H E name "spiral nebulae" is applied to certain faint telescopic objects which, in some cases, can be resolved into stars surrounding what appears to be a T mass of glowing gas. The shape of the whole nebula may be spherical, elliptical or, more characteristically, of a disc-like form with arms or trailers of starclouds winding in spirals round the central core. Nebulae of this latter type resemble our own galaxy in general shape and structure, although they fall far short of it in size. In recent years the study of the distances and spectra of these objects has attracted much attention and has led to some remarkable discoveries.The distances. The spiral nebulae lie far beyond the regions where the methods of distance-determination used for the stars of our galaxy can be applied, one method excepted. This is the method of deducing the distance of a star from the difference between its true and its apparent brightness. As a preliminary, therefore, it is necessary to explain how the brightness of a star or of a nebula is measured and how a knowledge of the brightness leads to the evaluation of the distance.The apparent brightness of a star can be measured visually by comparing it with an artificial star or with a set of fundamental stars. It is measured by a number called the apparent magnitude of the star and the scale of magnitudes is so adjusted that a first-magnitude star is IOO or 2.5 12 times as bright as one of the second magnitude and so on, the ratio between each pair of magnitudes being the same. It turns out that on this scale really bright objects have negative magnitudes. For instance, the full moon is of apparent magnitude -12.5 ; the planet Venus about -4.0;Sirius, -1-58 ; whilst the pole star is of about apparent magnitude + 2.0. Similarly photographic apparent magnitude can be defined by reference to the relative diameters, or the degrees of blackness, of the images of stars on the photographic plate. The photographic and the visual scales are calibrated so that stars of a certain spectral type have the same magnitudes in each. Stars of all other types then show systematic differences between photographic and visual magnitudes due to the different sensitivities of the eye and plate to light of different wave-lengths.It is clear that the apparent magnitude of a star depends not only on its intrinsic brightness or luminosity but also on its distance. A so-called absolute magnitude, either photographic or visual, is therefore defined. This is the magnitude which would be assigned to the star if it were at a distance of IO parsecs" from the sun.We can connect the apparent magnitude m, with the absolute magnitude M , and the distance D of the star as follows. Let I , be the total quantity of energy received * I parsec=3*zg8 light years=1*92 x 1o13 miles=3.og x 1or3 km. m, M D, I ,