REPORT OF COMMISSION V GV-39 
relative positions of stars close together, such as visual double stars, are less 
affected by plate and night errors, and an appreciably higher accuracy may be 
obtained. 
6. REDUCTION OF PHOTOGRAPHIC PLATES 
The long-focus photographic method is now applied to the study of the path 
of a star. The star may be under observation for parallax, in which case useful 
information may be obtained in a few years. Or the star may be under observa- 
tion for orbital motion, and hence, a prolonged interval of time,—several 
decades, or even centuries,—may be necessary to obtain the required observa- 
tional material. In all cases the path of the star is referred to and measured on a 
background of virtually 'fixed"' reference stars. While the largest known paral- 
lactic displacement for a star is less than 1", there are numerous stars whose 
annual proper motion exceeds 1”, the largest known annual motion being 10^.3 
for Barnard's large-proper-motion star. Appreciable displacements are the rule, 
at least for the more interesting nearby stars. Hence the measured positions 
must be properly adjusted or ‘reduced’ so as to permit a precise analysis of the 
star’s path. There is need only to consider differences in origin, scale, and orien- 
tation, when comparing the different plates of a series of observations of one 
and the same field. All that is necessary is to reduce the measurements by a 
linear transformation to a common origin, scale, and orientation. The effect of 
plate tilt and other higher order terms is generally negligible for long-focus 
instruments. 
[n order to permit a comparison of measured positions on different plates, 
a reduction is made to a standard frame as defined by the reference stars. Use 
is made of rectilinear coordinates closely oriented to the celestial directions of 
right ascension and declination. Let X’, Y’ and x’, y’ be the measured positions 
of central and reference stars as recorded at the measuring machine. The zero 
point is arbitrary, the scale and orientation are close to that of the adopted 
standard frame given by the configuration of n reference stars, at least three, 
and seldom more than four in number. The coordinates of the standard frame 
shall be denoted by the subscript s; the positions x,, y,, defining the standard 
frame of reference, are relative to their mean position, 1.e., 
[5] 7 Im] = 0. 
All measured positions can now be reduced to the scale, orientation and 
origin of the reference frame (x,, y,) through plate constants a, b, and c, which 
are given by the linear equations of condition, 
@:% d- boys -- 65 m X, — X! 
) 
AyXs 0 by, T Cy = Vs ae y 
For the central star the position, X, Y reduced to the standard frame is given 
by 
X = X'+a,Xo +b.Yo +c, 
Y = V' + a,Xo + byYo + Cy 
where X,, Y, are values of X, Y rounded off to a sufficient number of significant 
figures. 
7. DEPENDENCES 
For the case of linear plate constants, considerable time may be saved and 
insight gained by expressing the reduced position as an explicit linear function