from which _d_ = (_e_ cos [Greek: delta]_{1}) / (cos [Greek: delta]_{2} - cos [Greek: delta_{1}]). Now, in the Crossley reflector, the upper edge of the plate and the guiding eyepiece are just about 3-2/3 inches, or 1°, apart. If _e_ is given, the above formula serves to determine the maximum range of the slide for different positions of the telescope. It has been stated farther above that the smallest star disks, on a good photograph, are sometimes not more than 2´´ in diameter, or in a linear measure, about 1/20 mm. An elongation of this amount is therefore perceptible. There are many nebulæ in high northern declinations, and there are several particularly fine ones in about +70°. If, therefore, we take [Greek: delta]_{2} = 70°, [Greek: delta]_{1}, = 71°, _e_ = 0.05, and substitute these values, we find _d_ = 1.0 mm, which is the greatest permissible range of the plate in photographing these nebulæ. Before I realized the stringency of this requirement, by making the above simple computation, I spoiled several otherwise fine negatives by allowing the plate to get too far from the center, thus producing elongated star images. There is a corresponding elongation in declination, the amount of which can be determined by an adaptation of the formula for reduction to the meridian, but it is practically insensible. On account of the short focal length of the three-foot mirror, the photographic resolving power of the telescope is much below its optical resolving power. For this reason the photographic images are less sensitive to conditions affecting the seeing than the visual images. On the finest nights the delicate tracery of bright lines or caustic curves in the guiding star is as clear and distinct as in a printed pattern. When the seeing is only fair these delicate details are lost, and only the general form of the image, with its two principal caustics, is seen. A photograph taken on such a night is not, however, perceptibly inferior to one taken when the seeing is perfect. When, however, the image is so blurred that its general form is barely distinguishable, the photographic star disks are likewise blurred and enlarged, and on such nights photographic work is not attempted. The foregoing account of the small changes which have been made in the Crossley telescope and its accessories may appear to be unnecessarily detailed, yet these small changes have greatly increased the practical efficiency of the instrument, and, therefore, small as they are, they are important. Particularly with an instrument of this character, the difference between poor and good results lies in the observance of just such small details as I have described.