C. V. L. Charlier

“ German astronomers, Seeliger and others, have long used a stellar unit of distance corresponding to an annual parallax of 0′′.2, which has been called a “Siriusweite”. To this name it may be justly objected that it has no international use, a great desideratum in science. Against the theoretical definition of this unit it may also be said that a distance is suitably to be defined through another distance and not through an angle—an angle which corresponds moreover, in this case, to the harmonic mean distance of the star and not to its arithmetic mean distance. ”

“ For such large distances the secular parallax, which is caused by the progressive motion of the sun in space, may give better results, especially if the mean distance of a group of stars is simultaneously determined. Such a value of the secular parallax is also called, by Kapteyn, the systematic parallax of the stars.
When we speak of the proper motion of a star, without further specification, we mean always the secular proper motion. ”

“ The apparent magnitude of a star is changed as the star changes its distance from the observer, the intensity increasing indirectly as the square of the distance of the star. In order to make the magnitudes of the stars comparable with each other it is convenient to reduce them to their value at a certain unit of distance. As such we choose one siriometer. ”

“ Our knowledge of the stars is based on their apparent attributes, obtained from the astronomical observations. The object of astronomy is to deduce herefrom the real or absolute attributes of the stars, which are their position in space, their movement, and their physical nature. ”

“ Arguing from these statistics some astronomers have put forward the theory that the stars in space are divided into two classes, which are not in reality closely related. The one class consists of intensely luminous stars and the other of feeble stars, with little or no transition between the two classes. If the parallax stars are arranged according to their apparent proper motion, or even according to their absolute proper motion, a similar bipartition is revealed in their frequency distribution. ”

“ We shall, indeed, find that the mean proper motion of the stars down to the 6th magnitude 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. ”

“ All stars having an apparent magnitude brighter than 4m are directly drawn.
Instead of giving the galactic longitude and latitude of a star we may content ourselves with giving the galactic square in which the star is situated. For this purpose we assume the sky to be divided into 48 squares, all having the same surface. Two of these squares lie at the northern pole of the Galaxy and are designated GA1 and GA2. ”

“ Let us use the term spectral index (s) to define a number expressing the spectral character of a star. Then we may conveniently define this conception in the following way. Let A0 correspond to the spectral index s = 0.0, F0 to s = +1.0, G0 to s = +2.0, K0 to s = +3.0 M0 to s = +4.0 and B0 to s = -1.0. Further, let A1, A2, A3, &c., have [Pg 18] the spectral indices +0.1, +0.2, +0.3, &c., and in like manner with the other intermediate sub-classes. Then it is evident that to all spectral classes between B0 and M there corresponds a certain spectral index s. ”

“ 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. ”

“ A kilometre is, however, an inappropriate unit for celestial distances. When dealing with distances in our planetary system, the astronomers, since the time of Newton, have always used the mean distance of the earth from the sun as universal unit of distance. Regarding the distances in the stellar system the astronomers have had a varying practice. ”

“ On account of the refraction in the air the image of a star is, without the use of a spectroscope, really a spectrum. After some time of exposure we get a somewhat round image, the position of which is determined precisely by the mean wave-length. ”

“ The brightest of the near stars is Sirius (m = -1.6) , the faintest Proxima Centauri (m = 11) . Through the systematic researches of the astronomers we may be sure that no bright stars exist at a distance smaller than one siriometer, for which the distance is not already known and well determined. ”

“ The large instruments of our time hardly reach much farther, for visual observations. When, however, photographic plates are used, it is easily possible to get impressions of fainter stars, even with rather modest instruments. The large 100-inch mirror of the Wilson Observatory renders possible the photographic observations of stars of the 20th apparent magnitude, and even fainter.
The observations of visual magnitudes are performed almost exclusively with the photometer of Zöllner in a more or less improved form. ”

“ 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 whole system of the Galaxy then has a volume of 200 million cubic siriometers. Suppose further that the total number of stars in the Galaxy would amount to 1000 millions, a value to which we shall also return in a following chapter. Then we conclude that the average number of stars per cubic siriometer would amount to 5. This supposes that the density of the stars in each part of the Galaxy is the same. But the sun lies rather near the centre of the system, where the density is (considerably) greater than the average density. ”

“ The annual parallax can only be determined for near stars, nearer than, say, 5 siriometers. The direct picking out of these stars is not possible. The astronomers have therefore attacked the problem in the following way. The near stars must, on account of their proximity, be relatively brighter than other stars and secondly possess greater proper motions than those. Therefore parallax observations are essentially limited to (1) bright stars, (2) stars with great proper motions. Hence the selected attributes of the stars are m and μ. ”

“ A star of the 6th magnitude is 100 times fainter than a star of the first magnitude, a star of the 11th magnitude 10000 times, of the 16th magnitude a million times, and a star of the 21st magnitude 100 million times fainter than a star of the first magnitude. The star magnitudes are now, with a certain reservation for systematic errors, determined with an accuracy of 0m.1, and closer. ”

“ 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 by Kapteyn and Innes on the plates taken for the Cape Photographic Durchmusterung, and Barnard'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 10th magnitude, and lies at a distance of 0.40 sir. ”

“ The three classes I, II, III of Vogel correspond approximately to the colour classification into white, yellow, and red stars. Photography has now almost entirely taken the place of visual observations of spectra, so that Secchi's and Vogel's definitions of the stellar spectra are no longer applicable. The terminology now used was introduced by Pickering and Miss Cannon and embraces a great many types, of which we here describe the principal forms as they are defined in Part. II of Vol. XXVIII of the Annals of the Harvard Observatory. ”

“ Let us consider three attributes, say A, B and C, of the individuals of a population and suppose that the attribute C is positively correlated to the attributes A and B, so that to great or small values of A or B correspond respectively great or small values of C. Now if the individuals in the population are statistically selected in such a way that we choose out individuals having great values of the attributes A and small values of the attribute B, then we get a statistical series regarding the attribute C, which consists of two seemingly distinct normal frequency distributions. ”

“ The diameter of a star image increases with the time of exposure. This increase is due in part to the diffraction of the telescope, to imperfect achromatism or spherical aberration of the objective, to irregular grinding of the glass, and especially to variations in the refraction of the air, which produce an oscillation of the image around a mean position. ”

“ 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. ”

“ Type M has two other sub-types Ma and Mb.
Type N (Secchi's fourth type) . Banded spectra. The flutings are due to compounds of carbon.
Here are found only faint stars. The total number is 241. All are red. 27 stars having this spectrum are variables of long period of the same type as Md.
The spectral types may be summed up in the following way:—
The Harvard astronomers do not confine themselves to the types mentioned above, but fill up the intervals between the types with sub-types which are designated by the name of the type followed by a numeral 0, 1, 2, ..., 9. ”

“ 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. ”

“ 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. ”

“ These is also a photometric photographic catalogue of the stars nearest to the pole in Parkhurst'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 the polar sequence, [12] all lie in the immediate neighbourhood of the pole. ”

“ 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 by Argelander in the introduction to the B. D.
B. D. was planned and performed by the Swedish-Finn Argelander (born in Memel 1799) . ”

“ Generally they are rather faint, but we here find Betelgeuze, α Herculis, β Pegasi, α Scorpii (Antares) and most variables of long period, which form a special sub-type Md, characterized by bright hydrogen lines together with the flutings. ”

“ The reason is partly that we should otherwise necessarily have to deal with very large numbers, if they were to be proportional to the intensity, and partly that it is proved that the human eye apprehends quantities of light as proportional to m. ”