One branch of observatory work is that of determining the relative _magnitude_ of stars, the word magnitude being of course used in a conventional sense for brightness. There are, moreover, stars which vary in brightness or _magnitude_ from time to time; these are called variable stars, and the investigation of the amount and period of variation opens up another use for the equatorial, and an instrument is required for finding the value of the amount of light given by a star at any instant; in fact, a photometer is necessary. The methods of determining the brilliancy of stars are so similar in principle to those employed for ordinary light-sources that the ordinary methods of photometry may be referred to in the first instance. We may determine the relative brilliancy of two or more lights, or we may employ a standard light and refer all other lights to that. Rumford’s photometer, Fig. 165, is based upon the fact that if the intensity of the shadows of an opaque body be equal, the lights throwing the shadows are equal. Hence the lights are moved towards or from a screen until the shadows are equal; then if the distances from the screen are unequal the lights are unequal, and the intensities vary in the inverse ratio of the squares of the distances. This method is practically carried out in the telescope by reducing the aperture till the stars become invisible, and noting the apertures at which each vanishes in turn. The most simple method of doing this is that used by Dawes, which is simply an adjustable diaphragm limiting the available area of the object-glass; we can thus view a star, and gradually reduce the aperture until the star is _just visible_, or until it _just disappears_, the latter limit being perhaps the most accurate and most usually used; the aperture is read off on the scale attached. [Illustration: FIG. 165.—Rumford’s Photometer. ] The photometer of Mr. Knobel is, however, a very handy one; it consists of a plate of metal having a large V-shaped piece with an angle of 60° cut out of it; another plate slides over the first in such a manner that its edge forms a base for the V-shaped opening, thus forming an equilateral triangular hole, which is adjustable at pleasure by moving the second plate. The edge of the moveable plate is divided so that the size of the base of opening is known at once, and its area easily calculated. The annexed woodcut will give an idea of the second method which is possible. [Illustration: FIG. 166.—Bouguer’s Photometer. ] Let the gas flame be supposed to represent a constant light at constant distance; then the intensity of the light to be experimented upon (represented by the candle) is determined by moving it towards or from the mirror till the illumination of both the halves of the porcelain screen is equal. The instrument by which this kind of investigation is carried out by astronomers has been introduced by Zöllner, and is called the Astrophotometer.