ASTRONOMICAL PHOTOGRAPHY 739 



telescope is operated at full aperture since an astronomer desires all the light obtain- 

 able from a relatively faint source. Occasionally a diaphragm is used to stop down the 

 aperture for the sake of sharpening the focus near the periphery of the field, thus 

 increasing the effective area which may be satisfactorily utilized on a plate of a given 

 size. 



Focal Ratio and Scale. — The focal length of lenses employed in astronomical pho- 

 tography will be governed by the desired scale in the photographs to be obtained, and 

 by considerations depending upon the faintness of the objects to be photographed. 

 The speed of astronomical cameras or telescopes used for astronomical photography 

 varies inversely as the squares of their focal ratios when faint extended areas like 

 nebulae or comets are concerned. For stars yielding substantially point images, the 

 speed has been found to vary more nearly as the inverse first power of the focal ratio. 



In determining the relation of focal length to plate scale, it is convenient to 

 remember that there are 3438' in 1 rad. A telescope whose focal length is 3.438 m. 

 will yield a photograph of a given region of the sky in which the angular unit dimension 

 of 1' of arc will be represented by 1 mm. on the photographic plate. Hence the 

 relation : 



F = 3438s (2) 



where F is the focal length in mm. and s is the scale in mm. per 1' of arc. 



Some of the problems involving the measurement of small angular dimensions are 

 (1) measuring the distances between the components of double stars; (2) the small 

 annular drift of positions in stars, known as "proper motion"; and (3) the seasonal 

 variation in the position of a star known as "parallax." Here telescopes of a focal 

 length of 15 ft. and up are desirable to produce the requisite scale on the plates used. 

 Among the large telescopes in use for parallax programs in which the distance of the 

 nearer stars is determined from angular displacements of 0.01" or more is that of the 

 Yerkes Observatory of the University of Chicago, situated at Williams Bay, Wis. 

 The aperture of the Yerkes lens is 40 in., and its focal length is approximately 65 ft. 



For the scale of the plate to yield 1 mm. per 1" of arc a total length of 20.75 m. 

 is required. Here 



s = -oTro = 60 mm. per 1' (3) 



If the position of the star on such a plate can be measured with a microscopic 

 comparator to the precision of Hoo mm., the position of the star may be determined 

 to within 0.01" which is about the order of accuracy obtainable in parallax 

 determinations. 



The value of the reflector for positional work in astronomy is seriously handicapped 

 by the very limited field of the instrument. Distortion due to coma and spherical 

 aberration of a parabolic reflector become serious as we proceed away from the 

 optical axis of the mirror. For the purpose of producing a flat field over a considerable 

 area two devices have been perfected for use in connection with the reflector. 



Ross Corrector. — One of these is the Ross corrector of practically zero power which 

 usually consists of a doublet, one element of which is convex and the other concave. 

 The lens is placed somewhat inside the focal plane of the reflector and is so figured as 

 to reduce the coma formed in the images, which increases as the distance along the 

 radius from the center of the field increases. The specification of the lens must be 

 suited to each particular instrument employed. F. E. Ross of the Yerkes Observatory 

 has designed several such lenses. The one for the 100-in. telescope at Mount Wilson 

 has three separate elements. The reduction of coma is made possible at the sacrifice 

 of a certain amount of astigmatism but the increase in the usable field of the reflector 



