 and 0^.90, and in Messier 3, Messier 5,
and Messier 15 there is also a wide range of periods, the extremes
being
d d
032 and o 71 for Messier 3
o. 23 and 0.85 for Messier 5
0.30 and o 76 for Messier 15
Since for the periods PI and Pz we have
Pi^ [to
>2 \P1
and, introducing surface area A and mass /i,
PI
3/2
3/2
it is clear that either the masses or the surface areas must change
considerably throughout the range of periods found among
cluster variables.
It is decidedly contrary to our beliefs and our present evi-
dence that Class A stars of the same absolute magnitude should
differ in mass in the ratio of more than five to one. It is much
more reasonable to assume that the fixity of median magnitudes
and the general similarity of spectrum for cluster variables of
all periods mean essential identity of mass.
We are left, therefore, with the alternative of variety in the
sizes of cluster variables. But if we hesitate to accept large
and small cluster variables, we must then admit the failure of
the general relation connecting mean density and period.
27 Shapley, Mt. W. Contr. 92, 1914; 154, 4, 1917; Eddington, M. N. R. A. S..
7Q, i, 1918; The Internal Constitution of the Stars, 192, 1926; Scares, Mt. W.
Contr. 226, 40, 1921; Jeans, M. N. R. A. S., 85, 808, 1925; Russell, Dugan, and
Stewart, Astronomy, 2, 766, 1927.
HYPOTHESES OF CEPHEID VARIABILITY 57
a. Assumption of Diversity in Diameters. Let us consider
the first possibility diversity in size for stars of similar mass.
Since for uniformity of mass,
P oc
the surface areas for cluster variables must differ throughout
a range of at least four to one. To compensate for the increase
of radiant surface with period, there must be a corresponding
and exactly balancing decrease of surface brightness with period,
amounting to 2.5 log 4 = 1.5 magnitudes in extreme cases
and to 0.85 magnitudes in the case of the two distinct groups of
cluster variables in Messier 15, for which the mean periods are
0^.36 and 0^.64, respectively. The large differences in surface
brightness should correspond to conspicuous differences in
spectral class and color, the shorter periods requiring bluer
stars. The mean spectrum should differ by more than a whole
spectral class and the color index by half a magnitude in extreme
cases.
The observations on spectra for galactic short-period
Cepheids are not extensive, but they certainly do not support
this suggestion that the surface brightness and, therefore, the
size of cluster variables may differ in such measure and pro-
gressively with period. The spectra for the individual stars
vary on the average from Ao to F2. The median spectra show
little dispersion.
For galactic cluster-type variables for which a single random
determination of the spectrum is given in the Henry Draper
Catalogue, we find
Mean Penod
d Mean Spectrum Number
O 38 A5 Q 9
o 49 AS 6 8
o 59 A6 5 8
If we are to account for the constant luminosity by exactly
compensating changes in diameter and surface intensity, the
difference in spectrum between the first and last groups should
be five units (corresponding to a difference in surface brightness
58 VARIABLE STARS
expressed in magnitudes of 2.5 log -p = log ~ = 0.6],
A 2 3 * 2 /
which is, however, eight times as large as observed and cannot
be admitted.
b. Assumption of Differences in Color. The best evidence on
colors is derived from the two groups of cluster-type variables
in Messier 15, for which Bailey determined the periods and I
measured the average colors for each group, and from a similar
but smaller list of variables in Messier 5, for which the colors
are taken from my photovisual and photographic light curves
of individual variables.
For one group of 31 variables in Messier 15 the periods range
between 0^.57 and 0^.71, and for the other group, 29 variables,
between 0^.29 and 0^.44. No periods between 0*44 and 0^.57
were found, though in Messier 3 and some other clusters the
periods of this length predominate.
The mean median magnitudes, as noted above, are the same
for the two groups in Messier 15, within the errors of observa-
tion. This similarity holds also for the color indices, according
to the measures of color made with the 6o-inch reflector at
Mount Wilson for 39 variables in the cluster. 28 A composite
color curv>3 was derived which showed that no important color
differences exist between the two groups. 29 In summary, the
results are
Mean Mean C I. near C I near
Mean Penod Number Magnitude C. I. Maximum Minimum
Short (of 1 36) 22 16.00 +0.22 0.14: +036
Long (o d 64) 17 16.04 +0.28 0.02: +035
The difference in mean period would require a change in mean
color index of about three-tenths of a magnitude if the surface
brightness were balanced against a hypothetical change in size
with period.
28 Shapley, Mt. W. Contr. 154, 14, 1917.
29 Except, perhaps, near maximum where there is a suggestion that the variables
with longer periods are redder (in keeping with results for Cepheids with periods
longer than a day), but the observations are insufficient and uncertain at maxi-
mum where the long exposures are likely to decrease the observed range.
HYPOTHESES OF CEPHEID VARIABILITY 59
For Messier 5 the work on photovisual and photographic
magnitudes to test for differences in the velocity of light 30 also
gives results comparable to those above, showing the independ-
ence of color and period. The data are as follows:
Interval of
Penod
d
Mean
Penod
d
Number of
Variables
Mean Color Index
Maximum Median Minimurr
o 53 to o 61
558
9
+0 24 +0 39 +o 60
0.45 to 0.50
o 475
8
+0.23 +o 43 +0.58
The systematic excess of two-tenths of a magnitude in all these
color indices in Messier 5, which is more likely due to an error
in the zero point of photovisual magnitudes than to a differential
scattering of light in space, is of no consequence in the present
comparison of colors for the two groups.
c. Assumption of Nuclear Pulsations. From the foregoing
results it appears that the hypothesis of differences in the colors
and surface brightness, and therefore in the dimensions and
mean density, for cluster variables with different periods cannot
be maintained. The alternative of dispersion in mass has
already been rejected. The only remaining course seems to be
the admission of the failure for these variables of the simple
relation between the period and the mean density.
It may be that the pulsation period should be associated not
with the mean density of the whole star but with the density
in the interior and that the various periods indicate merely
stages in the development of a central nucleus which leaves the
total mass, the mean density, and the size and brightness of the
surface unaffected. This seems to me to be the only way out
of a difficult situation. 31 And it, of course, requires for cluster-
type Cepheids some modification of the pulsation hypothesis
or other theory that may quite satisfactorily account for the
classical Cepheids.
30 Ibid., H. Rcpr. 5, 1923.
31 Eddington's more rigorous expression P* = K/pf(y), which introduces the
ratio of the specific heats, would not help materially in reducing such a large
anomaly except in so far as the specific heats may be involved in the suggested
evolution of the nucleus.
6o
VARIABLE STARS
One might attempt to connect, speculatively, these changes
in period and nuclear readjustment with the hypothetical
transition, in an evolutionary scheme, from the giant branch
to the main sequence of stars, with the appeal to relatively
quick gravitational adjustment after a particular material
source of radiation has been exhausted.
In any case, the variables of the cluster type take on an added
importance. They are linked with the problems of distances
of clusters, Cepheid variation, and the interior structure and
evolution of stars at the critical point between giants and
dwarfs. It will be important in future studies to examine
individual variables for sudden or gradual changes of period
and of amplitude and to take the study of color into red and
violet light. My preliminary " violet" magnitudes indicate
for cluster variables smaller amplitudes than are shown by
photographic light. 32
23. Concerning Vestigial or Incipient Variation. The
most important irregularity in the general luminosity curve of
145
166
170
FIGURE IV, 4.
Photographic luminosity curve of stars of all colors in Mes-
sier 3 Ordmates and abscissae are numbers of stars and
magnitudes. Exclusion of variable stars gives the broken
line with circles.
globular clusters lies at about the median magnitude of the
cluster-type variables. It has been found for some clusters
that the excess of stars at that point over an otherwise smooth
luminosity curve is composed of blue stars. In Messier 3,
it is found that the surplus stars are mainly the cluster variables
82 Mt. W. Contr. 154, 16, 1917.
VESTIGIAL OR INCIPIENT VARIATION
61
90
60
30
themselves, supplemented by other stars that resemble the
variables in all characteristics except variability. The question
naturally arises whether or not the light of the other stars that
contribute to the excess is really constant. It may be that
these objects are variables of
small range, marking the
beginning or ending of typical
cluster variation.
In a photometric cata-
logue of the brighter stars
in Messier 3, which I pub-
lished at Mount Wilson in
collaboration with Miss
Davis, 33 there are about one
hundred typical cluster vari-
ables in the area studied,
which does not include the
dense and uncertain center.
These hundred variables are
only partially responsible for
the hump in the luminosity
curve, as may be seen from
Figure IV, 4, which shows the
photographic luminosity
curve for all stars in the sys-
tem from the fourteenth to
the seventeenth magnitude.
If we omit all known variables and plot the luminosity curve
for the remainder of the blue-white and the yellow-red stars
separately, from the twelfth to the seventeenth magnitude, as
in the lower part of Figure IV, 5, it is seen that the yellow-red
stars do not contribute to the special maximum. (Since the
photovisual magnitudes were used in this plot, the upper part
of the figure gives, for purposes of comparison, the general
photovisual luminosity curve, omitting variables.) The non-
33 Ibid. 176, 1920.
12
13
16
17
14 15
FIGURE IV, 5.
Luminosity curves in Messier 3. Above :
all colors; below dots and full line refer
to stars with color index greater than
+0.60; circles and broken line, color
index less than + o 60. Coordinates are
numbers of stars and photovisual
magnitudes.
62 VARIABLE STARS
variable blue stars, however, show the remarkable concentra-
tion between magnitudes 15.2 and 15.6. A smooth curve would
allow less than 15 stars to this interval; the actual number is
S3-
The stars that form the excess can be selected from the
catalogue on the basis of color and magnitude. In the future,
special attention should be directed to searching for possible
irregularities in these objects. We already have a preliminary
test of their stability in measuring the magnitudes for the
general catalogue of Messier 3, for the size of the residuals
from the several plates may be due to the variability of the
stars as well as to the errors of observation. In brief, we obtain
for the presumably invariable stars in the magnitude interval
15.2 to 15.6 (which includes the median magnitude of the
variables, 15.3) the following results:
Number of Stars Range of Color Index Mean Photographic Residual
33 o.oo to +o 20 103
IQ +0 20 tO +0 40 083
37 H-O 40 to +0 . 60 0.071
The mean residual for all magnitudes and colors (800 stars)
is 0.082, but as this includes many values for stars that were
later rejected because of uncertainty, it should be somewhat
diminished for a fair comparison with the tabulated results.
The interval of brightness near median magnitude was the most
satisfactory of all for photometric measurement, being neither
too bright nor too faint, and within it the accidental errors of
measurement should be distinctly less than for the rest of the
magnitude range. But the first line of the tabulation above
shows the average residual to be abnormally large for the stars
with colors and magnitudes like the variables. Moreover, two
or three overlooked variables are not responsible for this large
average deviation, for one half of the residuals exceed 0.10.
It seems reasonable to conclude that many of these stars are
slightly variable and that we here witness the beginning or end
of this type of Cepheid variation. At the maximum of the
magnitude-frequency curve of these 33 stars the brightness
A COMPOSITE LIGHT AND COLOR CURVE 63
is about a tenth of a magnitude fainter than the median magni-
tude of the variables.
24. A Composite Light and Color Curve for Cluster-
type Variables. From a combination of photometric work
done at Harvard and at Mount Wilson, it is possible to construct
150
000
050
FIGURE IV, 6
Light and color curves for variables in Messier 3 Above, full
line indicates photographic curve; broken line, photovisual.
Ordmates are magnitudes and color index, abscissae, frac-
tions of a day.
composite photographic, photovisual, and color index curves
of 103 typical cluster variable stars in Messier 3. The result
is essentially a highly accurate set of mean curves. Details
of Bailey's work on the variables and my discussion and stand-
ardization of the magnitudes are published elsewhere. 34 The
curves are shown graphically in Figure IV, 6, and numerically
14 H. A., 78, i, 1913; Mt. W. Contr. 154, 7, iQi7J Mt. W. Comm. 70, 1920.
VARIABLE STARS
TABLE IV, III. -MEAN PHOTOGRAPHIC AND PHOTOVISUAL LIGHT CURVES OF
CLUSTER-TYPE VARIABLES IN MESSIER 3
Phase
Pg. Mag
Color
Index
Pv. Mag.
Phase
Pg. Mag.
Color
Index
Pv. Mag.
000
14 90
o 07
14 97
o 371
16 07
+o 42
IS 65
on
14 93
o 06
14 99
o 283
16 08
+o 42
15 66
023
14 96
o 04
IS 00
294
16 09
+ o 43
15 66
034
15 oo
o.oi
IS 01
o 305
16 09
-f o 43
15 66
045
IS 04
+ 01
IS 03
o 317
16 10
+o 43
IS 67
057
IS ii
+o 05
IS 06
o 328
16 10
+ o 43
IS 67
068
IS 17
-f o 07
IS 10
339
16 10
-f o 43
IS 67
079
IS 23
+ II
IS 12
350
16 10
-Ho 43
IS 67
o 090
IS 32
+o 16
IS 16
o 362
16 10
-Ho 43
IS 67
102
IS 39
+o 18
IS 21
373
16 10
+ 43
IS 67
o 113
IS 48
+ 22
15 26
o 384
16 10
+ o 43
IS 67
o 124
IS 58
+ 26
IS 32
396
16 10
+ 43
IS 67
o 136
IS 67
+o 29
IS 38
o 407
16 10
-Ho 43
IS 67
o 147
IS 73
+ 31
IS 42
o 418
16 09
-Ho 43
IS 66
o 158
IS 79
+ o 33
IS 46
o 430
16 09
+ 43
IS 66
o 170
IS 84
-f o 34
IS SO
o 441
16 08
-Ho 42
15 66
o 181
IS 87
+ o 36
IS Si
o 452
16 06
+o 42
IS 64
o 192
IS 91
+ o 37
IS 54
o 464
16 01
-HO 40
15 61
o 204
H 94
+ o 38
IS 56
47S
IS 93
-Ho 38
IS SS
o 215
IS 98
+ 39
15 59
486
IS 77
+ o 33
IS 44
o 226
16 01
+ o 40
15 61
o 497
IS S3
-Ho 24
IS 29
237
16 03
-HO 41
15 62
509
15 22
+ II
IS II
o 249
16 04
+ o 41
IS 63
o 520
15 06
+ 02
IS 04
o 260
16 06
+o 42
IS 64
531
14 96
o 04
IS 00
in Table IV, III; in both places the adopted mean period is
For individual stars the light probably does not remain
constant for three hours at minimum, as it appears to do for
these mean curves. In other details, however, such as the
forms, the amplitudes of 1.2 and 0.7 magnitudes, and the
color variations, these results are essentially the same as
those customarily derived for the average isolated cluster-
type variable in the galactic system. In fact, the quantitative
agreement of the very remote variables in Messier 3 with the
local variables in such a phenomenon as color change is evidence
of the accuracy of the photovisual and photographic magnitude
scales relative to one another, and also of the absence of light
scattering in space.
CHAPTER V
THE DISTRIBUTION OF STARS IN GLOBULAR CLUSTERS
A FULL knowledge of the distribution of stars in time and
space is, of course, an unattainable dream. If we had, indeed,
a clear picture of the ages, arrangement, and masses of the stars
in even a single globular cluster, we should begin to know what
is going on in this universe; but we are denied complete informa-
tion. The distribution in time, or rather in stages of develop-
ment, can only be inferred from fragmentary data on the magni-
tudes and colors of the brighter stars. The distribution in space
is rather vaguely discernible through statistical conclusions based
on laborious star counts. The distribution in masses, at least
for giant and supergianl stars, is partially revealed in the general
luminosity curves and the mass-luminosity relation.
Thus, for globular clusters we may eventually attain some
idea of the distribution of mass and latent energy 1 ; we shall
probably have, at the most, an imperfect understanding of the
distribution in space, and nothing but surmises about the dis-
tribution in time. A good preliminary surmise concerning
stages of evolution is that all stars of a globular cluster origi-
nated at the same epoch and that their diversity in effective
age is a consequence both of the dispersion in masses and of
variety in dynamical experience. Other conjectures, however,
are equally entertaining.
25. Are Cluster Stars Arranged Spirally? In the early
days of visual and photographic observation of star clusters
it was natural that observers should look for a spiral arrange-
ment of the stars and very frequently find it. A relationship
between clusters and spiral nebulae was welcomed. The
1 See Chapter XIV, Section 73.
65
66 DISTRIBUTION OF STARS IN GLOBULAR CLUSTERS
coming of long-exposure photographs, which show in globular
clusters tens of thousands of stars in nearly spherical arrange-
ment, should have dispersed much of the interest in the arrange-
ment of the few hundred or thousand brighter stars; but the
subject has continued to attract attention.
Until recently, there has been a tendency to overemphasize
the superficial arrangement of stars in both galactic and globular
clusters. The laws of probability seem to be generally ignored
in considering stellar distribution, for as soon as a slight depar-
ture from radial symmetry is noted among the brighter stars,
we read of "lines of cleavage," "spiral paths," "lanes of nebu-
losity," and "channels of force." The significance that may
be attached to chance groupings and chance vacancies, however,
decreases remarkably with increasing exposure time. Nebulous
obscurations that are reported to conceal the brighter stars are
found, upon deeper penetration, to be ineffective for the more
numerous faint stars, and therefore they cannot be real.
Structural features other than flattening and central concentra-
tion may be present, but it is certainly inadvisable to conclude
definitely, from knowledge of only a small percentage of the
total number of the stars, that such structure exists. Probably
in only one globular cluster (Messier 22) have stars as faint as
the sun been photographed, and in only a few of those studied
for stellar distribution have stars other than giants or super-
giants been thoroughly examined.
In order to determine whether the frequently described
spiral structure in or near the center of globular clusters could
be seen on large-scale photographs, I made a series of exposures
on bright northern globular clusters some years ago with the
Mount Wilson reflectors. The exposures varied in length.
When only a few hundred stars were shown in a cluster, the spiral
structure could almost invariably be traced; if the exposures
were longer, the spiral arms became inconspicuous, or another
set of arms, sometimes with different center and pitch, was
found or imagined. The conclusion was reached that the
phenomenon is wholly illusory. Spiral structure is the easiest
ON THE LAWS OF DISTRIBUTION 67
form to visualize in centrally concentrated random groupings
especially when the number, pitch, thickness, origin, length,
symmetry, and defmiteness of the spiral arms are all arbitrary.
The a priori argument against the existence of spiral form
in the images of globular clusters is, of course, simply that the
clusters are three-dimensional. Cleanly traceable spiral arms
would mean a most remarkable and unbelievable arrangement
of stars in systems that are always nearly spherical. The
discussion of the ellipticity of globular clusters in the next
chapter will show how little they are flattened. Even the
images of the much sparser galactic clusters are very rarely
so elongated that we can assume them to be essentially
two-dimensional.
Pointing out that vestiges of spiral structure or other persist-
ent irregularities in globular clusters would indicate that the
systems are not in a completely steady state, ten Bruggencate 2
has discussed evidences of spiral arrangement, and especially
the data collected by Freundlich and Heiskanen. 3 In a dis-
cussion of our extensive Mount Wilson counts of stars in globu-
lar clusters, Heckmann and Siedentopf have recently concluded
that there are no actual traces of spiral structure in the several
globular clusters considered by them. 4
26. On the Laws of Distribution. The first detailed
numerical consideration of the space arrangement of stars in
globular clusters was made by Professor E. C. Pickering, who
examined the distribution in w Centauri, 47 Tucanae, and
Messier 13 6 and proposed general empirical relations connecting
surface density y with the distance from the center r in the forms
y = /(i-r*)<fe
and
y = J(i r) n dz
9 Sternhaufen, pp. 6j/., 1927.
8 Zeits. f. Phys., 14, 226, 1923.
4 Gott. Veroff., Heft 6, 1929.
H. A., 26, Chap. XI, 1897.
68 DISTRIBUTION OF STARS IN GLOBULAR CLUSTERS
Subsequently, much time has been devoted to studies of the
laws of the distribution of stars in globular clusters. Various
formulae relating the number of stars per unit volume AT with
distance from the center of the projected image r or with p,
the distance from the cluster center, have been derived (or
assumed) and applied to published counts of stars. We have,
for instance, from von Zeipel,
where R is the radius of the cluster and n is the number of stars
in the corresponding unit area of the projected image.
The problem of finding a law of space distribution from the
law of apparent distribution in a globular star system has been
solved by von Zeipel, who has been the leader in the attempt
to deduce the structure of clusters from observation of stellar
distribution. He was the first to utilize in this problem the
principles of the theory of gases. Analogies with the kinetic
theory have encouraged a number of theoretical and observa-
tional researches, but as yet no completely satisfactory repre-
sentation of the observations has been found. Whether
adiabatic cr isothermal distributions of gas most nearly simulate
star distributions in globular clusters is not yet decided finally. 6
It seems unnecessary to treat in detail the history, methods,
successes, and failures of these various investigations of dis-
tribution. No other phase of the study of globular clusters
has been so frequently and thoroughly described. Special
attention should be called, however, to the discussions by H. C.
Plummer, ten Bruggencate, Stromgren, Eddington, Jeans,
Parvulesco, and Martens. 7 A further important step has been
made by von Zeipel and Lindgren, who proceed, from the
assumption that the stars of different masses are distributed in
equilibrium in relation to surrounding stars, to the determina-
tion, from the observed distribution, of the mean masses for
8 See reference to Martens, Appendix C.
7 See references in \ppcndix C.
ON THE LAWS OF DISTRIBUTION 69
various color classes and absolute luminosities. They have
used the method with success in the study of the rich galactic
cluster Messier 37, and Wallenquist has further discussed their
analysis and applied the method to his own study of the magni-
tudes in Messier 36. Freundlich and Heiskanen have pro-
visionally applied it to the study of the distribution of stars in
globular clusters, but the observational material is yet too
uncertain for satisfactory results.
That the discussions of the adiabatic or isothermal distribu-
tions of stars in globular clusters have been very unsatisfactory
in practice is not surprising, since the data from which compari-
sons have been made are inherently faulty. The best chance
for improvement and successful application of the theory lies
in the few rich galactic clusters from which the foreground and
background stars can be satisfactorily differentiated. For the
globular clusters, however, the crowded centers and the attend-
ant difficulties with Eberhard effect and background contrast
vitiate the counts, except for the outer parts. Furthermore,
the available counts deal with only the few hundred or few
thousand supergiant stars; tens or hundreds of thousands of
fainter stars, which must play a major role in stellar distribution,
have not yet appreciably entered the investigations. Ten
Bruggencate has recognized the importance of ellipticity in
the distribution of stars in globular clusters, but otherwise
all discussions of the problem have ignored this lack of radial
symmetry.
The star counts that have been used for the study of globular
clusters are almost exclusively those of Bailey at Harvard and of
Pease and Shapley at Mount Wilson. Photographs on a
larger scale are needed. Special attention should be given to
the brighter and more open globular clusters (w Centauri,
N. G. C. 3201, N. G. C. 6397) and also to "giant-poor " anoma-
lous systems and those clusters like N. G. C. 2477 that are pos-
sibly intermediate between the globular and the galactic types.
Tables and figures of the distribution of the stars in globular
clusters are given for several of the brighter clusters by Picker-
DISTRIBUTION OF STARS IN GLOBULAR CLUSTERS
ing, Plummer, von Zeipel, and Heckmann and Siedentopf, to
whose work reference is made in the bibliography in Appendix
C. In conclusion, we must admit that the situation is not very
hopeful. The frequency is (roughly) inversely proportional
to the fourth power of the distance from the center. This
holds only for giant stars in the typical globular clusters; the
law of distribution of fainter stars is even less definitely known.
We find them more widely dispersed than the giants, but we can
100"
200"
300"
FIGURE V, i.
Energy distribution in Messier 3. Abscissae, distance from
center in seconds of arc. Ordi nates, left and dots, energy per
surface element in relative units, right and circles, in relative
magnitudes (After Hertzsprung.)
say nothing of their distribution within the central sphere of
ten parsecs diameter, where the crowding of brighter stars
" burns out" the photographs.
An indication of the distribution of brightness in a globular
cluster as a function of distance from the center is given in the
curves of Figures V, i and V, 2, which show for Messier 3 and
Messier 13 the distribution of light over the integrated images,
as determined by Hertzsprung 8 and Hogg, 9 respectively. In
both of these studies efforts were made to smooth out irregulari-
ties due to individual stars. The remarkable linear relation
8 A. N., 207, 89, 1918.
9 H. B. 870, 1929.
ON THE LAWS OF DISTRIBUTION 71
between distance and magnitude in Messier 3 is not found for
Messier 13. The similarity in form of the curves for photo-
visual and photographic magnitudes in Messier 13 is partic-
ularly noteworthy; the curves represent an inner region of the
cluster that is largely excluded from my survey of magnitudes
and colors. 10
If 4
08
12
16
?0
s
i
\
\
1
\
\
\
x
%
^
"^-^Sr
*
FIGURE V, 2.
Energy distribution in Messier 13. Ordmates arc magnitudes,
with an arbitrary zero point; abscissae are minutes of arc,
measured from the center. Circles and broken line represent
photovisual magnitudes; dots and continuous line, photographic
magnitudes
The distribution of light in the out-of-focus image of w Cen-
tauri has been investigated by Schilt, who measured the photo-
graph with a thermopile photometer. 11 He finds that the
measured intensities show a much larger increase of stellar
density toward the center than is revealed by Bailey's counts
10 Mt. W. Contr. 116, 1915.
11 A. J., 38, 109, 1928; Pop. Astr., 36, 296, 1928.
72 DISTRIBUTION OF STARS IN GLOBULAR CLUSTERS
of the brighter stars. 12 Nabokov's 13 study of Messier 13 gave
results closely comparable with those of Hogg.
27. Luminosity Curves for Clusters. Distribution in
absolute brightness as well as in space can be satisfactorily
studied as yet only for the giant and supergiant cluster stars.
Although, as we have seen, the space distribution is not inde-
pendent of the influence of dwarf stars, the fragmentary absolute
luminosity curves have a meaning and a certainty that are
essentially unimpaired by such forced neglect of the dwarfs.
With the use of more powerful telescopes, moreover, especially
on the borders of bright southern clusters in high galactic
latitude, we shall soon be able to extend both the general lumi-
nosity curves and the luminosity curves for specific color classes
to stars as faint as the sun or fainter. In the near future we
should therefore have for the globular clusters much more
satisfactory data on the frequency of luminosities than we now
have for stars of the galactic system.
The labor of determining magnitudes and colors on a satis-
factory photometric basis is so considerable that luminosity
curves will come slowly; for only three globular clusters are the
color and magnitude surveys at all extensive. It is necessary,
therefore, to resort for the time being to general luminosity
curves based on provisional magnitude scales, except for the
giant stars in the three systems for which results are herewith
presented.
a. Frequency Distribution of Giant Stars. Observations for
luminosity curves are listed in Chapter III above for the giant
and supergiant stars of various colors in the globular clusters
Messier 3, Messier 13, and Messier 22. Corrections have not
been made for superposed field stars; probably such corrections
would not materially alter the forms of the luminosity curves. 14
Figure V, 3 shows graphically the combined results from the
three clusters for six intervals of color class redder than fo.
H. A., 26, 213, 1897.
13 Rus. Astr. Journ., i, 109, 1924.
14 See Section 73 below for discussion of the field of Messier 22.
LUMINOSITY CURVES FOR CLUSTERS
73
Stars redder than k5 are grouped together, since the data are
insufficient for Class m alone; for classes b and a the observa-
tional limits of the three catalogues cut off the luminosity curves
so quickly that the plots would not be significant. Probably
Class f also is affected both by the confluence of giant and dwarf
stars and by the magnitude limitations of the catalogues.
The average dispersion is about half a magnitude, which is
probably well in excess of the observational errors.
TABLE V, I. COMPOSITE LUMINOSITY CURVE or MESSIER 3, MESSIER 13,
MKSSILR 22
Absolute
Color Class
All
Photovisual
Magnitude
All
Colors
fo to fs
f$ to go
go to gs
gS to ko
ko to ks
>k S
-4 oto -3 5
I
I
I
3
-3 5 to -3 o
i
I
II
13
3 o to 2 5
2
5
13
18
38
2 5 to 2 o
i
I
5
16
II
5
39
2 O tO I $
i
7
34
32
6
2
82
i 5 to i o
8
24
28
3^
4
I
97
i o to o 5
18
85
/i
20
i
195
o 5 to o o
103
136
73
7
i
320
o o to +o 5
9i
132
44
5
i
273
+o 5 to +i o
38
3i
8
i
78
+ i o to + 1 s
85
3i
i
117
Totals
346
449
264
1,255
The coordinates of the mean luminosity curves are given in
Table V, I. The tabulated quantities have been determined
directly from the color-magnitude arrays (not from the original
catalogues of magnitudes and color). Distance moduli used
for reduction from apparent to absolute photovisual magnitudes
are taken from Appendix A. The absolute photovisual magni-
tude limits of the catalogues are +0.4 for Messier 22, +0.5
for Messier 13, and +1.6 for Messier 3. The curves in Figure
V, 3 and the numbers in Table V, I are therefore without much
meaning fainter than M pv = +0.5. The preliminary maximum
at o.o for interval fo to f5 is probably related to the humps in
the general luminosity curves of these three clusters (Figure
74
DISTRIBUTION OF STARS IN GLOBULAR CLUSTERS
V, 4), which are caused mainly by an abundance of blue stars
and variables.
Until we have obtained data from other clusters, however,
there is little point in fitting the usual exponential curves to the
observations. Some of the asymmetries may be real in the
magnitudes and disappear in the corresponding curves for total
radiation or masses.
20
u.
kStokO*
P*.
>
120
100
80
60
40
20
f j
"''**
^
^
/
1
\
I I
\. I
\ 1
7
80
40
20
kOtogS
gStogO
A
KOtof
e
1 /
1 I
I I
\l
/
/
/ ^
\
/
V
r
.
\
i
<i
/
L
-
.//
V.
.jj
^
'
-30 -20 -10 00 +10 -30 -20 -10 00 +10
FIGURE V, 3.
Luminosity curves for six intervals of color class, based on colors in
Messier 3, Messier 13, and Messier 22. Coordinates are numbers of
stars and absolute photo visual magnitudes.
b. The Preliminary Maximum. General photographic lumi-
nosity curves based on provisional magnitude scales are given
in Figure V, 4 for eight globular clusters. All the plotted
material except that for N. G. C. 5053 is derived from my work
on Mount Wilson plates. The methods of estimating the
magnitudes and some of the numerical data are published
elsewhere. 15 The curves suggest two general comments,
which are followed below by a few special notes on the individual
clusters.
16 Mt W. Contr, 155, 1917; 175* 1919.
LUMINOSITY CURVES FOR CLUSTERS
75
i. There is a considerable variety in form of the general
luminosity curve, an indication of the impropriety of using any
method of parallax determinations that depends on the form
of only the brightest portion of the general luminosity curve.
50
-fl +2 -2
FIGURE V, 4.
Luminosity curves for eight globular clusters. Ordmates are numbers of stars;
abscissae are photographic absolute magnitudes (approximate).
2. Without exception, all the globular clusters show prelim-
inary maxima, which fall within half a magnitude of the median
magnitude of cluster- type variables, as indicated by the two
76 DISTRIBUTION OF STARS IN GLOBULAR CLUSTERS
heavy vertical lines in Figure V, 4. We have evidence in all
of these globular clusters, though it is not shown graphically
for N. G. C. 5053 and Messier 22, that the general luminosity
curve rises steeply and high for stars fainter than the critical
absolute luminosity near absolute magnitude zero. The
bunching of stars at this particular brightness is probably of
considerable significance in the economy of globular clusters.
The resultant hump in the luminosity curves has possibilities
in the measurement of distance.
3. Details concerning Figure V, 4:
(a) The preliminary maximum for Messier 3 is partially
due to the 150 known variable stars; when the cluster-
type variables are omitted from the diagram we have
the milder and fainter hump shown by the broken
line and small circles. The possible variability of
these "hump" stars has been considered above in
Section 23.
(b) For Messier 2, Messier 5, and Messier 15 the variable
stars have not been excluded, but they are not suffi-
ciently numerous, even in Messier 5, to contribute
much to the very conspicuous preliminary maxima.
(c) The somewhat fragmentary luminosity curve for
N. G. C. 5053 is derived from data published by
Baade, 16 with variables excluded.
(d) The preliminary maximum for Messier 13 is built
up largely by stars of small or negative color index;
the cluster has no definitely recognized cluster-type
Cepheids.
(e) For Messier 68 the two luminosity curves result from
stars in different selected areas, measured on two
plates. The curves are in fair agreement; a second
preliminary maximum at M = +1.4 is suggested.
(/) The fragmentary luminosity curve for Messier 22
is based on an unpublished catalogue, prepared at
Harvard from my Mount Wilson photographs. The
16 Hamb. Mitt., 6, No. 29, 1928.
LUMINOSITY CURVES FOR CLUSTERS 77
wide displacement of the maximum from absolute
magnitude zero suggests that the correct distance may
be 10 to 20 per cent larger than that given in Appendix
A; but further work on magnitudes of the fainter
stars is necessary before anomalies of the luminosity
curve can be taken seriously.
CHAPTER VI
THE FORMS OF GLOBULAR CLUSTERS
THE perfect sphere the form once commonly held to be an
essential attribute of celestial bodies is, according to observa-
tion and competent theory, a thorough illusion. There is
exceedingly small chance of null rotation, and rotation is the
end of sphericity. Oblateness, prolateness, and ellipsoidicity
characterize planets, stars, nebulae, and galaxies. We now
find that even the globular clusters belie their name. In a
universe of moving particles the conception of the perfect figure
vanishes with the growth of precision in measurement and
attentiveness to detail.
Passing reference has been made in preceding pages to the
ellipticity of globular clusters; Chapter VII will describe the
irregularities of various sorts in the apparent forms of galactic
clusters. The present chapter considers in some detail the
deviations from circularity in the photographic images of globu-
lar clusters. The non-circular images imply, of course, devia-
tions of the clusters themselves from sphericity.
28. Definitions and Difficulties. The term "ellipticity"
may be used in two senses, which are found to be practically
equivalent:
1. On photographs, especially those of small scale, the inte-
grated images of many globular clusters appear symmetrically
elongated the images are oval or elliptical.
2. In detailed star counts the density (number of stars)
at various distances from the center is systematically greater
along one axis of the projected image than along any other.
Both of these phenomena can be explained most naturally
by assuming that the clusters are oblate; that is, the gradient
78
DEFINITIONS AND DIFFICULTIES 79
of the space density of the stars differs in different directions
from the center and is usually symmetrical about a polar axis
and an equatorial plane. Probably the forms of the integrated
photographic images are related as directly to star density as
are the counts.
The ellipticity can be described in other terms, and possibly
other explanations of the observed forms and star counts might
be suggested; but in this chapter the foregoing interpretation
will be adopted. Flattening may be a consequence of the rota-
tion of the cluster or, in accordance with the theoretical work
of Jeans, 1 a result of the encounter of the cluster with another
stellar system; or both modes of deformation may be involved,
especially in clusters which show irregular elongation.
It is difficult to determine the actual bounds of a globular
cluster along various radii, or even the limits of the projected
image, because of
1. The unknown and possibly peculiar density laws in differ-
ent directions for a flattened stellar system.
2. The confusion with foreground stars.
3. The present lack, near the edges of individual clusters, of
sufficiently long exposures, made with large reflectors.
The planes of symmetry in globular clusters may be likened to
the galactic plane. Their discovery and measurement, however,
is sometimes difficult. Three factors are involved in their detec-
tion (i) the degree, (2) the orientation, and (3) the nature of the
oblateness of figure which is revealed by the elliptical images.
1. The ratio of the shortest diameter to the longest may be
near unity, so that only refined study, whatever the position
of the observer in space (in or out of the cluster), would be able
to detect the oblateness.
2. The cluster may be so oriented in space (polar axis nearly
parallel to line of sight) that whatever the ratio of its major
and minor axes the discovery of oblateness is impossible.
3. The absolutely brighter stars that enter our surveys may
not show the oblate form, the property of concentration toward
1 M. N. R. A. S., 74, 109, 1913; 76, 552, 1916; 82, 132, 1922.
8o THE FORMS OF GLOBULAR CLUSTERS
a plane being confined to the fainter stars. This consideration
is very relevant. In our galactic system the naked-eye stars
of the later spectral classes show practically no galactic con-
centration. In globular clusters the brightest stars, which
through their arrangement have given the name " globular"
to the systems, are also mainly giants of the redder spectral
classes.
In some of the brightest and most thoroughly studied globular
clusters Messier 13, Messier 22, w Centauri the ellipticity
is most pronounced. It is surprising, therefore, that the con-
spicuous elongation of globular clusters should have gone so
long undiscovered. Except for Bailey's star counts, 2 which
showed irregularities in the distribution of the brighter stars
for a few globular clusters, nothing very definite was known
of the important fact of deformation until the systematic star
counts on Mount Wilson photographs were analyzed. 3
Bailey's counts, like the earlier visual and photographic
inspections, generally dealt with but one or two thousand stars
in each cluster. The underlying ellipticity, although not
confined wholly to the faint stars, usually becomes evident
only when large numbers of stars are considered. But the
numerous faint stars frequently make their presence known
en masse as well as in detailed counts, so that the diffuse inte-
grated images of clusters can be used to study cluster forms
even if few or no individual stars are shown. The counts,
however, are frequently more searching. For example, in
Messier 13, described below, the Harvard plates do not show, on
inspection, the ellipticity revealed by the counts; they indicate,
if anything, a slight elongation in a direction 45 from the
major axis. The same is true of some other clusters. When
an integrated image is clearly elliptical, the numerical ellipticity
shown by star counts is very large. In a condensed cluster,
the Eberhard effect and other difficulties may interfere seriously
with the determination of the frequency of stars as a function
2 H. A., 76, No. 4, 1915-
8 Pease and Shapley, Mt. W. Contr. 129, 1917.
THE ELONGATION OF MESSIER 13
81
of the distance from the center; but errors arising from such
sources do not affect measures of the major axis of the cluster.
29. The Elongation of Messier 13. Among the various
globular clusters whose forms were investigated by the writer,
partly in collaboration with Mr. Pease, Mrs. Shapley, and Miss
Sawyer, the Hercules cluster, Messier 13, best illustrates the
nature of the ellipticity throughout a wide range in magnitude.
The stars in Messier 13 were counted on nine plates, and
the results arranged for analysis in a framework of 12 equal
radial sectors and a series of concentric rings. 4 The plates are
of various exposure times, ranging from one minute to five
hours. The counts of the total number of stars in each of the
12 equal sectors show the amount of ellipticity and its change
with magnitude. The counts for each of the zones between
concentric circles show how the degree and direction of ellip-
ticity varies with distance from the center of the cluster.
In Table VI, I the numbers of stars are given for six different
plates for each sector separately, but with the zones not differ-
entiated. For the two photographs of longest exposure Table
VI, II again gives the number of stars in different sectors but
divides the material into four zones for each plate. The central
regions are too much burned out to be included in the star counts.
Three figures illustrate the evidence, derived from these star
counts, for the ellipticity of Messier 13: Figure VI, i shows for
TABLE VI, I. ELLIPTICITY FOR DIFFERENT EXPOSURES IN MESSIER 13
1 s
TjIS
Numbers of Stars in Sectors
ri
o S5
15
45
75
105
135
165
195
225
255
285
315
345
m
6
5,800
163
149
211
235
214
213
154
154
174
2 S 6
235
198
15
7,700
296
264
433
396
420
314
284
230
259
401
309
305
22
14.150
734
672
744
859
814
638
569
583
684
825
852
738
37 5
16,600
749
770
913
1, 008
1,026
853
779
804
974
I, Oil
963
763
94
25,000
I,26l
1,340
1,475
1,590
1,580
1,431
1,338
1,343
1,486
1,590
1,580
I,36i
300
30,000
1,126
1,234
1,254
1,416
1,463
1,232
1,079
1,085
1,187
1,300
1,368
1,258
* Ibid.
82 THE FORMS OF GLOBULAR CLUSTERS
TABLE VI, II. ELLIPTICITY AND DISTANCE FROM CENTER IN MESSIER 13
(Results from Two Plates)
Number of Stars in Sectors
Distance
Center
iS
45
75
105
135
165
195
22 S
255
28 S
315
345
2 to 4
623
668
750
762
764
728
712
683
758
778
7 l8
670
4 to 6
358
36i
423
464
476
386
330
352
402
438
479
394
6 to 8
!68
207
212
236
226
2O2
188
194
214
2 4 8
249
198
8 to 10
112
104
90
128
114
"5
108
114
112
126
134
99
3 to 5
560
640
624
684
788
642
586
597
629
658
712
662
S to 7
362
374
410
471
431
360
302
292
358
396
424
394
7 to 9
2O4
220
22O
261
244
230
191
196
2OO
246
232
202
9 to ii
141
136
116
118
130
I2 9
131
124
130
IS7
134
IOO
100
800
1000
1300
1300
1100
X
90
180
Degrees
X
X
33
FIGURE VI, i.
Axis of symmetry of Messier 13, shown by frequency curves for
five plates Coordinates are numbers of stars and position
angles.
five plates frequency curves which permit the determination of
the position angle of the major axis of the cluster; Figure VI, 2
gives the amount and position angle of the elongation at differ-
THE ELONGATION OF MESSIER 13
ent distances from the center; Figure VI, 3 shows the relation
of the blue stars to the plane of symmetry. 5
To summarize the results derivable from these tables and
figures:
a. The cluster is conspicuously elongated, showing approxi-
mately 25 per cent more stars in the direction of the major
axis than in the direction perpendicular thereto.
300
100 1 -
ft 1 to 5'
7' to 9'
\
15
75
135
255
315
15
195
Degree.
FIGURE VI, 2.
Elhpticity of Messier 13 for different intervals of distance
from the center Ordmates are numbers of stars, and
abscissae are position angles.
b. The elliptical distribution appears in all magnitudes from
the thirteenth to the twentieth and fainter, though it is rela-
tively inconspicuous for the stars brighter than the fifteenth
magnitude. The ellipticity also shows throughout the cluster
from center to edge.
c. A close analogy with phenomena of galactic concentration
in our own stellar system is the decided preference shown by the
6 Shapley, Mt. W. Comm. 45, 1917.
8 4
THE FORMS OF GLOBULAR CLUSTERS
cluster stars with negative color indices for the sectors contain-
ing the major axis (Figure VI, 3). The Cepheid variables in
the cluster also lie near the major axis.
30. Ellipticity of Globular Clusters. Over half a million
stars have been counted in the course of the Mount Wilson and
Harvard studies of the forms of globular clusters. By means of
star counts the position angles of the major axes have been
found for 12 systems, and evidence of approximate circularity
or asymmetry adduced for a few others. 6 Direct estimates of
+4U
+20
-20
-40
A
A
/
/-
\ ~~
>.
/
s''
--/
^
x
\
/
^'
\
) 30 60 90 120 150 30 60 9(
Degrees
FIGURE VI, 3.
Relation of blue stars in Messier 13 to plane of symmetry. Full
line ani circles refer to stars of negative color index; broken line
shows the distribution of 10,000 stars between magnitudes 17
and 19. Coordinates are percentage deviations from the mean
number of stars and angles of direction from the center.
the position angles for the integrated images of most of these
clusters are found to agree closely with those determined from
the laborious counts; hence, further surveys of the forms have
been made with only the direct estimates of ellipticity on small-
scale plates. The work is described in the present section, and
the chapter ends with a section dealing with a number of sys-
tems on which special studies have been made.
a. C0mte and Estimates. In the first systematic study of
the forms of photographic images of the globular clusters,
results were obtained for 41 systems all that were bright
enough for satisfactory examination on the Franklin-Adams
8 Shapley, H., and Martha B. Shapley, Mt. W. Contr. 160, 1918.
ELLIPTICITY OF GLOBULAR CLUSTERS
star charts. 6 For 30 of the clusters the elongation seemed
sufficiently definite to justify a computation of the inclination
of the major axis to the galactic circle. For the brighter clus-
ters, for which counts of individual stars had been made on
Mount Wilson plates, we compared the estimates of the
position angles of the major axes with those derived from
the counts.
TABLE VI, III. COMPARISON OF COUNTS AND ESTIMATES
N G C
Messier
Position Angle of Major Axis
Counts
Estimates
Difference
o
5024
S3
1 60
170
IO
5U9
105
1 2O
-15
5272
3
Asym.
Asym.
SQ04
5
55
50
+5
6121
4
US
Ind.
6205
13
125
130
-5
6266
62
75
65
+ 10:
6273
19
15
15
o
6402
14
no
70
+40.
6626
28
50
45
+5
6656
22
25
25
7078
15
35
20
+ 15
7089
2
135
ISO
-15
The difference in position angles determined by the two
methods appeared satisfactorily small for these brighter clus-
ters, but a later investigation, 7 made on Harvard plates, shows
that for the faintest clusters the estimates of the direction of the
axis are less certain than was believed from the study of the
Franklin-Adams charts.
b. Orientation of Major Axes. The ellipticity and orienta-
tion given in columns 13 and 14 of Appendix A are based on the
newer Harvard investigation, except for starred values which
are taken from the earlier Mount Wilson counts. The ellip-
7 Shapley and Sawyer, H. B. 852, 1927.
86 THE FORMS OF GLOBULAR CLUSTERS
ticity is expressed as ten times the ratio of the minor to the
major axis. The orientations, with respect to the galactic
circle, are given only for those 39 clusters where the ellipticity
is 8 or less, or if 9, only when the orientation could be certainly
determined. 8 The orientation with respect to the galactic
circle is reckoned from the "galactic east" (direction of increas-
ing longitude) through the "galactic south"; negative angles
consequently indicate reckoning from the east in the opposite
direction.
c. Inclination to Galactic Circle. The data bearing on the
relation of the elongation to the plane of the Galaxy are col-
lected for 37 globular clusters in Table VI, IV. (N. G. C.
1866 and N. G. C. 1978, in the Large Magellanic Cloud, are
omitted from the table.) Successive columns are the number,
class, galactic latitude, distance above or below the galactic
plane in kiloparsecs, the degree of elongation, and the inclina-
tion of the major axis to the galactic circle.
Although the estimates here presented are probably better
than any previously made, I feel that they are not of much
significance except in the few cases where the ellipticity is
conspicuous and the orientation angle is given without a colon.
The average deviation of a position angle from the values
determined earlier on Franklin-Adams charts is about 30
an indication of the inherent difficulty of the estimates. Some
of the clusters are definitely asymmetrical. For most of those
not listed in Table VI, IV the deviations from circularity are
small, or the clusters are too faint or too involved in a star
field for useful determinations of form. Future star counts
will probably find the axes not now revealed. Notwithstanding
the difficulties and uncertainties, for all but 18 of the 93 clusters
in Appendix A the degree of ellipticity is estimated.
In the future, attention should be paid not so much to small
and difficult objects as to closer analyses of the distinctly asym-
metrical systems and of the brighter clusters in which the
degrees of ellipticity can be studied with respect to colors and
8 That is, position angles without a colon in H. B. 852.
ELLIPTICITY OF GLOBULAR CLUSTERS
8 7
TABLE VI, IV. ORIENTATION OF GLOBULAR CLUSTERS
N. G. C
Class
Galactic
Latitude
Distance from
Galactic Plane
Degree of
Elongation
Inclination to
Galactic Circle
o
Kpc.
104
III
-45
- 4 8
8
-55
362
III
-47
- 9 4
8
+65
1851
II
-34 5
- 8 i
9
-75
1904
V
-28
- 9 6
9
+ 5
2298
VI
-15
- 6 9
8
+39:
2419
VII
+ 23
+ 11 9
9
-56
2808
I
ii
- 3 i
8
+84
4833
VIII
-8 5
2 2
8
-80:
5024
V
+79
+ 17 9
9
-79
5053
XI
+78
+ 17 o
8
-61
SI39
VIII
+15
+ i 8
8
+30
5272
VI
+ 77 5
+ 11 9
8
+54
5897
XI
+ 29
+ 80
8
-44'
5904
V
+46
+ 7 8
9
+ 16
6101
X
-16
- 5 7
8
+35
6121
IX
+ 15
+ i 9
9
+ 72
6139
II
+ 6
+ 3 i
9
-64
6144
XI
+ i5
+ 48
8
22'
6205
V
+40
+ 66
9 5
-63
6235
X
+ 12
+ 5 9
8
+8 9
6266
IV
+ 7
+ 2 3
8
+ 16
6273
VIII
+ 9
-f 2 6
6
-28
6341
IV
+35
+ 64
8
+ 16
6356
II
+ 9
+ 7 8:
9
-14
6362
X
-18
- 4 7
8
+ 78-
6397
IX
-12 5
I 2
9
+73
6402
VIII
+ 14
+ 48
9
+ 76
6440
V
+ 2
+ I 7:
8
+ 10-
6441
III
- 6 5
2 2
8
+40
6517
IV
+ 6
+ 5 2.
8
- 4'
6626
IV
- 7
2O
9
+ 18
6638
VI
- 7 5
- 3 9
8
-27
6652
VI:
-13
- 5 3
8
ii'
6656
VII
- 9
i i
8
+ 18
6779
X
+ 8
+ 2 8
8
+ 12.
7078
IV
-28
- 6 i
8
+ 11
7089
II
-36
- 8 2
9
-80
magnitudes. From detailed investigations, as von Zeipel has
shown, we may hope to get information on the masses of stars of
88 THE FORMS OF GLOBULAR CLUSTERS
different colors and luminosities, using as criteria of mass the
distribution with respect to the centers and to the hypothetical
galactic planes within the clusters. 9
31. The Relation of Elongation to the Galactic Circle.
The inclination of the axis of Messier 13 to the galactic circle
is more than 60; the inclination of Messier 22 is less than 20.
The former is in high latitude, the latter is the nearest of all
globular clusters to the galactic plane. The question arises
whether or not the galactic system has influenced the orienta-
tion of the globular clusters. In order that the equatorial
plane of a cluster be parallel to the plane of the Galaxy, parallel-
ism of the major axis with the galactic circle is a necessary
though not a sufficient condition. We need to know the true
form, or an equivalent, and get another component of the
inclination, before we can fix the plane of the cluster in space;
at present there is little prospect of measuring the true
oblateness. 10
The estimates of orientation given in Table VI, IV are
admittedly uncertain, but the measures show definitely that
large and small values are scattered throughout all distances
from the galactic plane. There seems to be a slight tendency
in the mean toward smaller values of the orientation for small
values of R sin /3. Thus, we have:
Mean N,,hpr Mean
R sin ft Number Inclination
o
12 3 7 57
77 5 37
6 i 5 43
So 5 34
35 5 53
2.2 5 43
14 5 34
Grouped in order of inclination to the galactic plane, the
same data give:
9 Freundlich and Heiskanen, Zeit. f. Phys., 14, 226, 1923.
10 See discussion by ten Bruggencate, Sternhaufen, 72, 1927.
SEVEN PECULIAR CLUSTERS 89
Mean M..*Ka Mean
Inclination Number R sm ff
o
82 5 75
75 5 4i
62 5 96
46 5 66
28 5 38
17 5 39
10 7 55
The clusters in the direction of the galactic nucleus (X =
327, = o) have lower average inclinations than elsewhere,
according to the following means:
Mean Galactic v,, m K rtr Mean
Longitude Dumber Inclination
o o
39 6 39
203 5 52
277 6 52
308 5 64
321 5 36
33i 5 30
343 5 27
The equatorial planes in the clusters with low inclinations
of course may or may not be parallel to the galactic plane;
those with high inclinations are certainly not parallel.
The class of cluster appears to be unrelated to the inclination
of its axis to the galactic circle. Indeed, we may summarize
this investigation of the orientation of the axes of globular
clusters with the statement that there is no strong evidence
that they are not inclined at random in space.
32. Seven Peculiar Clusters. A few globular clusters that
depart considerably from a spherical form have been investi-
gated. They are of interest in connection with the possible
dissolution of clusters, and especially in considerations of
equilibrium and distribution laws.
a. Messier 62 (N. G. C. 6266). The asymmetry of Messier
62 was particularly noted by Sir John Herschel 11 in 1847,
11 Cape Results, 23, 1847.
90 THE FORMS OF GLOBULAR CLUSTERS
later by Bailey. 12 It is shown numerically in the following
counts based on a Mount Wilson photograph, where numbers
are given for 30 intervals of position angle, a central burned-
out area one minute in diameter being excluded:
Position Angle 15 45 75 105 135 165 195 225 255 285 315 345
Number of Stars 67 56 67 45 35 42 49 56 68 79 72 72
When opposite sectors are combined, the position angle of the
major axis appears to be about 75; the estimated values of the
angle 13 are 70 and 55.
Messier 62 is the most irregular globular cluster. Does
absorbing nebulosity cause its apparent asymmetry? Or
has collision or encounter deformed it?
b. Messier 3 (N. G. C. 5272) and Messier 5 (N. G. C. 5904).*
It is difficult to account for such pronounced and deep-seated
asymmetries in globular clusters as those of Messier 3, Messier
5, and Messier 62. For Messier 3 the distance from other
stellar systems is now, and probably for hundreds of millions
of years has been, extremely great; the galactic latitude is
+7 7. 5. There is no evidence of occulting matter in the cluster
or in front of it that might be responsible for a spurious appear-
ance of irregularity. The measure of asymmetry is illustrated
by the following data, 14 based on the counts of two Mount Wil-
son plates:
Position Angle 15 45 75 105 135 165 195 225 255 285 315 345
Number of Stars 244 234 246 220 198 242 222 282 292 321 303 263
Further work should be done on this cluster, as the counts on
different plates are not wholly consistent.
For Messier 5 we have comparable data from a long-exposure
plate showing 15,000 stars, made by Pease and counted by
Miss Davis, 15 the star numbers referring to a region between
3' and 15' from the cluster's center.
H. A., 76, 74, 1915-
"Mt. W. Contr. 160, 7, 1918; H. B. 852, 25, 1927.
14 Pease and Shapley, Mt. W. Contr. 129, 1917.
15 Shapley and Davis, P. A. S. P., 30, 164, 1918.
SEVEN PECULIAR CLUSTERS
Position
Angle I5
Number of
45 75 105 135 165 195 225 255 285 315 345
Stars
924 1016 972 861 693 783 870 978 1037 955 907 952
The asymmetry revealed by the counts for these three clus-
ters produces a surprisingly minor effect on the general appear-
ance of the clusters on photographs (see Plate I). The
same result enters for the strongly elliptical clusters they
generally appear essentially round (as Messier 13, whose ellip-
ticity is called 9.5 in Appendix A on the basis of its integrated
image), though the counts show from 25 to 100 per cent more
stars along one radius than along another.
c. Messier 19 (N. G. C. 6273).
Figure VI, 4 and the estimated
ellipticities in Table VI, IV show
that Messier 19 is the most elongated
globular cluster so far studied. The
circular coordinates of the diagram
are position angles; the radial coordi-
nates are relative numbers of stars
in each 30 sector. The position
angle of the major axis is 15, and
along this axis there are more than
twice as many stars as along the
minor axis. Photographs show no
evidence of a double nucleus. Since
the galactic latitude is +9, and the
major axis is inclined less than 30 to
the galactic circle, the equatorial plane of the cluster is probably
nearly parallel to the galactic plane.
Considering this extreme example, we conclude that the flat-
tening of clusters is systematically of a lower order than that
of spirals and the galactic system.
d. Messier 22 (N. G. C. 6656). The form of globular clusters
near the galactic plane may have an important bearing on the
relationship of the Galaxy and galactic clusters to the globular
systems. Messier 22, in galactic latitude 9 and one of the
FIGURE VI, 4.
Diagram of star density
Messier 19.
THE FORMS OF GLOBULAR CLUSTERS
nearest globular clusters, is significantly situated for a test of
deformation and the orientation of its central plane. On a
340
290
240
r
s
/
(~-
x
^
f
\
\/
>
w
f
30
90
1DO 210
270 330
FIGURE VI, 5.
Distnbution of stars in Messier 22. Ordmates
are numbers of stars*, abscissae arc position angles
photograph which shows more than 70,000 stars, most of which
are undoubtedly members of the cluster though it is located in
180'
FIGURE VI, 6.
Star density for Messier 22. Radial coordinates
show numbers of stars for 30 intervals of position
angle The unit of scale indicated along the zero
axis is one hundred.
the direction of a rich galactic star cloud, a detailed count has
been made. 16 The photograph shows stars from the twelfth
16 Shapley and Duncan Pop. Astr., 27, 100, 1919.
SEVEN PECULIAR CLUSTERS
93
to the twentieth magnitudes. The ellipticity is very pro-
nounced, as illustrated by the curves in Figures VI, 5 and VI,
6, which refer only to the annulus with internal and external
radii of 3'.6 and 6'.4. Near the center the counts would be
unsafe because of crowding and occultation; too far from the
center the cluster density falls off so that non-cluster stars would
vitiate the count.
The number of stars in the direction of the major axis is
nearly 30 per cent greater than the number along the minor
*w
+30
-30
'*"''X
s*-~~
--
\
/
/,
/
s"
-->
X
\
\
-
f
x
\
/
/
^J
120
150
90
120
150
30
Degrees
FIGURE VI, 7.
The distribution of stars in w Centauri. Ordmates are
percentage excesses along the various radii indicated by the
position angles (abscissae). The full line shows that the
position angle of the major axis for all stars is about 90.
For the variables alone (broken line) the axis is about the
same, but the relative excess is three times as great.
axis. The orientation of 18 and the high ellipticity, which
suggests that we see the cluster edgewise, indicate that it may
lie nearly parallel to the galactic plane.
c. co Centauri (N. G. C. 5139). The 128 cluster-type variables
in w Centauri appear to lie preferentially along the equatorial
plane of the system. Table VI, V and Figure VI, 7 illustrate
this remarkable distribution. 17 The data are obtained from
a Harvard plate, which shows the ellipticity for all distances
from the center.
The numbers of variables in opposite sectors are combined
in making the diagram. The relative amplitudes of the two
17 Mt. W. Comm. 45, 1917.
94
THE FORMS OF GLOBULAR CLUSTERS
TABLE VI, V. DISTRIBUTION OF 5,000 STARS IN w CENTAURI
(Results from Two Plates)
Number of Stars in Sectors
Width
of Zone
Mean
IS
45
75
IOS
135
I6 S
195
22 S
255
285
3IS
345
3 to 6
148
129
i$i
182
165
159
164
173
203
182
198
163
168
6 to 9
84
89
I5i
142
139
H3
105
H9
IS3
163
125
II?
125
9 to 12
66
81
96
74
64
79
64
68
88
97
74
68
77
12 tO 15
44
54
61
61
57
57
40
59
57
59
Si
45
54
.
260
i6
280
9 to 15
no
135
157
135
121
136
104
127
145
156
125
H3
130
3 to 15
342
353
459
459
425
408
373
419
Soi
501
448
393
423
Vari-
ables
8
6
17
12
9
5
2
16
ii
17
16
9
ii
curves show that the variables are three times as condensed
toward the supposed plane of symmetry as the stars in general,
and the latter exhibit such strong ellipticity that w Centauri
is easily seen to be elongated on all photographs.
/. Messier 15 (N. G. C. 7078). A series of long-exposure
photographs on the edges of Messier 15 show that as far from
the center as 15', corresponding to a linear distance of 200
light years and quite outside the limits usually seen on the
best photographs, the elongation of this cluster is in general
agreement with the results obtained for the central region, both
in direction and amount. 18 The stars involved in the extension
are extremely faint, and their frequency is, of course, relatively
low.
18 Pease and Shapley, Mt. W. Comm. 39, 5, 1917; Mt. W. Contr. 129, n, 1917;
Heckmann and Siedentopf, Gott. Verdff. Heft 6, 1929.
CHAPTER VII
THE STRUCTURE OF GALACTIC GROUPS
TURNING from the smooth and symmetrical globular clusters
to the typically irregular galactic groups, we note at once their
strong contrasts. The galactic clusters are of various forms.
The Pleiades suggested to the constellation makers Seven
Virgins, or perhaps a Hen with Chickens; Praesepe was the
Manger or the Beehive; the Hyades outlined the Face of the
Bull. It does not take a lively imagination, however, to recog-
nize the diversity and looseness which prevail in galactic clus-
ters, while symmetry and central compactness characterize
the globular systems.
The irregular boundaries make difficult the determination
of the diameters and forms of galactic clusters; they are not
easily untangled from the rich and fortuitously irregular star
fields in which frequently they are embedded. Nevertheless,
from star counts, studies of spectra, and measures of motion,
it is possible to deduce the extent and form of a fair proportion
of those now catalogued. In the following pages some of the
more significant results are reported. A consideration of the
distances of galactic clusters appears in Chapter XI, and of
anomalies in their distribution in Chapter XIV; their numbers,
classification, and distribution on the surface of the sky and
data on their spectral composition have been taken up in Chap-
ters II and III.
33. Elongation of Galactic Clusters. A cluster of
stars moving through a galactic field necessarily experiences
transformation. It is affected both by encounters with individ-
ual stars and by the deforming forces of the whole galactic
system. Jeans has shown that theoretically the form of a
95
96 THE STRUCTURE OF GALACTIC GROUPS
cluster at any time will depend upon its density and the length
of time it has been bombarded by members of the star field
which it penetrates. 1 The galactic clusters (again in contrast
with the globular clusters) are in low galactic regions where
they are necessarily undergoing continuous perturbation.
The observed irregularities of a cluster are therefore attribu-
table not only to the chance arrangement of its relatively small
population at a given time but also to various gravitational
transformations and to the inevitable loss of individual stars.
We naturally seek for evidence of some systematic effects
of such changes in the orientation of the galactic groups.
a. Only for the comparatively rich and compact galactic
groups is it possible to estimate the orientation, and even for
them the degree of elongation cannot be determined with suffi-
cient precision to be useful. The loose systems classes a, b,
and c are generally of too indefinite size and membership to
show significant boundaries. In the eighth column of the new
Harvard catalogue of galactic clusters (Appendix B) are mean
values, from two independent estimates, of the orientation,
with respect to the galactic plane, of the major axes of 57
objects. Twenty-four other clusters, of comparable richness
and symmetry, were examined and the orientation found to be
indeterminate (marked by "Ind" in the eighth column). The
two independent measures of the orientation agree surprisingly
well, and there is no doubt that for most of these clusters the
apparent elongation is correctly observed; but it is also possible
that occasionally superposed non-cluster stars may be respon-
sible for the appearance of elongation.
b. Of the 8 1 clusters suitable for examination 70 per cent show
measurable orientations. It is therefore appropriate to con-
clude that all are elongated, many so oriented as to avoid
detection. This is probably true, also, of both the loose groups
and faint clusters for which no measurements were attempted.
c. The orientations of the major axes of the galactic clusters
are best shown by Figure VII, i, where lines representing the
1 M. N. R. A. S., 82, 132, 1922.
ELONGATION OF GALACTIC CLUSTERS
97
directions of the major axes are plotted on an equatorial system
of coordinates on which the galactic circle is also drawn. The
mean value of the inclination is 44. The numbers of clusters
in successive 10 intervals of inclination, beginning with o
to 10, are 6, 8, 4, 7, 10, i, n, 6, 4.
d. Taken as a whole, the 57 clusters appear to be oriented
at random, within the uncertainty of the determinations. In
points of detail, however, we see that the average inclination
to the Galaxy differs from place to place, so that in some regions
the clusters appear to be mainly aligned with the galactic circle,
/ ~- "V.\
/--'.:,._.:; -7iir\\\'
FIGURE VII, i.
Orientation of major axes of galactic clusters, plotted on equatorial coordinates.
The black line represents the galactic circle. Dots show positions of clusters
for which no elongation is found.
in others, oriented approximately at right angles. The latter
condition is found, for example, in the clusters in Cassiopeia
and Perseus; in the opposite part of the sky, in the direction
of the galactic center, appears a decided tendency to parallelism
with the galactic circle. The mean orientation for intervals
of galactic longitude (Table VII, I) further illustrates the irregu-
larity but shows that we probably have little more than a ran-
dom distribution of inclination. The two high values at the top
of the table refer to the Cassiopeia-Perseus group of clusters,
and the last two entries to those in Sagittarius and Scorpio.
THE STRUCTURE OF GALACTIC GROUPS
TABLE VII, I. LONGITUDE AND INCLINATION
Mean
Galactic
Longitude
Number of
Clusters
Mean
Inclination
o
82 6
S
o
60
128 o
S
55
156 5
S
33
183 5
5
42
201 7
S
44
217 9
5
50
242 2
6
30
279 I
5
62
302 3
5
53
322 3
S
3i
337 6
6
33
TABLE VII, II INCLINATION AND DISTANCE FROM GALACTIC PLANE
Mean
R sin ft
Number of
Clusters
Mean
Inclination
Mean
Inclination
Number of
Clusters
Mean
ft sin ft
6 77
5
45
80
7
69
425
5
38
70
5
203
265
5
47
66
4
167
196
5
34
59
7
279
143
5
5i
47
5
215
100
5
52
40
5
131
62
5
47
29
6
281
30
5
39
18
5
175
17
6
53
12
4
222
6
6
47
4
4
108
e. The lack of correlation between orientation and distance
from the galactic plane is illustrated in Table VII, II for the
52 clusters with definite values for inclination and R sin ft.
The distances are expressed in parsecs.
The values of R sin ft depend on preliminary estimates of the
distances of galactic clusters. In means, however, they should
be sufficiently dependable for the comparison with the
inclinations.
"SHOULDER" EFFECT IN MESSIER 67
99
34. The "Shoulder" Effect in Messier 67 and Else-
where. In spectral composition Messier 67 appears as a third
type of galactic cluster, differing fundamentally from the
Pleiades and Hyades models. 2 Its colors and magnitudes were
the first to be systematically investigated in the Mount Wilson
work on open clusters. Not only was the relation of magnitude
to color found to differ from that in globular clusters, the
Pleiades, and the Hyades, but also a peculiarity in the distribu-
tion of its stars was brought to light. 3
TABLE VII, III. AVERAGE STAR DENSITY, PHOTOGRAPHIC MAGNITUDE, AND
COLOR INDLX IN MESSIER 67
Distance
from Center
Number
of Stars
Area
in
Square
Minutes
Number Stars
per Square
Minute
Av Pv
Magni-
tude
Average
Color
Index
Number of Stars
Background
Cluster
00-25
35
19 6
I 7 8
12 49
+i oo
6
29
25-45
64
44 o
i 45
12 85
+ i oo
13
51
45-65
49
69 i
o 71
12 52
+0 91
21
28
65-85
30
94 3
o 32
13 03
+o 81
28
2
8 5-10 5
34
119 5
o 28
13 06
+o 82
36
(-2)
10 5-1 i 5
20
69 i
o 29
13 ii
-ho 80
21
(-0
Total
232
125
107
A summary of the average star density, photovisual magni-
tude, and color index is given for 232 stars in Table VII, III.
There is no decrease of star density or change of average magni-
tude or color, outside a circle of 6'.s radius about the center
of the cluster, but inside that circle the density, brightness,
and redness of the stars increase towards the center. The
number of cluster stars, contained in the last two columns,
are obtained by assuming that the constant density outside the
circle of radius 6'.5 refers to the background or foreground stars.
The results indicate that less than half the measured stars
belong to the cluster and that even within a radius of 6'.5 from
the center, 27 per cent are not members of the system.
1 Chapter II, Section 4; Trumpler, P. A. S. P., 37, 316, 1925.
3 Shapley, Mt. W. Contr. 117, 1916.
100
THE STRUCTURE OF GALACTIC GROUPS
Although it seems conclusive, from this table, that the cluster
is composed of about 100 stars scattered over an area of radius
6'. 5, further study indicates that the evidence is misleading.
The background density, deduced from the table as 0.3 stars
per square minute, is nearly ten times as large as would be
expected for the galactic latitude and photovisual magnitude
concerned. This condition suggests that the cluster with
radius 6'. 5 is merely a well-marked nucleus of brighter and
redder stars in a much larger system. To test the matter
further, counts were made on Wolf-Palisa photographic charts
of all stars within a degree of the center of the cluster. From
this material, shown in Table VII, IV, it appears at once that
TABLE VII, IV. COUNTS OF STABS NEAR MESSIER 67 ON WOLF-PALISA CHART
40-
8
44-
8*48*
Means
o
+ 11 6
8
12
7
IO
9
ii
IO
8
19
12
IO
12
II
IO
IS
8
IS
IO
IS
7
10
10
10
7 13 12
10 S 9
10 6 12
6 13 14
II 8 9
7
12
7
13
I A
7
12
8
6
16
IS
12
13
IO
18
14
9
10
9
9 7
10 8
IO I
10 6
12 6
12
14
17
14
14
20
23 16 16
IS
ii
9
IO
14 7
+ 12 8
II
13
9
12
7
II
II
8
12
IS
U
II
IS
9
7
7
6
6
18
12
II
9
M
14
13
23
9
14
14
38 +
29
36
24
19
12
40+ 42+ 9
80+ 80+ 36
45+ 50+ 21
24 19 17
8 13 II
9 17 7
IS
13
IO
IS
10
6
8
6
9
14
22
IO
IO
6
6
ii
10
IO
8
6
IS
16 2
25 I
19 o
13 7
12 O
10 8
+ 13 18
9
M
ii
13
12
IS 5 U
3
9
6
ii
10 6
"Meanslio 2 ii 2 ii 8 I2~ 2 ij 5 18 8(22 2 22 i 14 3 10 8 10 6 9 7) 92
I I J i
the cluster extends far beyond the limits of the plates used for
the magnitude work. The real diameter may be as much as
one degree. Beyond 15' or 20' from the center the ratio of
background stars to cluster stars becomes large.
If the system of Messier 67 is roughly spherical in form, the
space occupied by the nucleus is about a hundredth of the
total volume of the cluster. The total membership is approxi-
mately 500 stars between photovisual magnitudes 10 and 15,
but only the central concentration of 150 stars would attract
attention in an ordinary survey of clusters. Without the
nucleus the slightly concentrated residue might long have
escaped discovery. Further research is needed to determine
ADDITIONAL REMARKS ON GALACTIC CLUSTERS 101
.04
\>2
n
S~-
^s
/^
S^
o 100 140 ja
FIGURE VII, 2
the number of cluster stars fainter than magnitude 15 and
their distribution in space; present evidence indicates that
such stars may be totally absent.
The "shoulder" effect found for Messier 67 appears to be
rather common among galactic clusters and is a characteristic
of high significance in their relation to the development of the
Galaxy. In a preliminary os
study of several clusters,
beginning in 1918, Trumpler
found a shoulder effect for the
Pleiades, Praesepe, and h
Persei. 4 It has later appeared
in studies of Messier n,
Messier 37. and other galactic Relatlon of radius to magnitude for h
. . Pcrsei Ordmates are distances from
Clusters and IS analogous, per- the center in degrees; abscissae, photo-
haps, to the wide scattering of graphlc ma ^ ltudes - < From Trum ^ r >
faint stars shown in studies of the globular clusters. Messier
1 1 may be but a nucleus of the Scutum cloud.
The dimensions of galactic clusters are much larger than
they appear at first to be. From his studies of the distribu-
tion of faint stars in the vicinity of the Pleiades, Praesepe,
and h Persei, Trumpler derived extreme diameters of 6, 6,
and i, respectively, and observed, also, that the brighter
stars are concentrated in the nuclei. A gradual change of
radius with magnitude (outside the nucleus) is shown for h
Persei in Figure VII, 2, based on data accumulated by van
Maanen and Trumpler. For the Pleiades and Praesepe the
" shoulder" effect appears to be more pronounced there is
a sharper contrast between nucleus and surrounding field.
35. Additional Remarks on Galactic Clusters. Investi-
gations now under way at the Lick and Harvard observatories
and elsewhere will soon add so effectively to our knowledge
of the structure and luminosity curves of galactic clusters
that a complete summary of the numerous recent special investi-
4 Allegheny Publ., 6, No. 4, 1922.
102
THE STRUCTURE OF GALACTIC GROUPS
gations is inappropriate in this place. Attention may be
called briefly, however, to a few studies which are indicative of
the considerable activity in this field. References to the
literature are given in Appendices C and D.
a. Messier 37. Von Zeipel and Lindgren have made valuable
contributions to the study of magnitudes and distributions in
the rich galactic system Messier 37. From the space distribu-
tion for different magnitudes and colors they have determined,
by the ingenious method devised by von Zeipel, the approximate
TABLE VII, V. LUMINOSITY CURVES FOR VARIOUS COLOR CLASSES IN
MESSIER 37
Color Classes
Limits of
Magnitude
b
a
f
g
k
m
]ll O
o
2
o
o
o
o
II O-ll 5
o
4
I
i
o
o
ii 5-12 o
12
o
5
o
o
12 0-12 5
7
21
o
10
o
o
12 5-13
8
18
o
i
o
o
13 0-13 5
20
16
3
o
i
13 5-i4 o
5
37
2
o
o
14 o-H 5
3
29
7
I
o
14 S-iS o
i
iQ
16
3
I
o
[iS o
2
3
9
I
o
mean masses of the stars of various spectral classes. The
method has been applied by Wallenquist to other galactic
clusters, and Freundlich and Heiskanen have attempted to
apply it to globular clusters, where, however, the available
data were found to be as yet too incomplete.
The data of von Zeipel and Lindgren on luminosity curves
for various color classes are given in Table VII, V. Tabulated
quantities are numbers of stars. Incompleteness at the fainter
magnitude limit is evident, but the results are definite in fur-
nishing the complete luminosity curve for color classes b and
g (giants) and in showing the significantly wide dispersion for
stars of color class a. The double maximum of the luminosity
ADDITIONAL REMARKS ON GALACTIC CLUSTERS 103
curve for Class A stars has been noted as a possible means of
estimating parallaxes. The method must be used with caution,
however, because of possible confusion with chance irregularities
when only small numbers of stars are considered.
b. Foundation for Proper Motions. Kiistner and Chevalier,
among others, have made accurate modern catalogues of posi-
tions in several galactic clusters. As a basis for future analyses
of proper motions, this work is of high importance, since reliable
measures of motions may soon be forthcoming for those galactic
clusters that are relatively bright and near; for globular
clusters the prospect is practically hopeless. The catalogues
of position also contain photographic magnitudes based on the
international standards.
c. Star Colors. Photographic and photo visual magnitudes
of stars in Messier 35, Messier 36, and other northern clusters,
as determined by Wallenquist, are appearing in a series of
papers. The results afford material for the discussion of bolo-
metric magnitudes, luminosity curves, density laws, and prob-
able mean masses, as well as star colors.
d. The Shapes of Moving Clusters. The structure of well-
known moving clusters and streams of stars, such as the groups
in Taurus, Ursa Major, Scorpio, and Perseus, has been treated
in some detail by B. Boss, Kapteyn, Eddington, Ludendorff,
Hertzsprung, Bottlinger, and especially by Rasmuson, from
the standpoint of measured motion. The group motions are
essentially parallel to the galactic plane. Rasmuson shows
that the Perseus and Ursa Major clusters are flattened at right
angles to the direction of motion, the Scorpio group is flattened
parallel to the galactic plane, and the Hyades cluster is nearly
spherical. These results on cluster forms are relevant to the
investigation of the orientation of galactic clusters, reported
in Section 33. The approximate sphericity of the Hyades had
been previously noted by L. Boss, and Turner first noted the
flatness of the Ursa Major system.
e. N. G. C. 7789. An investigation, made by Miss Mayberry
and the writer, of the luminosity distribution of 5,000 stars
104 THE STRUCTURE OF GALACTIC GROUPS
TABLE VII, VI. STAR COUNTS FOR N. G. C. 7789
Photographic Magnitude Interval
<i6
16-17
17-18
18-19
10-20
Total
Cluster Stars
Field Stars
347
592
2IO
2 5 6
155
666
266
1,178
126
i,47S
1,104
4,167
Ratio
59
o 82
o 23
o 23
o 09
in the faint northern cluster N. G. C. 7789 has shown that in
this cluster, as apparently in many others, the ratio of the
number of cluster stars to the number in the field soon begins
to decrease with decreasing brightness (Table VII, VI). 5
Apparently, most of the cluster stars have magnitudes between
15 and 19. It is well to observe, however, that this rapidly
decreasing ratio does not mean the total absence of dwarf
stars from the cluster, or even their relative scarcity. The
increase in the number of field stars is probably but an indica-
tion of depth of field and the narrow space limits of the cluster.
The additions to the field at any given apparent magnitude
can be of varied luminosities; but additions to the cluster
membership must be of specified absolute magnitudes.
8 Mt. W. Contr. 190, 7, 1920.
CHAPTER VIII
ON THE VELOCITY OF LIGHT
THE astronomical determination of the absolute speed of
light in vacua has not been attempted in recent years because of
its inaccuracy compared with measurements in the terrestrial
laboratory where the work is subject to control and the reduc-
tion from atmospheric pressure to vacuum is simple and certain.
The early procedure has, indeed, been reversed. The labora-
tory value of the velocity of light is adopted, and on this basis
the eclipses of Jupiter's satellites, which were the first recognized
indicators of the finite speed of light, serve now in the researches
on masses and motions in the Jovian system. 1
The classical laboratory method foreshadowed by Galileo
and brought to the practical stage by Fizeau 2 and Cornu, 3
and the one attempted by Wheat stone, 4 which was developed
by Arago 5 and Foucault, 6 were followed by the researches of
Newcomb and Michelson. In 1905 the velocity of light was
known with an accuracy of about 50 kilometers a second, or
0.000167 per cent. In 1924 the problem was taken up anew
at Mount Wilson, under Michelson's skilful supervision. 7
The velocity is now placed at 2.99796 X io 10 centimeters a
second. An accuracy to within 2 kilometers a second seems to
be attainable.
In comparison with the laboratory accuracy, the astronomical
measures, which depend on the diameter of the earth's orbit
1 Sampson, H. A., 52, Part 2, 1909.
2 C. R., 29, 90, 1849-
3 Paris Obs. Annals, 13, 1876.
4 Phil. Trans. Roy. Soc., 1834, 583.
6 Annuaire du Bureau des Longitudes, 1842, 287.
C. R., 30, 551, 1850; 55, 501, 792, 1862.
7 Mt. W. Contr. 329, 1927.
106 ON THE VELOCITY OF LIGHT
and the times of beginning and end of eclipses, have been of
little value. There is, in fact, little prospect of determining
accurately the absolute speed from astronomical measurements,
but there is a preliminary test for the relative speed of light of
different colors that can be made through the study of eclipsing
stars; and by means of globular clusters an exceedingly accurate
determination of the relative speed is possible, independently
of the actual speed of light.
In these tests of the dependence of speed on wave length,
which are of some importance in considering the nature of radi-
ation, advantage is taken of large sidereal distances and, also,
of certain properties of variable stars. We first consider briefly
the preliminary indication from eclipsing stars and then turn
to the more significant evidence provided by a remote globular
cluster.
36. Stellar Eclipses in Light of Different Wave
Lengths. The Nordmann-Tikhoff effect has been studied in
recent years by Y. and J. F. Cox, 8 by Russell, Fowler, and Bor-
ton, 9 and by others, none of whom has arrived at an unequivocal
explanation of the observed difference in times of mid-minima
for eclipsing stars when measured in light of different wave
lengths. Originally, the lag was investigated in the hope and
belief that it proved the absorption of light in space by inter-
stellar gas; later, the fact was appreciated that any measurable
difference in speed of light from nearby eclipsing stars would
mean an impossibly large amount of dispersing material.
The measurement of the difference in the time of an eclipse
in blue and in yellow or red light is an uncertain process, involv-
ing accurate light curves and freedom from systematic errors
dependent on wave length. From a comparison of extensive
photographic and visual observations made for six stars at the
Harvard Observatory (photographic work by Miss Leavitt
and visual work, except for W Ursae Majoris, by Wendell)
8 Bui. Obs. Lyon, 9, 113, 1927.
9 Russell, Fowler, and Borton, Ap. J., 45, 306, 1917.
ECLIPSES IN LIGHT OF DIFFERENT WAVE LENGTHS 107
Table VIII, I has been prepared from data computed by Russell
and his collaborators. It shows in the fourth column the
observed difference in time of mid-minimum, with its probable
error. The estimates of distance in the third column are
dependable enough for the computation of the differential
velocities, which are given in the last column. Although the
observed differences in time of mid-minimum are undoubtedly
real for some of these stars, the resulting computations show
such wide variance that the interpretation as differences
in velocity cannot well be maintained. The differences in
the fourth column for these six stars and for those discussed
TABLE VIII, I ECLIPSING STARS AND THE VELOCITY or LIGHT
Star
Period
Distance in
Parsecs
Pg.-Vis.
Velocity Differ-
ence in Meters
per Second
d
d
S Cancri
o 485
420
-fo 0085+9
+5 i
W Uelphini
4 806
890
-f o 0026
+o 7
SW Cygni
4 573
735
-fo 0042 9
+ i 4
U Sagittae
3 38i
295
-fo 0040 + 5
+34
RW Tauri
2 769
675
-o 0025
-o 9
W Ursae Majoris
o 334
50
o 0004 + 7
2 O
at Brussells 8 should probably be attributed to one or more
of the following causes:
1. Accidental observational errors. (Frequently visual and
photographic observations do not refer to the same minimum,
and the difference is merely inferred from mean light curves.)
2. Uneven distribution of color over the surface of the eclips-
ing pair, for which there is good evidence for a few stars.
3. The systematic errors dependent on color, such as the
humidity effect on photographic plates, which may make the
beginning of an exposure much less effective photographically
than the end and accordingly displace the mid-time of effective
exposure from that recorded.
8 Bui. Obs. Lyon, 9, 113, 1927.
108 ON THE VELOCITY OF LIGHT
The Nordmann-Tikhoff effect certainly merits further careful
study; meanwhile, the observations can be taken to indicate
that the difference in the velocity of blue and yellow light
must be exceedingly small. Table VIII, I shows, in fact, that
the two velocities are the same to one part in a hundred million.
In the following section we shall present much more conclusive
evidence for equality in the speed of light, using quantitative
material which comes incidentally from the study of globular
clusters.
37. Messier 5 and the Relative Speed of Blue and
Yellow Light. For the accurate measurement of the rela-
tive speed of blue and yellow light we need (i) a source that
emits light of various colors at controlled or predictable inter-
vals, (2) a measured base line of great extent, (3) a device for
receiving the signals sent over this base line in the form of
light of different wave lengths. The requirements can be met
by using the cluster-type Cepheid variables in distant globular
clusters as the source of the light signals and receiving the signals
simultaneously on blue- and yellow-sensitive photographic
plates through appropriate light filters. My studies of the
variable stars in Messier 5, resulting in the determination of
photographic and photovisual light curves for a large number of
individual stars, 10 have provided the material for the test
described in the following pages.
The steep rise to maximum brightness of a typical cluster-
type Cepheid variable makes the time of median magnitude
on the ascending branch more accurately determinable than
the times of maximum or minimum. Visual work by Wendell
at Harvard on the star RR Lyrae and by the writer at Princeton
on SW Andromedae was concentrated on the study of the rising
branch of the light curve; it was found that the time of median
magnitude can be determined to within 2 or 3 minutes. The
maxima are usually sharp, however, and can also be timed with
some success.
H. B. 763, 1922; H. Repr. 5, 1923; P. N. A. S., 9, 386, 1923.
RELATIVE SPEED OF BLUE AND YELLOW LIGHT 109
The astonishing accuracy of the mean period of the cluster-
type Cepheid led Barnard to propose the possibility of using the
period of a star of this type in the globular cluster Messier 5
as a standard timekeeper. 11 Many of the variables in this
cluster rise by a magnitude from minimum to maximum in
about 30 minutes, more than doubling the intensity of light
emission at minimum.
Professor Bailey's studies of Messier 5 revealed more than
90 cluster-type variables, with periods ranging from 6 to 20
hours and an average period of 13 hours. 12 The periods of most
of these variables are known to within a fraction of a second,
according to Bailey's work and the general revision undertaken
by the writer with the assistance of Miss Roper. 13
For the revision of the periods and for the test of the speed of
light I made five special series of photographs of Messier 5 in
1917, using the 6o-inch reflector of the Mount Wilson Observa-
tory. The exposures of 20 to 30 minutes that were necessary to
record the yellow light with an isochromatic plate and yellow
filter were interrupted in the middle for an exposure of i or 2
minutes on an ordinary plate sensitive to blue light. In this
manner the variable stars were photographed in two regions of
the spectrum at essentially identical times. Photographic and
photo visual observations were carried on throughout several
hours of the night. Each run of plates gives fragments of the
light curves of all the variables; but since the average period is
13 hours, for only a few stars in each series was the light rising
from minimum through median to maximum during a given
night's run on the cluster.
The measurement of the plates yielded 6,300 magnitudes,
from which 14 measures of the times of median magnitude both
in blue and in yellow light were obtained for n different vari-
ables. The results appear in Table VIII, II. The maximum
effective wave length for blue light is approximately 4,500
11 See Appendix C, Refs. 62, 65, 66, 67.
12 See Section 16; H. A., 78, Part 2, 1917.
13 H. B. 851, 1927.
no
ON THE VELOCITY OF LIGHT
A, and for yellow light, 5,500 A. The observed difference in
the times t of rise to median magnitude
t pg - t po
is given in thousandths of a day in the fourth column. Thus,
a positive residual would indicate that the yellow light is meas-
ured as arriving first.
TABLE VIII, II. DIFFERENCES IN TIMES OF MEDIAN MAGNITUDES
Number of
Vanable
Photographic
Range
Photovisual
Range
At
Weight
d
I
I 2
o 7
+o 009
3
001
2
4
I 4
o 9
0.005
I
8
I I
7
012
I
12
i 3
I O
-o 005
2
18
i 5
* 05
-f-o ooi
I
20
o 9
o 7
o ooo
2
H-o 003
I
28
I 2
o 8
+o 006
2
59
I
o 7
o 003
I
63
I 2
o 9
O OO2
3
64
I O
o 7
-ho 005
I
81
I I
o 8
-fo ooi
3
o 008
2
It is seen immediately that there is no measurable difference
in velocity, the values of AJ being of the order of the uncer-
tainties of measurement; six are positive, seven are negative,
and one is zero. The mean value of the difference in time
required for the passage of blue and of yellow light over the
distance from the cluster to the earth is
Blue yellow = o d .oooi2 0^.0007
= 10 seconds 60 seconds
We have determined in this experiment merely an upper limit
to the difference in speed. We find that since the distance to
the cluster is approximately 11,000 parsecs, light of these two
colors, which differ by 25 per cent in wave length, differs in
RELATIVE SPEED OF BLUE AND YELLOW LIGHT
in
time of arrival at the earth by no more than one minute after
traversing space for more than 35,000 years. In other words,
the relative size of the probable error indicates that the chances
are even that the speeds of blue and yellow light do not differ
by more than i part in 20,000,000,000; probably they do not
differ at all.
-80
-40 +40
FIGURE VIII, i
+ 80
Composite photographic (full line) and photovisual
magnitude curves for cluster-type variables in
Messier 5 Ordmates are magnitudes m hundredths;
abscissae are phases in thousandths of a day.
From ii determinations of the maxima for 9 variables in
Messier 5, a similar equality in speed was found for blue and
yellow light. In this result, also, the probable error exceeds
the observed average difference, but the determination has
much less weight than the one based on median magnitudes.
It might be argued that the simultaneous arrival of the blue
and yellow light signals is a coincidence and not a positive
indication that the speeds are the same the delay for one
average wave length with respect to another being an integral
multiple of the interval between successive maxima or successive
112 ON THE VELOCITY OF LIGHT
median magnitudes. Although this argument might have some
weight for a single star, it can be immediately rejected when
several variable stars, at the same distance from the observer
but with slightly differing periods, are involved in the test.
A graphical test of the preceding results is obtained by reduc-
ing the light curves of the variables, listed in Table VIII, II,
to two composite curves, one for blue and one for yellow light.
The curves in Figure VIII, i were made by reducing all the
variables to a mean period and a mean magnitude range. For
a given variable v, a suitable linear transformation of the light
intensities is effected by the equations
Lm = -2.5 log (i - A/oA/'/A/'o)
and
/ = i - io-- 4A -
in which Am and Al are the increments of magnitude and of
intensity measured from maximum, and the prime refers to
minimum light. For the reduction of the phases t to those
appropriate to a mean period PO, we have
t. = *0 - P/Po
The coincidence of the photovisual and photographic curves
in Figure VIII, i at median and also at maximum magnitude
again illustrates the equality in speed of light in the two colors.
But the essential equality in speed does not necessarily indicate
a perfectly transparent interstellar medium. As Groosmuller, 14
among others, has pointed out, a large amount of dust and gas
can exist in space without measurably affecting the speed of
light.
14 Hemel en Dampkring, 22, 153, 1924.
CHAPTER IX
THE TRANSPARENCY OF SPACE
IN all researches on the structure of the stellar universe the
possibility of the loss of light in its passage through interstellar
space must be recognized. The considerable space effect on
the colors of stars deduced 1 5 years ago by Kapteyn and others,
if it were finally verified, would be a most serious limitation in
the survey of distant clusters and nebulae. Indeed, only for the
sun's neighbors could we derive directly the true distances,
colors, or temperatures. A spurious redness would invalidate
our results and all stars would appear dimmed, the farther
away the more affected. Nine magnitudes would be lost at
the distance now assigned to the galactic center, and outside
galaxies could not be seen at all. The sidereal universe would
be effectively " closed " within a relatively short radius, not
because of some fundamental property of space-time, but
because of the nearly complete opacity of the regions within
i oo kiloparsecs.
Fifteen years ago, the possibility of this restricted horizon of a
few hundred thousand trillion miles or so brought little dismay
to astronomer or philosopher; but now that we have reached
some 50,000,000 parsecs and have tasted of the riches that lie
beyond our Galaxy, such cramping would be highly irritating.
Another illustration is afforded by the fact that if the loss
of the visual light due to absorption or scattering in space should
be as much as a millionth of one per cent in each 100,000,000
miles, stars 3,500 light years away would appear about two
magnitudes too faint. Uncertainty in the coefficient of scatter-
ing is, therefore, very serious in studies of the distances of faint
stars, especially if the coefficient is as large as that just
suggested.
"3
114 THE TRANSPARENCY OF SPACE
It is commonly assumed that any dimming that occurs will
act through Rayleigh scattering and vary as the inverse fourth
power of the wave length of the light. As the effect for blue
light is about double that for yellow, the colors of faint and
distant stars furnish an obvious method for the detection and
measurement of differential scattering.
In addition to the possibility of differential scattering we
must consider the blocking of light by meteoric particles or by
other means a phenomenon not directly revealed by star
colors but known to occur in extensive Milky Way regions
occupied by dark nebulosity. In the following pages we discuss
mainly the color tests.
38. Early Investigations of Light Scattering. At the
beginning of the work on star clusters at Mount Wilson (1915)
close attention was given to the problem of the scattering and
obstruction of light in space. 1 As recently as 1914 Kapteyn 2
had derived from star colors the coefficient, 3 expressed in stellar
magnitudes per parsec,
d = 0.0003
supporting his earlier findings of 1909 and corresponding to a
change of a tenth of a magnitude in color index for each 300
parsecs of distance. Among many others, Seeliger, Turner,
Kienle, 4 King, 5 Jones, 6 and van Rhijn 7 have considered the
question, and the last three, in 1915, had just derived positive
values of the absorption coefficient from a consideration of the
colors, distances, and proper motions of the available nearby
stars. 8
l Mt. W. Contr. 116, 1915.
2 Ibid. 83, 1914.
3 Unit of distance is one parsec.
4 For a full bibliography see Kienle's paper in the Jahrbuch der Radioaktivitdt
und Elektronik, 20, 6-9, 1923.
*H. A., 59, 182, 1912; 76, i, 1916.
M. N. R. A. S., 75, 4, 1914.
7 Dissertation, Groningen, 1915.
8 Shapley, Mt. W. Comm. 18, 1916.
EARLY INVESTIGATIONS OF LIGHT SCATTERING 115
The following values were then on record for the increase of
:olor index with each parsec of distance:
Observers Jones Kapteyn King Turner van Rhijn
Coefficient o 00047 o 00031 0.0019 o 0030 0.00015
Assuming tacitly that his value of the absorption coefficient
was a constant throughout space, Kapteyn proposed optimisti-
:ally that the excess of color index for distant stars over the
values found for nearby stars with similar spectra could be used
to measure the distances. Such scattering effects, however,
would doubtless depend on galactic coordinates (especially on
latitude) and on the density of nebulosity in the fields through
which the light travels.
The test for differential light scattering, based on colors of
nearby stars, consists usually in the correlation with proper
motion of the excess of redness over the average for a given
spectral class, making allowance for other possible factors.
Thus, a set of equations of the form
C. I. = a + bm + cp + dM
can be solved for the effects on the color index of (i) errors
in the scale of apparent magnitude m\ (2) scattering of light
in space (which should increase with decreasing parallax p)\
and (3) change of color with absolute magnitude M . But since
M = f(m, log p)
it appears that an unambiguous solution for the constants
a, 6, c, d is very difficult. Luminosity and distance effects
are not easily differentiated. Moreover, the magnitudes,
parallaxes, and luminosities near the sun are not well known
over any considerable range of distance.
In all work yielding positive results, the stars of small proper
motion have appeared to be redder. If the proper motion were
taken to be an infallible measure of distance, this excess of
redness might mean a scattering of light. On the other hand,
by recognizing relatively small proper motions as a character-
istic of highly luminous stars (a relation now firmly established),
n6 THE TRANSPARENCY OF SPACE
we see that the excess of redness becomes merely a correlate of
bright absolute magnitude. This alternative is now regarded
as the correct explanation of the observations that were earlier
interpreted as revealing light scattering in the solar neighbor-
hood; the work of Scares and others has clearly shown differ-
ences in color for giants and dwarfs.
There remains, however, some evidence of a tenuous localized
medium around the sun, which may account in part for the
earlier indications of a positive scattering coefficient. King
has recently reconsidered the question on the basis of new and
accurate magnitudes and colors for the bright stars. 9 He finds
support for the thesis that a local cloud of absorbing matter
extends to a distance of at least 30 parsecs, reddening the stars
at the rate of d = 0.0003 magnitudes per parsec but affecting
more distant stars only by a constant (and negligible) amount.
Similar localized effects have been found for nebulous stars,
and perhaps, also, in some galactic clusters; but the whole color
discrepancy measured by King is extremely small and uncertain
in amount, since the base line is relatively short.
If instead of being confined to stars in our immediate stellar
system the study of colors is extended to much more distant
objects, it can readily be decided whether general light scatter-
ing is to play an important part in stellar investigations. We
can, fortunately, take advantage of great distances in the pres-
ent study of globular clusters.
39. Blue Stars in Messier 13. After Kapteyn's work
on light scattering, and the contemporary results of King,
Jones, and van Rhijn, which independently confirmed it, the
discovery in 1915 of stars with negative color indices in Messier
13 was unexpected. A critical examination of photo visual
and photographic magnitude scales failed to assign the apparent
blueness of the cluster stars to observational error. Out of
495 stars with well-determined color indices, 86 were found to
be of color class b, and 63 of class a.
9 H. C. 299, 1927.
BLUE STARS IN MESSIER 13
117
With a scattering coefficient of 0.0003 (Kapteyn's last value)
and an assumed distance for the cluster of as little as 1,000
parsecs, practically no negative colors should appear if the stars
are of usual spectral classes. With the obviously better parallax
of o".oooi, the color index produced by Kapteyn scattering
f K
FIGURE IX, i
Frequency of color classes in Messier 13 (full line)
and in the neighborhood of the sun (Yerkes
actinometry). Coordinates are relative numbers
of stars and color classes.
should be +3.0 for stars of spectral class A, and many color
indices should be greater than +4 in a typical distribution of
spectral classes. (The direct correspondence of color class
with spectral class in this cluster had been provisionally verified
by the spectrograms made by Pease. 10 )
It is found that the range of color index observed in Messier
13 is the same as that found among nearby galactic stars, as
10 See Chapter III, Section 12.
Il8 THE TRANSPARENCY OF SPACE
illustrated in Figure IX, i. There are no color indices in the
cluster larger than +2. The largest admissible color excess
in the cluster appears to be about o m .i; and, even if this excess
is attributed entirely to light scattering, we derive d = o.ooooi,
a thirtieth of the value derived by Kapteyn and a fifteenth of
the value found by van Rhijn from a consideration of the stars
in the Yerkes Actinometry. The foregoing upper limit of
scattering is so small as to be entirely negligible in dealing with
nearby stars; but a more accurate value is desirable, and for-
tunately it can be found from studies of external stellar systems.
40. Faint Blue Stars in the Milky Way. The galactic
latitude of Messier 13 is +40. That light scattering is absent
in this direction is no proof that it does not occur elsewhere,
especially in low galactic latitudes where stars and diffuse
nebulosity are concentrated. To make the test more com-
prehensive with respect to galactic latitude and longitude, the
search for negative color indices has been carried out on several
distant cluster systems, on the assumption that a normal range
of color index and the presence of numerous blue stars are
sufficient evidence of the transparency of space in the directions
and to the distances considered. The results are in Table
IX, I, where the observed extremes of color are shown in the
fourth and fifth columns, and, in the next two columns, the
mean photovisual magnitude and mean color index for a group
(usually ten) of the faintest blue stars. The distances in the
last column are taken from the tables in Appendices A and B.
Similar results have been obtained for faint stars in four Milky
Way fields, 11 and Scares has found faint blue stars in the
Selected Areas that fall in low galactic latitude.
Considering the relatively large distances of the tabulated
objects, and their wide distribution, we appear justified in
generalizing the results of the study of Messier 13 and in con-
cluding that interstellar media, throughout the distances here
concerned, have no serious effect on the color of light. This
11 Shapley, Mt. W. Comm. 44, 1917.
N. G. C. 7006 AND THE SCATTERING OF LIGHT 119
conclusion does not bear on obstruction of light by recognized
diffuse nebulosity (dark and bright) or on the colors of nebulous
stars. 12
TABLE IX, I. TEST FOR SPACE TRANSPARENCY IN VARIOUS REGIONS
Cluster
Galactic
Color Index
Mean
Pv.
Mag
Mean
Color
Index
Dis-
tance
Long
Lat
Largest
Smallest
o
Kpc.
Messier 3
12
+78
+ i 77
-0 39
15 i
o 16
12 2
13
27
+40
+ i 42
-o 52
16 54
-0.34
10 3
IS
33
-28
+ i 50
O 21
16 o
0.14
13 I
38
139
+ i
+ 2 12
-o 45
13 5
0.16
I I
36
142
+ i
+ 1 50
o 30
12 5
-o 23
I 2
35
154
+ 3
+ 1 31
-0.15
ii 5
o 07
o 8
50
189
i
+ 2 00
0.04
12 3
0.02
o 8*
5
332
-N6
4-i 67
II
14 6
10
10 8
22
338
~ 9
+ 2 05
-o 45
14 34
-o 28
6 8
II
355
- 3
+ 2 06
o 16
14 32
-o 08
I 2
4i. N.G.C. 7006 and the Scattering of Light. Notwith-
standing the great distance and consequent faintness of N. G. C.
7006, the magnitudes and color indices of 38 of its supergiant
red stars have been measured. 13 The distribution of color in
this cluster has already been compared in Chapter III with
that of the brighter stars in Messier 13 and Messier 3. Even
at a distance more than five times that of Messier 13, no abnor-
mal redness appears in N. G. C. 7006; and there is no other
peculiarity in its star colors, although its radiation has traveled
through the scattering materials of space for an interval of
more than 180,000 years.
Comparing N. G. C. 7006 with Messier 3 and Messier 13,
we have, as mean color indices for the brightest 35 stars:
N. G. C. 7006 i 10
Messier 3 1.15
Messier 13 i 03
12 Scares and Hubble, Mt. W. Contr. 187, 1920.
13 Shapley, Mt. W. Contr. 156, 5, 1918; see, also, Shapley and Mayberry,
Mt. W. Comm. 74, 1921.
120 THE TRANSPARENCY OF SPACE
If interstellar media have any effect at all on the color indices
of stars in this distant system, the reddening apparently does
not exceed a tenth of a magnitude. The absorption coefficient,
therefore, expressed as change of color index for each parsec of
distance, is
d < 0.000002
42. The Coma-Virgo Group of Nebulae. With a pre-
liminary estimate of the distance of the Andromeda Nebula,
Lundmark and Lindblad found 14 for the coefficient of space
absorption
d < 0.000002
They used the method of effective wave lengths as an indicator
of color and obtained for Messier 31 and for fainter nebulae
values which were not appreciably different from those for
average stars.
A subsequent investigation of the integrated magnitudes
and colors in the cloud of 300 bright extra-galactic nebulae in
Coma and Virgo 15 permits a further consideration of light
scattering. The photographic magnitudes are derived from
Harvard plates. The visual magnitudes are from Holetscheck,
reduced to the Harvard scale by way of the corrections to the
faint magnitudes of the Bonn Durchmusterung, as evaluated
by Pickering and Pannekoek. The mean color index for 41
nebulae fainter than photographic magnitude 11.5 is +0.69
0.04, in good agreement with spectral class G, which is
normal for nebulae of this class. The color excess, if existent,
is, therefore, not likely to be greater than two tenths of a magni-
tude. The distance of the cloud of nebulae is of the order of
3 X io 6 parsecs, and therefore we find 16
d < 0.00000007
14 Ap. J., 50, 386, 1919. Through an error the value is printed ten times too
small.
18 Shapley and Ames, H. C. 294, 1926.
16 The value in H. C. 294 is erroneously printed ten times too large. See H. B.
841, 1926.
THK OBSTRUCTION OF LIGHT IN SPACE 1 21
This value is the color effect alone; the total loss photographi-
cally is about double the color-index change.
Apparently, we need not disturb ourselves further about the
general dimming of light in space, even when dealing with
external stellar systems, unless it happens that the diminution
differs from molecular scattering and has no effect on colors.
43. The Obstruction of Light in Space. Dark nebu-
losities effectively conceal at least one or two per cent of the
whole sky. Because of their presence in the Sagittarius region,
they hide a much higher percentage of the total number of
galactic stars. The question for consideration here is the extent
to which such diffuse nebulous material in the sky at large
obstructs starlight without affecting colors. That the effect
is inappreciable, outside the regions of recognized nebulosity,
has in the past been inferred rather than proved. The infer-
ence is based on (i) the practically complete absence of differ-
ential light scattering, indicating the meagerness of dust
particles of small dimensions and presumably, therefore, of
large dimensions; and (2) the fact that the angular dimensions
of globular clusters decrease systematically with decreasing
apparent brightness. The decrease of cluster diameter with
brightness also holds true for the magnitudes of the individual
stars in globular clusters.
The theoretical relation in transparent space, d IO -- 2m + const - )
is approximately maintained for globular clusters, 17 but the
agreement with theory has little meaning because neither
the available integrated magnitudes m nor the catalogued angu-
lar diameters d are on true scales representing luminosity and
linear dimensions. As far as it goes, the result for the globular
clusters indicates the essential transparency of space up to a
distance of 100,000 light years. The serious observational
difficulties in measuring the true angular diameters 18 and total
magnitudes, and the dispersion in linear dimensions leave us,
17 Shapley, H. B. 864, 1929.
18 See Chapter XIV, Section 72.
122
THE TRANSPARENCY OF SPACE
however, uncertain concerning general light obstruction near the
Galaxy, even though differential light.'scattering is inappreciable.
The uncertainties that attend a quantitative test of obstruc-
tion by means of globular clusters are largely avoided by the
use of extra-galactic nebulae. The boundaries of at least some
of these objects are more clearly defined on photographic plates
10
12
16
18
14
FIGURE IX, 2.
The relation of angular diameter to apparent photographic
brightness for 2,750 nebulae in the Coma- Virgo region.
Ordinates are logarithms of diameter; abscissae are total
magnitudes. (See H. B. 864.)
than are those of clusters, for which the limits are indiscernible
because of the confusion with foreground and background stars
and the irregularities in adjacent stellar distribution. Figure
IX, 2 shows the test of the transparency of space in the Coma-
Virgo region between the relatively bright Cloud A and the
clouds B, C, and D whose members average from three to
six magnitudes fainter. The magnitudes are photographic,
and the diameters are expressed in seconds of arc. 19 The
two broken lines in the figure connect the logarithms of the
10 Shapley and Ames, H. B. 864, 1929,
THE OBSTRUCTION OF LIGHT IN SPACE 123
means of the diameters for intervals of magnitudes (crosses)
and the mean magnitudes for intervals of angular diameters
(dots). The straight line gives the theoretical relation for
transparent space, m = 24.15 + 5 log d. The magnitude
24.15, for which the average galaxy here considered would have
an angular diameter of i", has, according to the diagram, an
uncertainty of a tenth of a magnitude. The observed value of
the constant would vary somewhat, of course, with the kind of
photographic plate and the method of measuring diameters.
Because of the possibility that the measured magnitude and
diameter of extra-galactic nebulae would be equally affected by
light obstruction, the foregoing test needs further consideration.
The nebulae in the Coma- Virgo region have been placed in six
grades, from a to f, in order of increasing central concentra-
tion. 20 Grade a represents an essentially uniform surface
brightness; for it an obstructing medium should affect total
magnitudes without disturbing angular diameters, and conse-
quently the theoretical relation would fail.
It is improbable that if there is an appreciable obstruction of
light in space the relation of diameter to apparent magnitude
would be the same for all grades. Those having marked central
concentration should exhibit a more rapid decrease in diameter
with decreasing apparent magnitude than is shown by the grades
of more even surface brightness. But this change of rate of
decrease is not observed in Figure IX, 3, which is the same as
the preceding figure except that the various grades are plotted
separately.
From the representation of the observations by the straight
lines in Figures IX, 2 and IX, 3 we conclude that space, at
least in the direction of Coma- Virgo, is effectively transparent
throughout a distance of more than 100,000,000 light years.
We may allow, tentatively, two-tenths of a magnitude for the
total obstruction, corresponding to a loss in light, expressed
in magnitudes per parsec, of
I < 0.000000007
20 Ibid., H. B. 862, p. 20, 1929; see, also, H. B. 869, p. 32, 1929.
124
THE TRANSPARENCY OF SPACE
This limiting value of loss through obstruction should be
considered as an indication of the size of the observational
uncertainties rather than as a positive measure of the amount
of absorbing material of all kinds in space. It depends on a
direct test and is about twenty times smaller than the earlier
value, which depended on inference. It is of higher weight
FIGURE IX, 3.
The relation of angular diameter to apparent photographic brightness
for nebulae in the Coma-Virgo region, plotted according to grades of
central concentration. (See H. B. 866.)
because of the much greater amount of material involved and
should give us confidence in our explorations of remote parts of
space.
Although we have shown that scattering and obstruction of
light in many directions in high galactic latitudes are probably
negligible, there is growing evidence of some general absorption
or scattering in the direction of a few of the Milky Way star
clouds an effect amounting to two or three tenths of a
magnitude.
CHAPTER X
THE PERIOD-LUMINOSITY CURVE
WE do not certainly know what a Cepheid variable star is
or how the variability arises or dies away. We have vast
accumulations of observations, but still too few; we have numer-
ous theories and interpretations, probably too many; and we
remain in the dark concerning some of the most fundamental
properties of the Cepheid. Nevertheless, in spite of our igno-
rance concerning them, the Cepheids are accepted as the most
useful type of star in the sky. Luckily, they are widely
spread- in the solar neighborhood, in the star clouds of the
Milky Way, in clusters, in the Magellanic Clouds, and in exter-
nal galaxies. Their spectral and temperature changes contin-
ually raise questions about the age and evolution of supergiant
stars. But by far their most intriguing characteristic is the
property of revealing candle power and distance simply through
the period of the variation in light. It is this property of the
Cepheids, empirically found, developed, and used, that in the
past 15 years has opened up the Galaxy and many remote
systems that lie beyond.
44. Historical Notes. The relation between the absolute
magnitude of a Cepheid variable and the logarithm of its period,
which I have called the " period-luminosity relation," was first
presented empirically in 1912 by Miss Leavitt in a brief study
of some of the variable stars in the Small Magellanic Cloud.
She dealt, however, with only the apparent magnitudes of 25
stars with periods in excess of i d .2 and did not consider matters
of absolute magnitude, distances, and the relation to cluster-
type variables. The high absolute luminosity of a few Cepheid
variables had already been inferred by Hertzsprung 1 from a
1 Zeit. f. Wiss. Phot., 5, 94, 107, 1907.
125
126 THE PERIOD-LUMINOSITY CURVE
consideration of their proper motions; and later he estimated
the distances and plotted the distribution of 45 galactic Ceph-
eids, 2 using Miss Leavitt's provisional linear relation between
magnitude and the logarithm of the period, and for the zero
point deriving a mean luminosity of typical Cepheids from
Boss' proper motions. Russell also noted the high luminosity
of the Cepheids in Boss' catalogue. 3
Practically all subsequent work on the period-luminosity
curve, and its development for use in the measurement of dis-
tances, has been done as an incidental but important part of
the systematic investigation of clusters at Mount Wilson and
later at Harvard. 4 There have also been some serious attempts
at theoretical interpretations of the period-luminosity relation,
including those of Eddington, 5 Scares, 6 and Shapley, 7 and some
vigorous critical discussions of the data on galactic Cepheids. 8
43. Miss Leavitt's Work on the Periods of Cepheids.
In her first discussion of the magnitude estimates of the brighter
Cepheids in the Small Magellanic Cloud, Miss Leavitt gave
the provisional periods of 16 variables and noted that the
brighter stars had the longer periods. 9 In her later communica-
tion 10 the number was increased to 25, with a wide range in period
and brightness. The essential data are reproduced in Table
X, I, in which successive columns contain the Harvard number
of the variable, its period, and the maximum and minimum
magnitudes on a provisional scale.
Miss Leavitt's plot of the periods and of maximum and mini-
mum magnitudes is reproduced in Figures X, i and X, 2.
A. N., 196, 201, 1913.
8 Science, N. S., 37, 651, 1913.
Shapley, Mt. W. Contr. 151, 1917; H. C. 280, 1925.
M. N. R. A. S., 79, 2, 1918.
8 Mt. W. Contr. 226, 40-56, 1921.
vibid. 154, 1917; 190, 7, 1920, H. C. 314, 1927; 315, 1927-
8 Kapteyn and van Rhijn, B. A. N., No. 8, 1922; Curtis, Bui. Nat. Res. Coun.,
2, 194, 1921; R. E. Wilson, A. J., 35, 35, 1923.
H. A., 60, 105, 1908.
10 H. C. 173, 1912.
WORK ON THE PERIODS OF CEPHEIDS
127
Apparently, neither Miss Leavitt nor Pickering felt certain at
that time that the Magellanic Cloud variables were of the
same type as galactic Cepheids. Miss Leavitt wrote:
TABLE X, I. Miss LEAVITT'S OBSERVATIONS OF CEPHEIDS IN THE SMALL
MAGELLANIC CLOUD
H. V.
Period
Maximum
Minimum
H. V.
Period
Maximum
Minimum
d
m
in
d
m
m
iSS
i 25336
14 8
16 i
1400
6 650
14 I
14 8
1436
I 6637
14 8
16 4
1355
7 483
14 o
14 8
1446
I 7620
14 8
16 4
1374
8 397
13 9
15 2
1506
I 87502
IS I
16 3
818
10 336
13 6
14 7
1413
2 I7J52
14 7
IS 6
1610
ii 645
13 4
14 6
1460
2 913
14 4
IS 7
1365
12 417
13 8
14 8
1422
3 SOI
14 7
IS 9
I3SI
13 08
13 4
14 4
842
1425
4 2897
4 547
14 6
14 3
16 i
IS 3
827
822
13 47
16 75
13 4
13
14 3
14 6
1742
4 9866
14 3
IS 5
823
31 94
12 2
14 i
1646
5 3ti
14 4
IS 4
824
65 8
II 4
12 8
I6J9
5 323
14 3
IS 2
821
127 9
II 2
12 I
1492
6 2926
13 8
14 8
40
100
120
60 80
FIGURE X, i.
Relation of period to maximum and minimum photographic
magnitudes for variables in the Small Magellanic Cloud.
Ordinates, magnitudes; abscissae, periods in days.
They resemble the variables found in globular clusters, diminishing
slowly in brightness, remaining near minimum for the greater part of the
time, and increasing very rapidly to a brief maximum.
128
THE PERIOD-LUMINOSITY CURVE
But that the importance of the observed relation did not
escape Miss Leavitt is shown by her remarks:
Since the variables are probably at nearly the same distance from the
earth, their periods are apparently associated with their actual emission
of light, as determined by their mass, density, and surface brightness . . .
Two fundamental questions upon which light may be thrown [by a study
12
13
14
15
16
00
04
1.6
20
08 12
FIGURE X, 2.
Relation of period to maximum and minimum magnitudes
for variables in the Small Magellanic Cloud. Coordinates
are photographic magnitudes and logarithms of the periods.
of the Magellanic variables] are whether there arc definite limits to the
mass of variable stars of the cluster type, and if the spectra of such vari-
ables having long periods differ from those whose periods are short.
46. The Visual Period-luminosity Curve. It will serve
no useful purpose to recount in detail the development of the
period-luminosity relation; the steps are given fully in the
various papers referred to in the bibliography, especially in
Mount Wilson Contribution 151, published in 1917. It will
suffice to reproduce in Figure X, 3 the original visual period-
THE VISUAL PERIOD-LUMINOSITY CURVE
129
luminosity curve and give a tabulation of the smooth curve in
Table X, II. In reproducing the table and curve, an arbitrary
correction of +o w .23, described below in Section 52, has been
applied to the absolute magnitudes. The plotted points in
the figure refer to the various clusters and the Small Magellanic
-5
-3
-2
2
-06
-02
+ 06
+ 10
+ 22
FIGURE X, 3.
The visual period-luminosity curve. Coordinates are absolute
visual magnitudes and logarithms of the periods The curve
is made up from five systems the Small Magellanic Cloud
(dots), w Centauri (crosses), Messier 5 (triangles), Messier 3
(squares), and Messier 15 (circled crosses). Most of the sym-
bols for periods less than a day represent averages of about
ten variables. The data are taken from Mount Wilson Con-
tribution 151, 1018; variable 50 in Messier 5 is omitted. The
line represents the period-luminosity curve.
Cloud, from which the data on the Cepheids were derived.
From this plot I have now removed the points referring to
galactic Cepheids, because their relative distances are not
accurately and independently known.
The observations on which the visual period-luminosity
curve was based were mainly photographic and were reduced
130
THE PERIOD-LUMINOSITY CURVE
to the visual system by means of a provisional period-color-
index relation based on the observations of spectra available
in 1917. From the determination of the period-spectrum rela-
tion, given later in this chapter, it has been shown that the origi-
nal reduction from photographic to visual magnitudes was very
rough, as was suspected at the time. Hence, the visual period-
luminosity curve here given should not be used without correc-
tion with a more accurate reduction from photographic to
visual magnitude.
TABLE X, II. COORDINATES OF THE VISUAL PERIOD-LUMINOSITY CURVE
Logarithm of
Penod
Absolute Visual
Magnitude
Logarithm of
Period
Absolute Visual
Magnitude
-0 6
II
+0 8
2 2O
-0 4
O 10
+ 1
-2 Q2
2
-o 15
-f I 2
-3 64
-o 41
+ 1 4
-4 36
-1-0 2
o 76
+ 1 6
-5 08
+0 4
-I 14
+ 1 8
-5 79
f o 6
-1 58
+ 2
-6 5:
It should be noted especially that high visual absolute magni-
tudes of Cepheids with periods in excess of 30 days are reduced
by at least half a magnitude by the later studies of the relation
of period to spectrum and color. But even with these modifica-
tions, the absolute magnitudes of the longest-period Cepheids
in the globular clusters and in the Magellanic Clouds remain
among the highest known. Only some of the novae and the
brightest supergiant stars of the Magellanic Clouds appear to
excel them in luminosity.
47. The Periods of 106 Variables in the Small Magel-
lanic Cloud. Since the practical use of the period-luminosity
relation soon became confined almost exclusively to photo-
graphic work, it seemed advisable to set up a well-determined
photographic period-luminosity curve for the study of the
distances of clusters, star clouds, and spiral nebulae. Granting
the generality of the relation, we deemed it best, moreover, to
VARIABLES IN THE SMALL MAGELLANIC CLOUD 131
base the curve on material from a single system. Hence,
we have made an effort to fix the form of the curve as accurately
as possible through a comprehensive study of the variable stars
in the Small Magellanic Cloud. The faintness of the variables
and the probable difficulties with the Eberhard effect and with
occasional wisps of obscuring nebulosity may produce large
accidental errors for the individual stars; but the number of
stars compensates for individual deviations.
The establishment of dependable magnitudes throughout the
Small Magellanic Cloud has been a laborious preliminary to
the study of the variable stars. In all, photographic magni-
tudes have been determined in the Cloud for 25 sequences,
involving a total of approximately 400 stars. The brightest
magnitude is 6.73, and the faintest in most of the sequences is
between 17 and 18. The magnitude scale is based on the pres-
ent International North Polar Standards, having been con-
nected through the Harvard Standard Regions Ci and C2,
in declination 15 and right ascensions i h and 3*. 11 It is
believed that the average deviation of the scale for sequences
in the Small Cloud is not over two per cent, throughout the
interval from the tenth to the seventeenth magnitudes, where
the Cepheid variables under discussion are found. Uncertain-
ties still remaining in the zero point of the magnitude scale,
at least for some of the secondary sequences, may be of the
order of two-tenths of a magnitude.
For 32 variables in the Small Cloud, periods were deter-
mined by Miss Leavitt. 12 For 74 the periods were originally
determined by Yamamoto, working with Harvard plates, and
later many were revised and checked by Miss Wilson or the
writer. 13
The 106 variables of the Cepheid class are well scattered
throughout the Cloud, and the magnitudes are referred to
"Shapley,H. 0.255,1924-
"Twenty-five were published by Miss Leavitt in H. C. 173, 1912, and the
others by Shapley, Yamamoto, and Wilson (loc. cit., infra).
" H. C. 280, 1925.
132 THE PERIOD-LUMINOSITY CURVE
many different sequences. In one field, in the densest part of
the Cloud, some of the variables are at least half a magnitude
fainter than is normal for their period. This discrepancy may
be due to the Eberhard effect or to an effect of uneven back-
ground. Except for these few stars, however, the relation of
median magnitude to period appears to be the same throughout
the whole of the Small Cloud ; but in the Large Cloud the cur-
rent study of the variable stars indicates more frequent disturb-
ance of magnitudes by the extensive nebulosities.
48. The Photographic Period-luminosity Curve. The plot
of the median apparent photographic magnitudes against loga-
rithms of the periods for the 106 individual variables is shown in
Figure X, 4. Points of low weight are enclosed in circles, and
the periods determined by MissLeavitt are indicated by crosses.
A few of the stars diverging most widely from the curve may not
be actual members of the system, but the fairly high galactic
latitude (33) makes rather unlikely the occurrence of typical
Cepheids except as members of the Cloud.
The deviations from the curve in Figure X, 4 are not larger
than might be expected in view of the difficulties of observation.
The average deviation in magnitude of the 32 Leavitt variables
is 0.19; for the 74 stars it is 0.25; for all, 0.23. The systematic
magnitude deviation from the curve is 0.063 for the Leavitt
variables and +0.049 f r the others, showing a negligible
systematic difference between the earlier and the later work.
Some of the dispersion in magnitude can be attributed to
the thickness of the Cloud in the line of sight, but between
the variables at the near and far edges this correction amounts
to only 0.14 magnitudes. If a. is the angular radius of a sen-
sibly spherical system, the maximum dispersion in magnitude
arising from the thickness is given with sufficient approxima-
tion for remote systems by
THE PHOTOGRAPHIC PERIOD-LUMINOSITY CURVE 133
The correction is thus independent of the distance and real
thickness. The diameter of the Small Cloud is 3.6, and the
extreme correction to mean values is, therefore, less than a
tenth of a magnitude.
13
/
10 A
/
138
142
146
150
154
158
162
166
170
/
/
/
/
* s
/
X
X
X
*/,
r
XX
y
*
X
<K
X '*
~
y
<
X*
IS
r *
c
s
'/*
17 - 4 c
3 -01 01 03 05 07 09 11 13 15 1.7 19 2J
FIGURE X, 4.
Photographic period-luminosity curve. Ordinates are apparent
magnitudes; abscissae are logarithms of the periods. Crosses refer to
periods determined by Miss Leavitt. Circles enclose values of low
weight.
As noted above, other factors contributing to residuals from
the period-luminosity curve are the Eberhard effect and obstruc-
tion by nebulosity. To these may be added actual deviations
of the periods and magnitudes from average conditions
that is, a true scattering which may arise from differences in
mass, structure, or other physical properties. We should also
consider errors in the periods and the observational uncertain-
ties for individual variables, which may easily amount to two
134
THE PERIOD-LUMINOSITY CURVE
tenths of a magnitude. Errors due to the failure to resolve
double stars are not likely to be serious.
In Figure X, 4 only two stars with periods shorter than a
day are included. There appear to be many others of this sort
in the Cloud, 14 but they are not considered in the present dis-
cussion because of the relative weakness of the magnitude scale
fainter than 17.0. These cluster- type variables will soon be
studied with a large reflector, when short-exposure photographs
and better magnitude sequences can be used.
By grouping the points plotted in Figure X, 4, first in order
of the logarithms of the period and then in order of apparent
magnitude, we get the two sets of means shown in Table X,
III. All magnitudes of Cepheids in this chapter are median
values: (max. + min.)/2.
TABLE X, III. DATA FOR THE PHOTOGRAPHIC PERIOD-LUMINOSITY CURVE
Mean
LogP
Mean
Magni-
tude
Num-
ber
Absolute
Magni-
tude
Mean
Magni-
tude
Mean
LogP
Num-
ber
Absolute
Magni-
tude
-0 194
17 2
2
12
17 oo
+o 054
4
-o 32
+0 253
16 51
17
-o 8i
16 44
o 437
33
-o 88
o 610
16.08
53
-i 24
IS 00
6?7
36
i 33
o 986
15.48
21
-i 84
IS 5i
o 871
17
-I 81
I 357
14 93
II
-2 39
IS 05
i 267
9
-2 27
I 961
12 9O
2
4 42
14 38
i 380
S
2 94
12 90
i 961
2
-4 42
The distance modulus for the Small Magellanic Cloud (see
Chapter XIII) is 17.32, and the absolute magnitudes for vari-
ables in the Cloud are therefore given by M = m 17.32.
In the fourth and eighth columns of Table X, III are the abso-
lute magnitudes corresponding to mean values of log P. The
plot of these quantities in Figure X, 5 gives the adopted
photographic period-luminosity curve, which is extended to
log P = 0.6 on the basis of the data embodied in the visual
period-luminosity curve, Figure X, 3. The curve is tabulated
for equal intervals of log P in Table X, IV. An adjustment of
the lower end of the curve may result from studies of the faintest
variables in the Magellanic Clouds.
"Shapley, P. N. A. S., 8, 69, 1922.
THE PHOTOGRAPHIC PERIOD-LUMINOSITY CURVE 135
TABLE X, IV. COORDINATES OF THE PHOTOGRAPHIC PERIOD-LUMINOSITY CURVE
Logarithm
of Period
Absolute Photo-
graphic Magnitude
Logarithm
of Period
Absolute Photo-
graphic Magnitude
-0 6
O OO
+0 8
-i 53
-o 4
O OO
+ 1
-i 89
2
o 07
+ 1.2
-2 26
-o 31
+ 1 4
-2.68
+ 2
o 61
+ i 6
-3.19
+04
-o 93
+ i 8
-3 81
+o 6
I 22
+ 2
4 60
The photographic period-luminosity curve can be shifted as
a whole, up or down the absolute magnitude axis, if such a
j
-A fi
/
-Ifi
/
1
_> n
/
-28
x
/
^-H
20
-16
-12
-08
-04
00
-0
/
y
/
X
x
x
/
X
6 -04 -02 00 02 64 06 08 10 12 14 16 18 21
FIGURE X, 5.
Adopted photographic period-luminosity curve. Coordinates are
absolute photographic magnitudes and logarithms of the periods.
Dots represent means for intervals of logarithms of periods; crosses,
for intervals of magnitude.
change is justified by future studies of the proper motions and
mean absolute magnitudes of galactic Cepheids; but, of course,
136 THE PERIOD-LUMINOSITY CURVE
this revision of the zero point would not affect the general form
of the curve.
49, The Period-spectrum Relation. In my first work
on star clusters the need of combining visual observations of
galactic Cepheids with photographic observations of the vari-
ables in globular clusters and the Magellanic Clouds led to a
preliminary attempt to determine the dependence of color index
(spectral class) on period for galactic Cepheids. 16 Attempts
to improve on the data through direct observations of Cepheid
spectra resulted in the discovery that the spectra of all Cepheids
are variable they show a systematic and continuous variation
of spectral class, synchronous with the changes in magnitude
and velocity, the type at maximum being earlier than the type
at minimum. 16
That the longer period Cepheids frequently show later spec-
trum classes (or redder color indices) than those of short period
has long been known, mainly from early work at the Harvard
and Lick observatories; but the data I obtained at Mount
Wilson on the changes of the spectra of 20 stars were not suffi-
cient to revise my preliminary period-spectrum curve. The
revision has recently become possible through a much more
extensive investigation made jointly with Miss Walton, using
Harvard plates. 17 The work is described here as a preliminary
to the derivation, in the following section, of a period-luminosity
curve for galactic Cepheids.
The determination of the median spectra and the spectral
variations for 70 Cepheid variable stars is based on the examina-
tion of more than 1,200 spectrum plates. The classifications
are by Miss Cannon. A discussion of the data brings out the
following points:
i. Among cluster-type Cepheids of the galactic system there
is a considerable scattering of median spectral class, but appar-
1B Shapley, Mt. W. Contr. 92, 16, 1914.
16 Ibid. 124, 2, 1916; Mt. W. Comm. 14, 21, 22, 27, 1915-1916.
17 H 0.313, 1927.
THE PERIOD-SPECTRUM RELATION
137
ently no progressive change of spectrum with variation in
period. 18
2. The average deviation from the mean spectrum-period
curve for all 70 Cepheids is 2.1 spectrum units.
3. No progressive dependence of spectral range on the length
of period, or on the median spectral class, is found. The aver-
age range is slightly more than one spectral subdivision.
AO
PO
GO
KO
MO
-04
04
2.0
2.4
2.8
0.8 1.2 1.6
FIGURE X, 6.
The relation of spectral class (ordmates) to logarithm of the period
(abscissae) for variable stars Open circles refer to RV Tauri variables,
crosses to long-period variables, dots to Cepheid variables, and the open
squares to the mean cluster-type Cepheids.
4. In Table X, V the mean spectrum and the logarithm of
the corresponding effective temperature are given for intervals
of the logarithm of the period (Figure X, 6) . The table includes
not only data for the cluster-type Cepheids, supplemented by
19 values from the Henry Draper Catalogue, and for classical
Cepheids, but also corresponding data for 1 1 RV Tauri variables,
assembled in two groups, and 389 long-period variables (Class
Me). The last three entries in the table for classes N, R, and
S are provisional, the temperatures not yet safely estimated.
Indeed, the tabulated temperatures for long-period variables
are none too dependable.
18 See Chapter IV, where the peculiar properties of cluster-type Cepheids are
considered in some detail.
138 THE PERIOD-LUMINOSITY CURVE
TABLE X, V. RELATION OP SPECTRUM TO PERIOD FOR VARIABLE STARS
LogP
Spectrum
Number
Log T
LogP
Spectrum
Number
Log r
0.32
AS
25
3 93
2 13
M2.4C
26
3 40
+o 31
F 7
2
3 78
2 25
M2 90
27
3 38
o 55
F 9 .i
8
3 76
2 35
M 3 . 3 e
65
3-365
0.71
Gi i
12
3 73
2 45
M4 ic
102
3 335
o 87
G2 9
18
3 7i
2 55
MS 4e
H3
3 28
15
G6 8
6
3 65
2 65
M6.ie
4 6
3 24
.29
G53
9
3 67
50
G5-7
5
3 66
2 57
N
27
3 42
63
Ki
2
3 60
2 58
R
5
2 56
S
27
56
G8
5
3 64
75
K 3
6
3 57
50. The Period-luminosity Relation among Galactic
Cepheids. That a period-luminosity relation exists for Ceph-
eid variables in star clouds, in clusters, and in spiral nebulae
is generally recognized. But the indication of a definite period-
luminosity relation for galactic Cepheids is admittedly not
strong. This might be taken as evidence for a greater real
dispersion in the properties of galactic Cepheids a somewhat
unlikely supposition.
The main reason for indefiniteness in the period-luminosity
relation among nearby Cepheids is obviously our ignorance of
the parallaxes and luminosities. There are few Cepheids
nearer than 200 parsecs; hence, few precise trigonometric
parallaxes are available. The proper motions, likewise, are
as yet scarcely sufficient for the derivation of a mean value of
the parallax, to say nothing of discriminating between the
absolute luminosities for different periods. The trigonometric
parallaxes of the Cepheids, as given in the system of the Yale
Catalogue, are at present as in Table X, VI. This material,
showing most of the parallaxes to be less than their probable
errors, strongly supports the deduction from proper motions
that the galactic Cepheids are certainly remote and highly
luminous.
GALACTIC CEPHEIDS
139
The trigonometric values are in the mean systematically
o".ooi larger than the values from the period-luminosity rela-
tion a quite negligible difference in view of the observational
errors. The individual differences for 10 out of the 16 stars
are actually smaller than the probable errors of the correspond-
ing trigonometric values.
TABLE X, VI. TRIGONOMETRIC PARALLAXES OF CEPHEID VARIABLES
Star
Parallax
Source
Per Lum
Parallax
Difference
Tr - P L
Polaris
//
o 007 -t o
//
007
G, F+
n
o 018
o on
SUCas
7
7
Mt. W
4
+ 3
SZTau
13
10
M, Mu
2
+ ii
RXAur
2
7
Mt. W
I
- 3
TMon
7
9
McC
I
8
RTAur
8
S
WSM
4
+ 4
fGem
5
6
A, M, S+
4
+ i
RYBoo
13
8
Mt. W
i
+ 12
RRLyr
8
4
A,W+
3
+ 5
UVul
10
McC
i
i
17 Aql
3
ii
McC
5
2
SSge
5
8
M, Mu
2
+ 3
XCyg
3
12
Sprl
I
+ 2
TVul
19
9
McC
3
+ 16
0Cep
7
7
M, Yk
22
- is
Cep
9
7
A, M
6
+ 3
The direct measures of parallax obviously do not yet suffice
as a test for dependence of luminosity on period. The proper
motion data compiled by R. E. Wilson 19 are, however, more
extensive and useful for the purpose.
All Cepheid variables for which the probable error of the
proper motion is less than ten thousandths of a second are
entered in order of period in Table X, VII. The median visual
magnitudes are from my compilation in Mount Wilson Contri-
bution 155 or from more recent Harvard data 20 ; the proper
motions are from Wilson's paper, and the spectral classes from
19 A. J., 35, 35,1923.
20 Walton, H. B. 845, 1927.
140
THE PERIOD-LUMINOSITY CURVE
Shapley and Walton 21 or, if italicized, from the Henry Draper
Catalogue. In grouping the material of this table for intervals
of the logarithm of the period, and for intervals of the reduced
TABLE X, VII. PROPER MOTIONS OF GALACTIC CEPHEIDS
Star
Median
Vis Mag.
Log
Period
Total P M
Reduced
P M
Spectrum
m
U Car
7 4
i 59
O OOI
OOI
G6 5
1 Car
4 3
i 55
021
O OI2
G 7
T Mon
6 2
i 45
o 030
021
G 4 S
RYSco
8 2
I 31
o 023
o 040
G3 5
W Vir
9 6
i 24
o 083
o 280
Pec.
YOph
6 3
i 23
o 003
O OO2
G2
X Cyg
TT Aql
7 6
I 21
I 14
o 018
o 015
o 014
O O2O
G4 5
G6
XX Cen
7 4
i 04
022
026
G5
f Gem
I OI
O OIO
O02
Cop
S Nor
7 I
o 09
009
009
Cop
Dor
S Mus
3 9
6 8
o 09
o 98
o 015
o 019
004
O2I
F S 5
Gi 5
K Pav
4 S
o 96
o 017
OOS
Ftp
SSge
U Vul
5 8
7 o
92
o 90
o 006
o 031
004
OJI
G 3
G4
W Gem
7 i
o 90
O OIO
OIO
Go 5
ER Car
7 i
o 89
o 014
015
F8
WSgr
R Mus
4 7
7 o
o 88
o 88
o on
o 008
004
008
Go 5
Gi 5
n Aql
U Aql
6 6
86
o 85
o 013
o 005
003
004
R 4
G3 5
XSgr
4 7
o 85
o 018
006
G 3 5
BB Sgr
6 8
o 83
o 049
045
04
USgr
6 9
o 83
o on
OIO
G 4
TCru
7 2
o 83
o 018
02O
G2 5
V Car
7 8
o 83
o 018
026
G S 5
STrA
6 9
o 80
o 009
O09
G2 5
RVSco
7 I
o 78
o 028
O3O
FS
R Cru
YSgr
V Cen
7 3
5 8
7 I
o 77
o 76
o 74
o 017
O O22
o 032
O20
013
034
G4
Go 5
Gi
Cep
APSgr
A I
7 3
o 73
o 70
o on
o 015
O03
OI7
G2
Fo
S Cru
7 o
o 67
o 044
O44
Gi S
T Vul
S 8
o 65
o ooo
OOO
F8p
BFOph
aUMi
6 8
2 I
o 61
o 60
o 003
o 046
003
005
G5
F8
SUCyg
6 6
o 58
o 024
020
FS s
RT Aur
5 3
o 57
o 024
Oil
F9
RTrA
7
o 53
o 026
026
Go
SZ Tau
7 I
o 50
O O22
O23
F8
SUCas
5 9
o 29
o 014
008
F6
RRLyr
7 2
-o 24
o 223
246
As 5
RR Cet
8 6
o 26
o 069
144
Ao
W CVn
o 3
o 26
o 042
192
SX Aqr
i 8
-o 27
o 027
247
SW Aqr
4
o 34
066
317
STOph
I 6
-o 35
o 009
075
U Tn
I 6
-o 35
o 023
192
ST Vir
o 8
o 39
o 018
104
RSBoo
3
o 40
o 014
064
A2 5
proper motion, we have the means of the Tables X, VIII and
X, IX. Leaving out of consideration cluster-type Cepheids,
21 H. C. 313, 1927.
GALACTIC CEPHEIDS
141
we have little indication here of a period-proper motion depend-
ence; and, since the reduced proper motion should be a direct
index of absolute magnitude, the correlation of period and
luminosity is low, as far as this material is concerned.
TABLE X, VIII. REDUCED PROPER MOTION
FOR INTERVALS OF LOG PERIOD
Mean Log
Penod
Number of Stars
Mean Reduced
P M
I 25
IO
//
o 015*
o 92
II
O 010
o 83
7
o 017
o 71
8
o 014
o 51
6
o 017
-o 32
9
o 176
* W Virgims omitted
TABLE X, IX. Loo P FOR INTERVALS OF
RIDUCFD PROPER MOTION
Mean
Reduced
P M
Number of Stars
Mean Log P
o 215
8
o 24
o 046
8
56
O 022
10
o 76
o 013
8
o 97
o 007
7
o 77
o 003
ii
o 94
A large systematic observational program on the proper
motions of Cepheid variables is now in progress at the McCor-
mick and Mount Wilson observatories. It may eventually
provide sufficiently accurate material for the direct test of the
existence of a period-luminosity relation for galactic Cepheids,
though observational errors and the peculiar motions of the
stars will make subdivision of the data for this spectral purpose
somewhat precarious. The direct attack is not too hopeful,
142 THE PERIOD-LUMINOSITY CURVE
but an indirect test is now possible; as shown in the next section,
we have a very definite astrophysical way of finding a period-
luminosity relation for galactic Cepheids.
51. A Theoretical Period-luminosity Relation for Galac-
tic Cepheids. The usefulness of photometric methods, such
as the period-luminosity relation, in the measurement of the
distances of clusters, star clouds, and nebulae, depends on the
uniformity of stellar laws throughout the universe. If Cepheids
of the galactic region differ systematically from those in the
Magellanic Clouds, the period-luminosity curve may perhaps
still be used for clusters and external galaxies, but not safely
for isolated Cepheids or galactic star clouds. It is, however,
a simple matter, as shown below, to prove definitely that the
period-luminosity relation is maintained for galactic Cepheids.
a. From the period-spectrum relation, given above in Sec-
tion 49, it appears that for Cepheids with periods less than one
day the average median spectral class is A6. For stars with
periods longer than a day the following values may be read
from the period-spectrum curve:
Median Spectrum Log P Median Spectrum Log P
F4 (o 16) G2 o 79
F6 o 30 64 1.04
F8 043 G6 1.38
Go o 59 G8 (i 70)
b. In a note on Cepheid variation and the period-luminosity
relation, 22 it was pointed out several years ago that if we start
with the general gravitational relation P 2 i/p, the total
luminosity of a Cepheid variable
L=7rr 2 / (i)
can be written, with close approximation,
L = k(pP*)**(C.I.) (2)
where p, P, r, and n are the mean density, period, radius, and
mass, respectively, and the surface brightness / is taken as
22 Shapley, Mt. W. Contr. 154, 4, 1918.
GALACTIC CEPHEIDS 143
primarily a function of color index. (Equation (i) is, of
course, rigorous; the approximation in (2) arises from writing
B
From equation (2) it follows that if the differences in median
color for typical Cepheids are ignored that is, if / = $ (C.I.)
is a constant the luminosity will decrease with the prod-
uct of the mass and the square of the period; and since the
range in the masses is believed to be small in comparison with
the wide range in period, a common mass may be assumed
provisionally, and the absolute magnitude is given approxi-
mately by
M = a + b log P
with a and b constants. This theoretical relation is of the
same form as and accurately represents the observed relation
for the Cepheids with periods from 3 to 15 days in the Magel-
lanic Clouds and globular clusters; it amounts to a preliminary
theoretical period-luminosity curve applicable to all Cepheids. 23
It would appear, therefore, that among the galactic Cepheids,
where direct observations are difficult because of insufficient
data on parallaxes and absolute magnitudes, the intrinsic
luminosity should necessarily increase with the periods, as
observed in the Magellanic Clouds. But the result obtained in
1917 was admittedly preliminary. Certain critical observations
were lacking.
c. The variation in J with P need no longer be neglected,
however, and with the observed relation of median spectral
class to period, it becomes possible to derive the period-
luminosity curve for the galactic Cepheids as a direct conse-
quence of the period-spectrum relation and freed from the
assumptions necessary above. 24
23 Subsequently, Eddington, Scares, and others have calculated period-
luminosity curves on the basis of the pulsation theory of Cepheids; M. N. R. A. S.,
79, 2, 1918; Mt. W. Contr. 226, 40 ff., 1921. See, also, Shapley, Mt. W. Contr.
190, 7, 1920; H. C. 314, 1927.
84 Russell has independently discussed the problem from another angle and
reached much the same conclusions (Mt. W. Contr. 339, 1927), using spectro-
scopic results by Adams and Joy (Mt. W. Comm. 100, 1927).
144 THE PERIOD-LUMINOSITY CURVE
A determination such as Eddington has attempted of the
actual absolute magnitude of a Cepheid from knowledge of its
period alone seems too uncertain for practical applications,
mainly because of our insufficient information concerning the
masses, the darkening at the limb which affects the mean
surface brightness, and the ratio of the specific heats which
enters into a more rigorous form of the relation of period to
mean density.
The relative intrinsic luminosities, however, can be simply
computed for typical Cepheids, since only the ratios of masses,
periods, and surface brightnesses are involved, and the uncertain
and undetermined factors cancel out or are of the second order.
With the relative luminosities determined for a series of galactic
Cepheids, the scale of absolute luminosities may be derived from
the mean parallax of the nearer variables.
d. Since the surface brightness of a star depends directly
on the fourth power of the absolute effective temperature T 9
which has been determined by several investigators for the
various spectral types, we may write, for two Cepheids of
different spectral class,
J jH
/o ^ TV
Then, from equations (i) and (2),
L
and we derive
Mo - M = 10 log ~ + I0 log + 5 log M (3)
to 3 -TO o ju
where M is the absolute bolometric magnitude. Equation (3)
is a definitive relation connecting the absolute magnitude,
temperature, period, and mass of a Cepheid variable and
involves no assumption beyond Stefan's law and the gravita-
tional relation P 2 p = const. Our problem is to solve the
equation for M in terms of P.
GALACTIC CEPHEIDS 145
We could write the first term on the right side of the preceding
equation as
j o 1( >g U = 2.5 log ( = (s - s) (4)
where 5 is the surface brightness expressed in stellar magnitudes.
Various kinds of evidence indicate that the difference in surface
brightness from one Harvard class to the next is a little more
than one visual magnitude. It will be best, however, not to use
an assumed constant value of (SQ s) but to deal directly with
the temperatures of the Cepheids as indicated by their spectra,
since the temperature scale is fairly well known over the range of
spectrum here involved.
e. Considering equation (3), we note that, since we are not
making, use of the data on parallaxes or proper motions (except
later to fix a zero point), both M and /* are unknown for any
given Cepheid, but P and T can be obtained from observations.
The mass-luminosity formula derived by Eddington would give
the necessary additional information for a complete solution,
but it is possible to keep clear of the theories underlying his
formulae and to use instead only the observed mass-luminosity
relation in the second approximation, after provisional absolute
magnitudes are derived from a preliminary solution.
For a first approximation, therefore, we take the masses
of Cepheids as equal, and equation (3) becomes
M o - M = 10 log T - 10 log To + log P - - log Po
s) O
= (10 log T - 37.40) + ( T J log P - 1.97) (5)
where TQ has been set at 5500, corresponding to a Class Go
star, and the corresponding value of log P from the period-
spectrum curve is 0.59.
/. For the computation (Table X, X) of the relative period-
luminosity relation (masses assumed equal) from equation (5),
I have used the scale of effective temperatures shown in the
first two columns of the table. The adopted values are those
i 4 6
THE PERIOD-LUMINOSITY CURVE
deduced from colors, spectrophotometric data, and spectrum
analysis on ionization principles. The logarithm of the period
is derived from the period-spectrum curve.
TABLE X, X. COMPUTATION OP A PRELIMINARY PERIOD-LUMINOSITY RELATION
Spectrum
T
LoP
10 Log T 37 4<>
10/3 Log P 1.97
M o - M
o
Ao
1 0000
0,56'
+ 2.6
-3-8:
I 2:
AS
8500
-0.31
+ i.9
-3-0
II
Fo
7400
0.06
+L3
2.2
-o 9
FS
6500
+0.23
+0.7
I 2
-o 5
F 7 5
6000
+o 40
+0.36
o 64
-o 3
Go
5500
+o 59
O
G2.s
5050
+o 85
-o 4
+o 9
+o 5
G S
4600
+ 1 22
-o 8
+ 2 I
+ i 3
G 7 .S
4300
+ 1 62
i i
+3 4
+ 2 3
A plot of the computed M o M , in the sixth column, against
the logarithm of the period gives the preliminary period-lumi-
nosity curve (bolometric) for galactic Cepheids. The range of
three and a half magnitudes in intrinsic bolometric luminosity,
TABLE X, XI. -COMPUTATION OP FINAL THEORETICAL PERIOD-LUMINOSITY
RELATION
Spectrum
M
Log/t
^Log*-
3 MO
Revised
A/o - M
Revised
M
Final
A/
LogP
Ao
-o 7
o 65
-o 4
-I 6
-o 3:
-o 3
-o 56:
A 5
-o 8
o 67
-o 3
I 4
- 5
-o 4
-o 31
Fo
I O
o 70
-0.3
I 2
~o 7
~o 6
o 06
FS
-i 4
o 76
2
~o 7
I 2
I 2
+o 23
F7-S
-i 6
o 80
O I
-o 4
-i S
~i 5
+o 40
Go
(-1 9)
o 86
O
(-1 9)
(-1 9)
+o 59
G2 5
-2 4
o 94
+0 I
+o 6
-2 S
-2 6
+0.85
GS
-3 2
i 13
+o S
+i 8
-3 7
-3 9
+ 1 22
G 7 .S
-4 2
i 42
+o 9
+3 2
-5 *
~5 7
+ 1 62
shown by this computation, indicates that the mass factor in
equation (3) is not negligible. In Table X, XI the relevant
correction to the magnitude is computed. Corresponding
to the provisional absolute magnitude in the second column,
GALACTIC CEPHEIDS 147
derived from Table X, X, the logarithm of the mass is read
from the observed mass-luminosity relation as compiled by
5 M
Eddington. 25 The computed correction, - log , gives the
3 Mo
revised values of MQ M in the fifth column, and the resulting
absolute bolometric magnitudes in the sixth column.
These improved values of the absolute magnitudes are used
for a new determination of the mass factor and lead to new
values of the absolute magnitudes, seventh column of Table
X, XI, which are considered final, since a third approximation
would not introduce sensible alterations. It is to be noted
that the mass-luminosity relation as presented by Eddington
is probably subject to modification as more data on masses
become available; but a considerable change can be allowed
without affecting either the legitimacy of the preceding compu-
tation or the final results. Nor will reasonable (and probable)
alterations of the assumed zero point of the period-luminosity
curve appreciably disturb the trend of the computed relation.
In Table X, XII the final bolometric magnitudes of the
seventh column of Table X, XI are reduced to visual and photo-
graphic values (the latter with zero point independently
adjusted) and compared with observation. The observed
visual period-luminosity relation is taken without change from
Mount Wilson Contribution 151, and the observed photographic
values are from Harvard Circular 280. The former involved
mainly the Cepheids in the Magellanic Clouds and in globular
clusters; the latter is based altogether on the Cepheids in the
Small Magellanic Cloud. The agreement of the values com-
puted by way of the spectrum-period curve of galactic Cepheids
with the observed values is surprisingly good. It should be
noted incidentally that since the computed values for spectral
classes Ao and 67.5 involve extrapolations they are of low
weight.
g. The negative residuals Ci in Table X, XII for the
stars of longer period suggest that the observed visual values
' 6 The Internal Constitution of the Stars, iqi. 1026.
i 4 8
THE PERIOD-LUMINOSITY CURVE
may be too bright. This is now known to be the case. In the
reduction from photographic to visual magnitudes for the origi-
nal construction of the visual period-luminosity curve, 26 the
color correction used for the longer-period Cepheids was too
great, as may be verified from the new spectrum-period curve.
The visual period-luminosity curve consequently gives the
absolute magnitudes too bright for periods greater than ten days;
the application of a suitable correction would tend to reduce
the corresponding negative residuals O Ci in Table X, XII.
TABLE X, XII. COMPARISON OF OBSERVED AND THEORETICAL PERIOD-LUMI-
NOSITY RELATIONS
Spec-
trum
LogP
Bolometric
Magnitude
Computed
Vis M
Observed
Vis M
- Ci
Computed
Pg M
Observed
Pg M.
- Ci
Ao
-o 56.
-o 3:
o i.
-0 3
2
-o 3-
2'
+ I
As
-o 31
A.
-o 3
-o 3
-o 3
-o 3
Fo
o 06
-o 6
-o 6
-o 6
O O
o 4
O f
O
FS
4 o 23
I 2
12
I O
+ 2
-0 8
o 4
-0 I
P? 5
+o 40
-I 5
-I 5
I 4
4-o i
10
i i
I
Go
-HO 59
(-1 9)
(-1 8)
-I 8
(0 0)
(-1 2)
-i 4
(-0 2)
G2 5
+o 85
-2 6
-2 4
-2 6
O 2
-I 7
-I 8
I
G S
+ 1 22
-3 9
-3 6
-3 9
-o 3
-2 8
^-2 6
-fo 2
G 7 5
-f I 62
-5 7-
-5 2
-5 4
-0 2
-4 J
-3 S
+ o 8
In fact, this necessary correction goes somewhat too far, chang-
ing systematically the signs of the residuals. It then appears
that a still more satisfactory agreement of both visual and
photographic observation with theory would be obtained if we
were to introduce Eddington's formulation of the pulsation
hypothesis and substitute P f P($y 4)"* for Pin the fore-
going discussion, 7 being the ratio of specific heats.
h. In summary, it is found that the period-luminosity curve
computed from spectroscopic observations of galactic Cepheids
is in close agreement with the observed visual and photographic
period-luminosity curves derived from clusters and star clouds.
This conclusion is reached independently of data on proper
motions, radial velocities, or trigonometric and spectroscopic
parallaxes; it is without assumption as to the theory of Cepheid
variation. We need have no hesitancy in accepting the com-
parability of Cepheid phenomena throughout known sidereal
2 Shapley, Mt. W. Contr. 151, 1917.
THE ZERO POINT 149
systems or in using the Magellanic period-luminosity curves
to measure the distances of galactic Cepheids.
52. The Zero Point. The foregoing sections of this chap-
ter have shown how definitely we have established the period-
luminosity relation for the Magellanic Clouds, for star clusters,
and indirectly for the Galaxy. The form of the curve and the
deviations from it are now fairly well known, but we remain for
the time being in a state of suspense with regard to the zero
point. Originally based on the parallactic motions of the few
bright Cepheid variables for which accurate proper motions
were available, the zero point has been the target of much dis-
cussion and suggested revision.
Kapteyn and van Rhijn believed that the large observed
proper motions of cluster-type Cepheids in the Galaxy show
them to be dwarfs and necessitate an enormous shift of the
zero point which I had adopted, 27 with consequent disaster for
my measures of galactic dimensions. Later discussions of the
proper motions and radial velocities of these variables indi-
cated, however, that they could not be used in the manner
adopted by Kapteyn and van Rhijn. 28 Many of the stars of
this type belong to the well-known high-velocity group, and
when allowance is made for their high space velocities, the
proper motion data are not in disagreement with the zero point
indicated by the classical Cepheids. Table X, XIII, giving the
radial velocities that are now available (mainly from Mount
Wilson) for cluster-type variables, shows that the galactic
members of this class have extraordinary speed a circumstance
which may be related to anomalies in their variations and is
certainly connected with their large proper motions and their
wide distribution in galactic latitude. There is nothing in
these motions to indicate that the cluster-type Cepheids are
dwarfs and the estimated distances of globular clusters seriously
wrong.
" B. A. N., I, 37, 1922.
M H. C. 237, 1922; R. E. Wilson, A. J , 35, 35, 1923.
THE PERIOD-LUMINOSITY CURVE
The most thorough study of the zero point is that by R. E.
Wilson. 29 He concluded that the distances that I had based on
the period-luminosity relation should be decreased by 20 or
30 per cent; but in view of the now generally accepted Kapteyn
TABLE X, XIII. RADIAL VELOCITIES OF CLUSTFR-TYPE VARIABLES
Designation
Star
Period
Amplitude in
Kilometers
Velocity in
Kilometers
001828
SW And
d
o 44
51
- 16
012700
RRCet
0.55
85
102
044515
RXEri
0.59
40
+ 66
044930
SU Aur
o 47
36
+ 23
045221
ULep
o 58
49
+ 114
07IS3I
RR Gem
o 40
5i
+ 70
100224
RRLeo
0.45
49
+ 34
113267
SUDra
0.66
43
-174
I2I370
SWDra
o.57
82
- 29
I329S4
RVUMa
o 47
61
-180
140238
WCVn
0.55
10
+ 20
142932
RSBoo
o 38
75
- 18
162618
VXHer
o 46
3i
-390
163358
RWDra
o 44
30
-109
183932
RZLyr
o 51
1 20
221
192242
RR Lyr*
o 57
- 60
193056
XZ Cyg"
o 47
-I 9 6
205230
UYCyg
o 56
6
- 36
205515
RVCap
o 45
70
- 86
211000
SW Aqr
o 46
7i
20
223564
RZ Cept
o 31
56
- 14
* Wilson, A. J, 35, 35, 1923
fLuyten, P. A. S. P., 35, 69, 1923; see Shapley, H. B. 773, 778;Leavitt (and
Luyten) H. C. 261, 1924.
correction to Boss' proper motions, this change in the zero point
by Wilson may be, as he himself has pointed out, largely effaced.
In the most recent discussions of Cepheid motions Oort gets
1.07 0.26 (m.e.) as the correction factor to my parallaxes,
using Mount Wilson measures of radial velocity. 30
* A. J., 35 35, 1923.
B. A. N.,4, 91, 1927.
CLUSTERS AND EXTERNAL GALAXIES 151
As far as they go, the trigonometric parallaxes in Table X,
VI and the Mount Wilson and Upsala spectroscopic parallaxes 31
support the system based on the period-luminosity curve. Van
Maanen has found satisfactory agreement of his trigonometric
parallaxes 32 with the values from the period-luminosity relation.
In view of Wilson's work, however, and of other indications
that the nearer galactic Cepheids give too bright a zero point, 33
I have made a provisional correction of +0.23 magnitudes, which
reduces to o.oo the absolute photographic magnitude of cluster-
type variables. The correction has been applied to the period-
luminosity curves and to all the computed distances appearing
in this volume. It amounts to a systematic decrease of 1 1 per
cent in the distances computed from older period-luminosity
curves.
Awaiting the completion in a few years of the McCormick and
Mount Wilson investigations of the proper motions of a large
number of galactic Cepheids, we adopt this corrected zero
point and the scale of distances dependent on it. The resulting
absolute magnitudes in clusters and Magellanic Clouds are
accordant with a large body of astronomical observations and
compatible with recent astrophysical theory. There seems to
be no serious inconsistency in the resulting luminosities, except
that the revision has made the maximum brightness of stars in
globular clusters surprisingly low. I am inclined to predict that
the correction to the zero point now adopted will never exceed
a quarter of a magnitude and that it may be in either direction;
but this prediction should be made with caution because of the
increasing evidence of peculiar drifts and of general heteroge-
neity in the star structure in the immediate vicinity of the sun.
53. The Period-luminosity Relation in Clusters and
External Galaxies. Figure X, 3 shows clearly that classical
Cepheids and cluster-type Cepheids are definitely related by the
81 Shapley, H. C. 237, 1922; Lindblad, Ap. J., 59. 37, 1924-
82 P. A. S. P., 32, 62, 1920.
88 See Appendix C for relevant papers by ten Bruggencate, Curtis, Doig,
Kicnle, Malmquist, and Stromberg.
152
THE PERIOD-LUMINOSITY CURVE
period-luminosity curve in some of the globular clusters as well
as in the Magellanic Clouds. The question has been raised
whether the relatively few long-period Ccpheids in globular
clusters are correctly described as typical. An examination of
the observational material leaves no doubt that the stars are
normal members of the class; Figure IV, 2 shows that variable
star No. 42 in Messier 5 has the usual form of light curve.
13
19
/
f
/ *
i
<*
20
/
9
20
FIGURE X, 7.
Hubble's period-luminosity curve for variables in
Messier 31. Coordinates are median apparent
photographic magnitudes and logarithms of the
periods.
Bubble's work on the Cepheicl variables in N. G. C. 6822,
a remote star cloud of the Magellanic Cloud type, and in the
bright spirals Messier 31 and Messier 33, establishes the period-
luminosity relation for those remote external systems. 34 Figure
X, 7 is a period-luminosity curve taken from Hubble's discus-
sion of Messier 31 (the Andromeda Nebula); in his discussions
of N. G. C. 6822 and Messier 33 similar plots may be found.
The new photographic period-luminosity curve, when applied
to these three external systems, gives the following distances:
Messier 31
Messier 33
N. G. C. 6822
247 kiloparsecs
236 kiloparsecs
192 kiloparsecs
"Hubble, Mt. W. Contr. 304, 1925; 310, 1926; 376, 1929.
LONG-PERIOD VARIABLES 153
54. Long-period Variables and the Pulsation Hypothe-
sis. The plot in Figure X, 6 of data given in Table X, V
(Section 49) shows a highly significant sequence for the differ-
ent types of variable stars. The apparently close relation of
cluster-type Cepheids and of RV Tauri variables to the classical
Cepheids has been generally admitted, but in the period-spec-
trum relation we appear to link up equally definitely the Ceph-
eid and long-period variables, 35
In the variability of spectrum and of color, in the form of
light curve and its frequent instability, in occasional inconstancy
of period, and in the property of high luminosity, the Cepheid
and long-period variables are similar. Their principal differ-
ences are distribution in the sky and range of variation, but
both these differences are apparent rather than real. As to
distribution, the selection of stars on the basis of luminosity
and distance may be mainly responsible for the differences in
galactic concentration. As to range of variation, the radio-
metric measures of Class M variables by Pettit and Nicholson
show that in total radiation the amplitude of the typical long-
period variable is not three or four magnitudes, as in visual
light, but is of the order of one magnitude, as for cluster-type
variables and classical Cepheids.
It appears, therefore, that the pulsation hypothesis, which
accounts for cluster-type and classical Cepheid variation more
satisfactorily than does any other theory hitherto proposed,
may be logically extended to RV Tauri 36 and long-period varia-
tion on the basis of the period-spectrum relation and the
observed similarities in bolometric absolute magnitude, radio-
metric variation, spectrum peculiarities, and other properties.
Dissimilarities among the four types are only those natural to
the different stages of development of the various groups that
is, differences in mean density, in average spectral class, in
visual absolute magnitude, and in mean distance and galactic
concentration for a given apparent magnitude,
36 Shapley, H. B. 861, 1928.
86 Gerasimovtf, H. C. 341, 1929.
154 THE PERIOD-LUMINOSITY CURVE
That the present period-luminosity law does not include the
long-period variable stars is admitted; but the law is of an
empirical nature. When dependable absolute bolometric
magnitudes are available, the red long-period variables may not
deviate widely. For class M variables, moreover, with their
low densities and temperatures, the internal pulsations would
probably be considerably masked; peculiar relations among
light, velocity, and spectrum variations should be expected,
since the heavily banded spectra may greatly affect photo-
graphic, visual, or even radiometric magnitudes. In the mean,
the fundamental relation P 2 p = constant, between period and
mean density, appears to hold for long-period variables.
The current investigations of galactic star clouds should
eventually show in what manner, if at all, the period-luminosity
relation can be extended to long-period variable stars. 37
37 Shapley H. Repr 53, 1928; Gerabimovi, H Repr 54, 1928.
CHAPTER XI
THE DISTANCES OF CLUSTERS
To the measurer of the sidereal universe star clusters are
beacon lights. They point the way to the center of the Galaxy
and to its edges, and throw light on problems of growth and
decay. They are parts of the higher galactic organization,
deeply involved in its complications and yet so significantly
placed that knowledge of their distances is knowledge of the
fundamental structure of the Galaxy itself. The globular
clusters are a sort of framework a vague skeleton of the whole
Galaxy the first and still the best indicators of its extent and
orientation. The galactic clusters, when near, reveal important
drifting tendencies of the stars and, when remote, are frequently
the informative nuclei in otherwise indefinite galactic star
clouds, thus outlining some of the inner structural detail of the
Galaxy. Both types of clusters contribute in fact and in half-
hidden intimation to the untangling of the story of sidereal
evolution.
Measures of the distances of globular clusters fortunately
can be based on Cepheid variables, either directly or through the
use of these stars in the calibration of other methods. The
galactic clusters, which not only are devoid of Cepheid variables
but also lack homogeneity in structure and similarity in absolute
dimensions, are more difficult to measure for distance, though
much nearer to the earth. In discussing the determination of
distances it will be convenient to treat the two types separately.
55. Distances of Globular Clusters Obtained from
Cepheids and Bright Stars. From the period-luminosity
curve given in the preceding chapter, distances 1 can be deter-
1 See special bibliography in Appendix D.
156 THE DISTANCES OF CLUSTERS
mined directly for all the globular clusters in which Cepheid
variables have been studied and magnitude scales determined.
The magnitudes of the brighter stars are nearly as useful.
In Table XI, I 2 are collected all the relevant observational
data now available from my own studies, and also, for N. G. C.
5053 and N. G. C. 5466, the magnitudes measured by Baade
with the Bergedorf reflector. For the sake of homogeneity,
the magnitudes measured at Bonn by Kustner for three globular
clusters (M3, M 15, and M 56) were not used.
a. The Observations. The new material represents a con-
siderable expansion over that in hand 12 years ago. The
determination, in 1917, of the parallaxes of 68 globular clusters
included only 7 for which the variable stars had been studied,
and for two of these the preliminary data could not be used
quantitatively. As the variable stars in clusters are fundamen-
tal in calibrating methods of determining distances, I have
given considerable attention since 1917 to the discovery and
observation of variable stars in clusters. Mount Wilson plates
and various series in the Harvard collection have been used for
this work. I am indebted to several assistants at Mount Wilson
and Harvard for aiding in this laborious research and especially
to Miss Sawyer, who has taken an active part in the recent
revision of cluster distances. 3
There are now 19 instead of 5 clusters in which variable stars
have been measured sufficiently to enter the new determination
of distances. Of the 730 variable stars in these 19 clusters,
524 have been studied enough to be useful in fixing the "median
magnitudes" for the clusters concerned.
In 1917 the absolute magnitudes of the high-luminosity stars
had been measured for only 28 clusters; we now have measures
on the brighter stars in 48 systems.
b. The Methods. For a new determination of distance and
distribution, I have followed in principle, though not in detail,
the methods developed and described in 1917. As before, the
2 From H. B. 869, 1929.
8 H. B. 869, 1929.
DISTANCES OF GLOBULAR CLUSTERS 157
reasonable assumption is made that the median absolute magni-
tude of variables with periods less than a day is constant from
cluster to cluster. The difference between the median magni-
tudes of the variables and the magnitudes of the brightest stars
is again found, on the average, to be so definite a quantity
that brighter star magnitudes themselves can be used as criteria
for those clusters where variable stars are lacking or have not
been analyzed. We go farther by taking measures of integrated
apparent brightness (total magnitude) and angular diameter as
criteria of relative distance, using these measures, after appro-
priate calibration, not only to strengthen the determination for
the 48 clusters whose variables and bright stars have been
studied in some detail (Table XI, I) but also for the other 45
clusters now known in the galactic system for which we
have as yet no measures of variables or of individual bright
stars.
c. The Results. A few of the essential details of Table XI, I
should be mentioned. The classes in the second column are
those described in an earlier chapter and listed for all globular
clusters in Appendix A. The apparent median magnitude of
cluster- type variables is in the third column. When a cluster
contains long-period Cepheids, their magnitudes are reduced
to the cluster-type median by means of the period-luminosity
relation and are combined with the magnitudes of the cluster-
type variables.
Since we have adopted zero as the absolute photographic
magnitude for cluster-type Cepheids, the third column actually
contains a direct determination for 19 clusters of the distance
modulus m M = 5 (log d i), where d is the distance
in parsecs and m is the apparent median photographic
magnitude.
The parenthetical numbers in the third column are the com-
bining weights assigned to the mean median magnitudes of the
variables in each cluster. These weights depend on the number
of variables, on the detail with which periods and light curves
are known, and on the estimated accuracy of the magnitudes.
158 THE DISTANCES OF CLUSTERS
TABLE XI, I. MAGNITUDES OF VARIABLES AND BRIGHT STARS
N. G. C.
Class
Photographic Magnitude
Preliminary
Modulus
Notes
Vanables
25 Br
6th Star
30th Star
104
III
13 09
12 4
n 4
14 33
Note i, 47 Tucanac
288
X
14 80
14 5
IS i
IS 87
Note 2
362
III
IS 5 (4)
14 12
13 5
14 8
IS 49
1904
V
15 29
15 01
IS 72
16 61
Messier 79
2808
I
14 9
14 3
IS 4
16 25
3201
4147
X
IX
1 6 I 2 (?)
13 52
16 58
13 3
16 23
13 8
16 93
14 57
16 99
Note 3
GP
4590
5024
5053
X
V
XI
15 90 (6)
16 19 (8)
14 80
IS 07
IS 6s
14 31
14 94
IS I
IS 08
IS 26
16 o
IS 87
16 36
16 15
Messier 68
Messier 53
GP
5139
VIII
14 37 (S)
12 91
12 6
13 I
14 22
w Centaun
5272
VI
IS 50 (8)
14 23
13 92
14 45
15 48
Messier 3
5466
XII
16 17 (6)
15 72
IS I
16 2
16 16
GP
S897
XI
IS IS
14 9
15 4
16 16
5904
V
IS 26 (8)
13 97
13 74
14 27
IS 26
Messier 5
6093
II
14 88
14 72
IS 09
16 24
6121
IX
14 27 (6)
13 88
13 3
14 4
14 29
Note 4, GP, Messier 4
6144
XI
I? 76
15 2
16 3
l6 22
GP
6171
X
IS 46
15 2
IS 9
16 57
6205
V
IS 20 (4)
13 75
13 45
13 92
15 10
Messier 13, Note s
6218
IX
13 97
13 56
14 31
IS 07
Messier 12
6229
VII
16 18
IS 90
16 37
17 36
6235
X
16 17
IS 7
16 8
17 28
6254
6266
VII
IV
i 6 40 (6)
14 06
IS 87
13 35
IS 6
14 38
16 i
IS 17
16 37
Messier 10
Irreg , Messier 62
6333
VIII
IS 61
15 08
IS 88
16 70
Messier 9
6341
IV
13 86
13 60
14 16
IS 18
Messier 92
6356
II
17 16
16 86
17 44
18 Si
6397
IX
12 6l
II 9
13 I
13 67
GP
6402
6535
VIII
XI
IS 44
IS 9
14 85
IS 3
15 86
16 4
16 56
16 89
Messier 14
6541
6626
III
IV
14 42 (4)
13 35
14 87
12 7
14 49
13 8
IS II
14 53
16 14
Note 3
Messier 28
6638
VI
16 22
IS 90
16 60
17 48
6656
VII
14 06 (5)
12 93
12 80
13 26
14 12
Messier 22
6712
IX
16 10
IS 65
16 36
17 17
6723
VII
15 33 (6)
14 20
13 7
14 8
IS 37
6752
VI
13 26
12 8
13 6
14 47
6779
X
IS 31
14 98
IS 70
16 39
Messier 56
6809
XI
13 58
12 9
14 2
14 58
Messier 55
6864
I
17 06
16 76
17 35
18 43
Messier 75
6934
VIII
IS 78
15 33
16 ii
16 91
6981
IX
16 80 (8)
IS 86
IS 53
16 20
16 86
Messier 72
7006
I
1 8 96 (6)
17 SO
16 99
17 89
18 91
7078
7089
IV
II
1-563(7)
IS 71 (4)
14 31
14 61
14 13
14 25
14 55
14 76
IS 63
15 81
Messier 15
Messier 2
7099
7492
V
XII
14 63
16 82
13 77
16 3
IS 04
17 I
15 80
17 22
Messier 30
NOTES TO TABLE XI, I
i. The long-period variables in 47 Tucanae (H. B. 783) could not be safely used m measur-
ing the distance.
a. The mean magnitude of the 25 brightest stars was determined at Mount Wilson to be
14.81, with a range of 1438 to 15.04.
3. The magnitudes of N G C 3201 and N. G. C. 6541 may be considerably in error due to
unsatisfactory companson sequences. They are not included in the determination of the
reduction curves for apparent integrated magnitudes and diameters, though they are
appropriately used m constructing Table XI, If
4. For N. G. C. 6121 the z
. . . . zero point of the magnitude scale depends on both Harvard and
Mount Wilson measures of Mount Wilson plates.
5. The mean magnitude of the 25 bnghtest stars was determined at Harvard to be 13.76
with a range of 13 4 to 14 i.
DISTANCES OF GLOBULAR CLUSTERS 159
The means of the third column are used in conjunction with the
distance moduli derivable from the next three columns to deter-
mine the preliminary modulus in the seventh column.
The fourth column of Table XI, I contains the mean magni-
tude of the 25 brightest stars (after the exclusion of 5 of maxi-
mum brightness in order to avoid, or at least to diminish, the
effect of optical doubles and of the chance superposition of
bright field stars). A weakness in using this method lies in the
dependence of the area in each cluster surveyed on the com-
pactness or distance of the cluster, or on the richness of the
foreground of galactic stars. Uniformity of selection was strenu-
ously sought, and we are convinced that for most clusters the
mean of the 25 brightest stars, as well as the magnitude of the
thirtieth star, would not be appreciably disturbed by including
or excluding too much of the dense central region.
In the fifth and sixth columns are given the apparent magni-
tudes of the sixth and thirtieth stars in each cluster; the sixth
star is the brightest object and the thirtieth the faintest
included in the means of the 25 brightest.
The difference between the median magnitudes of the cluster-
type variables (third column) and the magnitudes of the three
succeeding columns are found to depend on the class of the
cluster. Table XI, II gives the readings from the smooth
curves that represent the change of the difference with class.
In the earlier work, a single constant value, 1.28, for the differ-
ence between the median and the 25 brightest, was used, and the
two other sets of differences were not considered in deriving
distances. The range now found in med. 25 br. is from 0.92
(Class XII) to 1.34 (Class I).
The present method of using three different points in the
sequence of apparent magnitudes is essentially equivalent to
comparing, from one cluster to another, the general luminosity
curves for giant stars. Its advantage over previous practice
lies in the allowance it makes for abnormal distribution or even
small deviations from the average in limited groups of stars.
The method is obviously justified by the non-parallelism of the
i6o
THE DISTANCES OF CLUSTERS
three curves representing the relation of reduction factors to
class of cluster.
A comparison of the modulus from variable stars alone (third
column of Table XI, I) with the preliminary modulus (seventh
column) based on bright stars and variables together, indicates
how satisfactorily the data for bright stars agree with the
results from the variables. The agreement shows, in fact, to
what extent one typical cluster is comparable with another
inside the various classes.
TABLE XI, II. REDUCTION TO MEDIAN MAGNITUDE OF CLUSTER-TYPE VARIABLE
STARS
Class of Cluster
Medtan 25 Br
Median 6th Star
Median 3Oth Star
I
34
77
I 04
II
33
74
I Ol
III
32
71
98
IV
30
68
o 95
V
28
64
o 92
VI
i 24
60
o 89
VII
I 20
56
o 86
VIII
I 15
51
o 83
IX
I IO
46
o 80
X
i 05
40
o 77
XI
o 99:
34
o 74:
XII
o 92:
29
o 71:
d. Giant-poor Clusters. A number of the clusters of the more
open classes (classes IX to XII) were found upon examinations
for star frequency to be poor in giant stars. Their luminosity
curves are abnormal. Such objects are indicated by the letters
GP in the last column of Table XI, I. They were not used in
deriving differences in Table XI, II for normal clusters, and
the irregular cluster Messier 62 (N.G.C. 6266) was also
excluded.
The GP clusters with measured variables were used, however,
to determine special reduction factors for all the " giant-poor"
clusters. A study of these abnormal systems shows that the
following mean values can be satisfactorily used in reducing
DISTANCES OF GLOBULAR CLUSTERS 161
the magnitude measures to the standard median magnitude of
the cluster-type variables:
Median Mean of 25 = +o 44
Median Sixth brightest = -f o 94
Median Thirtieth brightest = -ho 03
e. The System of Weighting. For the typical clusters for
which bright star magnitudes have been measured (Table
XI, I), the reductions to "median magnitude" are made
directly with the aid of Table XI, II, and the three resulting
determinations for each cluster are combined with weights
2, i, i, for the mean of 25, sixth, and thirtieth, respectively, to
get the preliminary distance modulus. The modulus from
variable stars, when available, was, of course, included with
appropriate weight in the mean value in the seventh column
of Table XI, I. The final weight of each preliminary modulus
is, therefore, the weight in the third column (from the variable
stars) increased by four.
56. Distances of Globular Clusters Obtained from Diam-
eters and Integrated Magnitudes. Further steps in deriving
the distances of the clusters are now obvious and need only be
summarized. Plotting the values of the preliminary modulus
in Table XI, I against the integrated brightness and angular
diameter, 4 we get two empirical curves that may be used for the
derivation of the distance modulus of any globular cluster for
which the total magnitude and angular dimensions have been
measured.
a. Angular Diameters. The adopted diameters, which are
given for all globular clusters in Appendix A, are based on meas-
ures made at Harvard on photographs of Series A (Bruce 24-inch
refractor) and of Series AX and AY, which are made with short-
focus cameras; double weight is assigned to the large-scale
plates. It should be noted that the measured angular diameter
of a cluster depends on exposure time; the recorded diameters
d are, therefore, not exactly proportional to the parallaxes nor
4 H. B. 852, 1927.
162 THE DISTANCES OF CLUSTERS
related by the normal formula d = fcio- 2m to the integrated
apparent magnitudes iw. This limitation, however, does not
decrease their value as a measure of relative distances.
In general, the measures of diameter refer to the nucleus
or the main body of the cluster. Plates of long exposure, made
with large telescopes, when carefully counted and analyzed,
show that the clusters are of considerably greater extent than
is recorded in these "surface" measures of angular diameter.
The distribution of cluster-type variables also frequently indi-
cates the wide dispersion of cluster stars. For example, Bailey
notes the existence of variables 19' from the center of N. G. C.
3201, 5 though the "working diameter" in the catalogue is
7'.7, in agreement with the value given in the New General
Catalogue.
b. Integrated Apparent Magnitudes. The photographic mag-
nitudes for globular clusters are on a convenient but not the
conventional scale. They were measured by Miss Sawyer
on plates of the AX and AY series. 6 The scale is much more
open than in the customary Pogson system, and as a result the
integrated brightness listed in Appendix A ranges from the
third to nearly the thirteenth magnitude. If the scale were on
the usual bystem of stellar magnitudes, this difference of 10
magnitudes would indicate a factor of 100 in the relative dis-
tances, rather than the factor of 10 which is actually found.
The measures of brightness are, however, fairly accurate,
since much care was taken in the selection of plates and of
magnitude sequences. Photographic images of globular clus-
ters depend on the lenses, plates, and photographic development,
and for the brighter and larger clusters are necessarily uncertain
not only because of the size and texture of the photographic
image but also because of the scarcity of suitable comparison
stars and the general weakness of photographic sequences for
bright magnitudes. With the warning that these new measures
of brightness cannot be used for the computation of absolute
6 H. C. 234, 1922.
6 H. B. 848, 1927.
DISTANCES OF GLOBULAR CLUSTERS
163
magnitudes or for comparison with visual integrated magnitudes
for the determinations of color index or, as Dufay 7 has dis-
covered, used directly for the derivation of relative distances,
we can, however, proceed to make important indirect use of
them, when properly calibrated, to get at the distances of
clusters for which we have no data on individual bright stars
or variables.
10
06
02
140
150
180
160 170
FIGURE XI, i.
Relation of logarithm of diameter to distance modulus (abscis-
sae) for globular clusters
c. The Distance Moduli and Their Weights. The two curves
which were used for the derivation of distance moduli from
measures of diameters and of total magnitudes are shown in
Figures XI, i and XI, 2. Their coordinates are contained in
Tables XI, III and XI, IV. The actual moduli derived for
all 93 clusters are omitted 8 from Appendix A, but they may be
recovered if desired from the curves or tables of this chapter
and from the tabulated measures in the appendix.
7 Bui. Obs. Lyon, n, 59, 1929.
8 They are tabulated in Table III, p. 7, of H. B. 869, 1929.
1 64
THE DISTANCES OF CLUSTERS
Unit weight is assigned to each of these new determinations
of cluster distances. When other values are available, as in
48 of the clusters, the weight 4 is assigned to the modulus
depending on the bright stars, and the weight for the modulus
from variable stars is that given in Table XI, I above. For
instance, the four values of the modulus for Messier 3 (N. G. C.
5272) are 15.50 (variable stars), 15.45 (bright stars), 15.23
(diameters), and 15.0 (magnitudes). The corresponding
weights are 8, 4, i, i. The adopted mean modulus is 15.43,
corresponding to a mean distance of 12.2 kiloparsecs or about
40,000 light years.
140
150
160
170
180
FIGURE XI, 2
Relation of integrated magnitude to distance modulus
(abscissae) for globular clusters.
For the "giant-poor" clusters the modulus from the angular
diameter is derived from the curve for normal systems (Figure
XI, i) and the modulus from total magnitude is derived from a
smoothed curve based on the integrated magnitudes for only
those clusters that are deficient in giant stars. Loose globular
clusters, such as N. G. C. 288 and N. G. C. 3201, may approach
the deficient condition, but the variable reduction factors of
Table XI, II largely correct for minor systematic deviations
from average conditions of magnitude frequency.
The adopted mean modulus for each cluster is given in
Appendix A, followed by a letter indicating the quality of the
DISTANCES OF GLOBULAR CLUSTERS
165
determination. The assumed quality depends on the final
weight of the modulus and the accordance of the various deter-
minations. The letter "a" indicates the values of highest
weight; the letter "e" refers to the most uncertain determina-
tions, which are, unfortunately, still too numerous. The
distribution among the qualities is: a 13, b 25, c 23, d 17, and
TABLE XI, III. MODULUS-DIAMETER CURVE
Modulus
Log Diameter
14 o
I 30
14 5
I 20
15 o
i 05
15 5
o 89
16 o
o 67
16 5
o 42
17 o
o 24
17 5
O II
18 o
o 02:
18 5
9 92
TABLE XI, IV. MODULUS-MAGNITUDE CURVE
Modulus
Integrated Magnitude
14 o
3 *
14 5
3 7
15
4 5
15 S
5 6
1 6 o
6 7
16 S
8 i
17 o
9 4
i? 5
10 5
18 o
ii 4-
18 5
12 2:
The seven clusters for which the N. G. C. numbers are marked
with daggers in the first column of the catalogue (two of them
also appear in Table XI, I) may possibly be galactic clusters
or nebulous groups rather than normal globular clusters. They
166 THE DISTANCES OF CLUSTERS
are described in Chapter II, Section 6. An exponent n in
the first column refers to the notes at the end of the catalogue.
For clusters where there is good material on variable stars,
the determinations based on total magnitude and diameter
contribute but slightly to the finally adopted modulus. The
computed distances for nearly half of the clusters, however,
depend entirely on the relatively low weight determinations
of the apparent brightness and diameter. Efforts will be made
within the next few years to extend the work on variables and
magnitudes of individual stars. As a result, alterations in
the distances of individual clusters can confidently be expected,
but it is practically certain that the scale of the system of clus-
ters and of the Galaxy will not be affected thereby. The zero
point correction predicted in the last chapter is the only agent
likely to disturb the general scale of distances.
d. Comparison with Earlier Results. As previously noted,
we have made a systematic correction of n per cent to the
distances of globular clusters through making a provisional
alteration in the zero point of the period-luminosity curve.
On comparing the distances now given (Appendix A) with
those previously obtained through my investigations at Mount
Wilson, 9 the average difference is found to be 12 per cent (after
allowing for the systematic change). The revision of the
individual distances has therefore not been at all drastic,
though in a few cases where the early material was unexpectedly
weak it has been more than 30 per cent. Because of the great
increase in the basic photometric data and the number of globu-
lar clusters with Cepheid variable stars involved, the present
values are much more secure than those formerly determined.
At times during the past 12 years the scale of distances
has been challenged, and evidence or argument advanced to
show that I had derived cluster distances and galactic dimen-
sions that might be from five to one hundred times too large.
It is inadvisable to take space to reproduce here or even to
summarize these many discussions, because the general order
Mt. W. Contr. 152, 1918.
A WORKING CATALOGUE OF GALACTIC CLUSTERS 167
of distances, and consequent galactic arrangement, is now very
generally accepted. It should suffice to mention ten Brug-
gencate, Charlier, Crommelin, Curtis, Doig, Hopmann,
Kapteyn and van Rhijn, Lundmark, van Maanen, Malmquist,
Oort, Parvulesco, Perrine, Schouten, Scares, and R. E. Wilson
as principal contributors on one side or the other of the dis-
cussion and for the details refer to their papers in the general
bibliography (Appendix C).
57. A Working Catalogue of Galactic Clusters (Appendix
B). The discussion of the number and distribution of
galactic clusters in Chapter II, Section 7, was based on a new
and fairly homogeneous catalogue which is given in Appendix
B. Although intentionally incomplete, because of the adopted
restrictions which exclude poor or indefinite groups, and perhaps
overlooking a few clusters that fall within these limitations,
the catalogue is probably the most serviceable yet compiled
for the general study of galactic clusters. Miss Payne is respon-
sible for the classification of the individual clusters and for
the estimates of magnitudes and of numbers of stars. The
classifications (sixth column of the catalogue) are on the system
proposed in Chapter II. The galactic coordinates are on the
Harvard system (Pole at 12*40", + 28). 10 The angular diam-
eter is from Melotte's catalogue, except when italicized, in
which case the estimate was made by Miss Roper using Harvard
photographs; it is necessarily approximate and generally refers
to the obvious nucleus. Detailed star counts nearly always
extend the diameters.
The orientation, expressed as the position angle of the major
axis of an elongated cluster with reference to the galactic equa-
tor, was estimated independently by Miss Payne and the writer
on Harvard photographs for the more compact galactic dusters
(Melotte's Class II); the results, which are very accordant,
are discussed in Chapter VII. The ninth column of the cata-
logue indicates the approximate number of stars that could be
10 Pickering, H. A., 56, i, 1912.
1 68 THE DISTANCES OF CLUSTERS
assigned to each cluster on plates whose fainter magnitude
limits are as given in the following column. In the clusters
for which this fainter limit is not given, the majority of the
cluster stars are much brighter than the limit.
It is probable that many stars within the bounds of the cluster
are superposed members of the intermediate galactic field,
for these systems usually lie in rich regions in low galactic
latitude. Obvious bright foreground stars were not considered
in choosing the fifth star for each group and estimating its
magnitude. It is probable, therefore, that nearly always the
estimated magnitude in the eleventh column actually refers
to a star that is near the maximum luminosity in its cluster.
How bright absolutely that object may be depends, to some
extent, on whether it is a member of a Pleiades or a Hyades
type of cluster, and also on whether the cluster is poor or rich in
stars. No claim to accuracy is made for these estimated magni-
tudes; they are given as rough indicators of the brighter limit
of apparent magnitude and as a means of making preliminary
estimates of the distances and space distribution of galactic
clusters.
58. Parallaxes of Galactic Clusters. Direct trigono-
metric measures must necessarily fail to give useful information
on the distances of galactic clusters, even when they are as
near as the Pleiades. Measures of proper motions, and fairly
extensive studies of the spectral composition of some of the
nearer galactic clusters, have led to useful estimates of the
approximate distances. For ten systems, including the Pleiades,
the Hyades, Praesepe, Messier n, Messier 37, the double
cluster in Perseus, and the bright cluster in Coma Berenices,
the distance in kiloparsecs has been determined through more
or less detailed studies of motions, magnitudes, and spectra,
and is entered between the twelfth and thirteenth columns of
Appendix B. The sources are given in the notes at the end of
the catalogue. The accuracy of these ten values is not high,
except for the Hyades.
PARALLAXES OF GALACTIC CLUSTERS 169
For other galactic clusters no equally dependable measures
of the distances are yet available, though provisional photo-
metric or spectral parallaxes have been published by various
investigators. Doig 11 and Raab, 12 in particular, have analyzed
the spectral data and derived useful preliminary estimates for
many of the brighter groups. My own values for a number of
the galactic clusters 13 are systematically too great; the published
estimates were admittedly very provisional and gave distances
that now appear on the average to be two or three times too
large because of the tentative assumption that the brighter stars
were of exceptionally high luminosity.
Trumpler's spectroscopic and photometric researches on
galactic clusters, which have been in progress for some years,
should eventually give fairly accurate values of the distances
of many of the galactic clusters; his method involves the use
of luminosity curves for various spectral classes in the clusters 14
or, what is essentially the same, the use of a Russell diagram
for fixing the distance modulus. The final standardization
of his system of distances will probably await much serious work
on the absolute luminosity dispersion for stars of Class A.
Spectroscopic parallaxes should eventually give the distances
of a number of galactic clusters which contain late type stars;
and with the development of dependable spectroscopic methods
for early type stars, such as those foreshadowed by Miss
Williams 15 in analyses of absorption lines in Class A spectra, the
spectrum-line method may turn out to be the most dependable
one for measuring the distances of galactic groups. It will be a
procedure much less time-consuming than the Russell diagram
method.
Since the accurate determination of the distances of galactic
clusters is still mainly in the future, it seems worthwhile for
the time being to tabulate direct photometric estimates.
11 J. B. A. A., 35, 201, 1925.
12 Lund Medd. Set. 2, 28, 1922.
18 Mt. W. Comm. 62, 1919.
14 P. A. S. P., 37, 307, 1925.
H. C. 348, 1929.
1 70 THE DISTANCES OF CLUSTERS
Assuming that the fifth star in order of brightness in a galactic
cluster has an absolute magnitude like that of an average bright
Class A star, +0.5, we derive the distances given in the twelfth
column of Appendix B. In the thirteenth column are given the
distances corresponding to an assumed absolute magnitude of
0.5. Since we are dealing with objects selected on account of
high luminosity, these greater distances are probably more
nearly correct. 16 They have, therefore, been used in comput-
ing, in the next two columns, the linear diameter of each cluster
in parsecs and the distance of the cluster from the adopted
galactic plane. The wide range in linear diameters, reflecting,
in part, the difficulty of estimating the bounds of a galactic
cluster, is a striking feature of these computed results. The
smallest objects appear to be only a few light years in diameter,
and the largest more than 50. Not much weight can be put on
individual values of the distance, but it is practically certain
that these values are of the right order of magnitude and can
serve to give a correct idea of the distribution of galactic clusters
in space. The light they throw on galactic dimensions is
considered in the following chapter.
16 The assumption that the fifth star in the cluster is not more luminous than
0.5 implies, in general, that this star is not earlier in spectral class than B8.
For a duster of the spectral constitution and richness of the Pleiades, this
assumption would, therefore, give too small a distance. Trumpler has found
that about half the clusters he has classified are of the Pleiades type, but, as
pointed out in Section 15, this proportion is probably too large because of
observational selection. The clusters of the Pleiades type are apparently poor
in luminous stars of early type, for of fifteen enumerated by Raab, not one has a
fifth star of class as early as 65. The adopted method, therefore, probably does
not lead to serious systematic error.
CHAPTER XII
DIMENSIONS OF THE GALAXY
THE radius of the space-time world, the total mass of the
universe, the comparability of galaxies these basic problems
involve directly the measured dimensions of our galactic system.
The appeal of such deep and generally unanswerable questions
has encouraged the attempt to find the extent of the Galaxy
from measures of its star clusters. The attempt succeeds in the
gross but not in detail. The clusters dimly outline the size but
show little of the structure. We may confidently expect that
analyses of star motions, star clouds, and individual stellar
distances will in time reveal with more than present clarity
the significance of our galactic system in the total material
universe.
59. Membership in the Galaxy. By the term "Galaxy,"
or "the galactic system, " is meant the aggregate of stars and
nebulae for which the distributions appear to be organized
with respect to the galactic plane. Globular clusters are
therefore included, with galactic stars and galactic dusters
and nebulae; but the Magellanic Clouds and the extra-galactic
nebulae (spiral nebula family) are outside the organization.
Possibly, however, some of the remote globular clusters
(e.g., N. G. C. 7006, N. G. C. 4147, and Messier 75) are actually
independent, being either fugitives from the Galaxy or chancing
for the moment (cosmically speaking) to be moving in this
part of space. Some of the high-velocity stars of the sun's
neighborhood also may eventually escape from galactic control.
We need more information on speeds and masses and on the
phenomena of galactic rotation before we can pass judgment
on these questions of membership.
171
172 DIMENSIONS OF THE GALAXY
The complete freedom of the Magellanic Clouds from our
Galaxy is but a surmise based on relative masses, present posi-
tions, and radial velocities. Without accurate information
concerning their proper motions, we cannot safely assume from
radial components that they are receding from the Galaxy 1 ;
in fact, the increasing evidence that the Galaxy is in rapid
rotation argues for the affiliation of the Magellanic Clouds with
our Galaxy, or, at least, with a local group of galaxies that
would also include the three Andromeda nebulae, Messier 33,
and some others. 2
In measuring the Galaxy, we should at the start admit
indefinite limits, and also striking irregularities, not only in
the interior but probably also at the edges. The dimensions
discussed below are therefore not to be taken too literally as
marking the boundaries or even as giving sharp limits of star
density. At best, we measure or estimate the distances of the
remotest attainable stars or groups of stars which yield to
present methods and which appear to be members of the
Galaxy.
60. The Higher System of Globular Clusters. To illus-
trate the space distribution of the 93 known globular clusters
of the galactic system (Appendix A), the following rectangular
coordinates have been computed for all clusters:
X = R cos (X - 327) cos ft
Y = R sin (X - 327) cos ft
Z = R sin ft
where R is the distance in kiloparsecs, ft is the galactic latitude,
and (X 327) is the galactic longitude measured from the
direction to the center of the cluster system. The latitude,
longitude, distance, and R sin ft are given in Appendix A; the
computed quantities X and Y are given in Table XII, I.
a. Eccentric Position of the Solar System. A diagram of the
distribution of the globular clusters in the plane of the Galaxy
^uyten, H. C. 326, 327, 1928.
2 Shapley, H. Repr. 61, 1929.
THE HIGHER SYSTEM OF GLOBULAR CLUSTERS
173
(XY plane) is shown in Figure XII, i. Crosses indicate clusters
lying on the north of the galactic plane, and dots those on the
south; the smaller the symbol, the more distant is the object
from the plane. The equality of the division by the galactic
plane of the supersystem of clusters is remarkable 47 clusters
are on the north, 46 on the south.
TABLE XII, I. COORDINATES OF GLOBULAR CLUSTERS
N. G C.
R Cos/3
Cos (X -
327)
R Cos ft
Sm (X -
3-27)
N G C
R Cos/3
Cos (X -
327;
R Cos ft
Sin (X -
327)
N G C.
R Cos ft
Cos (X -
327)
R Cos ft
Sm (X -
327)
104
+ 2 8
- 3 9
6139
+ 27 7
- 8 5
6517
+47 o
+ 17 i
288
- o 5
I
6144
+ 17 3
2 4
6522
+ 35 8
+ 06
362
+ 4 5
- 7 5
6171
+ 19 4
+ 1 7
6528
+ 44
+ 1.2
1261
-13 7
6205
+ 40
+ 68
65^
+ 23 o
+ 12.3
1851
5 o
10 6
6218
+ 95
+ 2 9
6S39
+35 8
+ 13 8
1904
-12 3
-13 2
6229
+ 67
+ 21 8
6541
+ 86
- i 5
2298
10 4
-23 4
6235
+ 28 o
O
6553
+ 26 6
+ 26
2419
28 o
-OS
6254
+ 10
+ 2 9
6569
+ 29 I
+ 05
2808
+ 30
-IS 6
6266
+ 18 3
- i 6
6584
+ 18 6
- 5 9
3201
+ i i
9 o
6273
+ 16
- 7
6624
+ 21 7
+ I 2
4147
- 9
- 4 5
6284
+ 27 6
-05
6626
+ 16 2
+ 23
4372
+ 5 o
- 8 o
6287
+ 27 4
+ 05
6637
+ 18 4
+ 06
4590
+ 6 7
10 7
6293
+ 22 8
- o 8
6638
+ 29 o
+ 43
4833
+ 88
-13 o
6304
+ 25 o
i 8
6652
+ 23 o
+ 06
5024
+ 3 2
- 1.3
6316
+31 5
- o 8
6656
+ 63
+ I 2
5053
+ 3 5
I
6325
+46 o
+ 04
6681
+ 18 7
+ i o
SI39
-f 4 2
- 5
6333
+ 20 3
+ 2 I
6712
+ 23 2
+ 11 6
5272
+ 20
+ I 7
6341
+ 33
+ 86
6715
+ 18 6
+ I 9
5286
+ 16 o
-17 o
63*2
+ 39 I
+ 4 I
6723
+ n 7
+ 2
5466
+ 3 8
+ 34
6352
+ 18 4
- 6
6752
+ 67
- 3 o
5634
+ 19 8
- 5 8
6356
+48 5
+ 60
6760
+ 23 I
+ 16 8
14499
+ 14 o
18 o
6362
+ 12
- 8
6779
+ 9 I
+ 17 8
5824
+ 24 4
II 9
6366
+ 26 3
+ 9 I
6809
+ 79
+ I 2
5897
+ 15
- 4
6388
+ 16 6
- 4 2
6864
+40 7
+ 14 8
S904
+ 7 4
+ 06
6397
+ 5 I
2 I
6934
+ 14 I
+ 18 7
5927
+ 16 8
II.
6402
+ 17 7
+ 7 2
6981
+ 15 6
+ H 4
5946
+ 27 2
-17 o
6426
+ 31 3
+ 17 4
7006
+ 22 4
+48.0
5986
+ 15 4
- 6 2
6440
+49 5
+ 70
7078
+ 4 7
+ 10.6
6093
+ 16 5
- i 9
6441
+ 21
02
7089
+ 66
+ 9-2
6101
+ 14 7
-13 5
6453
+ 50 o
- o 4
7099
+ 86
+ 4-6
6121
+ 69
I O
6496
+ 21 2
- 4 5
7492
+ 6.4
+ 9 r
The direction to the center of the system, derived in Chapter
II from the apparent positions of globular clusters, is seen to
agree with the direction on the basis of space coordinates;
in Figure XII, i there are 46 positive values of Y and 46 negative
values, with Y = o for one cluster. (The remote system
174
DIMENSIONS OF THE GALAXY
N. G. C. 7006, with coordinates X = 22.4, Y = 48.0, falls
outside the limits of the diagram.)
The origin of coordinates for Figure XII, i that is, the
position of the observer is on the border of the globular cluster
system. The center of gravity of the system of clusters, indi-
cated by an open square, has the coordinates X = +16.4,
Y = 0.3 (or Y = +0.2 if the remote and isolated N. G. C.
7006 is included).
Y-OT
X
X
"
* *
X
*
J
X
f
(
^
*?*
V
* x x *
X
*x
X
-10
X
X
"
\
X
. x
X
X-20 -10
b
20 +30 +40 GO
FIGURE XII, i.
Distribution of globular clusters in the plane of the Galaxy.
is at the origin of coordinates.
The sun
Probably 10 or 20 globular clusters, within the limits of
space represented by the diagram, await discovery. Obscuring
nebulosity possibly conceals most of these systems, of which the
existence is intimated by the scarcity of observed points in the
right half of the figure. Of course, we need not assume high
regularity in distribution, or even approximate circularity in
the projected array; but it is probably observational difficulties
caused by nebulosity and by the small dimensions and faint
magnitudes of remote clusters, and not inherent irregularities,
that have produced the apparent incompleteness for X greater
than +30 kiloparsecs. On the left side of the diagram, from
THE HIGHER SYSTEM OF GLOBULAR CLUSTERS
175
X = o to X = 20, where the survey may be considered
sufficiently exhaustive, the complete absence of clusters from
one quadrant is even more striking and structurally significant
than the scarcity of values of X greater than +30.
The cluster at the extreme left is N. G. C. 2419 an object
in a region far from other clusters, found through studies of the
Lowell Observatory photographs. 3
Z=20
+10
-10
-20
x=-a
<
-
q
. .. '
<
:.V
.
."*
*."
OJ
*
** "
-20 -10 +10 +20 +30 --40
FIGURE XII, 2.
Distribution of globular clusters in the XZ plane.
b. The "Region of Avoidance." The same asymmetrical
position of the sun with respect to the supersystem of globular
clusters is shown in Figure XII, 2, where all 93 systems are
plotted on the XZ plane. The center of gravity that is,
the algebraic mean values of X and Z, indicated by an open
square is at X = +16.4, Z = +04. N. G. C. 2419 again
stands out on the extreme left.
The most interesting feature of Figure XII, 2, which repre-
sents a section perpendicular to the galactic plane, is the "region
of avoidance. " The scarcity of globular clusters in low galactic
latitudes, shown most clearly in Figure 4 of Chapter II, is
again in evidence. Here is a central section 2.5 kiloparsecs
(8,000 light years) in diameter, in which no globular cluster
has been found. On the other hand, there is only one galactic
8 Shapley, H. B. 776, 1922.
I 7 6
DIMENSIONS OF THE GALAXY
cluster out of the 249 listed in Appendix B that does not fall
well within this mid-galactic segment, and that duster, N. G. C.
2243, is of doubtful nature and uncertain distance. Practically
all known galactic stars and nebulae also fall within this " region
of avoidance. "
c. Projection on the YZ Plane.
Figure XII, 3 shows the
distribution of globular clus-
ters on the YZ plane, which
is perpendicular to the line
joining the sun and the cen-
ter of the system at galactic
longitude 327, galactic lati-
tude o. The "region of
avoidance" is again clearly
-20
At
.**
Y=-20
+20
-10 +10
FIGURE XII, 3.
Distribution of globular clusters in the
YZ plane.
shown, and also the essential
symmetry of the globular
cluster system, for the num-
bers of clusters in the four quadrants are 23, 24, 22, and 24.
Again N. G. C. 7006 is outside the diagram, with coordinates
Y = 48.0, Z = - 20.4.
61. The Distance to the Galactic Center. It appears to
be a tenable hypothesis that the supersystem of globular clusters
is coextensive with the Galaxy itself. Researches on variable
stars in the Milky Way 4 will eventually afford an instructive
check on this hypothesis. Until we have such direct measures
we can only assume that the galactic system is at least as large
as the system of globular clusters, and note that we have shown
rather convincingly that the globular clusters are galactic
members or associates.
The algebraic mean of the values of R cos (X 327) cos ft
gives a satisfactory indication of the distance to the center
of the cluster system and provisionally, therefore, of the dis-
tance to the center of the Galaxy. In so far as it depends on
4 Ibid., H. Repr. 51, 1928.
THE DISTANCE TO THE GALACTIC CENTER 177
the globular clusters now known, the uncertainty of the distance
does not exceed ten per cent. Further research on faint globu-
lar clusters, especially if new ones be found, will be more likely
to extend the system than to reduce it; on the other hand, the
distances of the more remote clusters are the least certainly
determined and must be given low weight. We shall adopt as
the distance to the center
R g = 1 6 kiloparsecs
= 52,000 light years
The galactic star clusters and the ordinary individual stars
are too near the sun to contribute effectively to the determina-
tion of the distance to the center; but the direction to the center,
as is well known, is confirmed by the counts of faint stars 5
and through the recent studies of galactic rotation by Oort,
J. S. Plaskett, Lindblad, Schilt, and others; it is shown, though
less definitely, by the distribution of Milky Way star clouds,
planetary nebulae, Class O stars, and other objects of high
luminosity. Most galactic objects, however, with the possible
exception of the novae and Cepheid variable stars, are too
faint absolutely and too infrequent in number to contribute in
current surveys of galactic regions at and beyond the center
of the cluster system.
Studies of the cluster-type Cepheids and the long-period
variables stars in the star clouds of the southern Milky Way
have led the writer and Miss Swope to a value of the distance of
the centrally located star clouds that is very much like the
value given above. 6 The variable star investigations of several
observers at Harvard tend to support this suggestion that the
heavy star clouds in Ophiuchus, Sagittarius, Scorpio, and
neighboring constellations are parts of a massive stellar nucleus
of the galactic system. The distribution of the cluster-type
Cepheids in these regions suggests that the nucleus extends
perhaps halfway from the center toward the sun. The speed
6 Nort, Recherches Ast. Obs. Utrecht, 7, 113, 1917; Scares, Mt. W. Contr.
347, 1927-
8 Shapley, H. Repr. 52, 1928.
178 DIMENSIONS OF THE GALAXY
of rotation about this nucleus is approximately 300 kilometers
a second at the sun's distance from the center.
One important feature of the galactic central region is that
the center itself lies behind heavily obscuring nebulosity.
The dark clouds are apparently but a part of those causing the
rift in the Milky Way that extends from Cygnus southward to
Centaurus; they seem to be largely responsible for the apparent
avoidance of the mid-galactic regions by globular clusters.
62. Galactic Dimensions. An inspection of Figures XII,
i, XII, 2, and XII, 3 gives only a rough idea of the total diam-
eter of the flattened galactic system. The most remote globular
clusters are the following:
Distance in Distance in
N. G. C. Kiloparsecs N. G. C. Kiloparseca
6325 46: 6517 50:
6342 40: 6528 44 4
6356 50: 6864 48 5
6440 50: 7006 56 8
6453 So:
Some of these values are uncertain; the distances may be greater
or less; but the superior distance of N. G. C. 7006, a cluster in
Vulpecula with -R = 56.8 kiloparsecs = 185,000 light years,
seems to be well attested by observations on its individual stars
and on its cluster-type Cepheids. 7
The greatest distance separating two of the clusters is
N. G. C. 7006 to N. G. C. 2298 = 80 kiloparsecs
Several other clusters are nearly as widely separated; N. G. C.
2298 in Puppis is 71.3 kiloparsecs from N. G. C. 6517 across the
sky in Ophiuchus, and N. G. C. 2419 in Lynx is 79 kiloparsecs
from N. G. C. 6453 in Scorpio. We may take such distances to
indicate the extreme dimensions of the galactic system, for
certainly most of these globular clusters, if not all, are integral
parts of the Galaxy.
It does not follow from the wide dispersion of globular dusters
that individual stars of the Galaxy are so widely dispersed, but
7 Shapley and Mayberry, Mt. W. Comm. 74, 1921.
THE SYSTEM OF GALACTIC CLUSTERS 179
it appears reasonable to maintain that the greatest diameter
of the Galaxy in its plane is not less than 70,000 parsecs, and
it may be 30 per cent larger. The thickness of the system differs
with distance from its center, being perhaps 10,000 to 15,000
parsecs at the galactic nucleus and one half as much out where
the solar system is located. Occasional isolated stars, however,
and, of course, the globular clusters extend to 20,000 parsecs
and more from the galactic plane, lying well outside the rela-
tively thin mid-galactic stratum.
Various studies of the extra-galactic nebulae, carried on,
for the most part, at Mount Wilson, Upsala, and Harvard, seem
to leave no doubt but that our galactic system is extremely
large compared with typical external systems. The Andromeda
nebula may have one fifth the diameter, but such gigantic
spirals appear to be rare. Among the hundreds of thousands,
possibly millions, of discoverable external systems or island
universes in the oceans of space, our own system tends to be
continental in dimensions. Whether it is comparable in form
and structural detail with typical spirals, or more analogous
with the irregular Magellanic Clouds, is a matter for the
researches of the immediate future. Extreme irregularity of
stellar distribution and heterogeneity of internal motion appear
to characterize the Galaxy; but such irregularities may be
normal in the arms of a great spiral, for all we now know, and
are therefore not conclusive evidence that the Galaxy is a
sheet of intermingling star clouds. In Chapter XIV this sub-
ject is again discussed and a revised hypothesis of galactic
structure is proposed.
63. The System of Galactic Clusters. Although the
loose star groups contribute as little as individual stars of
ordinary type to our knowledge of the dimensions of the Galaxy,
their space distribution may be mentioned here as bearing on
the structure of the nearer parts of the Milky Way. The
catalogue of 249 galactic clusters in Appendix B gives galactic
longitude, distance, and R sin ft (distance from the galactic
i8o
DIMENSIONS OF THE GALAXY
plane) ; these quantities are used in making the plots for Figures
XII, 4 and XII, 5, which supplement the figures in Chapter II
dealing with apparent distribution.
Features to be noted in the diagrams include:
90
240
270
FIGURE XII, 4
Distribution of galactic clusters in the galactic plane within four kilo-
parsecs of the sun (origin of coordinates, which are galactic longitude
and distance from the sun). Dots symbolize clusters north of the
galactic plane; circles, those south. Arrows represent clusters beyond
the limits and in the directions indicated. For clusters with galactic
latitude greater than 20, the projection on the plane R cos /3 is
plotted instead of the distance JR. The radial scale in kiloparsecs is
marked along the zero axis.
1. The contrast in galactic distribution of galactic and globu-
lar clusters (see Figure II, 5).
2. Close confinement of galactic clusters to the neighborhood
of the galactic plane.
3. The relative nearness of galactic clusters to the sun, which
results in a distribution free from effects of the obstructing
THE SYSTEM OF GALACTIC CLUSTERS
181
douds that contribute much to the anomalous distribution of
the globular clusters.
The nearest globular clusters are:
Distance in R sin/9 in
N. G. C. Name Light Years Light Year
104 47 Tucanae 22200 15600
5139 (o Centauri 22200 -f- 5900
6121 Messier 4 23500 + 6200
6397 Dunlop 366 18400 3900
6656 Messier 22 22200 3600
400
or
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120
FIGURE XII, 5.
Distribution of galactic clusters, (a) Galactic longitude
(abscissae) and R Sin /3 (in parsccs), full line indicates 10
algebraic mean R sin |8, smoothed over 30. (6) Smoothed
10 arithmetic means for same material, coordinates as for
(a). Three clusters are off at upper left.
The most remote galactic clusters, excluding those for which
the data are uncertain, are the following:
N. G. C.
Distance in
Light Years
R sin B in
Light Years
2236
27200
200
2259
51600
+3200
2324
22600
4-1900
H8
21600
-1800
H 9
21600
+ 400
6005
21600
-1500
It seems clear that larger telescopes will eventually reveal many
galactic clusters in remote parts of the Galaxy.
182 DIMENSIONS OF THE GALAXY
The most remote individual stars known in the Galaxy are
the novae and a few long-period Cepheid variables, of faint
apparent magnitude, studied by GerasimoviC, Miss Swope,
Miss Harwood, and others on Harvard and Nantucket plates.
Some of these appear to be well beyond the galactic nucleus,
with distances comparable with those of the remoter globular
clusters and the Magellanic Clouds. Since progress is rapid
in the discovery and study of faint variables, it will be advisable
to postpone the discussion of the part they play in the measure-
ment of the extent and orientation of the galactic system. It
may be 20 years or more before the detailed picture of the
structure of the galactic star clouds can be drawn.
CHAPTER XIII
STAR CLUSTERS IN THE MAGELLANIC CLOUDS
A PECULIAR importance attaches to the two clouds of Magellan.
They are near enough to be completely resolved into millions
of stars, remote enough to be viewed and worked objectively,
and rich in the various types of stars and nebulae. They
serve as keys to knowledge of distant galaxies, opening the way
from local regions to the outside universe.
Investigation into the structure and content of the Magellanic
Clouds will assist, first, in the interpretation of the Milky Way
clouds and the galactic system as a whole and, secondly, in
revealing the nature of the more distant and inaccessible star
clouds, such as N. G. C. 6822 and others of the Magellanic
type of extra-galactic nebula. Probably two or three per cent
of all recorded external systems are of this irregular kind.
In the Magellanic Clouds there are clusters of both the globu-
lar and the galactic type, and among the latter there is much
variety in richness, dimensions, and nebulosity. For both
types we can determine with some exactness the range in linear
dimensions and in real luminosities. The distances from the
observer can be assumed the same throughout each cloud; the
apparent magnitudes, therefore, differ from absolute magnitudes
only by an additive constant, and angular diameters from linear
diameters only by a simple factor.
64. A Summary of Clusters and Nebulae. In the New
General Catalogue and the Index Catalogues 41 clusters and
nebulae are listed within the limits of the Small Cloud and 301
within the Large Cloud. The descriptions, which are based
mainly on Sir John Herschers visual observations of about a
century ago, are meager. Photographic plates show many of
183
1 84 STAR CLUSTERS IN THE MAGELLANIC CLOUDS
the older descriptions to be quite inadequate and reveal scores
of clusters and nebulae that have not yet been catalogued and
described.
For the Small Cloud a catalogue by Shapley and Miss Wilson 1
gives 237 new objects, chiefly nebulous stars and groups of
stars. The Harvard photographs are incapable of differentiat-
ing clearly the nebulae or clusters that are fainter than the
fourteenth magnitude; objects of these classes that are abso-
lutely fainter than magnitude 3 are therefore as yet unlisted.
A manuscript catalogue of the star clusters in the Large Magel-
lanic Cloud, recently prepared from Harvard plates, contains
no new entries nearly doubling the number known from
Herschel's survey and subsequent investigations. No attempt
has yet been made to list the many nebulae that do not appear
in published catalogues.
Among the great number of nebulae in both Clouds, not a
single object has been found which could be assigned safely
to the spiral class. As would be expected from their total
absolute magnitudes, mainly between 3 and 7, the nebulae
are, for the most part, of the diffuse and irregular types, with
a meager sprinkling of planetaries.
In the Large Cloud many of the diffuse nebulosities are of
exceedingly high total luminosity, the greatest of them being
the famous "Looped Nebula," 30 Doradus. It is the largest
object of its class, except possibly for some of the diffuse nebu-
losities connected with spiral nebulae; its absolute brightness
probably exceeds magnitude 13, and its total diameter, includ-
ing the fainter wisps and loops of nebulosity, is 30 parsecs or
more. Many faint stars are involved, but apparently most of
the registered luminosity comes from the nebula itself. It
differs in this respect from the majority of the diffuse nebulae
in the Clouds; their apparently excessive luminosity is largely
that of involved bright stars or star clusters.
Compared with 30 Doradus the great Orion Nebula is a
pigmy. If the former were in the position of the Orion Nebula,
1 H. C. 275, 276, 1925.
THE GLOBULAR STAR CLUSTERS 185
it would extend over most of the constellation of Orion, and
its brightness would be so great that, even though 600 light
years distant, it would cast strong shadows on the surface of
the earth. 2
To catalogue and describe in detail the numerous dusters of
the Magellanic Clouds is inadvisable at the present time in
view of the new material that will soon be available. Hereto-
fore the instruments mainly responsible for our knowledge of
the structure of the Clouds have been the Lick Observatory
spectrograph at Santiago, Chile, which has given us the radial
velocities of bright line nebulae, and the Bruce 24-inch doublet
at the Boyden Station of the Harvard Observatory. On plates
of suitable exposure the Bruce telescope shows objects of the
eighteenth magnitude and fainter, but the sacle (i' = i mm.)
does not permit adequate resolution of the small clusters. The
new 6o-inch reflector of the Harvard Observatory will soon come
into use in the comprehensive study of the Magellanic Clouds.
Until its surveys have made considerable progress, we must
not only leave open the cataloguing and analysis of the clusters
and nebulae but also be content with somewhat provisional
values of the distances and dimensions of the Clouds themselves.
65. The Globular Star Clusters. Dunlop, Sir John Her-
schel, and others have described many of the compact star groups
in both Clouds as globular. The N. G. C. records 16 globular
clusters in the Large Cloud and two in the Small. On the
basis of photographic material, Bailey, Melotte, and others
have remarked that few if any of these objects are correctly
assigned. In fact, none of them is now retained as truly globu-
lar. On the other hand, the accepted globular clusters, listed
for both Clouds in Table XIII, I, are not described as such in
the N. G. C., though they all appear in that catalogue. The
2 Shapley and Wilson, H. C. 271, 1925. Allowance has been made in the
foregoing statements for the revision of the distance of the Large Magellanic
Cloud. A final determination has not been made, but it appears best to reduce
by half a magnitude the absolute magnitudes of clusters and nebulae previously
published.
1 86 STAR CLUSTERS IN THE MAGELLANIC CLOUDS
existence of these globular systems affords a valuable oppor-
tunity for the comparative study of globular and galactic types
and for the examination of the relation of globular clusters to
galaxies.
The first two clusters of Table XIII, I belong to the Small
Magellanic Cloud; the eight others to the Large Cloud. The
angular diameters and integrated magnitudes are given on the
same basis as in Appendix A for globular clusters in general.
The diameters, therefore, are not indicators of the extreme
bounds of the clusters they are rather measures of nuclei.
N. G. C. 416 in the Small Cloud is more uncertain than the
others and later may be dropped.
It is seen that the globular clusters in the Large Cloud range
from the compact Class II to the fairly open Class VII. In
earlier considerations of clusters in the Large Cloud 3 seven
objects were listed as possibly globular. Of these N. G. C.
1651 has now been definitely dropped, 4 and N. G. C. 1835
and N. G. C. 1856 have been added to the list. Later analysis
may show that some of the following N. G. C. objects are
globular clusters:
1711 1916 1986 2058 2133
1789 1926 2019 2065 2134
1852 1939 2031 2107 2157
1872 1944 2056 2108 2164
1903
In none of the globular clusters of the Magellanic Clouds
have variable stars been found, nor have their brighter stars
been measured individually. The final test as to whether these
doubtful objects are typical globular systems or merely open
groups involved in nebulosity will lie in future examinations
for variable stars and in the study of density and luminosity
laws.
The spectrum of N. G. C. 419, in the Small Cloud, resembles
Class K in its distribution of light and in the faint appearance
8 H. B. 775, 1922; H. C. 271, 1925.
4 It was included in H. B. 848, 849, and 852 as a doubtful object.
THE GLOBULAR STAR CLUSTERS
187
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i88 STAR CLUSTERS IN THE MAGELLANIC CLOUDS
of the G band and of lines H and K. The spectrum of N. G. C.
416 is too diffuse and faint to classify. The spectral class 6
of N. G. C. 1866, in the Large Cloud, is F8; that of N. G. C.
1835 is possibly GS, though for it and the other most compact
clusters of the Large Cloud the spectral images on the Harvard
objective prism plates are too difficult for classification.
Miss Cannon has thrown doubt on the globular nature of a
number of bright objects in both clouds by showing that their
integrated spectra are of early class; we have already seen that
practically all typical globular clusters belong to classes F and
G. 6 Thus, she finds:
N. G. C. Spectrum
294 A?
1872 A3
1903 A
2041 A3
2107 A?
2134 A
2157 A2
2164 AS
66. Distances of the Clouds Derived from Variables
and Globular Clusters. In the ninth column of Table XIII, I
a value of the distance modulus is given for each cluster, derived
from the measures of angular diameter and integrated photo-
graphic magnitude. In the use of these data we follow the
principles developed in an earlier chapter on the distances of
globular clusters of the galactic system. In getting mean
values of the modulus for each Cloud, weights were assigned as
follows:
Quality Weight
c 4
d 2
e i
While clusters of quality c may be accepted as almost certainly
globular, some doubt still attaches to those qualified as d and e.
H. B. 868, 1929.
See Appendix A.
DISTANCES OF THE CLOUDS 189
The mean modulus derived for the Small Magellanic Cloud
is nearly identical with the value, 17.55, previously derived from
107 Cepheid variable stars. 7 With the adopted revision of the
zero point of the period-luminosity curve 8 the distance modulus
from the variable stars becomes 17.32. Accepting this value,
we have for the Small Magellanic Cloud
TT = o".oooo345
Distance = 29 kiloparsecs
= 95,000 light years
Linear diameter = 6,000 light years
At this distance the integrated absolute magnitude is 7.12
for N. G. C. 419, the only object that appears definitely, from
the survey of existing plates, to be a globular cluster.
For the Large Magellanic Cloud the mean distance modulus
from eight globular clusters is 17.25, with a mean computed
error of only one tenth of a magnitude. But the Cepheid
variable stars should eventually give us a much more dependable
value of the modulus. The preliminary determination, 9 giving
a modulus from variables of approximately 17.7, was based on
few stars and somewhat provisional magnitude sequences.
The sequences are not yet wholly satisfactory, but a current
unpublished study at Harvard has produced periods of about
50 Cepheid variable stars in the Cloud and yields a value of
17.10 for the distance modulus. Adopting this value, we obtain
the following results for the Large Magellanic Cloud:
TT = o" .000038
Distance = 26.2 kiloparsecs
= 86,000 light years
Linear diameter = 10,800 light years
The corresponding mean absolute photographic magnitude of a
7 Shapley, Yamamoto, and Wilson, H. C. 280, 1925; see, also, Shapley, H. C.
255, 1924.
8 See Chapter X.
9 Shapley, H. C. 268, 1924.
190 STAR CLUSTERS IN THE MAGELLANIC CLOUDS
globular cluster in the Large Magellanic Cloud is 7.46
(weighted mean). The absolute values range from 9.1
to 6.5 an indication of the degree of uncertainty involved
in assuming a constant integrated absolute magnitude for
globular clusters. The spread is considerably less if the cluster
N. G. C. 1866 is assigned to the foreground rather than to the
Magellanic Cloud, and it would be very small indeed (7.2
to 6.5) if the newly admitted N. G. C. 1856, when analyzed
with a large telescope, proved to be a nebulous open group.
67. On the Relation of the Clusters to the Magellanic
Clouds. The angular diameters of the globular clusters in the
Large Cloud are at most two or three minutes of arc; the angular
diameter of the Cloud as a whole is slightly more than seven
degrees. 10 Enormous and rich as we know a typical globular
cluster to be, it is obviously small compared with ordinary
external galaxies. The clusters of the various sorts, however,
are important in the general appearance of the Clouds and
especially in the make-up of the high-luminosity population.
The distribution of the nebulous groups throughout the
Clouds is much the same as the distribution of the Cepheid
variable stars and of the general stellar population; on the
other hand, the accepted globular clusters in the Large Cloud
are almost exclusively to the north, and N. G. C. 1866 and
N. G. C. 1831 lie quite outside the main structure of the Cloud.
There are, however, a half-dozen variable stars, apparently of
the Cepheid class, in the same region, and long exposures on
small-scale plates show that these outlying clusters and variables
are within the observable bounds of the Cloud.
The asymmetrical distribution of the globular clusters in the
Large Cloud has led some to surmise that the globular clusters
of the galactic system may also be eccentrically arranged with
respect to the general galactic structure and, therefore, that
they cannot be used, as I have used them, in estimating galactic
dimensions. But this one-sided distribution of the globular
"Ibid.
RELATION OF CLUSTERS TO MAGELLANIC CLOUDS 191
clusters in the Large Cloud is modified by the inclusion of
N. G. C. 1835 and N. G. C. 1856 in the list accepted at present,
and it would be quite altered if a considerable proportion of the
list of suspected globular clusters prove to be typical systems.
The two clusters N. G. C. 1789 and N. G. C. 1944, both of
which are strongly suspected as globular, lie far from the center
of the Cloud on the south directly across from the outlying
globular clusters of Table XIII, I.
It is of significance that the 808 known variable stars in the
Large Cloud and the 969 in the Small Cloud 11 avoid the numer-
ous open clusters. In this respect the Clouds are like the
galactic system, where open clusters are free of variable stars
of all kinds. 12 The globular systems in the Magellanic Clouds
are, of course, too compact to have been searched as yet for
variables.
Possibly the most striking fact arising from the study of
globular clusters in the Magellanic Clouds is the low absolute
magnitude of their brightest stars when compared with the
brightest objects in the open and nebulous groups. If the new
values of the distance moduli are correct, there is scarcely a
star in the ten accepted globular systems of the two Clouds
that exceeds 3 in absolute photographic magnitude. This
result, however, is in complete agreement with the condition
found in globular clusters of our own galactic system. In
contrast, the individual stars in scores of the nebulous groups
appear to exceed 3 in absolute photographic magnitude,
and in many they attain the excessively high luminosities of
5 and 6. This again is in agreement with the data on
absolute magnitudes in galactic clusters, especially in those
early-spectrum groups in Orion, Scorpio, and elsewhere that
are associated with bright nebulosity.
It may be remarked in conclusion that, notwithstanding their
remoteness, isolation, and high galactic latitudes, the Magellanic
Clouds may be more closely allied to our galactic system than
" Leavitt, H. A., 60, No. 4, 1908.
" See Chapter IV, Section 20.
IQ2 STAR CLUSTERS IN THE MAGELLANIC CLOUDS
heretofore suggested. 13 There is growing evidence for galactic
rotation, and from a preliminary value of its velocity we com-
pute that the observed high-speed recession of the Clouds
should be assigned almost wholly to the rotation of the Galaxy.
Apparently, the Clouds are not in rapid motion with respect to
the galactic nucleus or the system of globular clusters.
18 H. Repr. 61, 1929.
CHAPTER XIV
DATA BEARING ON THE ORIGIN OF THE GALAXY
IT is encouraging to see how fragile and futile are the majority
of astronomical theories and speculations and how temporary
are the most conservative " interpretations"; for the futility
of speculations emphasizes the importance and durability
of observations and indicates the steady progress of the science.
Nevertheless, interpretations must be ventured in order to
fill in the picture where observations do not or cannot touch, and
also to guide further measurement and analysis.
It was not unexpected that the working hypothesis of the
origin and growth of the galactic system, suggested several
years ago as an aid in the study of the observations then avail-
able on clusters, nebulae, and star clouds, would soon require
extension and repair. The current researches on extra-galactic
nebulae and on the variables in the Milky Way contribute
vigorously now and will add still more in the near future, to
the theory of the Galaxy and comparable systems. Meanwhile,
various data bearing on galactic origin and structure can be
assembled in this chapter and tentatively appraised; in the
final section a modified hypothesis of galactic structure is
advanced.
68. The Earlier Interpretation. In the discussions of
galactic origin and behavior that grew out of the earlier work on
clusters and the local star system, 1 it was suggested that the
discoidal galactic system, originating from the combination of
independent star clouds and clusters, has long been growing,
by assimilating such groups, to its present relatively enormous
size. Its diameter was found to be of the order of 90,000
1 Mt. W. Contr. 157, Sec. 7, 1918.
193
IQ4 DATA BEARING ON THE ORIGIN OF THE GALAXY
parsecs, and the center was located in the remote star clouds
of the southern Milky Way. Evidence was then found (1918)
that the galactic system is moving with high speed through
space, with respect to the brighter extra-galactic nebulae,
toward some ill-defined point high in the northern hemisphere. 2
Subsequent investigations of this motion by Wirtz, Lundmark,
Stromberg, and others confirmed the general direction, the
speed, and the uncertainty of apex.
The moving Galaxy was visualized as collecting in the course
of time subordinate external systems and gradually dismember-
ing and absorbing them. The local cloud was mapped out
and described as one of these minor elements, though previously
it had been treated as the major part. The Galaxy was con-
sidered not a single spiral nebula but rather an organization
of many half-digested star clouds and clusters, moving in an
extensive stratum of stars and galactic nebulae.
It was suggested that the obvious dynamical equilibrium of a
globular cluster, acquired originally at a great distance from
external perturbing matter, results in a delicate adjustment that
readily breaks down under stresses such as those prevailing in a
large galactic system; further, that faint stars in a globular
cluster, as in the galactic system, are of small mass 3 and, there-
fore, of more than average velocity, so that in their motions
in the cluster they frequently attain great distances from the
center. When such globular systems approach or mingle with
other clusters or the dense stellar fields in the mid-galactic
segment, the dwarfs will preferentially become scattered
through encounters. The massive cluster stars, which are
mostly of high luminosity, and which are concentrated to the
center and endowed with low peculiar velocities, will retain
their cluster organization longer in a disrupting neighborhood.
A globular cluster thus becomes a galactic cluster which slowly
dissolves into the galactic field. Flattening and distortion of
* Ibid. 161, Sec. VII, 1919.
3 In view of subsequent work on the mass-luminosity relation there is now little
of the hypothetical about this suggestion.
THE EARLIKR INTERPRETATION 195
galactic clusters and star clouds arise through the "encounter
machinery" discussed by Jeans and through rotation. Star
streaming appears to be a complication of the various motions
in and of the local system and the general galactic field.
On the provisional interpretation sketched above, our galactic
system appears to be in an advanced stage of the survival of
the most massive. Once an enormous mass has accumulated
in such a celestial organization, subsequent accretions should
be numerous and relatively easily acquired. The Magellanic
Clouds (and we should now include their analogues among
the extra-galactic nebulae) are possibly similar growths. The
Clouds, however, are relatively so near and are so much smaller
than the Galaxy in mass and dimensions that the possibility of
ultimate assimilation into the galactic fields is not excluded,
notwithstanding their present large positive velocities in the
line of sight; they are, indeed, not receding rapidly if we correct
for "galactic rotation."
In earlier work on the galactic problem, I found it necessary
to conclude that the spiral nebulae are not comparable to our
Galaxy in size. The conclusion was based largely on observa-
tions of novae. Assuming the novae in spirals to be comparable
in luminosity to those in the Galaxy, in 1917 I computed the
distance of the Andromeda Nebula 4 to be approximately a
million light years; but even at this great distance (rather an
overestimate) it was shown to be much smaller than our Galaxy.
The lack of comparability between galactic system and spiral
nebula appears now more certain than before; ours is a Continent
Universe if the average spirals are considered Island Universes.
In view of this incomparability in dimensions and mass, and
especially because of the evidence for proper motions in the
spiral arms, I temporarily abandoned the hypothesis that
the nebulae of the spiral family are stellar in composition. But
the stellar composition of at least some of them has now been
proved; the arguments against the Kant-Herschel theory of a
plurality of universes have gone down under the weight of
4 P. A. S. P., 29, 216, 1917.
196 DATA BEARING ON THE ORIGIN OF THE GALAXY
novae and variable stars. The two results that seem most
convincing in establishing the stellar character of the spiral
family of nebulae are Landmark's observation of the generality
of the Magellanic type of star cloud among the extra-galactic
nebulae 5 and Bubble's work on the Cepheid variables in several
typical bright spirals.
69. The Research on Milky Way Variable Stars. The
measurement of the size of the galactic system, discussed in
Chapter XII, depends primarily on the Cepheid variable stars
and other stars of high luminosity in globular clusters. It is
unsatisfactory to continue to base estimates wholly on the
distribution of globular clusters. Direct measurements, how-
ever, are difficult for two reasons: (i) there is interference by
obscuring clouds in low galactic latitudes, and (2) extensive
labor is necessary to map out the irregular star clouds and the
galactic boundaries by determining the distances of the stars
one by one.
The customary statistical method of deducing details of
galactic structure from rather indiscriminate counts of stars
and from measures of motions in the solar neighborhood is
very limited in scope and is, in fact, wholly inadequate for
analyses of regions characterized by galactic star clouds some
20,000 to 100,000 light years distant. The direct attack by
those photometric methods that reach far and give unambiguous
results on the problem appears to be the only satisfactory way
of working out details of galactic dimensions and structure.
In time, spectroscopic parallaxes and spectral parallaxes of
distant stars may be highly effective, but at present the best
approach seems to be through variable stars of all types.
To meet the need for more information on faint variable
stars, a long program of variable star investigations was inaugu-
rated in 1923 at the Harvard Observatory. The program has
5 Pop. Astro. Tidsk., 7, 64, 1926. He lists 21 systems as probably being of
the Magellanic type. At Mount Wilson and Harvard it has been pointed out
that two or three per cent of all external systems are irregular in form and
are probably star clouds (see Chapter XIII).
THE DISTRIBUTION OF GALACTIC CLUSTERS 197
been described elsewhere; 6 it will suffice here to mention briefly
a few of the results that already begin to throw light on the
origin of the Galaxy.
1. Since the starting of the variable star program, about
2,500 new variable stars have been discovered on Harvard
plates, nearly doubling the number previously known in the
galactic system. The variables are largely of the Cepheid and
long-period classes ; they are accordingly giants. For more than
half, the maximum magnitudes are fainter than 14, and they
are therefore at least 20,000 light years distant.
2. Indications of a massive nucleus of the Galaxy in the
Sagittarius region have already been described in Section 61,
above. 7
3. The diameter of the galactic nucleus, if we judge by the
variable star data and the long-exposure photographs of the
Milky Way, is something like 35,000 light years.
4. Long-period variable stars are found to be numerous in
Milky Way Field 185 and adjacent regions; we have, therefore,
hopes that this type of variable can also be calibrated and that
it will prove useful in estimating the distances of star clouds.
5. The distance to the Sagittarius clouds is practically the
same as the distance derived from the globular star clusters for
the center of the galactic system. It appears reasonable to
assume tentatively that these star clouds actually mark the
center of the larger galactic system and that it is their total
mass that is important in the motions of our local system.
70. Peculiarities in the Distribution of Galactic Clus-
ters. The clusters listed in the catalogue in Appendix B do
not extend deep into the galactic structure; they tell us nothing
of the center or of the boundaries. There is significance,
however, in certain peculiarities of their distribution. Already
we have noted that in contrast with globular clusters they are
rather uniformly dispersed in galactic longitude, and also that
6 Shapley H. Repr. 51, 1928.
7 See, also, H. Repr. 52, 1928.
198 DATA BEARING ON THE ORIGIN OF THE GALAXY
they are largely confined to the low galactic regions where
globular clusters are scarce. There are two additional features
of their distribution that are worth consideration:
1. The infrequency of galactic clusters in the first quadrant
of galactic longitude; there are very few of these systems in
the Aquila-Cygnus region of the Milky Way.
2. The narrow restriction of the clusters to low galactic
latitudes in the direction of the galactic center and their wide
dispersion in galactic latitude in the opposite part of the sky.
This second phenomenon is more conspicuous in the second
figure of Chapter II, in which ordinates are galactic latitudes,
than in the fifth figure of Chapter XII, in which the ordinates
are distances from the galactic plane. The distribution might
be explained as a consequence of the motions of galactic clusters
in long orbits about the nucleus in Sagittarius. When such
objects are seen from the earth's eccentric position in the
Galaxy, those in the direction of the center would appear to be
in lower latitudes than those away from the center, except
when the orbits lie exactly in the galactic plane. It is probable
that none of the galactic clusters beyond the center of the
Galaxy enters our catalogue.
The alternative and, I think, preferable interpretation is that
galactic star clusters are associated largely with particular
galactic star clouds. Irregularities of distribution and con-
centration in low galactic latitude are therefore merely con-
sequences of the distribution of such star clouds as the local
system in this part of the Galaxy. If the galactic clusters are
closely affiliated with various star clouds, we may find them
differing systematically in spectral and structural characteristics
from one part of the sky to another. We already have an indi-
cation of such diversity in the orientation of the axes of elonga-
tion, discussed in Section 33. The bright clusters of Auriga
(Messier 36, Messier 37, Messier 38) are rich and not strongly
condensed; many of the small condensed clusters of Sagittarius
are nebulous, and the groups in Carina are systematically
bright.
RADIAL VELOCITIES OF GLOBULAR CLUSTERS
199
71. Radial Velocities of Globular Clusters. The meas-
ured radial velocities of globular clusters range from 350
to +315 kilometers a second. From Table XIV,I it can be
seen that there is no clear dependence of velocity on class of
TABLE XIV, I. RADIAL VELOCITIES OP GLOBULAR CLUSTERS
N. G. C.
Class
ft
Spectrum
Angular
Diameter
PK
Mag.
Distance
Radial
Velocity
'
kpc
1851
II
-34.5
5 3
6 o
14 3
+315
1904
V
-28
3 2
8 i
20 4
+ 235
~~ 5024
V
+79
3 3
6 9
18.2
-180
- 5272
VI
+77 5
G
9 8
4 5
12 2
-130
- 5904
V
+46
G-
12 7
3 6
10 8
+ 10
- 6093
II
+ 18
KO
3 3
6 8
17 5
+ 70
6205
V
+40
GO
IO
4 o
10 3
-265
6218
IX
+ 25
9 3
6 o
II
+ 160
6229
VII.
+40
1.2
9 7
29 8
100-
6266
IV
+ 7
KO
4 3
7 o
18 6
+ SO
6273
VIII
4 9
GS-
4 3
6 8
16 3
+ 30
6333
VIII
+ 10
K?
2 4
7 4
20 8
+225
6341
IV
+35
Gs-
8 3
5 i
II 2
-160
6626
IV
- 7
G 5
4 7
6 8
16 6
o
6934
VIII
20
GO
i S
9 4
24 9
~3So.
7078
IV
-28
F
7 4
5 2
13 i
- 94
7089
II
-36
FS
8 2
5 o
13 9
10
7099
V
-48 5
F8
5-7
6 4
14.6
-125
cluster, galactic latitude, angular diameter, total magnitude,
or distance from the sun. The only appreciable correlation
appears to be that of speed with distance from the solar apex,
pointed out by Stromberg. 8 The dependence is in the sense
of increasing velocity with increasing distance from the solar
apex.
8 Mt. W. Contr. 292, 5, 1925. A suggestion of a dependence of velocity
(corrected for solar motion) on galactic latitude and therefore on mass of the
intervening star fields is discussed by ten Bruggencate (P. N. A. S., 16, in, 1930),
who seeks a trace of the red-shift, characteristic of the spectra of distant spiral
nebulae. The material is as yet insufficient to establish the correlation securely
or to discriminate among its possible interpretations.
200 DATA BEARING ON THE ORIGIN OF THE GALAXY
The simplest interpretation of the relation of speed to position
in the sky is that the apparent systematic drift of the clusters
is but the reflection of the motion of the local system in the
Galaxy. When corrected for this motion, the average speed
remains high approximately 100 kilometers a second; but as
a group, the globular clusters are essentially at rest, unlike the
extra-galactic nebulae, which show a large K term apparently
dependent on distance.
The radial velocities of globular clusters have been measured
mainly by Slipher at the Lowell Observatory. Except for two
or three clusters, all measures refer to the integrated images
and not to individual stars. The study of differential radial
motions in a globular cluster is one of our important future
problems. The successful measure of the proper motions in
globular clusters also must await the photographs of the
future. Van Maanen has shown that the proper motion of
Messier 13 as a whole and its average internal proper motion
are each less than o".ooi annually, an amount to be expected
from a consideration of the distance and the radial velocity. 9
The values of the annual proper motions are slightly larger for
Messier 2 and Messier 56 but are consistent, he finds, with
my estimated distances and the average radial velocities. 10
72. Dimensions and Star Densities of Clusters. In the
earlier hypotheses concerning the origin and growth of the
Galaxy, it was suggested that the galactic clusters probably
represent stages in the dissolution of a typical globular system.
The existing galactic clusters are necessarily in the process of
dispersion through encounters; but it is not equally evident
that existing globular clusters are doomed to assimilation by the
Galaxy and subsequent transformation. We have already
commented in Section 55 on the giant-poor clusters, and in
Section 8 we have called particular attention to N. G. C. 2477,
one of the richest and most globular-like of the accepted galactic
9 Ibid. 284, 1925.
10 Ibid. 338, 1927.
DIMENSIONS AND STAR DENSITIES OF CLUSTERS 201
clusters. Such transition types are, however, apparently
scarce, and in considering the possible relationships of the two
groups, it is well to examine further their comparative dimen-
sions and star densities.
It is impossible to say how many stars constitute a typical
globular cluster. Our photographs can reach only a little way
down the main sequence toward the dwarfs. When we attempt
to go farther, the high density of the central stars "burns out"
the photograph and conceals the information we might other-
wise obtain. From available counts on our most suitable
photographs of the brightest clusters we estimate 11 that in the
average globular cluster there are more than 20,000 stars
brighter than absolute magnitude +5. To the same magnitude
limit, the population of an average galactic cluster is less than
200 stars.
The diameter of a globular cluster is also indeterminate. It
is probable that the actual linear dimensions depend on the
brightness of the stars involved, becoming greater for stars of
lower luminosity and mass; the same dependence appears
also in galactic dusters. 12 From Table XI, III (Section 56),
which gives the relation of distance modulus to angular
diameter for normal globular clusters, we can compute the
following relation of linear diameter to distance :
Modulus Angular Linear
Distance m A/ Diameter Diameter
kpc ' pc
10 15.0 ii. 2 33
20 16.5 2.6 1 6
30 17-4 14 13
40 l8.0 I 02 12
SO l8.S 0.8S 12
The measured decrease of linear diameter with increasing
distance is, of course, mainly photographic. The loss of light
in space is here of minor significance. We under-measure the
angular diameters of remote dusters because of the failure of
outlying faint stars to rise to measurable prominence on the
11 See, for example, Pop. Astr., 27, 101, 1919.
12 See Figure VII, 2.
202 DATA BEARING ON THE ORIGIN OF THE GALAXY
photographic plate. I think we can safely take the diameter
of a typical globular cluster to exceed 35 parsecs; but the diam-
eter of the nucleus, in which the brightest stars are concen-
trated, appears to be only one third as large.
The average linear diameter of the galactic clusters for which
definite estimates can be made (Appendix B) is 6.24 parsecs.
Few galactic clusters exceed 20 parsecs in diameter. Trumpler
has determined preliminary distances from observations of
magnitudes and spectral types for 54 systems. He finds a
range in linear diameter from 3.5 to 25 parsecs, with the great
majority between 4.5 and 10 parsecs.
The number of stars per cubic parsec in a typical globular
cluster cannot be computed at present, except for the super-
giant stars. It is obvious, when the dwarfs are taken into
consideration, that the distances separating stars at the center
of a rich globular cluster are on a planetary rather than a
stellar scale. It seems probable that sooner or later we should
have evidence of stellar encounters in such crowded regions;
but only one nova in a globular cluster is now on record the
seventh magnitude object in Messier 80, which appeared in
1860.
The space density and the distances separating individual
stars can be more readily computed for galactic clusters when
reliable estimates on the parallaxes become available and we
have made sufficient allowance for superposed stars. Trump-
ler's study of one of the richest of the galactic clusters, Messier
n, provides material that illustrates the conditions in these
systems. He finds that the cluster is 1,250 parsecs distant.
It lies in the rich Scutum star cloud, which has a star density
nearly four times that of the average field of the galactic belt.
The cluster itself is made up of about 480 stars brighter than
magnitude 15.5, distributed over an area approximately a
quarter of a degree in diameter. The bright stars are concen-
trated within a central area of less than four minutes radius. 13
13 L. O. B.. 12, 10, 1925. The distance is revised in his later work, to 1340
parsecs.
ON THE MASSES OF GIANT STARS 203
For stars brighter than absolute magnitude +4.5 the relation
of density to distance in Messier n is found to be as follows:
Distance
from Center Stars per
in Parseca Cubic Parsec
o 27 83
O 60 80
96 33
1 32 95
1.68 49
2 04 22
2 40 OS
The central density of Messier n is much higher than that of
the average galactic cluster. In contrast with the density of
83 stars per cubic parsec for Messier n is that for Messier 37
of only 1 8 stars per cubic parsec for stars brighter than absolute
magnitude +4-5- The corresponding number for Messier
36 is 12 (Wallenquist), for the Pleiades, 2.8 (if the parallax is
taken as o".oo8), and, for the vicinity of the sun, o.on. The
average separation of stars at the center of Messier n is one
light year. Trumpler points out that "an observer at the cen-
ter of Messier n would find about 40 stars with parallaxes of
2" or more and which would appear three to fifty times as
brilliant as Sirius shines in our sky." It is quite probable,
moreover, that this display would be very dull compared with
the show at the center of the Hercules cluster.
73. On the Masses of Giant Stars. The correlation
tables for color index and apparent magnitude for three bright
globular clusters are given in an earlier chapter. Using the
observed mass-luminosity relation for galactic stars, we can
transform the color-magnitude array into a relation between
spectral class and mass. It is necessary to assume that we can
safely replace color class by spectral class for giant stars; the
uncertainties involved both in this assumption and in the tem-
perature scale, used for reduction from photovisual to bolo-
metric magnitude, are not negligible, but still they are not
serious enough to falsify the average results except for stars of
204 DATA BEARING ON THE ORIGIN OF THE GALAXY
extreme color. It is possible that the chief source of error
lies in the mass-luminosity curve itself, which depends mainly
on nearby double stars and possibly is inappropriately applied
to single stars, especially in a globular duster.
The computations of mass have been carried through 14 for
Messier 22. The color-magnitude array (Table III, V) includes
the stars brighter than the magnitude limit of the photovisual
plates and within five minutes of the center of the cluster. It
is of interest that more than six per cent of the stars have nega-
tive color indices, the cluster resembling 15 in this respect Messier
13 rather than Messier 3.
No correction has been made in the color-magnitude array for
superposed stars. The cluster lies in a rich star cloud in
Sagittarius, and probably 10 per cent of the stars included in
this discussion are not cluster members. The color-magnitude
array is, therefore, applicable both to the cluster and to the
star cloud, and the small dispersion in brightness of both
together suggests that the two are associated. The computa-
tion of the stellar masses in terms of the sun's mass for successive
intervals of magnitude and color is shown in Table XIV, II.
The distance modulus m pv M po = 14.1 6 is taken from Appen-
dix A; the reduction to bolometric magnitudes and the computa-
tion of the masses are made with the aid of tables given by
Eddington. 16 The masses of the reddest stars would have been
from 10 to 20 per cent less on Brill's scale of temperatures and
corrections to bolometric magnitude. 17 The values of photo-
visual magnitude and spectrum in Table XIV, II are read
directly from the curve drawn through the plot in Figure XIV,
i of the colors and magnitudes of individual stars that appear
in the color-magnitude array.
The following masses for the average giant stars of various
spectral classes in Messier 22 are derived from the smooth curve
14 H. B. 874, 1930.
" See Table III, II, Table III, III, and Mt. W. Contr. 155, 8, 1918.
18 Internal Constitution of the Stars, Chapter VII, 1926.
17 Babelsberg Veroff., 5, 16, 1924.
ON THE MASSES OF GIANT STARS
205
10 6
iff)
/
114
118
122
126
130
134
138
142
146
150
.
/
7
.
\
r '
-
-
:
m
^ /
.
m
'.:
..
. JT
%
c- -
;"i "*
fe*
6 -02 +02 +08 +10 +14 +18 + 2J
FIGURE XIV, i.
Color-magnitude array for Messier 22. Coordinates are photo-
graphic magnitudes and color indices.
206 DATA BEARING ON THE ORIGIN OF THE GALAXY
in Figure XIV, 2, where the data are plotted from the second
and fifth columns of Table XIV, II:
Ao
AS
FO
<4 8
<3-5
FS
Go
GS
4 o
4 9
7 o
Ko
Mo
10 8
16 5
24.0
TABLE XIV, II. THE MASS-SPECTRUM RELATION FOR MESSIER 22
Apparent
Pv Mag.
Spectrum
Absolute
Pv Mag
Absolute
Bol Mag
Mass
II 2
M 2 5
2 96
4 62
29
II 4
K 9 .o
-2 7 6
-4 10
22 4
H 6
K 5 8
-2 5 6
-3-72
17 8
II 8
K 3 o
-2 36
~3 13
14 i
12
Ki o
-2 16
-2 74
ii 7
12 2
GQ o
- 9 6
-2 41
10 o
12 4
G; o
- 7 6
2.IO
8 3
12 6
G 5 S
- 56
-I 8 4
7 4
12 8
G4 o
- 36
-I 58
6 5
13
G2 5
- 16
-I 30
5 9
13 2
Gl 2
o 96
-I 06
5 4
13 4
F 9 8
o 76
-o 80
4 8
13 6
F 7 8
o 56
-o 58
4 S
13 8
F 5 8
o 36
o 36
4 i
14 o
F3 o
o 16
-o 16
3 9
14.2
Ag 5
+o 04
+o 04
3 7
14-3
A6 8
+o 14
4-o 07
3 6
14 4
B7 5
-f o 24
-o 49
5 7
It is possible to give only upper limits of average mass for
classes Ao, AS, and Fo because of the incompleteness of the
observational material for the corresponding intervals of color
index.
For the rich galactic cluster Messier 37, von Zeipel and
Lindgren, in good agreement with the present results, find the
mass of the giant g$ stars 2.15 times as large as the average
mass of the b and a stars. 18 They have used space distribution
of the stars as a criterion and a measure of the masses for stars
of different types. 19
Proc. Swedish Acad., 61, No. 15, 126, 1921.
See Chapter V, Section 26.
EVOLUTION OF GLOBULAR AND GALACTIC GROUPS 207
The most interesting feature of Figure XIV, i is the small
dispersion in color for stars of a given photovisual magnitude.
Accepting the mass-luminosity relation, we can only conclude
that in a globular cluster such as Messier 22 the giant stars of a
given mass have a very small spread in surface temperature.
A mass-spectrum relation, as deduced from Figure XIV, i
and plotted in Figure XIV, 2, has heretofore never been derived
for a globular cluster.
/
/
/
/
/
/
/
/
/
/
^
/
AO FO UO K
MO
FIGURE XIV, 2.
Mass-spectrum curve for Messier 22.
74. On the Evolution of Globular and Galactic Groups.
In the existence of supergiant stars in globular clusters there
are some implications bearing directly on the principles of stellar
evolution that have not as yet received the emphasis deserved.
They bear indirectly on our problem of the development of the
galactic system.
1. Apparently all of the globular dusters show the presence
of numerous red supergiants, with the fainter stars always bluer.
It follows that there must be for the typical globular system an
"equilibrium in time" an essentially stationary age, as
remarkable as the observed dynamical equilibrium.
2. It would be unreasonable to assume exactly the same age
for all globular clusters and argue therefrom that they are now
similar in stage of development only because the same time
208 DATA BEARING ON THE ORIGIN OF THE GALAXY
interval separates them from the date of origin. Even the
different distances from the observer would, on account of
the finite speed of light, give them effective ages differing by
nearly 2 X io 5 years. It appears more reasonable to admit that
undisturbed globular systems are effectively permanent in spec-
tral composition. Is this because the time units we use in
measuring stellar evolution are still too anthropocentric or
because the clusters are timeless?
3. No theory of evolution at present in vogue can explain
supergiant stars that are stationary with respect to time
especially such exceptional objects as the low-density, high-
luminosity red stars with normal spectral properties. The
very act of radiation spells change; the loss of mass per second
in a cluster giant exceeds a thousand million tons.
4. Whether it is the same star that always remains bright,
massive (presumably), and red, or whether all cluster stars
progress systematically and their places are methodically
taken by others, we have as yet no way of knowing. It is, of
course, unreasonable to ask that new supergiants be born at
just the right rate to keep up appearances. It would be better
either to assume essential permanency in the arrangement as
now observed, thereby admitting that we have been much too
terrestrial in trying to force on stellar processes a time scale
easily conceivable to us; or to assume that stellar development
is not unidirectional that stars may, and perhaps often or
always do, move up the luminosity sequence as well as down
toward gigantism as well as toward small mass and low
luminosity. The part that meteoric matter plays in fueling
the stars is an open research of much difficulty and some
promise.
5. Time seems to leave its marks, however, on the clusters
along the Milky Way. Some of the globular clusters may be
affected in freedom, form, and eventual survival by contacts
with galaxies or other clusters. The marks of age are shown
best by the numerous disturbed galactic groups, with their
variety in structure and content. But even the Hyades type
THE GALACTIC SYSTEM AS A SUPER-GALAXY 209
of galactic cluster, with its yellow and white giants side by
side, leaves us again groping for rather far-fetched assumptions
to disembarrass ourselves of the apparent unevenness in the
rates of stellar evolution.
6. Finally, it is worth suggesting that we may have been using
our theories of stellar evolution too much as explanations and
not enough in their proper place as temporary guides.
75. The Galactic System as a Super-galaxy. The relation
of galactic and globular star clusters to each other and to star
clouds and galactic systems remains obscure in many respects.
In the foregoing sections we have pointed out contrasts and
similarities, alluding to the evidence for a massive galactic
nucleus, the singularities in the distribution of galactic clusters,
and the high-speed motion of the local system with respect to
the globular clusters.
The earlier hypothesis (Section 68) concerning the possible
origin and growth of the Galaxy has not been disproved.
Nevertheless, I think there is increasing evidence from outside
the galactic system that the interpretation should be amended.
There were difficulties with the earlier theory that are now
avoided or resolved such, for instance, as its incompleteness
in leaving the spiral nebulae out of the picture, the scarcity of
clusters intermediate between globular and galactic groups,
the singular distribution of dark nebulosities, and the slowness
or even impossibility of amalgamating clusters and star clouds
with no more potent resisting medium available than the
galactic star field with its infrequent encounters.
In brief, I propose the following picture of the galactic
system, 20 realizing, of course, that our researches in the next
few years, guided in part by the present hypothesis, may modify
or remake the picture.
i. Our galactic system, it now appears, is neither a spiral,
such as the Andromeda Nebula (Messier 31), nor a single unified
discoidal star system, like a Magellanic Cloud on a grand scale;
20 H. Repr. 61, 1929.
210 DATA BEARING ON THE ORIGIN OF THE GALAXY
it is rather a super-galaxy a flattened system of typical
galaxies.
2. In mass and population, therefore, the galactic system
should be compared with the Coma- Virgo Cloud of bright
galaxies, rather than with one of its members. Our local
system, a star cloud that is a few thousand light years in
diameter, appears to be a galaxy, similar to the Clouds of
Magellan or to a typical extra-galactic nebula. That all
types of spirals and Magellanic Clouds are systematically
smaller than our galactic system seems clearly established by
recent work on star clouds and on the Coma- Virgo system of
nebulae. 21 Five to ten thousand light years appears to be the
average diameter, and this is not over four or five per cent of the
diameter of the galactic system.
3. The Scutum star cloud, the Cygnus star cloud, and a half
dozen or so other distinct Milky Way star clouds are, or have
been, on this interpretation, typical galaxies, in the sense in
which the average spiral nebula is called a galaxy.
4. The three or four clouds of galaxies in Coma- Virgo appear
to have diameters approximating 2,000,000 light years, but
many of the less populous systems have diameters well under
1,000,000 light years; such, for instance, are the Ursa Major
group measured by Baade, 22 and the Pegasus group, N. G. C.
7317 to 7320.
5. In comparing our galactic system with a cloud of galaxies,
we note that it is considerably flattened and seems to be
unusually compact. But a newly discovered cloud of four or
five hundred galaxies in Centaurus likewise has a projected
length three or four times its width; 23 many of its component
systems are apparently in contact a phenomenon that is
occasionally observed in the Coma- Virgo clouds and elsewhere.
6. If our galactic system is a flattened cloud of galaxies, we
may raise the question as to the continuity of galactic star fields
21 Shapley and Ames, H. C. 294, 1926; H. B. 864, 865, 866, 868, 869, 1929;
H. B. 873, 1930.
22 Hamb. Mitt., 6, No. 29, 103, 1928.
23 Shapley, H. B. 874, 1930.
THE GALACTIC SYSTEM AS A SUPER-GALAXY 21 1
between the separate galaxies and the meaning of the galactic
nucleus that is marked out by globular clusters, novae, star
clouds, and the distribution of faint stars. It may be noted
that Pannekoek and others have pointed to anomalies in star
distributions, which, I think, may in part be accounted for by
large breaks in the sheet of galactic star clouds; but these
irregularities in star distribution are partly features of the local
system we are perhaps beginning the detection of the present
structure of our own spiral.
7. Viewing our local system as a galaxy possibly at one
time a typical ellipsoid or spiral we observe that (a) the
major part of the recorded obscuring nebulosity is concentrated
in the plane of the local system; also, that nearly all the con-
spicuous dark regions appear to be within 1,000 parsecs or so of
the sun, a distance which indicates that they are a remnant of
the peripheral dark ring of matter such as is observed in many
spiral nebulae; 24 (6) the inclination of the local system indicates
the original equatorial plane of the ellipsoid or spiral; (c) when
observed from the distance of the Coma- Virgo galaxies the Orion
Nebula with its involved stars, the Pleiades, and other groups
near the sun would appear as nebulous knots in the structure
of our local system; (d) from an outside point the local
system and the Cygnus star cloud would appear as galaxies in
collision. 25
8. The great star cloud in the Sagittarius region has interest-
ing analogies with the Andromeda Nebula. Its dimensions
appear to be approximately the same; novae are frequent, but
long-period Cepheids are scarce near its center. If Kepler's nova
(Nova Ophiuchi No. i, 17* 24 m .6 21 24' (1900)) is at the
distance of the cloud its absolute magnitude at maximum was
about the same as that of S Andromedae the abnormal nova
of 1885. At the distance of the Andromeda Nebula the angular
separations of stars in the Sagittarius Cloud would be only six
per cent of those now observed, the stars would be six magni-
24 Curtis, Lick, Publ., 13, 9, 1918.
26 Shapley, H. Repr. 8, 1924.
212 DATA BEARING ON THE ORIGIN OF THE GALAXY
tudes fainter, and the densest central region would be unre-
solved with present telescopic power.
In brief, it is proposed that our galactic system is a cloud of
ordinary galaxies, the considerable oblateness of the cloud
representing a stage in its normal collisional development.
This hypothesis makes our Galaxy less anomalous than it
appears on previous views, which conceived ours either as an
enormous discoidal star cloud unduplicated by any other
visible organization or as a spiral nebula forty or fifty times the
diameter of the average spiral system.
CHAPTER XV
A PARTIAL SUMMARY
MUCH of our present information on the dimensions of sidereal
systems, the transparency of space, the relative frequency of
supergiant stars, and the distance and direction of the galactic
center has developed from the study of star clusters, which have
also contributed effectively to research on such subjects as
Cepheid variation and the velocity of light. A brief synopsis
of the more interesting and significant results attained in the
course of the work described in the preceding chapters is given
below. The summary may be conveniently made under the
heads Variable Stars, Clusters, and the Galaxy.
VARIABLE STARS
In a study, not yet complete, of 45 globular clusters (43.7 per
cent of all now known) 886 variables have been found, mainly
by investigators at Harvard and Mount Wilson (see Table
IV, I). An unaccountable inequality is found in the number
of variable stars; 6 per cent of the clusters are wholly barren of
variables; 41 per cent contain no more than five each; whereas
in others, of the same neighborhood and class, scores of variables
are known in some more than 10 per cent of all the giant stars
show variation. Variability is unknown among the low-
luminosity stars in clusters, but the tests have been only
preliminary, except in o> Centauri, Messier 13, and one or two
others.
Of the 886 known variables, about 50 per cent have been
shown to belong to the duster type (that is, they are Cepheids
with periods less than a day) ; many of the remainder probably
are also of the same type, but their light curves have not been
measured or the periods found. These short-period Cepheids
213
214 A PARTIAL SUMMARY
are widely scattered, some appearing quite beyond the normally
recognized limits of the clusters. The lack of a high concentra-
tion to the center may be a result of high velocities; but practi-
cally nothing is yet known observationally of the differential
motions in globular clusters. (See papers by van Maanen and
Balanowsky in Appendix C.)
There are a number of classical Cepheids in globular clusters,
a few long-period variables, and a few irregular variables, but
as yet no certainly verified eclipsing stars. The frequency of
cluster-type Cepheids relative to that of classical Cepheids is
greater in clusters than near the sun, but various factors of
observational selection disturb the comparison. Investigations
show that the light curves, ranges of period, and color phenom-
ena for Cepheid variables in clusters and in the solar neighbor-
hood are essentially the same, although there are unexplained
differences in relative frequency of different types due, possibly,
to environment or age.
Few variable stars are associated with galactic clusters,
perhaps none are actual members. The relatively strong
galactic concentration of the classical Cepheids of the galactic
system is well known. The absence of galactic concentration
for duster-type variables may be attributable to the high veloc-
ities. (The space velocities of classical Cepheids are normally
low.) Likewise, the large proper motions of many of the
cluster-type Cepheids of the galactic system should no longer
be taken as indicating nearness and low luminosity, since their
radial velocities prove their rapid motion in space (Table X,
XIII). '
The relation of logarithm of period to absolute magnitude,
called the period-luminosity curve, has been extended, from
the preliminary work of Miss Leavitt on apparent magni-
tudes for 25 variable stars in the Small Magellanic Cloud, to
several hundred stars in a dozen star clusters and clouds
(Chapter X). It is found by Hubble to hold also in some extra-
galactic nebulae. The great majority of Cepheids fit in with
VARIABLE STARS 215
this empirical period-luminosity curve; the exceptions are
few but probably of much importance. The curve can be cal-
culated rather satisfactorily on the basis of the pulsation theory
of Cepheid variation, though the latter is hardly complete.
The visual period-luminosity curve, developed and used in my
earlier discussion of the distances of clusters, is now fully
replaced by the photographic period-luminosity curve derived
from the Magellanic Clouds and globular clusters.
With the period-luminosity curve, the relative distances of
all normal Cepheid variables can now be determined with con-
siderable accuracy from measures of periods and apparent
magnitudes. The absolute values of the distances will become
equally accurate when current investigations of the proper
motions and radial velocities of the nearer Cepheids have fixed
securely the zero point of the period-luminosity curve.
An important relation has also been found between length of
period and the spectral class or color the period-spectrum
curve which holds generally for classical galactic Cepheids.
The longer the period, the redder and brighter is the variable
a clear connection of low density with high luminosity for giant
stars (Section 49). In one direction the period-spectrum rela-
tion extends to the cluster-type Cepheids, and in the other
through RV Tauri variables to the typical long-period variables.
On the basis of the period-spectrum curve for galactic Cepheids,
a relation between absolute magnitude and period can be
calculated (Section 51) which is identical with the observed
period-luminosity relation and shows again that galactic
Cepheids and those of clusters, Magellanic Clouds, and extra-
galactic nebulae are thoroughly comparable.
To test the accuracy of the dimensions of the Galaxy as
derived from globular clusters, an extensive investigation of
the faint variable stars in the Milky Way is in progress at the
Harvard Observatory. The study has resulted in the discovery
of two or three thousand new variable stars, in the determina-
tion of the distance to the star clouds in Sagittarius which
2i6 A PARTIAL SUMMARY
appear to compose the galactic nucleus, and in the acquisition
of much material for statistical and descriptive studies of
variable stars of all types. It is found that the long-period
variable star, which is a giant at maximum, may be of great
importance in future investigations of the distances of the Milky
Way star clouds and of such star clusters as contain variables
of this class (Section 69).
The cluster-type variables in distant systems afford a means
of testing with extraordinary accuracy the relative velocity of
blue and yellow light. No difference in speed is found through-
out a journey of 40,000 years for light waves differing in length
by 25 per cent.
A difficulty for all Cepheid theories that involve the gravita-
tional relation between period and mean density (P 2 i/p) is
found in the essential constancy of median magnitude, color,
and surface brightness for all periods less than one day (Sections
21 and 22). Probably nuclear differences are concerned in the
production of the variety of periods. There appears to be a
possibility, through careful photometry of globular clusters, of
witnessing the beginning or the dying out of Cepheid variation
in stars that are much like these cluster variables in color and
magnitude (Section 23).
CLUSTERS
Whatever its meaning and interpretation, the period-
luminosity curve for Cepheids affords a powerful practical
method of measuring the distances of all stellar systems
globular clusters, star clouds, and nebulae that contain
Cepheid variables. It has been possible to develop other useful
methods for measuring the distances of clusters, employing
variously the magnitudes, spectra, and colors of stars of high
luminosity, as well as integrated apparent magnitudes and
angular diameters. By using two or more of these various
methods the distance of the average globular duster is deter-
mined with an estimated probable error of 15 per cent (aside
from uncertainty of the zero point).
CLUSTERS 217
Many contributions to knowledge of the transparency of
space have been made in the course of the study of clusters.
The obstruction of light by dark nebulae in special regions is
well known. The differential scattering of light in interstellar
space is found to be negligible in both high and low galactic
latitudes (Chapter IX). General obstruction (non-selective
diminution of light) throughout space is neither proved nor
disproved, but it appears on present evidence to be of small
practical importance in the measurement of distances up to
100,000,000 light years.
The distances of the globular clusters now known range from
18,000 to 184,000 light years. The galactic clusters are, on
the average, much nearer; but for many of them the distances
are not yet accurately known. Ninety-three globular systems
are catalogued in Appendix A. Ten others are members of the
Magellanic Clouds (Table XIII, I). The globular clusters
appear very definitely to be a part of the Galaxy. They are
distributed throughout an oblate system, symmetrical with
respect to the galactic plane. Although they are concentrated
toward the galactic plane, only two are actually within four
degrees of it. The galactic clusters, on the other hand, are
almost exclusively in the low latitudes that are essentially
devoid of globular clusters.
The globular clusters seem to be fairly uniform in size,
content, and total intrinsic brightness. There is diversity in
central condensation, however, and occasionally other diver-
gences from normal structure appear. On the basis of these
variations, a scheme of 12 classes of globular clusters has been
developed (Section 5).
The diameters of typical globular clusters are of the order
of 35 parsecs (Chapter XIV). The galactic clusters are, on
the average, much smaller, but they are more varied in size and
richness. An increase in diameter with decreasing brightness
is shown for galactic clusters, giving rise in clusters such as
Messier 67 and the Pleiades to the appearance of a concentrated
2i8 A PARTIAL SUMMARY
nucleus in a widely dispersed larger system (Section 34). The
same wide dispersion of the fainter and less massive stars
apparently holds for globular clusters.
A catalogue of 249 galactic clusters is given in Appendix B,
with new data on magnitudes, dimensions, orientation, and
distances (see Sections 7 and 57). In making this catalogue, a
new and comprehensive classification of galactic clusters based
on richness and apparent concentration has been developed
and employed.
The maximum luminosities of stars in globular clusters,
if the distances which I derive are not too small, rarely if ever
exceed 3.5 visually, and therefore do not attain the high
values found in the Magellanic Clouds and in the galactic
clusters of B stars. If we except a few stars, the maximum
is, in fact, about 2.5. The classical Cepheids are always
found among the brightest objects; in the clusters and in the
Magellanic Clouds some are of extraordinary luminosity,
many of them exceeding absolute visual magnitude 4.
For several globular clusters a preliminary maximum in the
general luminosity curve is found at or near zero absolute
magnitude. There may be some association of the observed
excess (which is probably composed nearly altogether of white
stars) with the cluster- type variables (Section 27) and with the
fainter part of the period-luminosity curve. But to interpret
this phenomenon fully we need further detailed work on magni-
tudes and colors.
The globular clusters in the Large Magellanic Cloud show a
spread in integrated absolute photographic magnitude from
6.5 to 9.1, but if two of the objects, which possibly are not
globular cluster members of the Cloud, are excluded, the
extreme values are 6.5 and 7.2. The only cluster in the
Small Magellanic Cloud that appears certainly globular has
the absolute photographic magnitude 7.1 (Section 66). The
assumption of the general comparability of globular clusters
is supported by this relatively small dispersion, though "giant-
CLUSTERS 219
poor" globular clusters must be segregated in using magnitudes
and angular diameters for the determinations of relative
distances (Sections 55 and 56).
There is a scarcity of forms intermediate between globular
and galactic clusters, but with further research it should be
possible to work out the details of the relationship between the
types and an explanation of the peculiar contrast in space dis-
tribution. Obscuring nebulosity throughout the Galaxy will
play a part in this explanation.
From star counts and from small-scale photographs it is
found that many globular clusters are distinctly elliptical in
projected outline, probably being oblate spheroids. The data
in Chapter VI indicate, indeed, that most of the globular
clusters are non-spherical, and for 37 the degree and orientation
of the flattening is definitely measurable on average photographs.
There are tempting analogies between the distribution of
stars in globular clusters and certain features in the kinetic
theory of a gas; but the observations are regrettably insufficient
and the approach to such a comparison must be cautious. In
the attempt to find density laws we encounter three seriously
perturbing factors, discussed in Chapter V: (a) non-sphericity
of clusters and the impossibility of evaluating the true ellip-
ticity, with the consequence, therefore, that the differences in
the density laws along the various radii must be ignored; (b)
the Eberhard effect in condensed regions; (c) the magnitude
limitations, which make us attempt interpretations of the
distribution of a million or so dwarfs and giants on the basis of
partial counts of a few hundred, or a thousand or so, high-
luminosity (massive) stars. But whatever the true density
laws, there appears to be a preferential concentration of bright
stars (possibly massive objects) at the centers of globular
dusters.
Stars of all common colors and spectral classes have been
recorded in both globular and galactic clusters, and in the latter
various degrees of nebulosity are found. Many kinds of
220 A PARTIAL SUMMARY
peculiar stars are also present. It seems that in clusters prac-
tically all the materials exist that constitute star clouds and
galaxies.
In spectral composition the galactic clusters of the Milky
Way are of two principal kinds (Trumpler proposes a more
elaborate subdividing): (a) the Hyades model, with giant
red-yellow stars as well as white giants and the main series of
ordinary dwarf stars; (b) the Pleiades model, with no yellow-red
giants or supergiants, all the stars falling along the main branch
of a Russell diagram, the redness increasing with decreasing
brightness. For both kinds of cluster, supergiant stars are
relatively uncommon, occurring most frequently as class B
stars in the Pleiades type.
In all globular clusters so far investigated the most luminous
stars are found to be red, with a progressive change toward
blueness for the next few fainter magnitudes. This relation of
magnitude to color appears to differ from the average conditions
for galactic giant stars; but in the Galaxy the general non-
homogeneity is obvious and the stellar sources are much con-
fused. From the color-magnitude arrays (Section 12) it is
possible, on fairly reasonable assumptions, to compute the
mean masses of the giant stars in globular clusters for various
intervals of color or spectrum. The computation of average
masses for Messier 22 (Section 73) shows values in terms
of the sun's mass as follows: Mo, 24.0; Ko, 10.8; Go, 4.9; Fo,
<3.6;Ao, <4.8.
The coexistence in the globular clusters of blue stars fainter
than absolute magnitude zero and red supergiants brighter than
2.5, and also the yellow and white giant stars in the Hyades
and other galactic clusters, gives rise to inquiries concerning
the speed and direction, or even the generality, of the evolution
of stars. The current theories of giant stars require that the
duration of the total giant stage, if contraction is the main
source of the energy of radiation, can scarcely exceed 100,000
years. But the color-luminosity relation appears to be identical
THE GALAXY 221
in near and remote clusters, though because of the finite velocity
of light many such clusters differ from each other in age by more
than 100,000 years. There is thus little if any evidence of
ageing in the typical globular clusters; stellar evolution is almost
immeasurably slow, and contraction, of course, must be aban-
doned as the source of the energy of radiation. The somewhat
anomalous consequences are discussed in Section 74.
THE GALAXY
Minimum dimensions of the galactic system are found from
the distances separating some of its stars and star clusters.
Revising earlier values, we now find 70 kiloparsecs as the
diameter in the galactic plane (Chapter XII). The diameter
perpendicular to the plane is probably about one tenth as great,
with, however, a quantity of far outlying stars that are probably
affiliated (Section 62).
The center of the Galaxy, judged from the distribution of
clusters and of several kinds of high-luminosity stars, is in the
general direction of 17* 30, 30 (Sagittarius) and approxi-
mately 16 kiloparsecs distant from the sun. Around this
massive nucleus (Section 61) the neighboring galactic stars
appear to move with a velocity of some 300 kilometers a second
and a period well in excess of 100,000,000 years.
Examination of the colors in the distant Milky Way star
clouds reveals the presence of stars of all common spectral
types, indicating that these remote regions probably do not
differ fundamentally from the solar neighborhood.
The brighter early class stars the B's, and many A's are
members of a local cloud, which contains also many stars of
other types and some of the nearby galactic clusters and diffuse
nebulae. The local system is also considerably flattened, and
its central plane is found, in confirmation of Gould's work on the
bright stars and Charlier's investigation of the brighter B's, to
be inclined some 10 or 15 to the Milky Way plane. The sun,
as Newcomb and others have shown, is north of the galactic
222 A PARTIAL SUMMARY
plane (hence the dip of the galactic circle); it is also about
55 parsecs above the central plane of the local cloud and 90
parsecs from the center which lies in the direction of Carina,
approximately at right angles to the direction to the center of
the Galaxy. Other values of the distance of the sun to the
central planes and to the center of the local system have been
derived by different investigators; the most dependable work
gives distances and directions in general agreement with those
quoted above.
In variety of stars, nebulae, and clusters, and in irregularity
of structure, the Magellanic Clouds afford a fair parallel to our
own Galaxy; in dimensions, however, they probably approach
the star clouds of the Milky Way, and of course are much
inferior to the galactic system in diameter, volume, and total
mass. They are of the same general diameter as many external
galaxies (extra-galactic nebulae), and though differing from true
spirals and elliptical nebulae in form, they appear to be exactly
comparable with a small subclass of irregular extra-galactic
nebulae.
A higher organization is shown in the Coma- Virgo cloud of
external galaxies, which contains 300 or more true spirals, double
nebulae, spherical nebulae, and various sorts of elliptical and
spindle systems. The distance of this supergroup is found to
be of the order of 3,000,000 parsecs. A number of more remote
clouds of extra-galactic nebulae are on record, some at distances
in excess of 40,000,000 parsecs, but they are not yet investigated
in detail.
In total mass and stellar population, the galactic system is
more nearly comparable to the whole Coma- Virgo cloud than
to any one of its individual members. In the last section of the
preceding chapter the tentative theory is advanced that our
galactic system is in fact a super-galaxy a flattened cloud of
ordinary galaxies.
APPENDIX A
CATALOGUE OF GLOBULAR CLUSTERS
THE material on which is based the catalogue of globular clusters
has been described in the text. For three clusters, N. G. C. 4372,
N. G. C. 6356, and N. G. C. 6864, special notes appear at the end of
the catalogue. Daggers after the N. G. C. numbers in the first
column indicate questionable objects (Section 6). Galactic coordi-
nates are on the Harvard system (pole i2 h 40, +28). The values
of the ellipticity and orientation are described in Section 30. The
magnitudes and diameters are explained in Chapter XI, and in that
chapter and in Chapter XII is described the derivation of the
distances listed in the last three columns of the catalogue.
The distance of N. G, C. 4147 is 19.5 kiloparsecs according to
a preliminary study of its two cluster-type Cepheids reported in a
letter from Dr. Baade.
223
224
APPENDIX A
CATALOGUE OF GLOBULAR CLUSTERS
N. G. C.
Name
R. A
1900
Dec.
1900
Galactic
Angu-
lar
Diam-
eter
Inte-
grated
Magni-
tude
Class
Spec-
trum
Number
of Varia-
bles
Long
Lat.
h m
e /
/
104
47 Tuc
o 19 6
-72 38
272
-45
23
3
III
Gs
7
288
o 47 8
-27 8
157
-88
IO O
7 2
X
2
362
A 62
o 58 9
-71 23
268
-47
5 3
6 o
III
Gs
14
1261
395
~5S 36
237
-51 5
2 O
8 5
II
G
1851
A 508
5 10 8
-40 9
212
-34 5
5 3
6 o
II
3
1904
M 79
5 20 I
-24 37
194
-28
3 2
8.1
V
5
2298
6 45 4
-35 54
213
-IS
1.8
10 I
VI
2419
7 31 4
+39 6
I 4 8
+ 23
I 7
II
VII
2808
9 IO
-64 27
249
II
6 3
5 7
I
Ko
3201
A 445
10 13 5
-45 54
244
+ 9
7 7
7 4
X
61
4147
12 SO
4-19 6
226
+ 79
I 7
io 3
IX
A?:
s
4372 n
12 2O I
72 7
269
10
12 O
7 8
XII
4590
M 68
12 34 2
26 12
269
+36
2 9
7 6
X
28
4833
12 52 7
70 20
271
- 8 5
4 7
6 8
VIII
5
5024
M S3
13 8 o
+ 18 42
305
+ 79
3 3
6 9
V
40
SOS3
. .
13 II 5
+ 18 13
309.5
+ 78
3 5
io S
XI
9
5139
a Cen
13 20 8
-46 47
277
+ 15
23
3
VIII
132
5272
M 3
13 37 6
+ 28 S3
8
+ 77 S
9 8
4 5
VI
G
1 66
5286
A 388
13 39 9
-so 52
280
+ 10
I 6
8 5
V
Go
O
5466
14 I o
+ 29 o
8
+ 72 S
5 o
IO O
XII
14
5634
14 24 4
5 32
310 5
+48 5
I 3
io 4
IV
4499
14 45 o
8l 49
275
20
3 I
115
XI
5824
14 57 8
-32 40
301
+ 21
I
9 3
I
F8
5897
IS II 7
20 39
312
+ 29
7 3
7 3
XI
S904
M 5
15 13 5
+ 2 27
332
+ 46
12 7
3 6
V
G.
84
5927
15 20 8
SO 19
294
+ 4
3 O
8 8
VIII
S946t
15 28 2
-50 19
295 5
+ 3-5
I 3
io 6
IX.
5986
A 552
IS 39 5
-37 27
305
+ 12
3 7
7
VII
F8
I
6093
M 80
16 ii i
22 44
320.5
+ 18
3 3
6 8
II
Ko
4
6101
16 14 4
-71 58
284 5
-16
3 8
9 5
X
6121
M*" 4
16 17 5
-26 17
319
+ 15
14 o
S 2
IX
F
33
6139
16 21 o
38 36
310
+ 6
i 3
9 8
II
6i44
16 21 I
-25 49
319
+ 15
3 3
10 3
XI
6171
16 26 9
-12 50
332
+ 22
2 2
8 9
X
6205
M 13
16 38 I
+36 39
27
+40
IO O
4
V
Go'
7
62x8
M 12
16 42 o
- I 46
344
+ 25
9 3
6 o
IX
6229
16 44 2
+47 42
40
+40
I 2
9 7
VII:
6235
16 47 4
22 O
327
+ 12
I 9
10 8
X
6254
M io
16 51 9
- 3 57
343
+ 22
8 2
5 4
VII
6266
M 62
16 54-9
-29 58
322
+ 7
4 3
7 o
IV
Ko
26
6273
M 19
16 56 4
-26 7
324 5
+ 9
4 3
6 8
VIII
G S :
6284
16 58 4
24 3^
326
+ 9
U
10 O
IX.
F.
6287
16 59 i
-22 34
328
+ 10
7
10 4
vii
6293
17 4 o
-26 26
325
+ 7
9
8 8
IV
GS
3
6304
17 8 2
29 20
323
+ 5
5
92
VI
K:
6316
17 10.3
28 I
325 .5
+ 5
i
*
9 .9
III
GS
6325
17 II 9
23 38
327.5
+ 6
7
II 9
IV:
6333
M 9
17 13.3
-18 25
333
+ 10
a 4
7 4
VIII
K?
I
6341
M 92
17 14 I
+43 15
36
+35
8 3
5 I
IV
Gs:
14
CATALOGUE OF GLOBULAR CLUSTERS
CATALOGUE OP GLOBULAR CLUSTERS. (continual)
22$
N. G. C.
Ellip-
ticity
Orien-
tation
Photographic Magnitude
Adopted
Modulus
Qual-
ity
Dis-
tance
? sin ft
ft COS
Var.
Bright
6th 30th
o
kpc
kpc
kpc
104
8
-ss
13 09
12 4
13 4
14 17
b
6 8
-48
4 8
288
9
14 80
14 5
IS I
IS 81
b
14 S
-14 S
o 5
362
8
+ 65
15 5
14 12
13 5
14 8
IS SS
b
12 9
-94
8 8
1261
9 5
16 72
c
22
-17 2
13 7
1851
9
-75
IS 78
c
14 3
- 8 I
II 7
1904
9
+ 5
15 29
15 oi
IS 72
16 54
b
20 4
-96
18 o
2298
8
4-39
17 12
d
26 S
-69
25 6
2419
9
-56
17 41
d
30 3
+ 11 9
28 o
2808
8
+ 84
14 9
14 3
15 4
16 05
b
16 3
- 3 I
16 o
3201
9
14 52
13 52
13 3
13 8
14 81
c
9 2
+ I 4
9 i
4147
16 8
16 58
16 23
16 93
16 93
b
24 2
+ 23 7
4 6
4372
9
14 91
e
9 6
- I 7
9 S
4590
9
15 90
14.80
14 3i
15 08
IS 95
a
IS S
+ 9 i
12 6
4833
8
-80
16 01
c
15 9
22
15 7
S024
9
-79*
IS 07
14 94
IS 26
16 30
a
18 2
+ 17 9
3 S
S053
8
-61
16.19
15 65
IS I
16 o
16 20
a
17 3
f 17 o
3 6
5139
8
4-30
14 37
12 91
12 6
13 I
14 IS
b
6 8
+ I 8
6 6
5272
8
+ 54
IS 50
14 23
13 92
14 45
IS 43
a
12 2
+ 11 9
2 6
5286
9 S
16 89
d
23 9
+ 4 2
23 S
5466
9
16 17
IS 72
15 I
16 2
16 16
b
17 o
+ 16 2
S i
5634
I 4499
9
17 49
c
31 4
+ 23 2
20 S
5824
9
17 32
e
29 I
+ 10 4
27 2
5897
8
-44
IS IS
14 9
IS 4
16 07
b
16 4
+ 80
IS 5
5904
9
+ 16
IS 26
13 97
13 74
14 27
IS 17
a
10 8
+ 7 8
7 5
5927
9
16 56
d
20 5
+ I 4
20 I
S946f
9
17 54
d
32 2
+ 20
32 i
5986
. ...
16 14
c
16 9
+ 35
16 6
6093
IO
14 88
14 72
IS 09
16 22
a
17 5
+ 54
16 6
6101
8
+35
16 60
d
20 8
~ S 7
20
6121
9
+ 72*
14 27
13 88
13 3
14 4
14 30
b
7 2
+ I 9
7 o
6139
9
-6 4
17 34
d
29 3
- 3 I
29 I
6144
8
22
IS 76
IS 2
16 3
16 29
b
18 I
+ 4 8
17 S
6171
9
IS 46
IS 2
IS 9
16 63
b
21 2
+ 79
19 6
6205
9-5
*-6 3 *
15 20
13 75
13 45
13 92
IS 07
a
10 3
+ 66
7 9
6218
13 97
13 56
14 31
IS 21
b
II
+ 46
9 9
6229
16 18
IS 90
16 37
17 37
b
29 8
+ 19 2
22 8
6235
8
+ 89'
16 17
IS 7
16 8
I? 28
c
28 6
+ S 9
28 o
6254
9
14 06
13 35
14 38
15 26
b
II 2
+ 4 2
10 4
6266
8
+ 16
16 40
IS 87
IS 6
16 I
16 35
c
18 6
+ 23
18 4
6273
6284
6
-28
16 06
c
16 3
+ 26
16 i
27 7
6287
9
17 24
d
28
+ 49
27 S
6293
9
16 82
c
23 I
+ 28
22 9
6304
9 5
17 02
c
25 3
+ 22
25 2
6316
9
17 52
d
31 8
+ 2.8
31.6
6325
....
18 3
e
46'
+ 48
46-
6333
9
IS 61
16.76
IS 08
16 61
b
20 8
+ 36
20 S
6341
8
+ 16.
13.86
13 60
14 16
IS 24
b
II 2
+ 64
9 2
226 APPENDIX A
CATALOGUE or GLOBULAR CLUSTERS. (continued)
N. G. C.
Name
R A.
1900
Dec.
1900
Galactic
Angu-
lar
Diam-
eter
Inte-
grated
Magni-
tude
Class
Spec-
trum
Number
of Varia-
bles
Long
Lat.
h m
O f
o
o
/
6342
17 15 3
19 29
333
+ 8
0.5
11.4
IV
6 3 52t
17 17 5
48 22
309
- 8
2.5
7.9
XI:
6356*
17 17 8
17 43
334
+ 9
i .7
8.6
II
Ko
6362
A 225
17 21 5
-66 58
293
-18
6.7
7-1
X
i?
6366
17 22 4
~~ 4 59
346
+ 15
4:
12. 1
XI
6388
17 29 o
-44 40
313
- 8
3 4
7.1
III
K
6402
M 14
17 32 4
- 3 II
349
+ 14
3
7 4
VIII
6397
A 366
17 32 7
-53 37
304.5
12 5
19 o
4 7
IX
G?
a
6426f
17 39 9
-f- 3 13
356
+ 15
I 3
12 2
IX:
6440
17 43 O
2O 2O
335
+ 2
O 7
II 4
V
6441
17 43 4
37 i
321
65
2.3
8 4
III
Ko
64S3
t
17 44 7
-34 36
322.5
-55
o 7
II 2
IV
6496
17 51 8
-44 14
315
-10 5
2 2
9-7
XII
6517
17 56 4
8 57
347
+ 6
O.4
12. 1
IV
6522
17 57 2
-30 2
328
- 5
o 7
II. O
VI
. .
6528
17 58 4
-30 4
328 5
5
o 5
II. 8
V
. . .
6S3St
17 58 7
- o 18
355
+ 9 5
i 3
ii. 9
XI:
6539t
17 59 4
- 7 35
348
+ 5
i 3
12 6
X:
z
6541
A 473
18 8
-43 44
317
12
6 3
5 8
III
G
z
6SS3
18 3 2
-25 56
332.5
- 5
I 7
IO O
XI
. . .
o
6569
18 7 2
-31 51
328
-75
I 4
10 2
VIII
6584
A 376
18 IO 6
-52 IS
309 5
17
2 5
8 3
VIII
o
6624
18 17 3
-30 24
330
10
2.0
8 6
VI
Mo
6626
M 28
18 18 4
-24 55
335
7
4 7
6 8
IV
Gs
9
6637
M 69
18 24 8
32 25
329
II
2 8
7.5
V
K2
6638
18 24 8
-25 34
335 5
- 7.5
I 4
9 2
VI
66S2
18 29 2
33 4
328 5
13
I 7
8 7
VI:
KS
6656
M 22
18 30 3
-24
337
- 9
17 3
3 6
VII
21
6681
M 70
18 36.7
-32 23
330
-13 5
2.5
7.5
V
. . .
6?i2t
18 47.6
8 50
353 5
6
2 . 1
9.9
IX:
I
6715
M 54
18 48.7
-30 36
333
-15
2.1
7.1
III
F8
6723
A 573
18 52 8
-36 46
328
19
5-8
6.0
VII
GS?
17
6752
A 295
19 2
-60 8
303
-26 5
13 3
4 6
VI
Go
X
676of
19 6 I
+ o 52
3
- 5
I 9
IO 9
IX:
6779
M 56
19 12 7
4-30 o
30
+ 8
i 8
8.8
X
X
6809
M 55
19 33 7
31 10
336
-25
IO.O
4 4
XI
2
6864"
M 75
20 2
22 12
347
27
I 9
8 6
I
Go*
IX
6934
20 29 3
+ 74
20
20
I 5
9 4
VIII
Go
698 x
M 72
20 48 O
12 55
3
-34
2.O
8 6
IX
29
7006
20 56 8
+ 15 48
32
21
I I
ii 8
I
. . .
XX
7078
M"IS
21 25 2
+ 11 44
33
-28
7 4
5.2
IV
P
74
7089
M 2
21 28 3
I 16
21
-36
8 2
5 o
II
PS
10
7099
M 30
21 34 7
-23 38
355
-48 5
5 7
6 4
V
F8
3
7492
23 3 I
-16 10
22
-64
3 3
10 8
XII
9
NOTES TO APPENDIX A
N. G. C. 4372. The distance depends only on the diameter measure. The cluster appears
to be partially obscured by one of the streamers from the Coal Sack nebula. A special
investigation of the magnitudes is being made on Harvard plates.
N. G. C. 6356, 6864. The distance depends only on the magnitudes of the bright stars,
since the integrated bnghtness and diameter appear to be abnormally large. There may be
obscuring nebulosity in the field of N. G. C. 6356.
CATALOGUE OF GLOBULAR CLUSTERS
CATALOGUE OF GLOBULAR CLUSTERS. (continued)
227
N. G. C
Ellip-
ticity
Orien-
tation
Photographic Magnitude
Adopted
Modulus
Qual-
ity
Dis-
tance
Ksin0
Rcos/9
Var.
Bright
6th
30th
"
kpc
kpc
kpc
6342
18.0:
e
40:
+ 56:
39 S:
6352t
9
16.48
d
19 7
- 2.7
19.4
6356
6^62
9
g
-'4
+ 78
17 16
16 86
17 44
18 51
15 9O
e
d
SO-
+ 7.8
49:
6366
17 34
e
29:
+ 7 5-
28:
6388
9 5
16 20
c
17 3
-24
17 2
6402
9
+ 76
IS 44
14 85
IS 86
16 48
a
19 7
+ 48
19 I
6397
9
4-73
12 6l
ii 9
13 I
13.76
c
S 65
X.2
5 5
6 4 26f
9
17 85
e
37 I
+ 9 6
35 9
6440
8
+ 10
4- in
18.5
e
so:
+ 1.7:
SO:
6441
6453
8
-f4O
18 5
e
SO.
-48.
21 O
So:
6496
16 90
d
24 o
-40
21 6
6517
8
4
18 5:
e
So
+ 5 a-
So:
6522
17.78
e
36 o
-32
35 8
6528
18 24
e
44 4
-39
44 I
6S3St
IS 9
IS 3
16 4
17 13
d
26 7
+ 4 4
26 3
6539t
9
17 94
e
38 7
+ 3 4
38 4
6S4I
9
14 4?
U 35
12 7
13 8
14 76
c
8 9
- I 8
8 7
6SS3
9
17 14
c
26 8
-23
26 7
6569
9 5
17.35
c
29 5
-3
29 2
6584
M\<*A
9
16 56
c
20 S
-60
19 6
0024
6626
IO
9
+ 18
14 87
14-49
IS ii
16 10
a
16 6
a o
16 4
66?7
16 36
18 7
3 6
18 4
v)J,57
6638
9
8
27
16 22
15.90
16.60
17 36
b
29 6
- 3.9
29 3
6652
8
ti
16 87
d
23 6
53
23.0
6656
8
+ 18
14 06
12 93
12.80
13.26
14 16
a
6 8
Z.I
6.7
6681
9 S
16 41
c
19 2
-4.S
18 8
6?i2t
16 10
15.6s
16.36
17 10
d
26.2
- a. 7
26.0
6715
10
16 44
d
19 4
SO
18 7
6723
9 5
IS 33
14 20
13.7
12 8
14.8
Tl ft
IS 44
b
v
12 3
-41
II. 7
6752
6?6ot
* " " *
13
I3.O
17 28
c
28 6
as
28 5
6779
8
+ 12
....
IS 31
14 98
IS-70
16 54
h
20 3
+ a 8
2O O
6809
9
....
13 58
12.9
14 2
14 74
b
8 8
-37
8 o
6864
9
17 06
16 76
17-35
18 43
d
48 S
22
43 2
6934
9
.
IS 78
15.33
16 ii
16 98
b
24 9
-85
a3 4
6981
1 6. 80
15 86
IS S3
16.20
16 84
a
23 3
-13 o
19 3
7006
18.96
17.50
16 99
17.89
18 77
b
56 8
-20 4
53
7078
8
-II
15.63
14.31
14 13
14- SS
15 60
a
13 I
- 6.1
II 6
7089
9
-80*
15.71
14 61
14 25
14 76
IS 72
a
13 9
- 8 a
II 3
7099
9
14 63
13 77
IS 04
IS 82
b
14 6
10.9
9.7
7492
9
16 82
16 3
17. 1
17 oi
c
25. a
-aa 7
XX X
228
APPENDIX B
I
- - - - *
S 1
V O ^-M M MMO<N M
1 1 +++ 1 I+I++I 1 1 1 l+l+l+l 1 l+l+l
V V
00 rfM OO ro
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u 0.0 00^t^oo looo^^ooo^ioo, r^orc
oO^M^Mro
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OtO rOOtN 10
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3+
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II
TJ- o t* foo oo o i>-oo N oo ooo o 10 100 POOO o oo MNOOOON
PI M M O tfr OtOO M O^OOtOOvOtOv Ovoo M Otoo O f*5 Oi } O\ N O\
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0.00. OVM o
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T+i TT+
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10 10 IO
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^OA
++++++++++++++++++++++++++++
++++++
-I
00 COO IO M rfoO 00 O O> N *tN 00 O * N * O O rooO N O toO
K Ot^iOl^iOOtN MO x}- 1~ t^ O\ M M to ioO lOiOrOt^iOMQO C< t^ ^
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M M M M* 3 5$ u> IOO O OO^OOOO-J O OjjJ ?fO* tOiOrt
M^&
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M M M M M M
CATALOGUE OF GALACTIC CLUSTERS
229
< N ro if in
f) O CO -<t M O O 10 *t Ot f*)O 00 O ^tO M r* I>.M t (M oo M 1000 ro Ot M d O O O
i/} M MM PI ro o O* "t >O >-t ioci MMMvoddMro
+++++++ +++ I I I I M I ++H-+ I + -f ++ I + I -
A A V V V
CO N (*)vO ^
A
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fO M 00 O O tO ^ N 00 >O <*)O O
t^OO^O Ok O*.OO\NOON\O OOO>OO N vo O> i/>/jt/>o <N N t^O O t* w r
MI^OM M Mot*t"O M POM f-00 r>-NO r-t*. ooO^O^w O> O^ O-i woooo irtOoo M roOs
^ > NM XOW W ^ * f y\ P ' 00 ^ JJ^ N M OOOP O O O W rO"H M TfM W M ^-M C
A M rt- . v v v
N Qi n n 00 QO . o O M\OOO u)OoO 00 to WOO 00 t^ O 00 O O O M O W)00 10 i/J OMfl o <O O>
OfOO *} *)MnOO*MrONrto < 'l 1 ^fO^t'<l- O <*JO (*) OO\O^O>-"ooOt-iOi-"NOt*
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t*oMM^tM^tN(ot-t^ > MOOO'OOrofOHiooo>HOO^MioroOTtH^-M^t wio f*5 /> M fJ OO fO
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l/>TtM^^Tf<v)>-it/)*)NO'<t-OtOI/)NOO
^ ''
**
t^oo ^lOrfMoo ^tNO M o>flO O O Tf *}O oo O Tf O oo wjoo N P oo t r- t^O rO^O oo oO o t~ n 1000 to i^ c*
\O roioio^tc* *>Ot'*'t^*f)io t^.\o "-" *OO*r>.MO OoooOMOOfOwj^tO ^tw f*JM o M ^r'jHeor^'
^J- fO *5 f* M *) rj- <* M M t-t to M N ^M M M N M M M M M n w M S POM N row
++++++++++++++ I + I 4-++++ I ++ I + I I + I I I I + I I + M I I I I I
O 1000 O t>. fj too
NO O\00 OOOMPO'ti-<NN < PO s -t-O 'too O O
j- rf *t -3- if) \f> M H M HI ro f*> fO fO <*> CO fj *) 't *t ^t O M>
n fOrf 4 O
M I^M t p>)Tf rOTfuiO NH
oo 00 o o N N ww>OO
230
APPENDIX B
&
M
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>0
a 1
'
J
++++l + l-f++-h-f++4-?l
** ^ M M M OOO M MM
1 + 1 1 + 1 HhH 1 1-4-1 +-H-+ 1 1 +
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SH3XSQT) 3I1DVTVO JO
232
APPENDIX B
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234 APPENDIX B
NOXES TO APPENDIX B
1 Messier 103
2 Distance from Wallenquist, Ups. Medd. 42, 1929
3 h and x Persei; fifth star assumed of magnitude 2 m .s. Trumpler (P. A. S. P.,
38, 352, 1926) gives a distance of 2.3 on the basis of the mean magnitude for
Class Ap
4 Messier 34
6 Messier 45; the diameter from Russell, Dugan, and Stewart corresponds to an
angular radius of nearly two degrees
8 Distance and diameter from Russell, Dugan, and Stewart
7 Messier 38
8 Messier 36; distance from Wallenquist, Ups. Medd. 32, 1927
9 Messier 37; distance from von Zeipel and Lindgren, Swedish Acad., 6z, No. 15,
1921
10 Messier 35
11 Scarcely resolved
12 Eccentric in an elliptical diffuse nebula
13 S Monocerotis in cluster
14 Messier 41
18 Messier 50
16 r Canis Majoris in cluster
17 Messier 46; an important photographic catalogue by Chevalier (see App. C)
18 Messier 93
19 Praesepe, Messier 44; distance from Russell, Dugan, and Stewart
20 Messier 67
21 Diffuse nebula in a coarse cluster
22 Carinae involved
23 Coma Berenices; distance from Russell, Dugan, and Stewart
24 *Crucis
26 Not resolved; a photograph of N. G. C. 6540 appears in Pop. Ast. Tidsk..
8, 62, 1927
26 Mount Wilson plate
27 Messier 6
28 Messier 7
29 Messier 23
30 Messier 21
31 Messier 24
82 Messier 16
33 Messier 18
34 Messier 17; nebulosity
* Messier 25
86 Messier 26; Trumpler finds a distance of 2.75 (L. O. B., 14, 122, 1929)
87 Messier 1 1 ; distance from Trumpler
88 Messier 71
89 Messier 29
40 Messier 39
41 Messier 52; distance from Wallenquist, Ups. Medd. 42, 1929
APPENDIX C
BIBLIOGRAPHY
THE bibliography of star clusters contains only a few entries
prior to 1875 but is essentially complete from then to 1930.
Bibliographies of earlier papers have been compiled by Holden
(Reference 261 below) and Knobel (Reference 316). Some papers
on Cepheid variables, mainly my own, are included in the bibli-
ography because of their bearing on the period-luminosity and
period-spectrum relations which have been of importance in cluster
work. A few articles on the Magellanic Clouds and the structure
of the Galaxy are also listed.
The topical bibliographies in Appendix D should facilitate study
in a few special fields.
1. ADAMS, W. S., The Radial Velocities of the Brighter Stars in the Pleiades,
Ap. J., 19, 338, 1904-
2 . and A. VAN MAANEN, A Group of Stars of Common Motion in the h
and \Persei Clusters, A. J., 27, 187, 1913.
-, The Spectra of Some Individual Stars in the Hercules Cluster,
P. A. S. P , 25, 260, 1913.
4. and H. SHAPLEY, The Spectrum of 5 Cephei, Mt. W. Comm. 22, 1916.
5. and , Note on the Cepheid Variable SU Cassiopeiae, Mt. \V.
Contr. 145, 1918.
6. ALDEN, H. L., Trigonometric ParaUax of the Pleiades, Amer. Astr. Soc., 4,
349, 1922.
7. ANDREINI, A., Distanze e Dimensioni cosmiche, Livorno, 1921.
8. AUWERS, A., AuseinemSchreibendes IlerrnGehcimrath Auivcrs . . . , A. N.,
114, 47, 1886 (Nova in Messier 80).
9. BAADE, W., Sieben Ver&nderliche in der Umgebung des Kugerlhaufens M 53,
Hamburg Mitteilungen, 5, No. 16, 1922.
10. , Bemerkung zu der Arbeit von H. Kienle und P. ten Bruggencate uber
die absolute Helligkeit der Plejadensterne, Zeit. f. Phys., 31, 604, 1924.
ii. , 5 isolierte Haufenver Underlie he in der Umgebung des Kugclhaufens
N. G. C. 5466, Hamb. Mitt., 6, No. 27, 1926.
ia. , Der kugelfiirmige Sternhaufen N. G. C. 5466, Hamb. Mitt., 6, No. 27,
1926.
13. , 17 neue Ver&nderliche im Kugelhaufen M 53 (N. G. C. 5024),
Hamb. Mitt., 6, No. 27, 1926.
235
236 APPENDIX C
14. , Der Sternhaufen N. G. C. 5053, Hamb. Mitt., 6, No. 29, 1928;
A. N., 232, 193, 1928. (See Chapter II, Section 8 above for a discussion
of this abnormal cluster.)
15. BACKHOUSE, I. W., Note on Mr. A. S. Eddington's Moving Cluster of Stars
in Perseus, M. N. R. A. S., 71, 523, 1911.
16. BAILEY, S. I., w Centauri, Astr. and Ap., 12, 689, 1893.
17. , Variable Stars in Clusters (Abstract), Amer. Astr. Soc., I, 49, 1898.
18. , The Periods of the Variable Stars in the Cluster Messier 5, Ap. J., 10,
255, 1899-
19. , Note on the Relation between the Visual and Photographic Light
Curves of Variable Stars of Short Period, Ap. J., 10, 261, 1899.
20. , The Rate of Increase in Brightness of Three Variable Stars in the
Cluster Messier 3, Amer. Astr. Soc., I, 100, 1900; Science, 12, 122, 1900.
21. , co Centauri, H. A., 38, i, 1902.
22. , Variable Stars in the Clusters Messier 3 and Messier 5, H. C. 100,
1905.
23. , The Number and Distribution of Stellar Clusters and Nebulae, Amer.
Astr. Soc., i, 268, 1906.
24. , Note on the Magnitude of the Stars in Messier 3 (Abstract), J. R.-
A. S. Can., 5, 337, ipn.
25. , Variable Stars in the Cluster Messier 3, H. A., 78, i, 1913.
26. , Variable Stars in the Cluster Messier 5, H. A., 78, 103, 1917.
27. , Variable Stars in the Cluster Messier 15, H. A., 78, 199, 1919.
28. , Globular Clusters, VJS. d. A. G., 48, 418, 1913.
29. , On the Number of the Globular Clusters (Abstract), Pop. Astr., 22,
558, 1914.
30. , Globidar Clusters, H. A., 76, No. 4, 1915.
31. , Cluster Variables with Double Maxima, H. C. 193, 1916.
32. , Note on the Form of the Light Curve of Variable Stars of Cluster Type,
(Abstract), Pop. Astr., 25, 307, 1917.
33. , Note on the Variable Stars in the Globular Cluster M 15 (Abstract),
Pop. Astr., 25, 520, 1917.
34. , Note on the Magnitudes of the Variables in M 15 (Abstract), Pop.
Astr., 26, 683, 1918.
35. , Globular Clusters, H. C. 211, 1918.
36. , Variable Stars in M 22 (Abstract), Pop. Astr., 28, 518, 1920.
37. , Variable Stars in the Cluster N. G. C. 6723, H. C. 266, 1924.
38. , Photographic Work at Arequipa with the Bruce 24-inch Refractor,
N.G. C. 3201, H. C. 234, 1922 (Variable Stars in N. G. C. 3201;.
39 . } Eight New Variable Stars near N. G. C. 6809, H. B. 813, 1925.
40. , Clusters and Nebulae, H. Repr. 29, 1926.
41. BALANOWSKY, J., (Photometric Study of 42 Stars in the Cluster h Persd),
Pulk. Bui., 7, 199, 1920 (in Russian).
42. , &tude des amas stettaires h et \Pers6e, Pulk. Bui., 9, 277, 1924.
43. , Die Eigenbewegung des kugelf'ormigen Sternhaufens Messier 92
(N. G. C. 6341), Pulk. Bui., xi, 167, 1928; C. R. Acad. U. R. S. S., No.
21, 364, 1927.
BIBLIOGRAPHY 237
44. BALL, R., and E. A. RAMBAUT, On the Relative Position of 223 Stars in the
Cluster x Persei, Trans. Roy. Irish Acad., 30, Part 4, 1892.
45. BANNISTER, R. D., Positions of the Stars in a Cluster Whose Center Is at R. A.
1 8*34"* and Declination +5 17' Determined from Photographic Plates,
A. J., 3*> 165, 1918. (This cluster is I. C. 4756.)
46. BARABASCHEFF, N., Uber die Helligkeitsverteilung im Sternhaufen M 13,
A. N., 220, 299, 1923.
47. BARNARD, E. E., The Cluster G. C. 1420 and the Nebula N. G. C. 2237, A. N.,
122, 53, 1889.
48. , Photographic Nebulosities and Star Clusters connected with the Milky
Way, Astr. and Ap., 13, 177, 1894.
49 . f Triangulation of Star Clusters, Amer. Astr. Soc., I, 77, 1899.
50. , Note on Some of the Variable Stars of the Cluster Messier 5, A. N.,
147, 243, 1898.
51. , Triangulation of Star Clusters, Science, 10, 789, 1899.
52. , Note on the Exterior Nebulosities of the Pleiades, M. N. R. A. S.,
59, 155, 1899; 60, 258, 1900.
53. , Some A bnormal Stars in the Cluster 3/13 Ilerculis, Ap. J., 12, 1 76, 1900.
54. , Micrometrical Measures of Individual Stars in the Great Globular
Clusters, Science, 17, 330, 1903.
55. , Discovery and Period of a Small Variable Star in tlie Cluster M 13
Uerculis, Ap. J., 12, 182, 1900 (Previously discovered by Bailey; cf.
Barnard, Ap. J., 29, 72, 1008).
56. , Micrometrical Measures of Individual Stars in the Great Globular
Clusters, Amer. Astr. Soc., I, 193, 1902.
57. , On Some of the Variable Stars in the Cluster M 5 Librae, Amer.
Astr. Soc., i, 193, 1902.
58. , Visual Observations of a Variable Star in the Cluster M 3 (N. G. C.
5272), A. N., 172, 345, 1906.
59. , On the Motion of the Stars in the Cluster Messier 92, A. N., 176, 1 7,
1007.
60. , Second Paper on the Motion of the Stars in Messier 92, A. N., 176,
21, 1907.
61. ,OntheColorsof Some of the Stars in the Globular Cluster M 13 Hcrcu-
lis, Ap. J., 29, 72, 1908.
62. f (^ fa Constancy of the Period of the Variable Star, M 5 (Librae)
No. 33, Amer. Astr. Soc., I, 298, 1908.
63. , On the Proper Motion of Some of the Small Stars in the Dense Cluster
M 92 Herculis, Amer. Astr. Soc., I, 323, 1909.
64. , On the Motion of Some of the Stars of Messier 92 (Hercules), A. N.,
182, 305, 1909; Pop. Astr., 18, 3, 1910.
65. , On the Period and Light Curve of the Variable Star No. 33, M 5
(Libra) and on the Possible Use of Such a Star as a Time Constant, A. N.,
184, 273, 1909.
66. , The Variable Star No. 33 in the Cluster M 5, A. N., 196, n, 1913.
67. , On the Change in the Period of the Variable Star Bailey No. 33 in the
Cluster M 5 (Abstract), Pop. Astr., 27, 522, 1919.
238 APPENDIX C
68. , Remeasurement of Hall's Stars in the Pleiades (Abstract), Pop. Astr.,
*7 523, 1919-
69. , Variable Stars in the Cluster M n (N. G. C. 6705), Pop. Astr., 27,
485, 1919.
70. , On the Comparative Distances of Certain Globular Clusters and the
Star Clouds of the Milky Way, A. J., 33, 86, 1920.
71. BATTERMANN, H., Triangulation zwischen den acht hellsten Sternen der
Plejadengruppe, A. N., 122, 353, 1889.
72. BAXENDELL, J., Notes on Pogson's Observations of U Geminorum, T Scorpii,
and R Librae, A. J., 22, 127, 1902 (Nova in Messier 80).
73. BECKER, F., Die Kugelformigen Sternhaufen, Himmelswelt, 32, 105, 1922.
74. , Sternhaufen und Nebelflecken, Hevelius, p. 354, 1922.
740 , Die Verleilung der Spektren in zwei 0/enen Sternhaufen, A. N.,
236, 327, 1929-
75. BELLAMY, F. A., A New Cluster in Cygnus, with Right Ascensions and
Declinations of 103 Stars Included in It, M. N. R. A. S., 64, 662, 1904.
76. BELOPOLSKY, A., Dber die Veranderungen in dem Sternhaufen N. G. C. 5272,
A. N., 140, 23, 1895.
77. BELOT, E. , VOrigine Possible des Amas d'Etoiles, C. R., 164, 513, 1917.
78. BERGSTRAND, 0., Sur le Groupe des Etoiles d Helium dans la Constellation
d 'Orion, N. Acta S. S. U., Reg. Soc. Sci. Ups., Ser. 4, Vol. 5, No. 2, 1919.
79. BHASKARAN, T. P., Proper Motions of Stars in the Cluster M 41 (N. G. C.
2287), M. N. R. A. S., 79, 59, 1918.
80. BICKERTON, A. W., The New Astronomy, III. Star Clusters and Nebulae,
Knowledge, 34, 413, 1911.
81. BIGOURDAN, G., Les Nebuleuses de la Rtgion des Pleiades, Bui. Astr., 28,
417, 1911 (History of discoveries, and description of the nebulosities,
rather extensive bibliography).
82. , Observations de Nebuleuses et d'Amas Stellaires, Ann. Obs. Paris,
Observations, 1884, 1888, 1890-1907.
83. BOHLIN, K., Der Zweite Sternhaufen im Hercules, Messier 92, Stockholm
Publ., 8, No. 3, 1906.
84. , Ausmessung des Zweiten Sternhaufens im Hercules (Messier 92),
A. N., 174, 203, 1907.
g^ . 1 Q n tfo Galactic System with Regard to Its Structure, Origin, and
Relations in Space, Swedish Acad. Proc., 43, No. 10, 1909.
86. Bos, W. H. VAN DEN, Photovisual Magnitudes of 55 Stars in Praesepe, from
Plates taken at Potsdam, B. A. N., I, 79, 1922.
87. Boss, B., Systematic Proper-Motions of Stars of Type B, A. J., 26, 163, 1910.
(See also A. J., 27, 33, 1911; 27, 67, 1912; 28, 12, 15, 1913; 28, 174, 1914.)
88. , A Convergent Point for Four Clusters of Small Proper Motion Stars,
A. J., 30, 22, 1916.
89. Boss, L., Convergent of a Moving Cluster in Taurus, A. J., 26, 31, 1908.
90. BOTTLINGER, K. F., Die Eigenbewegung der Btirengruppe, A. N., 198, 153,
1914.
91. BOURGET, H., Photographic des Nebuleuses et des Amas stellaires, Bui. Soc.
Astr. France, 14, 57, 1900.
BIBLIOGRAPHY 239
92. BREDICHIN, T., Mesures micromelriques du groupe de Persee, Ann. Moscow
Obs., 4, No. 2, 1878.
93. BRONSKY, M., and A. STEBNITZKY, Les Positions des Etoiles dehet x Persee
et de leurs Environs, Mem. St. Petersburg Acad. Sci., 2, Ser. 8, No. 7,
1894.
94. BROWN, F. L., Measures of the Cluster N. G. C. 6633, A. J., 31, 57, 1918.
95. BRUGGENCATE, P. -iEK,Die Bedeutung derFarbenhelligkeits-diagrammenfur das
Studium der Siernhaufen, Probleme der Astronomic, Festschrift fiir Hugo
von Seeliger, p. 50, 1924.
96. , Uber die Resle einer Spiralstruktur in Sternhaufen, Zeit. f. Phys.,
24, 48, 1923.
97. , Uber eine Absorption des Lichtes bei ojfenen Sternhaufen, Zeit. f.
Phys. 29, 243, 1924.
98. , The Absorption of Light in Open Star Clusters, B. A. N., 4, 51, 1927.
99. , Sternhaufen, Berlin, 1927.
IOO ^ Q H ifa Determination of the Spacial Distribution of the Stars in
Globular Clusters from the Intensity Distribution in Their Projections,
B. A. N., 4, 195, 1928.
101. , Bemerkungen uber ellipsoidformige Sternhaufen t A. N., 232, 417,
1928.
102 . f Die Dichteverteilung in rotationssymmetrischen Sternhaufen, A. N.,
232, 423, 1928.
1020. , The Radial Velocities of Globular Clutters, P. N. A. S., 16, in, 1930.
103. CERASKI, W., Uber die Anzahl der Sterne in den Plejaden, A. N., 108,
245, 1884.
104. , Etude Photometrique sur VAmas Stellaire Coma Berenices, Moscow
Annals, Ser. 2, 6, 33, 1917.
105. , Une nouvelle Variable 16.1904 Persei au Cluster x Persei, A. N.,
165, 126, 1904.
106. CHAPMAN, S., Some Problems of Astronomy, II. Globular Clusters, Obs., 36,
112, 1913.
107. CHARLILR, C. V. L., Preliminary Statistics of Nebidae and Clusters, Lund
Medd. 56, 1913. (Arrays and diagrams based on the N. G. C. and the
I. C.; correlations of distribution, brightness, and size.)
108. , Stellar Clusters and Related Celestial Phenomena, Lund Medd.,
Ser. 2, 19, 1918.
109. CHASE, F. L., Triangulation of the Principal Stars of the Cluster in Coma
Berenices, Trans. Yale Obs., i, Part V, 1896.
no. CHASE, H. S., A Comparison of the Positions of the Stars in Praesepe Derived
by Dr. B. A. Gould from Photographs with the Positions Observed by
Professor Hall, A. J., 8, 167, 1889.
in. CHEVALIER, S., Etude Photographique de VAmas d* Etoiles Messier 67
(N. G. C. 2682), Ann. Z6-S< Obs., 8b, 1914.
112. , Etude Photographique de VAmas d'Etoiles Messier 46 (N. G. C.
2437), Ann. Z6-S& Obs., pd, i, 1916.
113. , Amos d'Etoiles Messier 22 (N. G. C. 6656), Ann. Z6-S4 Obs., 100,
i, 1918.
240 APPENDIX C
114. CnfcvREMONT, A., D&ouverte d'une Etoile variable dans VAmas Messier
2 du Verseau, Bui. Soc. Astr. France, 12, 16, 90, 1898.
115. CHRETIEN, H., Sur I 1 Analyse statistique des Amas d'Etoiles, C. R., 157,
1047, 1913.
1 1 6. CLERKE, A. M., The Yale College Measurement of the Pleiades, Nature, 36,
372, 1887.
117. COEBERGH, C. L. A. M., Parallaxbepalingen van Sterrenhoopen, Hem. en
Damp., 1918.
1 1 8. COLLINDER, P., Sur la Distribution et les Couleurs des Etoiles dans I 9 Amas
M 34, Ark. Mat. Astr. Fys., 198, No. n, 1926.
119. , De dppna Stjdrnhoparna i Vintergatan och i Angrdnsande Stjarn-
system, Pop. Astr. Tid., 8, 36, 1927.
120. COMMON, A. A., Faint Stars near Alcyone, M. N. R. A. S., 44, 412, 1884.
121. , The Photographic Nebulae in the Pleiades, M. N. R. A. S., 46, 341,
1886.
122. , Note on some Variable Stars near the Cluster 5 M t M. N. R. A. S.,
50, 517, 1890.
123. COMSTOCK, G., A New Member of the Taurus Cluster, A. J., 34, 33, 60, 1922.
124. CROMMELIN, A. C. D., The Distances of Globular Clusters, Obs., 45, 138, 1922.
125. CURTIS, H. D., Descriptions of Nebulae and Clusters Photographed with the
Crossley Reflector, L. O. B., 7, 81, 1912; 8, 43, 1913.
126. , Search for Faint Members of the Taurus Cluster, P. A. S. P., 27,
243, 1915.
I2 7. t Finding List for General Catalogue Numbers, P. A. S. P., 29, 180, 191 7.
128. , Descriptions of 762 Nebulae and Clusters Photographed with the
Crossley Reflector, Lick Publ., 13, 9, 1918.
129. , The Scale of the Universe, Bui. Nat. Res. Coun., 2, 194, 1921.
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138. , Note on the Distance of M n Aquilae (N. G. C. 6705), J. B. A. A.,
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139. , The Spacing of the Nearby Stars compared with Globular Clusters,
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BIBLIOGRAPHY 241
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156. , Kritische Bemerkungen liber Sterngruppen, mit Bertlcksichtigung der
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242 APPENDIX C
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BIBLIOGRAPHY 243
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185. FLEMING, W. P., Note on Mr. Packer's Variables near M 5 Librae, Sid. Mess.,
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186. , Two New Variable Stars near the Cluster 5 M Librae, A. N., 125,
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189. AND V. HEISKANEN, Uber die Verteilung der Sterne verschied-
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190. GAULTIER, E. C., Catalogue Annuel des Grandeurs Photographiques de 300
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192. GIFFORD, A. C., The Average Distance Apart of Stars in a Globular Cluster,
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193. GORE, J. E., Globular Star Clusters, Knowledge, 17, 232, 255, 1894.
194. , Messier's Nebulae, Obs., 25, 264, 288, 321, 1902.
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196. GOULD, B. A., Photographic observations of star clusters, 1897.
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198. AND W. KRUSE, Photometrische Vermessung des Sternhaufens N. G. C.
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199. , Photometrische Helligkeilen und Farben in dem Stemhaufen M 34
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200. , Photometrische Stern- und Farbenfolge in dem zerstreuten Stemhaufen
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201. GUSHEE, V. M., A Study of Proper Motions in the Cluster N. G. C. 663, A. J.,
32, 117, 1919.
202. GUTHNICK, P., Kugelhaufen, inbesondere uber gemeinsam mit Herrn R.
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204. GYLLENBERG, W., Die Ausmessung des Sternhaufens I. C. 4996, Lund Medd.
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205. HAGEN, J. G., On the Extension and Appearance ofN. G. C. 6822, Atti Pont.
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206. HAHN, R., Mikrometrische Vermessung des Sternhaufens S 762, Abh. d.
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244 APPENDIX C
207. , Mikrometrische Vermessung des Sternhaufens S 762, A. N., 129,
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208. HALE, G. E., Photographs of Star Clusters Made with the Forty-inch Visual
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210. HARTMANN, J., Die Bewegung der elf hellslen Plejadensterne, A. N., 199,
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211. HAYN, F., Eigenbewegungen und Parallaxe derPlejaden, A. N., 198, 147, 1914.
212. , K dialog von 70 Plejadensternen fur das Aquinoktium von 1900.0,
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213. , Nachtrag zum Katalog der Plejaden in A. N., 209, 355, A. N., 211,
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214 . > j)i e piejaden, Abh. der Math.-Phys. Kl. d. Sachs. Akad. d. Wiss.,
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215. , Der Sternhaufen Praesepe, Leipzig Ver5ff ., 2, 1927.
216. HECKMANN, O., Photographische Vermessung der Praesepe, A. N., 225, 49, 1925.
217. , Analysis of ten Bruggencate's "Sternhaufen" VJS. d. A. G., 62,
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218. , Photographische Vermessung der Sterngruppe Coma Berenices, G6tt
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219. and H. SIEDENTOPP, Uber die Struktur der Kugelformigcn Stern-
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221. HEINEMANN, K., Photographische Photometrierung und Vermessung des
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223. HELMERT, F. R., Der Stern-Haufen im SternbUde des Sobieski'schen Schildes,
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229. , Uber die Verteilung Galaktischer Objekte, A. N., 192, 261, 1912.
230. , Uber die Helligkeit der Plejadennebel, A. N., 195, 449, 1913.
231. , Comparison between the Distribution of Energy in the Spectrum of
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232. , N. G. C. 1647, Mt. W. Rep., 9, 222, 1914.
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BIBLIOGRAPHY 245
234. , Effective Wave-lengths of 184 Stars in the Cluster N. G. C. 1647, Mt.
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235. , Prufung, der photographischen Grossenskda der hellen Plejadensterne,
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236. , Photographische Sterngrdssen von 233 Praesepesternen t A. N., 203,
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237. , The Nature of Globular Clusters, Obs., 40, 303, 1917.
238. , Ein schwacher Verdunkelungsveranderlicher in Praesepe, A. N.,
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239. , Photographische Sterngrdssen von 308 Praesepesternen, A. N., 205,
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240. , Photographische Messung der Lichtverteilung im mittleren Gebiet des
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241. , Bemerkungen zur Hyadengruppe t A. N., 209, 113, 1919.
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243. , Bearbeitung der J. F. J. Schmidtschen Beobachtungen und Bestimmung
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245. , Effective Wavelengths of Stars in the Pleiades, Mem. Danish Acad.,
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246. , Stars possibly belonging to the group of the Hyades selected from a
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247. , Remarks on some Double Stars in the Hyades, B. A. N., I, 87, 1922.
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249. , On the Motion ofPraesepe and of the Hyades, B. A. N., I, 150, 1922.
250. , On the Motions of the Clusters x andhPersei, B. A. N., I, 151, 1922.
251. , Notes on the Magnitude Scale of the Plejades, B. A. N., I, 152, 1922.
252. , Further Remark on the Motion of the Clusters \ and h Persci, B. A. N.,
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253. , A Star in the Pleiades possibly belonging to the System of the Hyades,
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254. 9 The Pleiades, M. N. R. A. S., 89, 660, 1929.
255. HINKS, A. R., On the Galactic Distribution of Gaseous Nebulae and of Star
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256. HINS, C. H., B. D. +13 688, a Star of the Hyades?, B. A. N., 2, 60, 1924.
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258. HOFFMEISTER, C., Ver Under liche in Sternhaufen, G. u. L., Appendix II, 1920.
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246 APPENDIX C
261. HOLDEN, E. S., Index Catalogue of Books and Memoirs Relating to Nebulae
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263. , List of New Nebulae and Clusters Discovered in the Zone Observations
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264. , Bemerkungen zur Plejadengruppe, A. N., 108, 439, 1884.
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266. , Characteristic Forms within the Cluster in Hercules^ P. A. S. P., 3,
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267. HOLETSCHEK, J., Vber den Helligkeitseindruck von Nebelflecken und Stern-
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268. , Vber den Helligkeitseindruck von Sternhaufen, Wiener Berichte, no,
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269. , Vber den Helligkeitseindruck einiger Nebelflecken und Sternhaufen,
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270. , Beobachtungen uber den Helligkeitseindruck von Nebelflecken und
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271. HOPMANN, J., Die Sternhaufen, Naturwiss., 8, 740, 1920.
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275. , *Die ojfenen Sternhaufen N. G. C. 6885 bei 20 Vulpeculae und M 36
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276. , Vergleich der Hamburger und Bonner Vermessungen des kugel-
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283. and others, (Estimates of Color 0/47 Tucanae), U. C. 31, 1915.
284. , Centennial proper motions of Stars near w Centaurus, U. C. 45,
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285. , Nebulae, Clusters, etc., on Sydney Plates, U. C. 48, 1920.
286. , Nebulae and Clusters in the Melbourne Zone, U. C. 53, 1921.
287. , Variable Stars in and near the Cluster <> Centaurus, U. C. 59, 1923.
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290. , Globular Star Cluster, N. G. C. 5824, U. C. 66, 1925.
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299. , An Investigation of the Cluster M 37 (N. G. C. 2099) for Proper-
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300. JUNG, J., Die Radial geschwindigkeiten von elf Plejadensternen nach Spektro-
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302. , , and , The Proper Motion of the Hyades, Groningen
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305. KEELER, J. E., Photographs of Nebulae and Clusters made with the Crossley
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306. KEMPF, P., Beobachtungen von Nebelflecken und Sternhanfen mit einem
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307. , Beobachtungen von Nebelflecken und Sternhanfen, Pots. Publ., 8,
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309. and P. TEN BRUGGENCATE, Die Absolute Helligkeit der Plejaden-
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310. , Die Gestalt der Kugelftirmigen Sternhaufen, Naturwiss., 15, 243,
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311. , Zur Entfernungsbestimmung von Sternsystemen, A. N., 230, 243,
1927-
248 APPENDIX C
312. , Die Dichteverteilung in Ellipsoidfdrmigen Sternhaufen, A. N., 232,
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313. , Die Absorption des Lichtes und die Grenze des Sternsystems, Zs. f.
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314. KLEIN WASSINK, W. J., Stars belonging to the Cluster Praesepe, B. A. N.,
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316. KNOBEL, E. B., Reference Catalogue of Astronomical Papers and Researches. 4,
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319. KoHLSCHthTER, A., Die Spektren der Hyaden und der Praesepe, A. N., axx,
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320. KONIG, A., Photographische Vermessung der Plcjaden, A. N., 222, 177, 1924.
321. KOPFF, A., Uber die Haufigkeitsfunktion beim Kugelsternhaufen M 13,
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322. KOSTINSKY, S., Uber die Eigenbewegung der Sterne in der Umgebung der
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3220. , Durchmusterung der Eigenbewegungen in der Umgebung der Stern-
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326. KREIKEN, E. A., Proper Motions of Stars belonging to thePlejadcs, B. A. N.,
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327. KRETZ, W. C., The Positions and Proper Motions of the Principal Stars in
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328. KRITZINGER, H. H., Beobachtungen der Helligkeit einiger Nebel und Stern-
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329. KRUSE, W., Mikrometrische Vermessung des Sternhaufens N. G. C. 6633,
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330. KUSTNER, F., Der kugelfSrmige Sternhaufen Messier 56, Bonn Verflff., 14,
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331. , Der kugelftirmige Sternhaufen Messier 15, Bonn Verdff., 15, 1921.
33 2. , Der kugelformige Sternhaufen Messier 3, Bonn Verflff., 17, 1922.
333* > Ausmessungen der vier ojfenen Sternhaufen N. G. C. 7789, Messier
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333d. LAGRULA, J., fitudes sur les Occultations d'Amas d'fitoiles par la Lune t
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339. , Neuer Veranderlicher 4, 1921 Canum Venaticorum vom XX Cygni-
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358. , Nachtrag zu der Abhandlung, "Der grosse Sternhaufen im Herkules
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359. f Bemerkungen zu Herrn Zurhettens Abhandlung "Der Sternhaufen
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360. , Vber die RadialgeschwindigkeUen von 0, e, Ursae Majoris und
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250 APPENDIX C
361. LUNDBORG, A., Nebulosor och stjarnhopar, Pop. Astr. Tid., 4, 16, 1923.
362. LUNDMARK, K., and B. LINDBLAD, Photographisch effektive Wellenltingen fur
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363. and , Photographic Effective Wave-Lengths of Nebulae and
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364. , The Relations of the Globular Clusters and Spiral Nebulae to the
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365. , The Parallax of the Coma Berenices Cluster, L. O. B., 10, 149, 1922.
366. , Die Stellung der kugelformigen Sternhaufen und Spiralnebel zu
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367. , Determination of the Apex of Globular Clusters, P. A. S. P., 35, 318,
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368. , Avlagsna StjOmsystem (Tre Extragalaktiska System nu bekanta),
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369. , Plejadernas Avstand, Nord. Astr. Tid., 5, 73, 1924.
370. , De MagalKaeska Molnens Avstand, Pop. Astr. Tid., 5, 146, 1924.
371. , De Mdrka Nebulosornas Utbredning, Ups. Medd. 12, 1926 (abstract
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3710. , Are the Globular Clusters and the Anagalactic Nebulae Related?,
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372. LUYTEN, W. J., Note on the Cluster N. G. C. 6633, M. N. R. A. S., 8z, 213,
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373' > On the Distances of the Cepheids, P. A. S. P., 34, 166, 1922.
374. , Note on some Stars belonging to the Hyades Cluster, P. A. S. P., 36,
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375- , Proper Motions of Eleven Cluster Type Variables, H. B. 847, 1927.
376. MAANEN, A. VAN, The Proper Motions of 1418 Stars in and near the Clusters
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377. , Investigations on Proper Motion, First Paper. The Motions of
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378. , Remarks on the Motion of the Stars in and near the Double Cluster
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379. , Investigations on Proper Motion, Third Paper. The Proper Motion
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380. , Note on the Parallax of Cepheid Variables, P. A. S. P., 32, 62, 1920.
381. , Investigations on Proper Motion, Eleventh Paper. The Proper
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382. , Investigations on Proper Motion, Twelfth Paper. The Proper
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383. , Over de Eigenbeweging van en in de drie bolvormige Sterrehoopen
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384. MACKLIN, H. E., The Clusters h and x Persei, M. N. R. A. S., 8x, 400, 1921.
385. , Note on the Proper Motions of Stars of the Clusters h and x Persei,
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386. MACPHERSON, H., The Distances of Star-Clusters, Obs., 42, 126, 1919.
BIBLIOGRAPHY 251
387. MALMQUIST, K. G., ttber die Enlfernung des ofenen Haufens N. G. C. 752,
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3880. MARTENS, ERIK, A Research on the Spherical Dynamical Equilibrium-
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402. NANGLE, J., The Cluster near K Crucis, J. B. A. A., 18, 384, 1908.
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252 APPENDIX C
414. OORT, J. H., On a Possible Relation between Globular Clusters and Stars of
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415. , Additional Notes concerning the Rotation of the Galactic System,
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416. PACKER, D. E., On a New Variable Star near the Cluster 5 M Librae, Sid.
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417. , New Variable Stars near the Cluster 5 M Librae, Sid. Mess., 10,
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420. PANNEKOEK, A., Luminosity Function and Brightness for Clusters and
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421. , New Reduction of von ZeipeVs Magnitudes in Messier 3, B. A. N.,
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422. PARASKEVOPOULOS, J. S., Integrated Magnitude of 47 Tucanae, H. B. 824,
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425. PARIJSKI, N., V Essai sur I 9 estimation de la masse et du nombre d' etdlles de
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434. PEASE, F. G., The Star Cluster N. G. C. 6760, P. A. S. P., 26, 204, 1914.
435- , Spectra of Stars in the Hercules Cluster M 13, P. A. S. P., 26, 204,
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436. , Spectra of Stars in the Hercules Cluster M 13, Mt. W. Rep., 9, 219,
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437. , Spectra of Stars in the Hercules Cluster M 13, Mt. W. Rep., 10,
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BIBLIOGRAPHY 253
439. , and , Note on the Elliptical Form of Messier 13, Amer. Astr.
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440. and , Axes of Symmetry in Globular Clusters , Mt. W. Comm.
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441. , A Planetary Nebula in the Globular Cluster Messier 15, P. A. S. P.,
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442. PERRINE, C. D., A Division of the Stars in some of the Globular Star Clusters,
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444. , Some Results derived from Photographs of the Brighter Globular Star
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445. , The Nature of Globular Clusters, Obs., 40, 166, 1917.
446. , Spcctroscopic Notes on Southern Clusters, Nebulae and Red Stars,
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447. , Distances of the Galactic Cepheids, Magcllanic Clouds, and Globular
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449. PETER, B., Bestimmung der Qrter von 27 Sternen dcr Plejadengruppe am
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451. , Bestimmung dcr relativen Coordinaten dcr Sterne A und Z im Stern-
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452. PETTIT, H. S., TJte Proper Motions and Parallaxes of 359 Stars in the Cluster
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453. PICKERING, E. C., Variable Star in Chester G. C. 3636, A. N., 123, 207, 1889.
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454. ? Spectrum of Pleione, A. N., 123, 95, 1889.
455. , Variable Stars near 47 Tucanae, A. N., 125, 129, 1894.
456. , Variable Star Clusters, H. C. 2, 1895; A. N., 139, 137, 1895; Ap. J. f
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457- , The Cluster Messier 5 Serpentis, N. G. C. 5904, A. N., 140, 285, 1896.
458. , Distribution of Stars in Clusters, II. A., 26, 213, 1891.
459. , Measurement of Positions (Stars in Messier 5), H. A., 26, 226, 1891.
460. , Spectra of Stars in Clusters, H. A., 26, 260, 1891.
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462. , Variable Star Clusters, H. C. 24, 1898; A. N., 146, 113, 1898; Ap. J ,
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463. , Variable Stars in Clusters, H. C. 33, 1898; A. N., 147, 347, 1898;
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464. , Variable Stars in Clusters. Rate of Increase of Light. H. C. 52, 1900;
A. N., 153, us, 1900; Ap. J., 12, 159, 1900.
254 APPENDIX C
465. PICKERING, W. H., The Distance of the Pleiades; the Distance of Coma
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466. PIHL, O. A. L., The Stellar Cluster \ Persei micrometrically surveyed,
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467. PINGSDORF, F., Der Sternhaufen in der Cassiopeia, Messier 52, Dissertation,
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468. PITMAN, J. H., Parallaxes of nine Stars in the Pleiades, Amer. Astr. Soc.,
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469. PLUMMER, H. C., The Positions of Seventy Stars in the Cluster M 13 Herculis,
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470. , On the Problem of Distribution in Globular Star Clusters, M. N.
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471. , Star Clusters, Nature, 94, 674, 1915.
472. , The Distribution of Stars in Globular Clusters, M. N. R. A. S., 76,
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473. , An Analysis of the Magnitude Curves of the Variable Stars in Four
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474. PLUMMER, W. E., The Great Cluster in Hercules, M. N. R. A. S., 65, 801,
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475. PORRO, F., Variabli sos peltate, M 3, A. N., 127, 197, 1891.
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477. PROCTOR, M., K Crucis, J. B. A. A., 25, 193, 1915.
478. PROCTOR, R. A., On the Resolvability of Star-Groups Regarded as a Test of
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479. PUMMERER, P., Der Sternhaufen G. C. 392, Publ. Kttffner'schen Stern w., 6,
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480. RAAB, S., A Research on Open Clusters, Lund Medd., Ser. 2, 28, 1922.
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482. , Photographies de Nebuleuses et d? Amas d 1 fitoiles, Bui. Soc. Astr.
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483. RAIMOND, J. J., Jr., The Mean Parallax of the Hyades, B. A. N., 3,221, 1926.
484. , Proper Motions of 12 Bright Pleiades, B. A. N., 4, 135, 1928.
485. RASMUSON, N., A Research on Moving Clusters, Lund Medd., Ser. 2, 26, 1921.
486. , Rbrliga stjarnhopar, Pop. Astr. Tid., 3, 43, 1922.
487. , A New Research on the Scorpio-Centaurus Cluster, Lund Medd.
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488. REBEUR-PASCHWITZ, E., Bemerkung betrejfend den Sternhaufen G. C. 1360
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489. REBOUL, M., La Distance des Amas d' toiles, Bui. Soc. Astr. France, 32,
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490. , Sur les Dimensions du Systeme Galactique, Bui. Soc. Astr. France,
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491. , Distances des nuages stellaires et de la Voie Lactic, Bui. Soc. Astr.
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BIBLIOGRAPHY 255
492. VAN RHIJN, P. J., The Proper Motions of 2088 Stars and the Motion of the
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496. , Notes on Photographs of Nebulae taken with the 6o-inch Reflector
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498. ROBERTS, I., (Photographs of Nebulae and Clusters), M. N. R. A. S., 47,
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505. , Radial Velocities of Clusters, Mt. W. Rep., 15, 250, 1919.
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512. , Uber den grossen Sternhaufen im Herkules, M 13, Abh. d. Preuss.
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513. , Uber die Liapunow'schen Messungen im Sternhaufen Messier 13,
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514. , Uber den Sternhaufen um theta Orionis, A. N., 147, 149, 1898.
256 APPENDIX C
515. SCHILLER, K., Photographische Helligkeiten und Mittlere drier von 251
Sternen der Plcjadengruppe, A. N., 171, 337, 1906.
516. SCHILT, J., On the Detection of Orbital Motion in Star Clusters, P. A. S. P.,
38, 327, 1926.
517. , The Distribution of Light in the Central Part of the Globular Cluster
co Centauri, Pop. Astr., 36, 296, 1928; A. J., 38, 109, 1928.
518. SCHOUTEN, W. J. A., On the Determination of the Principal Laws of Statis-
tical Astronomy, Dissertation, Amsterdam, 1918.
519. , The Parallax of Some Stellar Clusters, Obs., 42, 112, 1919.
520. , fiber dieParallaxe einiger Sternhaufen t A. N., 208, 317, 1919.
521. , The Parallax of the Pleiades, Obs., 42, 240, 1919.
522. SCHULHOF, L., Vergleich der Messungen von Ferguson, 1863-64, mit den
Beobachtungen von Bessel, A. N., 83, 193, 1874.
523. SCHULTZ, H., Note in Regard to U 92, A. N., 66, 47, 1865.
524. , Globular Clusters Motions, Upsala, 1873.
525. , Mikrometrisk Bestamning of 104 Stjernor inom teleskopiska Stjcrn-
gruppen 20 Vulpeculae, Proc. Swedish Acad., Supplement, 12, Sec. i,
No. 2, 1886.
526. , Beobachtungen des telescopischen Sternhaufens Gen. Cat. Nr. 4976,
A. N., 108, 371, 1884.
527. SCHUR, W., Die drter der helleren Sterne derPraesepe, Gttttingen Mitt., 1895.
528. , Heliometrische Bestimmung der gegenseitigen Lage der Sterne A und
Z in Perseus, A. N., 132, 95, 1892.
529. , fiber die Bestimmung der Parallaxe der Sterne der Praesepegruppe
durch Photographische Aufnahmen, A. N., 137, 221, 1895.
530. , Vermessung der beiden Sternhaufen h und x Persei mit dem sechszdl-
ligen Heliometer der Sternwarte in Gottingen, Gbttingen Mitt., 6, 1900.
531. SCHWARZSCHILD, K., and W. VILLIGER, Aufnahmen des Sternhaufens h
Persei mit Spiegeln von sehr grossem OffnungsverhcUtniSy A. N., 174, 133,
1907.
532. , fiber die Ritumliche Bewegung derPraesepe, A. N., 196, 9, 1913.
533. S&COLEY, B., fiber die Verteilung der Riesensterne in Sternhaufen nach dem
Color-index, Rus. Astr. Journ., x, No. 2, 69, 1924.
591. SEARES, F. H., and H. SHAPLEY, Color Variation of the Cluster Type Variable
RS Bootis, P. A. S. P., 26, 202, 1914.
534. and , Distribution of Colors among the Stars of N. G. C. 1647
and M 67, Mt. W. Comm. 17, 1915.
615. and , Color Variation of the Cluster Type Variable RS Bootis
(abstract), Pop. Astr., 23, 19, 1915.
535- , Color-Indices in the Cluster N. G. C. 1647, Mt. W. Contr. 102, 1916.
536. and H. Shapley, The Variation in Light and Color of RS Boittis,
Mt. W. Contr. 159, 1918.
537. , The Relation of Color Index to Spectrum in the Pleiades, P. A. S. P.,
34, 56, 1922.
538. SEE, T. J. J., On the Theoretical Possibility of Determining the Distances of
Star Clusters, etc., A. N., 139, 161, 1895.
539- , Measures of Double Stars in the Great Nebula and Cluster in Carina,
M. N. R. A. S., 57, 541, 1897.
BIBLIOGRAPHY 257
540. , Dynamical Theory of the Globular Clusters and of the Clustering Power
inferred by Herschel from the observed Figures of Sidereal Systems of High
Order, Proc. Amer. Phil. Soc., 51, 118, 1912.
541. , Confirmation de la Valeur de la "thorie de la capture" dans V Evolu-
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Soc. Astr. France, 28, 476, 1914.
542. SELGA, M., Cumulos estelares en moviminto, Rev. Soc. Astr. Esp., 6, 12, 1916.
543. SELLACK, C. S., Photographie Sudlicher Sterngruppen, A. N., 82, 65, 1873.
544. SHAPLEY, HARLOW, New Variables in the Center of Messier 3, Mt. W. Contr.
91, 1914.
545. , On the Nature and Cause of Cepheid Variation t Mt. W. Contr. 92,
1914.
546. , Miscellaneous Notes on Variable Stars, Mt. W. Contr. 99, 1915.
547. and M. B. SHAPLEY, A Study of the Light Curve of XX Cygni t Mt. W.
Contr. 104, 1915.
548. , On the Changes in the Spectrum, Period, and Light Curve of the Cepheid
Variable RR Lyrae, Mt. W. Contr. 112, 1916.
549. , Studies based on the Colors and Magnitudes in Stellar Clusters, I.
The General Problem of Clusters, Mt. W. Contr. 115, 1915.
550. II. Thirteen Hundred Stars in the Hercules Cluster (Messier 13), Mt. W.
Contr. 116, 1915.
551. ///. A Catalogue 0/311 Stars in Messier 67, Mt. W. Contr. 117, 1916.
552. IV. TheGalactic Cluster Messier n, Mt. W. Contr. 126, 1917.
553 V. Color-Indices of Stars in the Galactic Clouds, Mt. W. Contr. 133, 1917.
554. VI. On the Determination of the Distances of Globular Clusters, Mt. W.
Contr. 151, 1918.
555. VII. The Distances, Distribution in Space, and Dimensions of 69 Globular
Clusters, Mt. W. Contr. 152, 1918.
556. VIII. The Luminosities and Distances of 139 Cepheid Variables, Mt. W.
Contr. 153, 1918.
557. IX. Three Notes on Cepheid Variation, Mt. W. Contr. 154, 1918.
558. X. A Critical Magnitude in the Sequence of Stellar Luminosities, Mt. W.
Contr. 155, 1918.
559. XI. A Comparison of the Distances of Various Celestial Objects, Mt. W.
Contr. 156, 1918.
560. XII. Remarks on the Arrangement of the Sidereal Universe, Mt. W. Contr.
157, 1918.
561. XIII. The Galactic Planes in 41 Globular Clusters, Mt. W. Contr. 160,
1919 (with M. B. Shapley).
562. XIV. Further Remarks on the Structure of the Galactic System, Mt. W. Contr.
161, 1919 (with M. B. Shapley).
563. XV. A Photometric Analysis of the Globular System M 68, Mt. W. Contr.
175, 1920.
564. XVI. Photometric Catalogue 0/848 Stars in Messier 3, Mt. W. Contr. 176,
1920 (with H. N. Davis).
565. XV IL Miscellaneous Results, Mt. W. Contr. 190, 1920.
258 APPENDIX C
566. XV 111. The Periods and Light Curves of 26 Cepheid Variables in Messier 72,
Mt. W. Contr. 195, 1920 (with M. Ritchie).
567. XIX. A Photometric Survey of the Pleiades, Mt. W. Contr. 218, 1921 (with
M. L. Richmond).
568. , The Variations in Spectral Type of Twenty Cepheid Variables,
Mt. W. Contr. 124, 1916.
439. F. G. PEASE and, on the Distribution of Stars in Twelve Globular
Clusters, Mt. W. Contr. 129, 1917.
5. W. S. ADAMS and, Note on the Cepheid Variable SU Cassiopciae,
Mt. W. Contr. 145, 1918.
536. F. H. SEARES, and, The Variation in Light and Color of RS Bootis,
Mt. W. Contr. 159, 1918.
j6 9 . and M. B. SHAPLEY, The Light Curve of XX Cygni as a Contribution
to the Study of Cepheid Variation, Mt. W. Comm. 14, 1915.
534. F. H. SEARES and, Distribution of Colors among the Stars of N . G. C.
1647 and M 67, Mt. W. Comm. 17, 1915.
570. , Studies of Magnitudes in Star Clusters, I. On the Absorption of Light
in Space, Mt. W. Comm. 18, 1916.
571. //. On the Sequence of Spectral Types in Stellar Evolution, Mt. W. Comm
19, 1916.
572. 777. The Colors of the Brighter Stars in Four Globular Systems, Mt. \V.
Comm. 34, 1916.
573. IV. On the Color of Stars in the Galactic Clouds Surrounding Messier 1 1, M.
W. Comm. 37, 1917.
574. V. Further Evidence of the Absence of Scattering of Light in Space, Mt. W.
Comm. 44, 1917.
575. VI. The Relation of Blue Stars and Variables to Galactic Planes, Mt. W.
Comm. 45, 1917.
576. VII. A Method for the Determination of the Relative Distances of Globular
Clusters, Mt. W. Comm. 47, 1917.
577. VIII. A Summary of Results Bearing on the Structure of the Sidereal Universe,
Mt. W. Comm. 54, 1918.
578. IX. The Distances and Distribution of Seventy Open Clusters, Mt. W. Comm.
62, 1919.
579. X. Spectral Type B and the Local Stellar System, Mt. W. Comm. 64, 1919.
580. XI. Frequency Curves of the Absolute Magnitude and Color Index for 1152
Giant Stars, Mt. W. Comm. 69, 1920.
581. .X77. Summary of a Photometric Investigation of the Globular System Messier
3, Mt. W. Comm. 70, 1920.
582. XT77. Variable Stars in N. G. C. 7006, Mt. W. Comm. 74, 1921.
583. , A Short Period Cepheid with Variable Spectrum, Mt. W. Comm. 21,
1916.
4. , W. S. ADAMS and, The Spectrum of B Cephei, Mt. W. Comm. 22,
1916.
S g 4 . f Discovery of Eight Variable Stellar Spectra, Mt. W. Comm. 27, 1916.
585. , F. G. PEASE and, Axes of Symmetry in Globular Clusters, Mt. W.
Comm. 39, 1917. (This is the same as Ref. 440.)
BIBLIOGRAPHY 259
586. , and S. B. NICHOLSON, On the Spectral Lines of a Pulsating Star.
Mt. W. Comm. 63, 1919.
587. , Photometry of Star Clusters, Mt. W. Rep., 14, 205, 1918.
588. , Limit of Brightness in Clusters, Mt. W. Rep., 16, 243, 1920.
589. , Spectroscopic Parallaxes ofG and K Stars in Clusters, Mt. W. Rep.,
16, 242, 1920.
590. , Absolute Magnitudes of Cluster Stars, Mt. W. Rep., 17, 265, 1921.
sgl . f F. H. SEARES and, Color Variation of the Cluster-Type Variable RS
Bo'dtis, P. A. S. P., 26, 202, 1914.
592. , Note on the Color of the Faint Stars in the Orion Nebula, P. A. S. P.,
27, 40, 1915.
593. , (New Variable Stars in the Hercules Cluster), P. A. S. P., 27, 134,
238, 1915.
594. , The Colors of Fifteen Variables in Messier 3, P. A. S. P., 28, 81, 1916.
595. , Six Cepheids with Variable Spectra, P. A. S. P., 28, 126, 1916.
596. , Outline and Summary of a Study of Magnitudes in the Globular
Cluster Messier 13, P. A. S. P., 28, 171, 1916.
597. , Light Elements of Variable No. 37 in Messier 3, P. A. S. P., 29, no,
1917.
598. and H. DAVIS, On the Variations in the Periods of Variable Stars in
Messier 3, P. A. S. P., 29, 140, 1917.
599. and , Messier's Catalogue of Nebulae and Clusters, P. A. S. P.,
29, 177, 1917.
600. , Descriptive Notes Relative to Nine Clusters, P. A. S. P., 29, 185, 1917.
601. , A Faint Nova in the Andromeda Nebula, P. A. S. P., 29, 213, 1917.
602. , Note on the Magnitudes of Novae in Spiral Nebulae, P. A. S. P., 29,
213, 1917.
603. , The Dimensions of a Globular Cluster, P. A. S. P., 29, 245, 1917.
604. , Globular Clusters and the Structure of the Galactic System, P. A. S. P.,
30, 42, 1918.
605. and H. DAVIS, Note on the Distribution of Stars in the Globular Cluster
Messier 5, P. A. S. P., 30, 164, 1918.
606. , Note on the Distant Cluster N. G. C. 6440, P. A. S. P., 30, 253, 1918.
607. , On Radiation and the Age of Stars, P. A. S. P., 31, 178, 1919.
609. , Nineteen New Variable Stars, P. A. S. P., 31, 226, 1919.
610. , On the Existence of External Galaxies, P. A. S. P., 31, 261, 1919.
6 1 1. and J. C. DUNCAN, Novae in the Andromeda Nebula, P. A. S. P.,
31, 280, 1919.
612. , Photometric Parattaxes of Nine Cepheid Variables, P. A. S. P., 32,
162, 1920.
613. , The Local Cluster, A. N., 213, 231, 1921.
614. , Neuer Veriinderlicher 2, 1922 Coronae Australis in N. G. C. 6541,
A. N., 215, 391, 1922.
615. , F. H. SEARES and, Color Variation of the Cluster-Type Variable RS
Bo'dtis (Abstract), Pop. Astr., 23, 19, 1915.
6 1 6. , New Variables in the Center of Messier 3 (Abstract), Pop. Astr.,
23, 20, 1915.
260 APPENDIX C
617. , On ike Nature and Cause of Cepheid Variation (Abstract), Pop.
Astr., 23, 20, 1915.
6 1 8. , Magnitudes and Colors in the Hercules Cluster (Abstract), Pop.
Astr., 23, 640, 1915.
619. , The Colors of Fifteen Variables in Messier 3, Pop. Astr., 24, 257, 1916.
620. , Discovery of Eight Variable Stellar Spectra, Pop. Astr., 24, 354, 1916.
621. , The Colors of the Brighter Stars in Seven Globular Clusters (Abstract),
Pop. Astr., 25, 35, 1917.
622. , Notes on the Spectra of Cepheid Variables (Abstract), Pop. Astr.,
25. 36, 1917-
623. , F. G. PEASE and, Note on the Elliptical Form of Messier 13 (Abstract),
Pop. Astr., 25, 374, 1917.
624. , Notes on Stellar Clusters (Abstract), Pop. Astr., 25, 379, 1917.
625. and J. C. DUNCAN, The Globular Cluster Messier 22 (N. G. C. 6656)
(Abstract), Pop. Astr., 27, 100, 1919.
626. , The Galactic System, Pop. Astr., 31, 316, 1923.
627. , On the Distribution of Stars in Globular Clusters, Obs., 39, 452,
1916.
628. , Note on the Explanation of the Absence of Globular Clusters from the
Mid-galactic Regions, Obs., 42, 82, 1919.
629. , Note on Changes in the Period and Light-Curve of the Cluster Variable
SW Andromedae, M. N. R. A. S., 81, 208, 1921.
630. and A. J. CANNON, The Local System and Stars of Class A, H. C.
229, 1922.
631. , Notes Bearing on the Distances of Clusters, H. C. 237, 1922.
632. and A. J. CANNON, The Distribution of Stars of Spectral Class B,
N. C. 239, 1922.
633. and , The Distribution of Stars of Spectral Class M, H. C.
245, 1923-
634. , On the Dwarf Variable Stars in the Orion Nebula, H. C. 254, 1924.
635. , The Magellanic Clouds, I. The Distance and Linear Dimensions of
the Small Cloud, H. C. 255, 1924.
636. , The Magellanic Clouds, II. The Luminosity Curve for Giant Stars ;
H. C. 260, 1924.
637. , The Magellanic Clouds, III. The Distance and Linear Dimensions
of the Large Cloud, H. C. 268, 1924.
638. and H. H. WILSON, The Magellanic Clouds, IV. The Absolute
Magnitudes of Nebulae, Clusters, and Peculiar Stars in the Large Cloud, H.
C. 271, 1925.
639. and , The Magellanic Clouds, V. The Absolute Magnitudes
and Linear Diameters of 108 Diffuse Nebulae, H. C. 275, 1925.
640. and , The Magellanic Clouds, VI. Positions and Descriptions
of 170 Nebulae in the Small Cloud, H. C. 276, 1925.
641. , I. YAMAMOTO, and H. H. WILSON, The Magellanic Clouds, VII.
The Photographic Period-Luminosity Curve, H. C. 280, 1925.
642. and M. L. WALTON, The Magellanic Clouds, VIII. Note on the
Spectral Composition of the Foreground, H. C. 288, 1925.
BIBLIOGRAPHY 261
643. , Note on Obscuring Cosmic Clouds in High Galactic Latitudes, H. C.
281, 1925.
644. and M. WALTON, Investigations of Cepheid Variables, I. The Period-
Spectrum Relation, H. C. 313, 1927.
645. , Investigations of Cepheid Variables, II. The Period-Luminosity
Relation for Galactic Cepheids, H. C. 314, 1927.
646. , Investigations of Cepheid Variables, III. Cluster Type Variables
and Theories of Cepheid Variation, H. C. 315, 1927.
647. and M. WALTON, Investigations of Cepheid Variables, IV. Beta
Doradus, a new Fourth Magnitude Cepheid, H. C. 316, 1927.
648. , Dimensions of Messier 3, H. B. 761, 1921.
6 49 . f Note on the Velocity of Light, H. B. 763, 1922.
650. , Parallax of Messier 5, H. B. 763, 1922.
651. , Giant Stars near the Pleiades, H. B. 764, 1922.
652. , Spectral Classification of Faint Pleiades, H. B. 764, 1922.
653. , The Absolute Magnitude of Cluster Type Variables, H. B. 765, 1922.
654. , New Cluster Type Variable in the Small Magellanic Cloud, H. B. 765,
1922.
655. , Star of High Velocity, H. B. 773, 1922. (RZ Cephei.)
656. , Group of New Globular Clusters, H. B. 775, 1922.
657. , Approximate Distance and Dimensions of the Large Magellanic
Cloud, H. B. 775, 1922.
658. , New Globular Clusters, H. B. 776, 1922.
659. , N. G. C. 2419, H. B. 776, 1922.
660. , New Faint Cluster Variable (near N. G. C. 6362), H. B. 777, 1922,
(variable discovered by S. I. Bailey.)
661. , Absolute Magnitude of RZ Cephei, H. B. 778, 1922.
663. , Five New Variable Stars, H. B. 781, 1923 (variables discovered by
A. J. Cannon, I. E. Woods, and S. I. Bailey).
664. , Globular Cluster Containing Long Period Variables, H. B. 783, 1923.
665. , Nine New Variables in HighGalactic Latitude, H. B. 791, 1923.
666. , Note on the Distance of N. G. C. 6822, H. B. 796, 1923.
667. , Angular Dimensions of Magellanic Clouds, H. B. 796, 1923.
668. , Photographic Magnitudes in Messier 13, H. B, 797, 1924.
669. , Proof of Variability of Fourteen Stars in Orion Nebula, H. B. 803,
1924.
670. , Note on a Star Cloud in Sagittarius, H. B. 804, 1924.
671. , Comparison of Messier 33 and the Large Magellanic Cloud, H. B. 816,
1925.
672. , The Absorption of Light in Space, H. B. 841, 1926.
673. and H. B. SAWYER, The Galactic Cluster N. G. C. 6231, H. B. 846,
1927.
508. , H. B. SAWYER, and, Photographic Magnitudes of Ninety-five Globular
Clusters, H. B. 848, 1927.
674. , The Distance of Messier 22, H. B. 848, 1927.
675. and H. B. SAWYER, A Classification of Globular Clusters, H. B. 849,
1927.
262 APPENDIX C
676. , The Periods of Seventy-three Variables in Messier 5, H. B. 851, 1927.
677. and H. B. SAWYER, Apparent Diameters and Ellipticities of Globular
Clusters, H. B. 852, 1927.
678. and A. AMES, The Coma-Virgo Galaxies, I. On the Transparency of
Inter-galactic Space, H. B. 864, 1929.
679. , Relation of Apparent Magnitude to Angular Diameter for Globular
Clusters, H. B. 864, 1929.
680. and H. B. SAWYER, The Distances of Ninety-three Globular Star
Clusters, H. B. 869, 1929.
68oa. ,The Mass-spectrum Relation for Giant Stars in the Globular Cluster
Messier 22, H. B. 874, 1930.
681. , Note on the Problem of Great Stellar Distances, P. N. A. S., 8, 69,
1922.
682. , On the Relative Velocity of Blue and Yellow Light, H. Repr. 5, 1923.
683. and A. J. CANNON, Summary of a Study of Stellar Distribution, II.
Repr. 6, 1924.
684. , The Distribution of the Stars, H. Repr. 8, 1924.
685. , The Magettanic Clouds, H. Repr. 25, 1925.
686. , Studies of the Galactic Center, I. The Program for Milky Way
Variable Stars, H. Repr. 51, 1928.
687. and H. H. SWOPE, Studies of the Galactic Center, II. Preliminary
Indication of a Massive Galactic Nucleus, H. Repr. 52, 1928.
688. , Studies of the Galactic Center, III. The Absolute Magnitudes of Long
Period Variables, H. Repr. 53, 1928.
689. , Star Clusters and the Structure of the Universe, Scientia, 26, 269,
353, JQIQ; 27, 93, 185, 1920.
690. , The Size of the Galaxy, Scientific American Monthly, 4, 197, 339,
1921.
691. , The Scale of The Universe, Bui. Nat. Res. Coun., 2, 171, 1921.
692. , The Magcllanic Clouds, Festschrift fur Hugo von Seeliger, p. 438,
1924.
693. , Globular Clusters, Cepheid Variables, and Radiation, Nature, 103, 25,
1918.
694. , Star Clusters and their Contribution to the Knowledge of the Uni-
verse, Proc. Amer. Phil. Soc., 58, 337, 1919.
695. , Star Cluster, Encyclopaedia Brittanica, 1929.
696. SHAPLEY, M. B., The Color-Curve of XZ Cygni, Mt. W. Contr. 128, 1917.
697. SHAW, H. K., Note on the Nebulae and Star Clusters shown on the Franklin-
Adams Plates, M. N. R. A. S., 76, 105, 1915.
698. SHILOW, M., Grdssenbestimmung der Sterne im Sternhaufen 20 Vulpeculae,
Bui. St. Petersb. Acad. Sci. 2nd Series, 5, No. 3, 243, 1895.
699. SILBERSTEIN, L., The Radial Velocities of Globular Clusters and de Sitter's
Cosmology, Nature, 113, 350, 1924.
700. , The Curvature ofde Sitter's Space-time derived from Globular Clusters,
M. N. R. A. S., 84, 363, 1924.
701. , New Determination of the Curvature Radius of Space-time, Nature,
124, 170, itpo.
BIBLIOGRAPHY 263
702. SITTERLY, B. W., On the Distance and Motion of the Cluster Praesepe, A. J.,
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703. SLIPHER, V. M., On the Spectrum of the Nebula in the Pleiades, Lowell Obs.
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704. , Spectrographic Observations of Nebulae, Pop. Astr., 23, 21, 1915.
705. , Radial Velocities of Star Clusters, J. R. A. S. C., xx, 335, 1917.
706. , Spectrographic Observations of Nebulae and Star Clusters, Pop. Astr.,
25i 36, 1916.
707. , Spectrographic Observations of Nebulae and Star Clusters, P. A. S. P.,
28, 191, 1916.
708. , Spectrographic Observations of Star Clusters, Pop. Astr., 26, 8, 1918.
709. , Further Notes on Spectrographic Observations of Nebulae and Clusters,
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710. , The Radial Velocity of Additional Globular Star Clusters, Pop. Astr.,
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711. SMART, W. M., Proper Motions of Stars in the Pleiades, M. N. R. A. S., 81,
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712. , The Proper Motion of the Cluster N. G. C. 2168 (M 35), M. N. R.
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713. SMITH, A., The Pleiades Cluster, Engl. Mech., 74, 469, 1901.
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717. , Observaci6n estereoscdpica del Cumulo estelar del Centauro, Bol. del
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718. SPRAGUE, R., Star Clusters, Pop. Astr., 1, 407, 1894.
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724. STRATONOFF, W., (Ansahl d cr Plejad ensterne auf Photogr aphischen Aufnah-
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725. , Note Sur les Pleiades, A. N., 144, 137, 1898.
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264 APPENDIX C
730. STRdMGREN, E., Om Bevargelsesmulighedeme I Sljernhobe, Nord. Astr. Tid.,
6, 21, 1925.
731. - , Ober Bewegungsformen in Globular Clusters, A. N., 203, 17, 1916.
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200, 217, 1914.
741. - , Preliminary Results on the Constitution of the Pleiades Cluster, Pop.
Astr., 26, 9, 1918.
742. - , A Study of the Pleiades Cluster, P. A. S. P., 32, 43, J 92o.
743. - , The Physical Members of the Pleiades Group, P. A. S. P., 33. 214,
1921; L. O.B., 10, no, 1921.
744. - , Comparison and Classification of Star Clusters, Publ. Allegheny
Obs., 6, 45, 1922.
745. - , The Cluster Messier n, L. O. B., 12, 10, 1925.
746. - , Spectral Types in Open Clusters, P. A. S. P., 37> 37, 1925.
747. - , Note to Mr. Doig's Letter on Spectral Types in Open Clusters,
P. A. S. P. 38, 114, 165, 1926.
748. - , B-Type Stars with Bright Hydrogen Lines in the Cluster x Persei,
P. A. S. P., 38, 350, 1926.
749. - , Bright Line Stars in the Cluster \Ptrsei, Obs., 50, 93, 1927.
7490. - , Diameters and Distances of Open Star Clusters, P. A. S. P., 41, 249,
1929.
750. - , Magnitudes, Spectral Types and Radial Velocities in the Open
Cluster Messier 39 (N. G. C. 7092), P. A. S. P., 40, 265, 1928.
7$oa. - , Preliminary Results on the Distances, Dimensions t and Space
Distributions of Open Star Clusters, L. O. B. 14, 154, 1930.
751. TURNER, H. H., Some Measures of Photographs of the Pleiades at the Oxford
University Observatory, M. N. R. A. S., 54, 489, 1894.
752. - , Note on the Changes of Period in the Variable Bailey No. 33 in the
Cluster MS, M. N, R, A, S., 80, 640, 1920,
BIBLIOGRAPHY 265
753- , Further Note on Barnard's Observations of Variable Bailey No. 33
in the Cluster Jf 5, with a Suggestion that the Comparison Star kisa Short-
Period Variable, M. N. R. A. S., 8x, 74, 1921.
754. TRZCINSKI, P., Mglawice i zbiorowiska gwiardowe (Nebulae and Clusters),
Wsz. 21, 193, 1902 (in Polish).
755. VALENTINER, W., Ausmessung des Sternhaufens G. C. 4410, Astr. Beob.
Mannheim, 3, 1879. (This is N. G. C. 6633.)
756. VALIER, M., Das Rdtsel der kugelformigen Sternhaufen, Astr. Zeit., 13, 62,
1919.
7560. VANDERLINDEN, II. L., Longueurs d'Onde Effectives des Stoiles de I 1 Amos de
Praescpe, Belg. Acad. Me"m. Series II, 10, Part 2, 1929.
757. VOGEL, II., Spektra ciniger Nebelflecken und Sternhaufen, Bothkampf Bcob.,
i, 156, 1872.
758. , Der Sternhaufen x Persei, Leipzig, 1878.
759- Muthmassliche starke Eigenbewegung eines Sterns im Sternhaufen
G. C. 4440, A. N., 116, 257, 1887.
760. VOGT, H., Photometrische Untersuchungen und Helligkeitsbestimmungen in
den Sternhaufen h und x^ersei, Heidelberg Veroff., 8, No. 3, 1921.
761. , Photometrische Vermessung des Sternhaufens G. C. 1119 (M 38),
A. N., 212, 73, 1920.
762. , Ptwtometrische Vermessung des Sternhaufens N. G. C. 6633, A. N.,
216, 373, 1922.
763. , Fldchcnhelligkeiten von Nebelflecken und Sternhaufen, A. N., 221,
n, 1924.
764. , Photometrische Vermessung der Sternhaufen N. G. C. 752 und I. C.
4665, A. N., 221, 41, 1924.
765. VORONTSOV-VELYAMINOV, B., Catalogue of Integrated Magnitudes of Star
Clusters, A. N., 226, 195, 1925.
766. , Integral Magnitudes of South Star Clusters, A. N., 228, 325, 1926.
767. , Photographic Magnitudes of Globular Clusters, A. N., 236, i, 1929.
7670. VYSSOTSKY, A., Some Results of a Photometric Study of the Double Cluster
in Perseus, Pop. Astr., 36, 350, 1928.
768. WALLENQUIST, A., Stjarnhopen Messier 36, Nord. Astr. Tid., 8, 140, 1927.
769. , Colors and Magnitudes in the Open Cluster Messier 36, N. G. C.
1960, Upsala Medd., 32, 1927.
770. , A Research based on the Bolomctric Magnitudes in the Cluster Messier
37 (N. G. C. 2099), Upsala Medd., 36, 1928.
771. , Om Fotometriska Undcrsokningar av dppna och klotformiga stjarn-
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772. , A Photometric Research on Two Open Clusters in Cassiopeia (Messier
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773. , A Photometric Investigation of the Open Cluster Messier 35 (N. G. C.
2168), Bosscha Ann., 3B, 1929.
773fl. , On the masses of the stars in stellar clusters and their relation to
the theory of Eddington, Proc. Fourth Pac. Sci. Cong , Java, 1929.
774. WATERS, S., The Distribution of the Clusters and Nebulae, M. N. R. A. S.,
33i 558, 1873.
266 APPENDIX C
775 . 1 Q n TWO Distribution Maps of the Nebulae and Clusters in Dr.
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775<*. WEGNER, U., Vber die Verteilungsfunktion in Kugelsternhaufen, Zeit. f.
Phys., 49, 386, 1928.
776. WILSON, F., Clusters and Nebulae Visible with Small Optical Means ; J. B.
A. A., 27, 72, 1916.
777. WILSON, H. C., The Number and Distribution of the Stars in the Vicinity of
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77 8. t The Hyades Group of Stars, Pop. Astr., 20, 359, 1912.
779. , Radial Velocity of the Praesepe Cluster from Objective-Prhm
Neodymium Plates, Pop. Astr., 31, 93, 1923.
780. WILSON, R. E., On the Radial Velocities of Five Nebulae in the Magcllanic
Clouds, P. N. A. S., i, 183, 1915.
781. , The Radial Velocity of the Greater Magellanic Cloud, Lick Publ.,
13, 185, I9 i8.
782. , The Proper Motions and Mean Parallax of the Cepheid Variables,
A. J., 35> 35> 1923-
783. WINLOCK, A., Positions of Stars in Globular Clusters, H. A., 38, 235, 1901.
784. WINNECKE, F. A. T., On the Visibility of Stars in the Pleiades to the Naked
Eye, M. N. R. A. S., 39, 146, 1878.
785. WIRTZ, C., Sternhaufen, Nebelflecke und Weltraum, Astr. Schr. d. Bundes d.
Sternfreunde, i, 1922.
786. , Einiges zur Statistik der Radialbewegungen von Spiralnebcln und
Kugelsternhaufen, A. N., 215, 349, 1922.
787. , Triangulation der Hyaden-Gruppe, A. N., 160, 17, 1902.
788. , Flachenhelligkeiten von 566 Nebelflecken und Sternhaufen nach photo-
metrischen Beobachtungen am w-cm Refraktor der Vniversitatsslernwarte
Strassburg, 1911-1916, Lund Medd., Ser. 2, 29, 1923.
789. , Einiges zur Statistik der kugelfbrmigen und offenen Sternhaufen,
A. N., 220, 293, 1924.
790- , Totalhelligkeit des Kugelsternhaufens M 3 = N. G. C. 5272, Kiel
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791. WOLF, M., Die Aussen-Nebel der Plejaden, Munch. Abh., 20, Part 3,
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793- , Photographische Messung der Sternhelligkeiten im Sternhaufen G. C.
4410, A. N., 126, 297, 1890.
794. , Bewegte Sterne in der Umgebung der Plejaden, A. N., 218, 81,
1922.
795- > DM Sternleeren bei Messier n Scuti, A. N., 229, i, 1927.
796. WOOD, H. E., Note on Southern Star Clusters, U. C. 75, 444, 1927.
797- WOODS, I. E., Variable Stars in the Cluster, N. G. C. 3201, H. C. 216, 1919.
7Q 8. , Variable Stars in the Cluster, N. G. C. 6362, H. C. 217, 1919.
799. , New Variable in N. G. C. 6541, H. B. 764, 1922.
800. WORSSELL, W. M., (Star Clusters and Nebulae from the Wolf-Pdisa Chart
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BIBLIOGRAPHY 267
801. YOUNG, A. S., Rutherfurd Photographs of the Stellar Clusters hand \Persei,
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802. ZEIPEL, H. VON, La Theorie des Gaz et les amas globidaires, C. R., 144, 361,
1907.
803. , Catalogue de 1571 Etoiles conlenues dans Vamas globulaire Messier 3,
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805. , La Loi des luminosites dans I 9 amas globulaire Af3, Ark. Mat. Astr.
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808. , Om Sljttrngruppen M 37, Pop. Astr. Tid., 2, 132, 1921.
809. and J. LINDGREN, Photometrische Untersuchungen der Sterngruppe
M 37 (N. G. C. 2099), Proc. Swedish Acad., 61, No. 15, 1921.
810. , Om stjarngruppernas Natur> Pop. Astr. Tid., 4, i, 1923.
811. ZINNER, E., Untersuchungen uber dieFarbenund Grossen indenSternhaufen,
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812. ZURHELLEN, W , Der Stcrnkaufcn Messier 46, Bonn Veroff., n, 1909.
APPENDIX D
SPECIAL BIBLIOGRAPHIES FOR STAR CLUSTERS
(Numbers refer to titles in Appendix C)
Pleiades: i, 6, 10, 52,* 68, 71, 81,* 99, 103, 116, 120, 121,* 153, 165-168, 182,
187,* 190, 197, 209-214, 226,* 230,* 233, 235, 245, 251, 253, 254, 259, 264,
292, 300, 309, 320, 326, 351, 369, 377, 390, 397, 413, 426, 432, 449, 454, 465, 468,
476, 484, 501, 515, 521, 537, 567, 651, 652, 703,* 711, 713, 715, 724, 725, 728,
740-743, 751, 777, 784, 791,* 792,* 794.
Hyades: 89, 123, 126, 241, 242, 246, 247, 249, 253, 256, 302, 319, 374, 4".
483, 778, 787-
Praesepe: 86, no, 215, 216, 236, 238, 239, 249, 314, 315, 319, 404, 527, 529,
532, 702, 7S6a, 779-
Coma Berenices: 104, 109, 173, 218, 327, 365, 412, 465.
h and x Persei: 2, 41, 42, 44, 92, 93, 105, 133, 172, 222, 225, 250, 252, 301, 322,
336, 352, 376, 378, 379, 384, 385, 392, 427, 45i, 452, 466, 500, 503, 528, 530, 531,
714, 727, 748, 749, 758, 760, 7673, 801.
Ursa Major: 90, 156, 203, 227, 257, 317, 346, 360.
Catalogues of clusters: 30, 82, 127, 140, 141, 148-151, 194, 263, 270, 289, 305,
391, 480, 599.
Number and distribution: 23, 28-30, 40, 48, 70, 85, 99, 106-108, 119, 136, 143,
163, 178, 193, 229, 255, 364, 366, 429, 549, 555, 560, 562, 577, 578, 628, 680, 689,
774, 775-
Spectra: 3, 74a, 78, 142, 177, 179, 180, 259, 319, 432, 433, 435~437, 44*, 446,
454, 460, 501, 504, 506, 537, 589, 652, 694, 703-710, 722, 723, 746-750, 757-
Motions: i, 2, 15, 43, 59, 60, 63, 64, 79, 87-90, 154-157, 170, 173, 176, 195, 201,
210, 211, 227, 244, 249, 250, 252-254, 282, 284, 288, 298-300, 302, 303, 314, 3i5,
322, 326, 327, 347, 360, 367, 376-379, 381-383, 385, 4", 414, 415, 427, 431, 448a,
452, 476, 484-487, 492, 505, 507, 524, 532, 542, 699-702, 704-712, 728, 729,
735, 740, 750, 759, 779, 794.
Variable stars: 8, 9, 11-14, 17-22, 25-28, 30-39, 50, 55, 57, 58, 62, 65-67, 69,
72, 76, 105, H3, 114, 122, 130, 131, 133, 185, 186, 202, 238, 258, 287, 338, 339,
341, 416-418, 423, 453, 455-457, 461-464, 473, 475, 497, 506, 544, 566, 575, 582,
593, 594, 597, 598, 609, 614, 616, 619, 631, 634, 660, 664, 669, 674, 676, 738, 752,
753, 797-799-
See Table IV, I for bibliography of discoveries.
Period-luminosity curve: 99, 146, 343~345, 388, 554, 557i 565, 631, 641, 645,
646, 653, 681, 782.
* Refers to nebulosity in the Pleiades.
268
INDEX
Absorption coefficient, H4jf., 120
Adams, W. S , 33, 143
Ames, 120, 122
Andromeda Nebula (M3i), 5, 120,
152, 172, 179, 195, 209, 211
Arago, 105
Auwers, 52
B
Baade, i8/., 44, 46, 76, 156, 210, 223
Bailey, 7, 9, i4/., 43/> 46, 50. 5*i S3/,
63, 69, 71, 80, QO, 109, 162, 185
Balanowsky, 214
Barnard, 4, 43, 46, 53, i9
Bayer, 3
Becker, 41
Bohlin, 7, 15
Borton, 106
Boss, B., 103
Boss, L., 103
Bottlinger, 103
Brill, 204
ten Bruggencate, 26, 33, 67jf., 88, 151
167, 199
Cannon, A. J., 23, 136, 188
Catalogues of clusters, 4, i4jf>, 224,
228, 268
Centaurus cloud of nebulae, 210
Cepheids, 44, 48/., 148, 215
classical, 52, 54, 182
in clusters, 152
in extra-galactic nebulae, 196
in galactic system, 1 26/.
in Small Magellanic Cloud, I26/.
proper motion, 140
spectra, 136, 140
cluster-type, S3/.
Cepheids, cluster-type and velocity of
light, io8/.
hypotheses of variation, 55$"., 216
in galactic system, 57, 136, 177
light curves, 63, 108, in
proper motion, 140
spectra, 136, 140
(See also Variable stars.)
Charlier, 167, 221
Chevalier, 103, 234
ChvSremont, 46, 51
Clerke, 15
Clusters, 216-221
comparison of galactic and globular,
6jf., 21, 180, 200
historical notes, 3Jf.
in Magellanic Clouds, iB^ff.
number, 14 ff.
relation to galactic system, 155, 194,
207, 209
(See also Globular clusters and
Galactic clusters )
Color and mass, 203^".
and relative speed of light, io6jf.
as test of light scattering, nojf.
changes in variables, 49, 64
correction for Cepheids, 148
distribution in globular clusters,
3/-
of stars in galactic clusters, 32/., 103
of stars in Milky Way, n8/.
Color class and spectral class, 27
Color index, 25/, 63, 99, ntf.
and period, 130, 136
of extra-galactic nebulae, 120
Color-magnitude arrays, 26jf., 73, 102,
203^., 220
Coma- Virgo nebulae, 120, 122, 210,
222
Common, 43
Cornu, 105
Cox, J. F., and Y., 106
Crommelin, 167
269
270
STAR CLUSTERS
Curtis, 151, 167
Cygnus Star Cloud, 210
Davis, H., 46, 50, 90
Distance modulus from diameters and
integrated magnitudes, 163-166
of globular clusters, 157^., 201
of Small Magellanic Cloud! 134
system of weighting, 161
Distribution, laws of, 67^.
Boig, 33. 35, S3, 151, 167, 169
Dreyer, 4, 14
Dufay, 163
Dugan, 56, 234
Duncan, 92
Dunlop, 185
Eberhard, 44
Eberhard effect, 12, 26, 3o/., 44, 69,
80, i3i/., 219
Eclipsing stars, 44, 49
and the velocity of light, io6/.
Eddington, 56, 59, 68, 103, 126, 14^-,
I47/., 204
Evolution of clusters, 207 ff.
of stars, 30, 60, 220
Path, 23
Fizeau, 105
Fleming, 32, 34, 4*
Foucault, 105
Fowler, M., 106
Freundlich, 67, 69, 88, 102
Galactic clusters and galactic star
clouds, 198
angular diameters, 167, 228
apparent distribution, 17, 96, 167,
1 80
classification, Sff., 167, 218, 228
diameter, 170, 202, 217, 228
distance from galactic plane, 170,
1 80, 228
from solar system, 180
Galactic clusters, galactic coordinates,
167, 228
inclination to galactic plane, 97^.
number of stars, 167
orientation, 96, 98, 103, 167, 228
parallaxes, i68/.
peculiarities in distribution, 1977.
spectra, 34/.
structure, 95^., 103
(See special index for individual
clusters.)
Galactic system, and external nebulae,
iQS
as a supergalaxy, 2ogjf. t 222
dimensions, 17 iff., I78/., 193, 215
distance to center, 1767., 221
membership, 17 1/.
origin, 193
relation to clusters, 194
to local system, 194
to Magellanic Clouds, 172, 195
rotation, 172, I77/., 192, 195
Galileo, 3, 105
Gerasimovifc, i$3/., 182
"Giant-poor" clusters, 69, 160, 218
Giant stars in clusters, 28
frequency distribution, 72
masses, 2O3jf , 220
Globular clusters, center of system,
22, I73/.
classification, nff.
containing variables, 43jf , 156
diameters, 161, 2oi/, 217, 224
distances, is$ff, 21 6/
from Cepheids and bright stars,
155-161
from diameters and magnitudes,
161-167
distribution, 13, 20
among classes, 1 2
of colors, 30^.
of stars, 65^, 8o/., 162, 203, 219
ellipticity, 78, 8ijf., 219
and distance from galactic plane,
88
direct estimates, 84/.
forms, 78, 219
in Magellanic Clouds, 185$"., 218
absolute magnitude, 190
angular diameter, 190
distribution, 1907.
spectra, i86/.
INDEX
271
Globular clusters, inclination to galac- Kepler, 211
circle, 86
Kienle, 114, 151
number of stars (see Star densities). King, . S., ii4jf.
orientation, 85,
period-luminosity relation, 1517.
photographic magnitude, 12, 162
radial velocities, 199
rectangular coordinates, i72jf.
relation to solar system, 172
spectra, 2^ff.
(See index to clusters.)
Gould, 4, 221
Graff, 33
Groosmuller, 112
Guthnick, 46
H
Halley, tf.
Hardcastle, 7
Harwood, 182
Heckmann, 67, 70, 94
Heiskanen, 67, 69, 88, 102
Henry, 4
Herschel, J , 4, 14, 89, 183^.
Herschel, W., 4, 195
Hertzsprung, 33, 35^, 70, 103, 125
Hinks, 7, IS
Hipparchus, 3
Hogg, 32, 70, 72
Holetscheck, 120
Hopmann, 167
Hubble, 16, 19, 22, 46, 119, 152, 196,
214
Hyades type, o/ , 32. 168, 208, 220
Ihle, 3
Innes, 46
Jeans, 56, 68, 79, 95, 195
Jones, ii4jf.
Joy, 143
Kant, 195
Kapteyn, 103, ii4/., 126, 1407., 167
Kirch, 3/.
Kustner, 103, 156
Larink, 44, 46
Leavitt, 46, 48, 106, I26/., 13 1/., 150,
214
Light scattering in space, 64, ii3/.,
124, 217
Lindblad, 40, 120, 151, 177
Lindemann, E., 53
Lindgren, 33, 68, 102, 206, 234
Local system, i94/., 200, 210, 22i/.
Looped Nebula, 184
Lowell Observatory, 16
Ludendorff, 4, 103
Lukk, 2
Luminosity curves, 61, 72^., 102
of "giant-poor" clusters, 160
preliminary maximum, 74, 218
Landmark, 167, 194, 196
Luyten, 150
M
van Maanen, 33, 37, 39, 101, 151, 167,
200, 214
Magellanic Clouds, 7, 171, 222
clusters, 16, iSjjf., 218
diameters, 189
distance modulus, 134, 189
magnitude of bright stars, 191
recession from galaxy, 192, 195
relation to clusters, igoff.
to galaxy, 172, 183, 195
variables, 487, i26/f., 147, 191
Magnitude and color, 26, 73, 99, 102
integrated, of galactic clusters, 167
of globular clusters, 162, 224
of variables, 47, 55, 75, 125, 130, 151
(See also Period-luminosity curve.)
Malmquist, 151, 167
Martens, 68
Mass, and distribution, 102
and spectrum, 2o6/.
loss per second, 208
of giant stars, 203^., 220
of stars in clusters, 68, 87
of variables, 143
272
STAR CLUSTERS
Mass-luminosity relation, 145, 147,
203/.
Mayberry, 119, 178
Melotte, 7, 9, 16, 167, 185
Messier, 4
Messier 33, 152, 172
Michelson, 105
Moving clusters, 6/., 103
N
Nabakov, 72
Nebulae, extra-galactic, 16, 120, 122,
ISI/., 171, 179, 210, 222
and galactic system, 195
Cepheids, 196
in Magellanic Clouds, 184
Nebulosity, obscuring, 2, 2i/., 66, 121,
174, 178, 211
Newcomb, 105, 221
N. G. C. 6822, 7, 152, 183
Nordmann-Tikhoff effect, 106, 108
Nort, 177
O
Oort, 150, 167, 177
Opik, 2
Packer, 43
Pannekoek, 120, 211
Parallaxes of galactic clusters, i68jf.
of globular clusters, 156
spectral, 34
spectroscopic, 151
trigonometric, 151
Parvulesco, 68, 167
Payne, 167
Pease, 2$/., 69, 8o/., 90, 94, 117
Period-luminosity relation, 1 25^
Period-spectrum relation, 136^., i42/.,
215
Perrine, 7, 167
Pickering, E. C., 32, 43, 67, 69, 120,
127
Planes of symmetry in globular
clusters, 79
Plaskett, J. S., 177
Pleiades type, o/., 32, 34, 42, 168, 170,
220
Plummer, H. C., 68, 70
Pogson, 162
Prager, 46
Proper motion, 103, 115
of galactic Cepheids, 140, 149, 151
of globular clusters, 200
Ptolemy, 3
Pulsation hypothesis, 59, 143, 148,
R
Raab, 33, 35, i6o/.
Radial velocity, of globular clusters,
199
of stars in clusters, 50
of variables, 1407.
Rasmuson, 103
"Region of avoidance," 1757.
van Rhijn, ii4jf., 118, 126, 149, 167
Ritchie, 53
Roper, 109, 167
Russell, H. N., 56, io6/., 126, 143, 234
Russell diagram, 10
Sagittarius star cloud, 211
Sampson, 105
Sanford, 26, 50
Sawyer, H. B., n, 15, 19, $o/., 81, 85,
156, 162
Schemer, 4
deviations from curve, 1327. Schilt, 71, 177
for galactic Cepheids, i38/., 142^. Schouten, 167
in clusters and external galaxies, Schultz, 4
Scutum star cloud, 210
Scares, u, 22, 33, 56, 116, n8/., 126,
143, 167, 177
Seeliger, 114
Shapley, M. B., 81, 84
" Shoulder" effect, 90/.
photographic, 130, i32Jf.
relative, 145
theoretical, 146, 148
visual, i28/., 215
zero point) 126, i49Jf., 166
INDEX
273
Siedentopf, 67, 70, 94
Slipher, V. M., 23, 50, 200
Spectra and magnitudes, 35
and masses, 2o6/.
and periods of variables (See Period-
spectrum relation),
integrated, 2$ff.
of clusters in Magellanic Clouds,
1 88
Spectral class in galactic clusters, o/.,
32/., 42, 170, 220
in globular clusters, 25, 220
Class A in galactic clusters, 34, 40
absorption lines, 169
as means of estimating parallax,
I02/.
Star counts, 69, 8o/., 84> 8ojf., 9o/ ,
i<>3/-
Star density, in globular clusters,
82-94, 201
in galactic clusters, 202/.
in Messier 67, 99
in Messier 37, 102
Star streaming, 195
Stewart, J. A., 56, 234
Stromberg, 151, 194, 199
Stromgren, E., 68
Supergalaxy hypothesis, 2oojf., 222
Supergiant stars in clusters, 69, 2077.,
220
Swope, 46, 177, 182
Variable stars, in clusters, 19, 26, 43jf.,
2l$ff.
discovery, 43, 45/. 213
frequency, 467.
general properties, 47/.
in galactic clusters, 53, 214
hypotheses of Cepheid variability,
55tf.
in Magellanic Clouds, i26Jf.
long period, 51, i 3 7/., 1537., 177
Milky Way survey, 1967., 215
proper motions and spectra, 140
radial velocities, 150
RV Tauri type, 1377., 138, 153
(See also Cepheids )
Velocity of light, iosff. t 216
W
Wallenquist, 69, IO2/., 203, 234
Walton, 53, 136, 1397.
Waterfield, W. F. H., 53
Wendell, 106, 108
Wheatstone, 105
Williams, E , 169
Wilson, H. H , 131, 1847.
Wilson, R. E., 126, 139, I4O/., 167
Wirtz, 194
Wolf, R., 3
Woods, I. E., 44, 46
Transparency of space, 113^., 217
Trumpler, 6, 10, 337., 37jf., 99, 101,
i6o/., 202, 220, 234
Turner, 2, 103, 1147.
Yamamoto, 131
Z
von Zeipel, 4, 33, 68, 70, 87, 102, 206,
234
INDEX TO CLUSTERS
(See also tables on pages 12, 24, 87, 158, 173, 186, 188, 224-234)
Messier ? (N. G. C. 7089): 46, 51, 55,
75/- 85, iQQ/.
Messier 3 (N. G. C. 5272): 14, 19, 25/,
28/., 31, 44/, 48/., 54/., 6o/.,
7o/, 85/., 90, 119, 129, 156, 164,
199, 204, Plate I.
Messier 4 (N. G. C. 6121): 6, n, 45,
85, 181, Plate I.
Messier 5 (N. G. C. 5904): 3, 43f-
48, 52, 54/., 58/, 75/., 85, 90,
io8jf , 119, 199, 129, 152
Messier 6 (N. G. C. 6405): 34/.
Messier 7 (N. G. C. 6475): 34/-, Plate
II
Messier 8 (N. G. C. 6523): 22
Messier n (N. G. C. 6705): 2, 4, 6,
10, 27, 36/, 53, 101, 119, 168, 2O2/.
Messier 13 (N. G. C. 6205): 3, s/, 23,
25^, 45, 48/., 67, 70, 72/., 8ojf.,
91, 116, n8/., I90/., 203/, 213
Messier 14 (N G. C. 6402). 85
Messier 15 (N. G. C. 7078): 46, 54^,
75/., 85, 94, 119, 199, "9, 156
Messier 16 (N. G. C. 6611): 6, Plate II
Messier 19 (N. G. C. 6273): 6, u, 14,
85, 91, 199, Plate I
Messier 21 (N. G. C. 6531): 9
Messier 22 (N. G. C. 6656): 3, 14, 2o/.,
45, 49/-, 66, 72/, 80, 85, 91, 119,
181, 204jf , 207, 220
Messier 28 (N. G. C. 6626) : 45, 85, 199
Messier 34 (N. G. C. 1039): 9/., tfff.
Messier 35 (N. G. C. 2168)- 6, 103, 119
Messier 36 (N. G. C. 1960): 10, 69,
103, 119, 198, 203
Messier 37 (N. G. C. 2099): o/., 33,
69, ioi/., 168, 198, 203, 206
Messier 38 (N. G. C. 1912): 9, 119, 198
Messier 50 (N. G. C. 2323): 119
Messier 56 (N. G. C. 6779): 46, 156
Messier 62 (N. G. C. 6266): u, 45,
85, 8o/., 160, 199, Plate I
Messier 67 (N. G. C. 2682): 10, 27, 30,
99/, 217
Messier 68 (N. G. C. 459o): 27, 45, 55,
75/.
Messier 72 (N. G. C. 6981). u, 46, 55
Messier 75 (N. G. C. 6864): 46, 178,
223
Messier 80 (N. G. C. 6093): 45, 52,
199, 202
Messier 103 (N. G. C. 581): 6
H 8: 181
Kg: 181
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
N.
G. C. 288: n,45, 164
G. C. 362:45
G. C. 416: iS6ff.
G. C. 419: i86/., 189
G. C. 1647:33
G. C. 1651:15
G. C. 1783: 187
G. C. 1789: 191
G. C. 1806: 187
G. C. 1831: 187, 190
G. C. 1835: i86Jf., 191
G. C. 1846: 187
G. C. 1851: 45, 199
G. C. 1856: i86/., ioo/.
G. C. 1866: 86, i87/., 190
G. C. 1904: 45, 199
G. C. 1944: 191
G. C. 1978: 86, 187
G. C. 1981:6
G. C. 2236: 181
6.0.2243:176
G. C. 2259: 181
G. C. 2298: 178
G. C. 2324: 181
G. C. 2419: 16, 175, 178
G. C. 2477; 9> i8/., 69, 200, Plate II
275
276
N. G. C. 3201: 6, ii, 45, 69, 162, 164
N. G. C. 3S3: 34/, 4i, Plate II
N. G. C. 3766: 41
N. G. C. 4H7: xi, 13, 24, 30, 45, i?i,
223
N. G. C. 4372: 22, 223
N. G.C.4833: 45
N. G. C. 5024: 45, 85, 199
N. G. C. 5053: n, i8/, 30, 45, 74jf.,
156
N. G. C. 5286: 45
N. G. C. 5466: n,45, 156
N. G. C. 5927: 14
N. G. C. 5946: 15
N. G. C. 5986: 45
N. G. C. 6005: 181
N. G. C. 6144* 22
N. G. C. 6218: 199
N. G. C. 6229: 45, 199
N. G. C. 6284: 13
N. 6.0.6293:45
N. G. 0.6325: 178
N. 6.0.6333:45, i99
N. 0.0.6341:45, 199
N. G. C. 6342: 178
N. G. 0.6352: 15
N. G. 0.6356: 178, 223
N. 0.0.6362:45
N. 0.0.6397:45, 69, 181
N. G. C. 6426: 15
N. G. C. 6440: 178
N. G. C. 6453: 13, 178
N. G. C. 6517: 178
N. 0.0.6528:178
N. G. 0.6535: 15
N. G. C. 6539: 15, 45
N. G.C.654i:45
STAR CLUSTERS
N. G. C. 6553: i3, 45
N. G. C. 6569: 13, 22
N. G. C. 6584: 45
N. G. C. 6624: 13, 24
N. G. C. 6633: 53
N. G. C. 6712: 15, 45, 181
N. G. 0.6723:46
N. G. C. 6752:46
N. G. C. 6760: 15
N. G. C. 6809: 46
N. G. C. 6934: 199
N. G. C. 7006: 28/, 46, 119, 171, 174,
176, 178, Plate I
N. G. C. 7099: 46, 199
N. G. C. 7492: 11,46
N. G. C. 7789: IQ3/.
LC. 2602:347.
I. C. 4499: ii
co Centauri (N. G. C. 5139): 3 5 ",
i3/., 45, 48/., 53/., 67, 69, 71, 80,
85, 93/-i 129, 181, 213
Ooma Berenices: 3, 10, 18, 34/ , 168
K Crucis: 4
Hyades: 2, 4, 9, *8, 23, 32, 34/., 95,
99, 103, 168
Perseus, double cluster in (N. G. C.
860 and N. G. C. 884): 3/, 10,
33 36, 97, 101, 103, 168
Pleiades: 3/., 6/., 9, 18, 22, 32/., 95,
99, 101, 168, 170, 203, 211, 217
Praesepe: 3/., 7, 10, 18, 34, 95, 101,
168
Scorpio, cluster in: 3, 7, 97, 103, 191
47 Tucanae (N. G. C. 104) : 45, So/ ,
67, 181, plate I
Ursa Major: i, 3, 7/, 103
