SpectralColour-indextypeindexB0-1.0-0.46B5-0.5-0.23A00.00.00A5+0.5+0.23F0+1.0+0.46F5+1.5+0.69G0+2.0+0.92G5+2.5+1.15K0+3.0+1.38K5+3.5+1.61M0+4.0+1.84
Colour-indexSpectralindextype-0.4-0.70B3-0.2-0.80B70.0+0.10A1+0.2+0.50A5+0.4+0.90A9+0.6+1.30F3+0.8+1.70F7+1.0+2.10G1+1.2+2.50G5+1.4+2.90G9+1.6+3.30K3+1.8+3.70K7+2.0+4.10M1
From each catalogue of visual magnitudes of the stars we may obtain their photographic magnitude through adding the colour-index. This may be considered as known (taking into account the high coefficient of correlation betweensandc) as soon as we know the spectral type of the star. We may conclude directly that the number of stars having a photographic magnitude brighter than 6.0 is considerably smaller than the number of stars visually brighter than this magnitude. There are, indeed, 4701 stars for whichm< 6.0 and 2874 stars havingm′< 6.0.
Radial velocity of the stars.From the values of α and δ at different times we obtain the components of the proper motions of the stars perpendicular to the line of sight. The third component (W), in the radial direction, is found by theDopplerprinciple, through measuring the displacement of the lines in the spectrum, this displacement being towards the red or the violet according as the star is receding from or approaching the observer.
The velocityWwill be expressed in siriometers per stellar year (sir./st.) and alternately also in km./sec. The rate of conversion of these units is given in§5.
Summing up the remarks here given on the apparent attributes of the stars we find them referred to the following principal groups:—
I.The position of the starsis here generally given in galactic longitude (l) and latitude (b). Moreover their equatorial coordinates (α and δ) are given in an abridged notation (αδ), where the first four numbers give the right ascension in hours and minutes and the lasttwo numbers give the declination in degrees, the latter being printed in italics if the declination is negative.
Eventually the position is given in galactic squares, as defined in§2.
II.The apparent motion of the starswill be given in radial components (W) expressed in sir./st. and their motion perpendicular to the line of sight. These components will be expressed in one component (u0) parallel to the galactic plane, and one component (v0) perpendicular to it. If the distance (r) is known we are able to convert these components into components of the linear velocity perpendicular to the line of sight (UandV).
III.The intensity of the lightof the stars is expressed in magnitudes. We may distinguish between theapparentmagnitude (m) and theabsolutemagnitude (M), the latter being equal to the value of the apparent magnitude supposing the star to be situated at a distance of one siriometer.
The apparent magnitude may be either thephotographicmagnitude (m′), obtained from a photographic plate, or thevisualmagnitude (m) obtained with the eye.
The difference between these magnitudes is called thecolour-index(c=m′-m).
IV.The characteristics of the stellar radiationare the mean wave-length (λ0) and the dispersion (σ) in the wave-length.The mean wave-lengthmay be either directly determined (perhaps aseffectivewave-length) or found from the spectral type (spectral index) or from the colour-index.
There are in all eight attributes of the stars which may be found from the observations:—the spherical position of the star (l,b), its distance (r), proper motion (u0andv0), radial velocity (W), apparent magnitude (morm′), absolute magnitude (M), spectral type (Sp) or spectral index (s), and colour-index (c). Of these the colour-index, the spectral type, the absolute magnitude and also (to a certain degree) the radial velocity may be considered as independent of the place of the observer and may therefore be considered not as only apparent but also asabsoluteattributes of the stars.
Between three of these attributes (m,Mandr) a mathematical relation exists so that one of them is known as soon as the other two have been found from observations.
In this chapter I shall give a short account of the publications in which the most complete information on the attributes of the stars may be obtained, with short notices of the contents and genesis of these publications. It is, however, not my intention to give a history of these researches. We shall consider more particularly the questions relating to the position of the stars, their motion, magnitude, and spectra.
Place of the stars.Durchmusterungs.The most complete data on the position of the stars are obtained from the star catalogues known as “Durchmusterungs”. There are two such catalogues, which together cover the whole sky, one—visual—performed in Bonn and called theBonner Durchmusterung(B. D.), the other—photographic—performed in CapeThe Cape Photographic Durchmusterung(C. P. D.). As the first of these catalogues has long been—and is to some extent even now—our principal source for the study of the sky and is moreover the first enterprise of this kind, I shall give a somewhat detailed account of its origin and contents, as related byArgelanderin the introduction to the B. D.
B. D. was planned and performed by the Swedish-FinnArgelander(born in Memel 1799). A scholar ofBesselhe was first called as director in Åbo, then in Hälsingfors, and from there went in 1836 to Bonn, where in the years 1852 to 1856 he performed this greatDurchmusterung. As instrument he used aFrauenhofercomet-seeker with an aperture of 76 mm, a focal length of 650 mm, and 10 times magnifying power. The field of sight had an extension of 6°.
In the focus of the objective was a semicircular piece of thin glass, with the edge (= the diameter of the semicircle) parallel to the circle of declination. This edge was sharply ground, so that it formeda narrow dark line perceptible at star illumination. Perpendicular to this diameter (the “hour-line”) were 10 lines, at each side of a middle line, drawn at a distance of 7′. These lines were drawn with black oil colour on the glass.
The observations are performed by the observer A and his assistant B. A is in a dark room, lies on a chair having the eye at the ocular and can easily look over 2° in declination. The assistant sits in the room below, separated by a board floor, at theThiedeclock.
From the beginning of the observations the declination circle is fixed at a certain declination (whole degrees). All stars passing the field at a distance smaller than one degree from the middle line are observed. Hence the name “Durchmusterung”. When a star passes the “hour line” the magnitude is called out by A, and noted by B together with the time of the clock. Simultaneously the declination is noted by A in the darkness. On some occasions 30 stars may be observed in a minute.
The first observation was made on Febr. 25, 1852, the last on March 27, 1859. In all there were 625 observation nights with 1841 “zones”. The total number of stars was 324198.
The catalogue was published byArgelanderin three parts in the years 1859, 1861 and 1862[7]and embraces all stars between the pole and 2° south of the equator brighter than 9m.5, according to the scale ofArgelander(his aim was to register all stars up to the 9thmagnitude). To this scale we return later. The catalogue is arranged in accordance with the declination-degrees, and for each degree according to the right ascension. Quotations from B. D. have the form B. D. 23°.174, which signifies: Zone +23°, star No. 174.
Argelander's work was continued for stars between δ = -2° and δ = -23° bySchönfeld, according to much the same plan, but with a larger instrument (aperture 159 mm, focal length 1930 mm, magnifying power 26 times). The observations were made in the years 1876 to 1881 and include 133659 stars.[8]
The positions in B. D. are given in tenths of a second in right ascension and in tenths of a minute in declination.
The Cape Photographic Durchmusterung[9](C. P. D.). This embraces the whole southern sky from -18° to the south pole. Planned byGill, the photographs were taken at the Cape Observatory with aDallmeyerlens with 15 cm. aperture and a focal-length of 135 cm. Plates of 30 × 30 cm. give the coordinates for a surface of 5 × 5 square degrees. The photographs were taken in the years 1885 to 1890. The measurements of the plates were made byKapteynin Groningen with a “parallactic” measuring-apparatus specially constructed for this purpose, which permits of the direct obtaining of the right ascension and the declination of the stars. The measurements were made in the years 1886 to 1898. The catalogue was published in three parts in the years 1896 to 1900.
The positions have the same accuracy as in B. D. The whole number of stars is 454875.Kapteynconsiders the catalogue complete to at least the magnitude 9m.2.
In the two great catalogues B. D. and C. P. D. we have all stars registered down to the magnitude 9.0 (visually) and a good way below this limit. Probably as far as to 10m.
A third great Durchmusterung has for some time been in preparation at Cordoba in Argentina.[10]It continues the southern zones ofSchönfeldand is for the present completed up to 62° southern declination.
All these Durchmusterungs are ultimately based on star catalogues of smaller extent and of great precision. Of these catalogues we shall not here speak (Compare, however,§23).
A great “Durchmusterung”, that will include all stars to the 11thmagnitude, has for the last thirty years been in progress at different observatories proposed by the congress in Paris, 1888. The observations proceed very irregularly, and there is little prospect of getting the work finished in an appreciable time.
Star charts.For the present we possess two great photographic star charts, embracing the whole heaven:—TheHarvard Map(H. M.) and theFranklin-AdamsCharts(F. A. C.).
The Harvard Map, of which a copy (or more correctly two copies) on glass has kindly been placed at the disposal of the Lund Observatoryby Mr.Pickering, embraces all stars down to the 11thmagnitude. It consists of 55 plates, each embracing more than 900 square degrees of the sky. The photographs were taken with a small lens of only 2.5 cms. aperture and about 32.5 cms. focal-length. The time of exposure was one hour. These plates have been counted at the Lund Observatory by HansHenie. We return later to these counts.
TheFranklin-AdamsChartswere made by an amateur astronomerFranklin-Adams, partly at his own observatory (Mervel Hill) in England, partly in Cape and Johannesburg, Transvaal, in the years 1905-1912. The photographs were taken with aTaylorlens with 25 cm. aperture and a focal-length of 114 cm., which gives rather good images on a field of 15 × 15 square degrees.
The whole sky is here reproduced on, in all, 206 plates. Each plate was exposed for 2 hours and 20 minutes and gives images of the stars down to the 17thmagnitude. The original plates are now at the observatory in Greenwich. Some copies on paper have been made, of which the Lund Observatory possesses one. It shows stars down to the 14th-15thmagnitudes and gives a splendid survey of the whole sky more complete, indeed, than can be obtained, even for the north sky, by direct observation of the heavens with any telescope at present accessible in Sweden.
The F. A. C. have been counted by the astronomers of the Lund Observatory, so that thus a complete count of the number of stars for the whole heaven down to the 14thmagnitude has been obtained. We shall later have an opportunity of discussing the results of these counts.
A great star map is planned in connection with the Paris catalogue mentioned in the preceding paragraph. ThisCarte du Ciel(C. d. C.) is still unfinished, but there seems to be a possibility that we shall one day see this work carried to completion. It will embrace stars down to the 14thmagnitude and thus does not reach so far as the F. A. C., but on the other hand is carried out on a considerably greater scale and gives better images than F. A. C. and will therefore be of a great value in the future, especially for the study of the proper motions of the stars.
Distance of the stars.As the determination, from the annual parallax, of the distances of the stars is very precarious if the distanceexceeds 5 sir. (π = 0″.04), it is only natural that the catalogues of star-distances should be but few in number. The most complete catalogues are those ofBigourdanin the Bulletin astronomique XXVI (1909), ofKapteynandWeersmain the publications of Groningen Nr. 24 (1910), embracing 365 stars, and ofWalkeyin the “Journal of the British Astronomical Association XXVII” (1917), embracing 625 stars. Through the spectroscopic method ofAdamsit will be possible to enlarge this number considerably, so that the distance of all stars, for which the spectrum is well known, may be determined with fair accuracy.Adamshas up to now published 1646 parallax stars.
Proper motions.An excellent catalogue of the proper motions of the stars isLewis Boss's “Preliminary General Catalogue of 6188 stars” (1910) (B. P. C.). It contains the proper motions of all stars down to the sixth magnitude (with few exceptions) and moreover some fainter stars. The catalogue is considered by the editor only as a preliminary to a greater catalogue, which is to embrace some 25000 stars and is now nearly completed.
Visual magnitudes.The Harvard observatory has, under the direction ofPickering, made its principal aim to study the magnitudes of the stars, and the history of this observatory is at the same time the history of the treatment of this problem.Pickering, in the genuine American manner, is not satisfied with the three thirds of the sky visible from the Harvard observatory, but has also founded a daughter observatory in South America, at Arequipa in Peru. It is therefore possible for him to publish catalogues embracing the whole heaven from pole to pole. The last complete catalogue (1908) of the magnitudes of the stars is found in the “Annals of the Harvard Observatory T. 50” (H. 50). It contains 9110 stars and can be considered as complete to the magnitude 6m.5. To this catalogue are generally referred the magnitudes which have been adopted at the Observatory of Lund, and which are treated in these lectures.
A very important, and in one respect even still more comprehensive, catalogue of visual magnitudes is the “Potsdam General Catalogue” (P. G. C.) byMüllerandKempf, which was published simultaneously with H. 50. It contains the magnitude of 14199 stars and embracesall stars on the northern hemisphere brighter than 7m.5 (according to B. D.). We have already seen that the zero-point of H. 50 and P. G. C. is somewhat different and that the magnitudes in P. G. C. must be increased by -0m.16 if they are to be reduced to the Harvard scale. The difference between the two catalogues however is due to some extent to the colour of the stars, as has been shown by Messrs.MüllerandKempf.
Photographic magnitudes.Our knowledge of this subject is still rather incomplete. The most comprehensive catalogue is the “Actinometrie” bySchwarzschild(1912), containing the photographic magnitudes of all stars in B. D. down to the magnitude 7m.5 between the equator and a declination of +20°. In all, 3522 stars. The photographic magnitudes are however not reduced for the zero-point (compare§6).
These is also a photometric photographic catalogue of the stars nearest to the pole inParkhurst's “Yerkes actinometry” (1912),[11]which contains all stars in B. D. brighter than 7m.5 between the pole and 73° northern declination. The total number of stars is 672.
During the last few years the astronomers of Harvard and Mount Wilson have produced a collection of “standard photographic magnitudes” for faint stars. These stars, which are called thepolar sequence,[12]all lie in the immediate neighbourhood of the pole. The list is extended down to the 20thmagnitude. Moreover similar standard photographic magnitudes are given in H. A. 71, 85 and 101.
A discussion of thecolour-index(i.e., the difference between the photographic and the visual magnitudes) will be found in L. M. II, 19. When the visual magnitude and the type of spectrum are known, the photographic magnitude may be obtained, with a generally sufficient accuracy, by adding the colour-index according to thetable 1in§15above.
Stellar spectra.Here too we find the Harvard Observatory to be the leading one. The same volume of the Annals of the Harvard Observatory (H. 50) that contains the most complete catalogue of visual magnitudes, also gives the spectral types for all the stars there included,i.e., for all stars to 6m.5. MissCannon, at the Harvard Observatory, deserves the principal credit for this great work. Not content with this result she is now publishing a still greater work embracing more than 200000 stars. The first four volumes of this work are nowpublished and contain the first twelve hours of right ascension, so that half the work is now printed.[13]
Radial velocity.In this matter, again, we find America to be the leading nation, though, this time, it is not the Harvard or the Mount Wilson but the Lick Observatory to which we have to give the honour. The eminent director of this observatory,W. W. Campbell, has in a high degree developed the accuracy in the determination of radial velocities and has moreover carried out such determinations in a large scale. The “Bulletin” No. 229 (1913) of the Lick Observatory contains the radial velocity of 915 stars. At the observatory of Lund, where as far as possible card catalogues of the attributes of the stars are collected,Gyllenberghas made a catalogue of this kind for the radial velocities. The total number of stars in this catalogue now amounts to 1640.[14]
Finally I shall briefly mention some comprehensive works on more special questions regarding the stellar system.
Onvariable starsthere is published every year byHartwigin the “Vierteljahrschrift der astronomischen Gesellschaft” a catalogue of all known variable stars with needful information about their minima &c. This is the completest and most reliable of such catalogues, and is always up to date. A complete historical catalogue of the variables is given in “Geschichte und Literatur des Lichtwechsels der bis Ende 1915 als sicher veränderlich anerkannten Sterne nebst einem Katalog der Elemente ihres Lichtwechsels” vonG. MüllerundE. Hartwig. Leipzig 1918, 1920.
Onnebulaewe have the excellent catalogues ofDreyer, the “New General Catalogue” (N. G. C.) of 1890 in the “Memoirs of the Astronomical Society” vol. 49, the “Index catalogues” (I. C.) in the same memoirs, vols. 51 and 59 (1895 and 1908). These catalogues contain all together 13226 objects.
Regarding other special attributes I refer in the first place to the important Annals of the Harvard Observatory. Other references will be given in the following, as need arises.
The number of cases in which all the eight attributes of the stars discussed in the first chapter are well known for one star is very small, and certainly does not exceed one hundred. These cases refer principally to such stars as are characterized either by great brilliancy or by a great proper motion. The principal reason why these stars are better known than others is that they lie rather near our solar system. Before passing on to consider the stars from more general statistical points of view, it may therefore be of interest first to make ourselves familiar with these well-known stars, strongly emphasizing, however, the exceptional character of these stars, and carefully avoiding any generalization from the attributes we shall here find.
The apparently brightest stars.We begin with these objects so well known to every lover of the stellar sky. The following table contains all stars the apparent visual magnitude of which is brighter than 1m.5.
The first column gives the current number, the second the name, the third the equatorial designation (αδ). It should be remembered that the first four figures give the hour and minutes in right ascension, the last two the declination, italics showing negative declination. The fourth column gives the galactic square, the fifth and sixth columns the galactic longitude and latitude. The seventh and eighth columns give the annual parallax and the corresponding distance expressed in siriometers. The ninth column gives the proper motion (μ), the tenth the radial velocityWexpressed in sir./st. (To get km./sec. we may multiply by 4.7375). The eleventh column gives the apparent visual magnitude, the twelfth column the absolute magnitude (M), computed frommwith the help ofr. The 13thcolumn gives the type of spectrum (Sp), and the last column the photographic magnitude (m′). The difference betweenm′andmgives the colour-index (c).
1234567891011121314NamePositionDistanceMotionMagnitudeSpectrum(αδ)SquarelbπrμWmMSpm′sir.sir./st.m′1Sirius(064016)GD7195°- 8°0″.8760.51″.32- 1.56-1m.58-0m.3A-1.582Canopus(062152)GD8229-240.00729.50.02+ 4.39-0.86-8.2F-0.403Vega(183338)GC230+170.0942.20.35- 2.910.14-1.6A0.144Capella(050945)GC5131+ 50.0663.10.44+ 6.380.21-2.8G1.135Arcturus(141119)GA2344+680.0752.72.28- 0.820.24-1.9K1.626α Centauri(143260)GD10284- 20.7590.33.68- 4.690.33+3.2G1.257Rigel(050908)GD6176-240.00729.50.00+ 4.770.34-7.0B8p0.258Procyon(073405)GC7182+140.3240.61.24- 0.740.48+1.5F51.179Achernar(013457)GE8256-590.0514.00.09..0.60-2.4B50.8710β Centauri(135659)GC10280+ 20.0375.60.04+ 2.530.86-2.9B10.4511Altair(194508)GD115-100.2380.90.66- 6.970.89+1.2A51.1212Betelgeuze(054907)GD6168- 80.0306.90.03+ 4.430.92-3.3Ma2.7613Aldebaran(043016)GD5149-190.0782.80.20+11.631.06-1.2K52.6714Pollux(073928)GC6160+250.0643.20.07+ 0.821.21-1.3K2.5915Spica(131910)GB8286+51....0.06+ 0.341.21..B20.8416Antares(162326)GC11320+140.0297.10.03- 0.631.22-3.0Map3.0617Fomalhaut(225230)GE10348-660.1381.50.37+ 1.411.29+0.4A31.4318Deneb(203844)GC251+ 1....0.00- 0.841.33..A21.4219Regulus(100312)GB6196+500.0336.30.25..1.34-2.7B81.2520β Crucis(124159)GC10270+ 30.00825.80.06+ 2.741.50-5.6B11.09sir.m′Mean.........23°.50″.1347.30″.563.26+0m.64-2m.1F1+1.13
The values of (αδ),m,Spare taken from H. 50. The values ofl,bare computed from (αδ) with the help of tables in preparation at the Lund Observatory, or from the original toplate Iat the end, allowing the conversion of the equatorial coordinates into galactic ones. The values of π are generally taken from the table ofKapteynandWeersmamentioned in the previous chapter. The values of μ are obtained from B. P. C., those of the radial velocity (W) from the card catalogue in Lund already described.
There are in all, in the sky, 20 stars having an apparent magnitude brighter than 1m.5. The brightest of them isSirius, which, owing to its brilliancy and position, is visible to the whole civilized world. It has a spectrum of the type A0 and hence a colour-index nearly equal to 0.0 (observations in Harvard givec= +0.06). Its apparent magnitude is -1m.6, nearly the same as that of Mars in his opposition. Its absolute magnitude is -0m.3,i.e., fainter than the apparent magnitude, from which we may conclude that it has a distance from us smaller than one siriometer. We find, indeed, from the eighth column thatr= 0.5 sir. The proper motion of Sirius is 1″.32 per year, which is rather large but still not among the largest proper motions as will be seen below. From the 11thcolumn we find that Sirius is moving towards us with a velocity of 1.6 sir./st. (= 7.6 km./sec.), a rather small velocity. The third column shows that its right ascension is 6h40mand its declination -16°. It lies in the square GD7and its galactic coordinates are seen in the 5thand 6thcolumns.
The next brightest star isCanopusor α Carinæ at the south sky. If we might place absolute confidence in the value ofM(= -8.2) in the 12thcolumn this star would be, in reality, a much more imposing apparition than Sirius itself. Remembering that the apparent magnitude of the moon, according to§6, amounts to -11.6, we should find that Canopus, if placed at a distance from us equal to that of Sirius (r= 0.5 sir.), would shine with a lustre equal to no less than a quarter of that of the moon. It is not altogether astonishing that a fanciful astronomer should have thought Canopus to be actually the central star in the whole stellar system. We find, however, from column 8 that its supposed distance is not less that 30 sir. We have already pointed out that distances greater than 4 sir., when computed from annual parallaxes, must generally be considered as rather uncertain. As the value ofMis intimately dependent on that ofrwe must consider speculations based on this value to be very vague. Another reason for a doubt about a great value for the real luminosity of this star is found from its type of spectrum which, according to the last column, is F0, a type which, as will be seen, is seldom found among giant stars. A better support for a large distance could on the other hand be found from the small proper motion of this star. Sirius and Canopus are the only stars in the sky having a negative value of the apparent visual magnitude.
Space will not permit us to go through this list star for star. We may be satisfied with some general remarks.
In the fourth column is the galactic square. We call to mind that all these squares have the same area, and that there is therefore the same probabilitya prioriof finding a star in one of the squares as in another. The squares GC and GD lie along the galactic equator (the Milky Way). We find now from column 4 that of the 20 stars here considered there are no less than 15 in the galactic equator squares and only 5 outside, instead of 10 in the galactic squares and 10 outside, as would have been expected. The number of objects is, indeed, too small to allow us to draw any cosmological conclusions from this distribution, but we shall find in the following many similar instances regarding objects that are principally accumulated along the Milky Way and are scanty at the galactic poles. We shall find that in these cases we maygenerallyconclude from such a partition that we then have to do with objectssituated far from the sun, while objects that are uniformly distributed on the sky lie relatively near us. It is easy to understand that this conclusion is a consequence of the supposition, confirmed by all star counts, that the stellar system extends much farther into space along the Milky Way than in the direction of its poles.
If we could permit ourselves to draw conclusions from the small material here under consideration, we should hence have reason to believe that the bright stars lie relatively far from us. In other words we should conclude that the bright stars seem to be bright to us not because of their proximity but because of their large intrinsic luminosity. Column 8 really tends in this direction. Certainly the distances are not in this case colossal, but they are nevertheless sufficient to show, in some degree, this uneven partition of the bright stars on the sky. The mean distance of these stars is as large as 7.5 sir. Only α Centauri,Sirius, Procyon and Altair lie at a distance smaller than one siriometer. Of the other stars there are two that lie as far as 30 siriometers from our system. These are the two giants Canopus and Rigel. Even if, as has already been said, the distances of these stars may be considered as rather uncertain, we must regard them as being rather large.
As column 8 shows that these stars are rather far from us, so we find from column 12, that their absolute luminosity is rather large. The mean absolute magnitude is, indeed, -2m.1. We shall find that only the greatest and most luminous stars in the stellar system have a negative value of the absolute magnitude.
The mean value of the proper motions of the bright stars amounts to 0″.56 per year and may be considered as rather great. We shall, indeed, find that the mean proper motion of the stars down to the 6thmagnitude scarcely amounts to a tenth part of this value. On the other hand we find from the table that the high value of this mean is chiefly due to the influence of four of the stars which have a large proper motion, namely Sirius, Arcturus, α Centauri and Procyon. The other stars have a proper motion smaller than 1″ per year and for half the number of stars the proper motion amounts to approximately 0″.05, indicating their relatively great distance.
That the absolute velocity of these stars is, indeed, rather small may be found from column 10, giving their radial velocity, which in the mean amounts to only three siriometers per stellar year. From the discussion below of the radial velocities of the stars we shall find that this is a rather small figure. This fact is intimately bound up with the general law in statistical mechanics, to which we return later, that stars with large masses generally have a small velocity. We thus find in the radial velocities fresh evidence, independent of the distance, that these bright stars are giants among the stars in our stellar system.
We find all the principal spectral types represented among the bright stars. To the helium stars (B) belong Rigel, Achernar, β Centauri, Spica, Regulus and β Crucis. To the Sirius type (A) belong Sirius, Vega, Altair, Fomalhaut and Deneb. To the Calcium type (F) Canopus and Procyon. To the sun type (G) Capella and α Centauri. To the K-type belong Arcturus, Aldebaran and Pollux and to the M-type the two red stars Betelgeuze and Antares. Using the spectral indices asan expression for the spectral types we find that the mean spectral index of these stars is +1.1 corresponding to the spectral type F1.
Stars with the greatest proper motion.Intable 3I have collected the stars having a proper motion greater than 3″ per year. The designations are the same as in the preceding table, except that the names of the stars are here taken from different catalogues.
In the astronomical literature of the last century we find the star 1830 Groombridge designed as that which possesses the greatest known proper motion. It is now distanced by two other stars C. P. D. 5h.243 discovered in the year 1897 byKapteynandInneson the plates taken for the Cape Photographic Durchmusterung, andBarnard's star in Ophiuchus, discovered 1916. The last-mentioned star, which possesses the greatest proper motion now known, is very faint, being only of the 10thmagnitude, and lies at a distance of 0.40 sir. from our sun and is hence, as will be found fromtable 5the third nearest star for which we know the distance. Its linear velocity is also very great, as we find from column 10, and amounts to 19 sir./st. (= 90 km./sec.) in the direction towards the sun. The absolute magnitude of this star is 11m.7 and it is, with the exception of one other, the very faintest star now known. Its spectral type is Mb, a fact worth fixing in our memory, as different reasons favour the belief that it is precisely the M-type that contains the very faintest stars. Its apparent velocity (i.e., the proper motion) is so great that the star in 1000 years moves 3°, or as much as 6 times the diameter of the moon. For this star, as well as for its nearest neighbours in the table, observations differing only by a year are sufficient for an approximate determination of the value of the proper motion, for which in other cases many tens of years are required.
Regarding the distribution of these stars in the sky we find that, unlike the brightest stars, they are not concentrated along the Milky Way. On the contrary we find only 6 in the galactic equator squares and 12 in the other squares. We shall not build up any conclusion on this irregularity in the distribution, but supported by the general thesis of the preceding paragraph we conclude only that these stars must be relatively near us. This follows, indeed, directly from column 8, as not less than eleven of these stars lie within one siriometer from our sun. Their mean distance is 0.87 sir.