id="section_8"/>8.

Photographic magnitudes. The magnitudes which have been mentioned in the preceding paragraphs all refer to observations taken with the eye, and are called visual magnitudes. The total intensity of a star is, however, essentially dependent on the instrument used in measuring the intensity. Besides the eye, the astronomers use a photographic plate, bolometer, a photo-electric cell, and other instruments. The difference in the results obtained with these instruments is due to the circumstance that different parts of the radiation are taken into account.

The usual photographic plates, which have their principal sensibility in the violet parts of the spectrum, give us the photographic magnitudes of the stars. It is, however, to be remarked that these magnitudes may vary from one plate to another, according to the distributive function of the plate (compare L. M. 67). This variation, which has not yet been sufficiently studied, seems however to be rather inconsiderable, and must be neglected in the following.

The photographic magnitude of a star will in these lectures be denoted by m′, corresponding to a visual magnitude m.

In practical astronomy use is also made of plates which, as the result of a certain preparation (in colour baths or in other ways), have acquired a distributive function nearly corresponding to that of the eye, and especially have a maximum point at the same wave-lengths. Such magnitudes are called photo-visual (compare the memoir of Parkhurst in A. J. 36 [1912]).

The photographic magnitude of a star is generally determined from measurements of the diameter of the star on the plate. A simple mathematical relation then permits us to determine m′. 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.

The zero-point of the photographic magnitudes is so determined that this magnitude coincides with the visual magnitude for such stars as belong to the spectral type A0 and have m = 6.0, according to the proposal of the international solar conference at Bonn, 1911.

Determinations of the photographic or photo-visual magnitudes may now be carried out with great accuracy. The methods for this are many and are well summarised in the Report of the Council of the R. A. S. of the year 1913. The most effective and far-reaching method seems to be that proposed by Schwarzschild, called the half-grating method, by which two exposures are taken of the same part of the sky, while at one of the exposures a certain grating is used that reduces the magnitudes by a constant degree.

9.

Colour of the stars. The radiation of a star is different for different wave-lengths (λ). As regarding other mass phenomena we may therefore mention:—(1) the total radiation or intensity (I), (2) the mean wave-length (λ₀), (3) the dispersion of the wave-length (σ). In the preceding paragraphs we have treated of the total radiation of the stars as this is expressed through their magnitudes. The mean wave-length is pretty closely defined by the colour, whereas the dispersion of the wave-length is found from the spectrum of the stars.

There are blue (B), white (W), yellow (Y) and red (R) stars, and intermediate colours. The exact method is to define the colour through the mean wave-length (and not conversely) or the effective wave-length as it is most usually called, or from the colour-index. We shall revert later to this question. There are, however, a great many direct eye-estimates of the colour of the stars.

Colour corresponding to a given spectrum.

Spectrum corresponding to a given colour.

The signs + and - indicate intermediate shades of colour.

The preceding table drawn up by Dr. Malmquist from the colour observations of Müller and Kempf in Potsdam, shows the connection between the colours of the stars and their spectra.

The Potsdam observations contain all stars north of the celestial equator having an apparent magnitude brighter than 7^m.5.

We find from these tables that there is a well-pronounced regression in the correlation between the spectra and the colours of the stars. Taking together all white stars we find the corresponding mean spectral type to be A0, but to A0 corresponds, upon an average, the colour yellow-white. The yellow stars belong in the mean to the K-type, but the K-stars have upon an average a shade of white in the yellow colour. The coefficient of correlation (r) is not easy to compute in this case, because one of the attributes, the colour, is not strictly graduated (i.e. it is not expressed in numbers defining the colour).[5] Using the coefficient of contingency of Pearson, it is, however, possible to find a fairly reliable value of the coefficient of correlation, and Malmquist has in this way