Lectures on Stellar Statistics | Page 3

the stars.
When we speak of the proper motion of a star, without further specification, we mean always the secular proper motion.
4. Terrestrial distances are now, at least in scientific researches, universally expressed in kilometres. 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. 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. The same objection may be made to the unit "parsec." proposed in 1912 by TURNER.
For my part I have, since 1911, proposed a stellar unit which, both in name and definition, nearly coincides with the proposition of SEELIGER, and which will be exclusively used in these lectures. A siriometer is put equal to 10^6 times the planetary unit of distance, corresponding to a parallax of 0".206265 (in practice sufficiently exactly 0".2).
In popular writings, another unit: a light-year, has for a very long time been employed. The relation between these units is
1 siriometer = 15.79 light-years, 1 light-year = 0.0633 siriometers.
5. In regard to time also, the terrestrial units (second, day, year) are too small for stellar wants. As being consistent with the unit of distance, I have proposed for the stellar unit of time a stellar year (st.), corresponding to 10^6 years. We thus obtain the same relation between the stellar and the planetary units of length and time, which has the advantage that a velocity of a star expressed in siriometers per stellar year is expressed with the same numerals in planetary units of length per year.
Spectroscopic determinations of the velocities, through the DOPPLER-principle, are generally expressed in km. per second. The relation with the stellar unit is the following:
1 km./sec. = 0.2111 sir./st., = 0.2111 planetary units per year, 1 sir./st. = 4.7375 km./sec.
Thus the velocity of the sun is 20 km./sec. or 4.22 sir./st. (= 4.22 earth distances from the sun per year).
Of the numerical value of the stellar velocity we shall have opportunity to speak in the following. For the present it may suffice to mention that most stars have a velocity of the same degree as that of the sun (in the mean somewhat greater), and that the highest observed velocity of a star amounts to 72 sir./st. (= 340 km./sec.). In the next chapter I give a table containing the most speedy stars. The least value of the stellar velocity is evidently equal to zero.
6. Intensity of the radiation. This varies within wide limits. The faintest star which can give an impression on the photographic plates of the greatest instrument of the Mount Wilson observatory (100 inch reflector) is nearly 100 million times fainter than Sirius, a star which is itself more than 10000 million times fainter than the sun--speaking of apparent radiation.
The intensity is expressed in magnitudes (m). 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.
This depends upon a general law in psycho-physics, known as FECHNER's law, which says that changes of the apparent impression of light are proportional not to the changes of the intensity but to these changes divided by the primitive intensity. A similar law is valid for all sensations. A conversation is inaudible in the vicinity of a waterfall. An increase of a load in the hand from nine to ten hectograms makes no great difference in the feeling, whereas an increase from one to two hectograms is easily appreciable. A match lighted in the day-time makes no increase in the illumination, and so on.
A mathematical analysis shows that from the law of FECHNER it follows that the impression increases in arithmetical progression (1, 2, 3, 4, ...) simultaneously with an increase of the intensity in geometrical progression (I, I^2, I^3, I^4, ...). It is with the sight the same as with the hearing. It is well known that the numbers of vibrations of the notes of a harmonic scale follow each other in a geometrical progression though, for