Lectures on Stellar Statistics Part 3

III. _The intensity of the light_ of the stars is expressed in magnitudes. We may distinguish between the _apparent_ magnitude (_m_) and the _absolute_ magnitude (_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 the _photographic_ magnitude (_m'_), obtained from a photographic plate, or the _visual_ magnitude (_m_) obtained with the eye.

The difference between these magnitudes is called the _colour-index_ (_c_ = _m'_-_m_).

IV. _The characteristics of the stellar radiation_ are the mean wave-length (?_0) and the dispersion (s) in the wave-length. _The mean wave-length_ may be either directly determined (perhaps as _effective_ wave-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 (_u_0_ and _v_0_), radial velocity (_W_), apparent magnitude (_m_ or _m'_), 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 as _absolute_ attributes of the stars.

Between three of these attributes (_m_, _M_ and _r_) a mathematical relation exists so that one of them is known as soon as the other two have been found from observations.

FOOTNOTES:

[Footnote 1: Meddelanden frn Lunds Observatorium, No. 41.]

[Footnote 2: Meddelanden frn Lunds Astronomiska Observatorium, Serie II, No. 14.]

[Footnote 3: Annals of the Harvard Observatory, vol. 50.]

[Footnote 4: In order to deduce from _M_ the apparent magnitude at a distance corresponding to a parallax of 1? we may subtract 3m.48. To obtain the magnitude corresponding to a parallax of 0?.1 we may add 1.57. The latter distance is chosen by some writers on stellar statistics.]

[Footnote 5: The best colour-scale of the latter sort seems to be that of OSTHOFF.]

[Footnote 6: Compare H. A. 50 and H. A. 56 and the remarks in L. M. II, 19.]

CHAPTER II.

SOURCES OF OUR PRESENT KNOWLEDGE OF THE STARS.

18. 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.

19. _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 the _Bonner Durchmusterung_ (B. D.), the other--photographic--performed in Cape _The Cape Photographic Durchmusterung_ (C. P. D.). As the first of these catalogues has long been--and is to some extent even now--our princ.i.p.al 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 by ARGELANDER in the introduction to the B. D.

B. D. was planned and performed by the Swedish-Finn ARGELANDER (born in Memel 1799). A scholar of BESSEL he was first called as director in bo, then in Halsingfors, and from there went in 1836 to Bonn, where in the years 1852 to 1856 he performed this great _Durchmusterung_. As instrument he used a FRAUENHOFER comet-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 gla.s.s, with the edge (= the diameter of the semicircle) parallel to the circle of declination. This edge was sharply ground, so that it formed a 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 gla.s.s.

The observations are performed by the observer A and his a.s.sistant 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 a.s.sistant sits in the room below, separated by a board floor, at the _Thiede_ clock.

From the beginning of the observations the declination circle is fixed at a certain declination (whole degrees). All stars pa.s.sing the field at a distance smaller than one degree from the middle line are observed.

Hence the name "Durchmusterung". When a star pa.s.ses 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 by ARGELANDER in 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 of ARGELANDER (his aim was to register all stars up to the 9th magnitude).

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 d = -2 and d = -23 by SCHoNFELD, 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.

20. _The Cape Photographic Durchmusterung_[9] (C. P. D.). This embraces the whole southern sky from -18 to the south pole. Planned by GILL, the photographs were taken at the Cape Observatory with a DALLMEYER lens 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 by KAPTEYN in 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. KAPTEYN considers 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 of SCHoNFELD and 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 11th magnitude, 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.

21. _Star charts._ For the present we possess two great photographic star charts, embracing the whole heaven:--The _Harvard Map_ (H. M.) and the _FRANKLIN-ADAMS Charts_ (F. A. C.).

_The Harvard Map_, of which a copy (or more correctly two copies) on gla.s.s has kindly been placed at the disposal of the Lund Observatory by Mr. PICKERING, embraces all stars down to the 11th magnitude. 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 Hans HENIE. We return later to these counts.

The _FRANKLIN-ADAMS Charts_ were made by an amateur astronomer FRANKLIN-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 a _Taylor_ lens 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 17th magnitude. 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-15th magnitudes 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 14th magnitude 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. This _Carte 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 14th magnitude 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.

22. _Distance of the stars._ As the determination, from the annual parallax, of the distances of the stars is very precarious if the distance exceeds 5 sir. (p = 0?.04), it is only natural that the catalogues of star-distances should be but few in number. The most complete catalogues are those of BIGOURDAN in the Bulletin astronomique XXVI (1909), of KAPTEYN and WEERSMA in the publications of Groningen Nr.

24 (1910), embracing 365 stars, and of WALKEY in the "Journal of the British Astronomical a.s.sociation XXVII" (1917), embracing 625 stars.

Through the spectroscopic method of ADAMS it 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. ADAMS has up to now published 1646 parallax stars.

23. _Proper motions._ An excellent catalogue of the proper motions of the stars is LEWIS 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.

24. _Visual magnitudes._ The Harvard observatory has, under the direction of PICKERING, made its princ.i.p.al 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.