Lectures on Stellar Statistics

by C. V. L. Charlier

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, I², I³, I⁴, ...). 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 the ear, the intervals between the notes are apprehended as equal. The magnitudes play the same rôle in relation to the quantities of light as do the logarithms to the corresponding numbers. If a star is considered to have a brightness intermediate between two other stars it is not the difference but the ratio of the quantities of light that is equal in each case.

The branch of astronomy (or physics) which deals with intensities of radiation is called photometry. In order to determine a certain scale for the magnitudes we must choose, in a certain manner, the zero-point of the scale and the scale-ratio.