In this the star is compared with a small image of a portion of the flame of a lamp attached to the telescope. It being found that, though the total light emitted by the flame varies with its size, the _intensity_ of the brightest part does not, appreciably. Two artificial stars are formed by means of a pin-hole, a double concave lens, and a double convex lens. These appear in the field by reflexion from the front and back faces of a plate of glass alongside the image of the real star, the light of which passes through the plate. The intensity of the artificial star is varied, first by changing the pin-hole, and finally by two Nicol’s prisms, the colour being first matched with that of the star by means of a third Nicol, with a quartz plate between it and the first of the other two Nicols. The instrument is provided with object-glasses of various sizes (and diaphragms) up to 2¾ inches, and, if fainter stars are to be examined, it can be screwed on to the eyepiece of an equatorial instrument. A second arrangement, like the first, but without the quartz plate arrangement, forms an artificial star from moonlight, for comparison of the light of that body with the artificial star. So far there is no difficulty, but this measure must be interpreted into magnitude, and we must know what magnitude a star is which just disappears with a given aperture of, say, one inch, and secondly, the ratio of light between the magnitudes, or how much less light is received from a star of the next magnitude in proportion to the given one. If now we were able to start a new scale of magnitude, it would be easy to say that a star just visible with an inch aperture on a fine night shall be called a ninth magnitude star, and fix a certain number of ninth magnitude stars for reference, so that the errors induced by hazy nights and variable eyes might be eliminated. An observer on a bad night could limit his aperture on a known star, when he might find that double the area given by an aperture of one inch was required as a limit for one of the stars of reference, and in that case he would know that half the usual amount of light from every star was stopped by atmospheric causes, and he would make the requisite corrections throughout his observations. We might also say that a star of a whole magnitude, greater or less than another, shall give us half or double the amount of light—in fact, that _this_ shall be the ratio between magnitudes. We are not, however, able to make these rules, for an arbitrary scale has been adopted for years, and we can only reduce this scale to a law, in such a manner as not to interfere greatly with the generally received magnitudes.