Before beginning an exposure the focus is adjusted by means of a high-power positive eyepiece. An old negative, from which the film has been partially scraped, is placed in one of the plate-holders, and the film is brought into the common focus of the eyepiece and the great mirror. The appearance of the guiding star, which varies somewhat with the position of the guiding eyepiece on its slide, is then carefully noted, and is kept constant during the exposure by turning, when necessary, the focusing screw of the eye-end. For preliminary adjustments a ground-glass screen is often convenient. On it all the _DM._ stars, and even considerably fainter ones, as well as the nebulæ of Herschel's Class I, are easily visible without a lens. Plates are backed, not more than a day or two before use, with Carbutt's "Columbian backing," which is an excellent preparation for this purpose. During the exposure the observer and assistant exchange places every half hour, thereby greatly relieving the tediousness of the work, though two exposures of four hours each, in one night, have proved to be too fatiguing for general practice. At the end of the first two hours it is necessary to close the slide and wind the clock. The brightness of the guiding star is a matter of some importance. If the star is too bright, its glare is annoying; if it is too faint, the effort to see it strains the eye, and changes of focus are not easily recognized. A star of the ninth magnitude is about right. In most cases a suitable star can be found without difficulty. In such an apparatus as that described above, the amount by which the plate may be allowed to depart from its zero position is subject to a limitation which has not, I think, been pointed out, although it is sufficiently obvious when one's attention has been called to it. It depends upon the fact that the plate necessarily moves as a whole, in a straight line which is tangent to a great circle of the sphere, while the stars move on small circles around the pole. The compensation for drift, when the plate is moved, is therefore exact at the equator only. Let the guiding star have the declination [Greek: delta]_{1}, and let a star on the upper edge of the plate (which, when the telescope is north of the zenith, and the eye-end is on the north side of the telescope, will be the southern edge) have the declination [Greek: delta]_{2}. Then if the guiding star is allowed to drift from its zero position through the distance _d_, the other star will drift through the distance _d_ (cos [Greek: delta]_{2} / cos [Greek: delta]_{1}). If the guiding star is followed by turning the right-ascension screw, the upper edge of the plate, as well as the guiding eyepiece, will be moved through the distance _d_. Hence there will be produced an elongation of the upper star, represented by _e_ = _d_ ((cos [Greek: delta]_{2} / cos [Greek: delta]_{1}) - 1)