Elements of Long-Focus 
Photographic Astrometry’ 
DR. PETER VAN DE KAMP, Director, Sproul Observatory, 
Professor of Astronomy, Swarthmore College, 
Swarthmore, Pennsylvania 
1. INTRODUCTION 
CCURATE positional measurements, obtained from photographic plates taken 
with astronomical telescopes, furnish astronomers with essential astro- 
metric data, which form the basis of studies in the field of celestial mechanics, 
the physical properties of stars, and the structure of our Milky Way system. 
No other technique exists that permits the observer to obtain as highly accurate 
a mapping of the sky. Less than a century old, photographic astrometry continues 
to be of the utmost importance in current research and in the planning for 
future research, and shows no sign of impending obsolescence. However, one 
must reckon with the possibility of appreciable reductions in exposure times 
through the development of image tube techniques. 
Experience has shown that in general, for positional work, refracting tele- 
scopes are superior to reflectors. This paper shall be limited to a description of 
the astrometric technique as applied to the jewels of optical astronomy,—the 
long-focus achromatic refractors. These are refracting telescopes with focal 
lengths of about 8 meters or more, and commonly of large aperture- about 40 
cm. or more—resulting in focal ratios up to f/20. The power of these instru- 
ments lies in the large-scale portrayal in the focal plane, of an observed star 
field of limited angular extent, usually less than a degree in diameter. 
The long-focus refractor is of particular importance in the study of small 
angular shifts of stars, such as the star’s parallactic displacement due to the 
earth’s annual motion around the sun, as distinguishable from the star's own 
angular motion across the sky (** proper motion"). Another fruitful application 
lies in the study of the orbital motion of double star components and of the or- 
bital motion or “perturbation’’ of a “single” star, due to the presence of an 
invisible companion star. 
2. THE LoNG-Focus REFRACTOR 
The long-focus refractor normally has a focal-ratio of between f 15 and 
f/20. The achromatic objective usually consists of a convex crown-glass lens 
and a concave flint-glass lens, which may be very close together, or separated 
by several centimeters. For example, here are the specifications for the objective 
of the (visual) Sproul refractor, given in a letter of October 15, 1924 from Charles 
S. Hastings to my predecessor, Dr. John A. Miller. See tabulation. 
The aperture of the Sproul refractor is 24 inches (61 cm.), the focal length 
36 feet (1,093 cm.), the focal ratio is f/18 (Figure 1). 
The scale value in the focal plane is defined as the number of seconds of arc 
per millimeter; for a focal length of F mm., the scale value is 206,265/F. For 
* Paper to be presented at the International Society of Photogrammetry at the Royal Insti- 
tute of Technology in Stockholm, Sweden, July 17-18, 1956; Commission V, Special Applications 
and Measurements. 
GV-32 
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