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 δ1, 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 δ2. 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 δ2 / cos δ1). 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 δ2 | — 1 | ) | |
| cos δ1 |
| from which | d = | e cos δ1 | . |
| cos δ2 - cos δ1 |
Now, in the Crossley reflector, the upper edge of the plate and the guiding eyepiece are just about 3⅔ 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 δ2 = 70°, δ1, = 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.