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_ (λ_0), (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._ _Sp._ _Colour_ _Number_ B3 YW- 161 A0 YW- 788 A5 YW 115 F5 YW, WY- 295 G5 WY 216 K5 WY+, Y- 552 M Y, Y+ 95 ----------------------------- Sum ... 2222 _Spectrum corresponding to a given colour._