REPORT OF COMMISSION V GV-41 
reference stars; almost any set of faint stars represents an acceptable close 
approximation to a fixed background. The choice depends of course on the 
exposure time and limitations due to required magnitude compensation. In any 
long-term astrometric problem it is important to study carefully any possible 
choice of reference stars, so that one will not be faced with early obsolescence, 
but instead will have a well-planned foundation for the present, and possibly 
future, configurations of reference stars. As to the number of reference stars, 
even for a central star at the origin, the accuracy does not increase much with 
the number of reference stars. Considering the extra work involved, generally 
not much accuracy is gained by using more than four reference stars. Graphical 
methods are very useful for an initial exploration and evaluation of the de- 
pendences for different configurations of reference stars; they are particularly 
effective for three-star combinations. 
The geometrical accuracy of the reduced position of the central star de- 
pends on the distribution of the dependences for the reference stars. In case of 
a central star of appreciable proper motion the dependences change and result 
in a corresponding change in accuracy for the changing dependence background. 
In that case, the error squared, or inverse weight of the position measured on 
the dependence background is proportional to 1+ [D2]. 
For any investigation spread over a limited time interval, greatest accuracy 
is maintained if the position of greatest dependence accuracy is reached about 
the middle of that interval. The absolute minimum value of [D?] in the con- 
figuration (xs, Vs) exists for the origin defined by [x,]— [y,] 20 where each of 
the dependences equals 1/». For any central star, therefore, to insure a satis- 
factorily small [D?] it is important to choose a configuration whose origin will 
not lie too far off the path of the star. 
9. STELLAR PARALLAXES 
Probably the most important single application of long-focus photographic 
astrometry is the determination of stellar distances, since these are basic in 
comprehending the structure of the stellar universe. The history of photo- 
graphic determinations of parallaxes, as developed by Schlesinger and others, 
is well known. Long-focus refractors at several observatories are engaged in the 
determination of parallaxes of various types of stars. As a rule, plates are taken 
near extreme parallactic displacement (shortly after dusk and before dawn) of 
the parallactic ellipse. Some twenty or thirty plates, containing two to four 
exposures each, spread over several years, yield a parallax determination with 
a probable error of about +”.010. Gradually a tendency has developed to in- 
crease the accuracy of individual parallax determinations by increasing the 
number of plates. 
As an example of a parallax determination of very high accuracy mention is 
made of the faint, twelfth magnitude star Ross 248 (Figure 4). A total of 350 
plates, on 164 observing nights were taken with the Sproul refractor over the 
decade 1937-1946. An analysis of the measured positions yields a parallax of 
--".320 4- ".003 (probable error), relative to the background of four faint, distant 
reference stars. 
The photographic method has yielded measurable parallaxes for thousands 
of stars. The 1952 edition of the Yale Catalogue of stellar parallaxes lists de- 
terminations for some six thousand stars. The nearest star, Alpha Centauri, 
has a parallax of 0".76. By a simple computation the distance to Alpha Centauri 
is found to be 270,000 times that of the sun, or 270,000 astronomical units. The 
corresponding light time is 4.3 years and the distance is thus conveniently ex- 
pressed as 4.3 light years (1 light year = 63,300 astronomical units = 9.46 X10"? 
kilometers, or 5.88 X 10"? miles).