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Comparisons have also been made against a standard consisting of a 
23x 23 cm Zeiss grid on which a representative sample of 33 grid intersections 
had been calibrated by the manufacturer to a stated accuracy of 0.8 microns 
(rms). In a typical comparison the discrepancy (after allowance for translation 
and rotation) between comparator coordinates and grid coordinates of the 33 cali- 
brated points amounted to 1.50 microns (rms). Of this, about 1.3 microns (i.e., 
[(1.5)3 - (0.8)? 12 can be attributed to the comparator. 
In addition to external evidence concerning accuracies, there is internal 
evidence arising as a by-product of the reduction of each plate. We refer here to 
the ranging residuals resulting from the adjustment. By virtue of the redundancy 
of the measuring process, each point generates four observational residuals. These 
may be regarded as closures of quadrilateration. As such, they should be consistent 
with the errors to be expected from combined errors of setting and errors of the 
comparator. Both the random and the systematic errors of the comparator will be 
reflected in the residuals. This means that if uncompensated systematic errors are 
sizeable in comparison with random errors, they will dominate the determination 
of the residuals and will reveal their presence in a plot of residual vectors. Thus 
the residuals from the adjustment provide a truly meaningful indication of total 
measuring accuracy, and the rms error of the residuals, representing as it does an 
ms error of closure, provides a particularly suitable criterion for quality control. 
The rms errors of closure on production models have been found to range 
typically from 1.5 to 2.0 microns for double settings on points marked by a Wild 
PUG Ill. The set of residuals obtained from measurements of a 5x5 array of PUG 
points evenly spaced at 45mm intervals is listed in Table 1. Inasmuch as double 
settings were made on each point, the rms error of setting was also determined. 
The rms error of an individual setting was found to be 1.7 microns which meant 
that the rms error of the mean of each pair of settings amounted to 1.2 microns. 
Inasmuch as the rms error of closure turned out to be 1.6 microns (Table 1), this 
suggests that the rms contribution of the comparator itself is on the order 
[(1.6)2 - (1.2)272 ~ 1.1 microns. 
By-products of the reduction are estimates of the standard deviations of 
the plate coordinates. In the above example, eighty percent of the standard 
deviations in x and y ranged between 1.1 and 1.3 microns; two points had 
standard deviations as large as 1.5 microns. These figures consider the total 
error propagation: that is, combined effect of the propagation of random mea- 
suring errors and the errors remaining in the recovered values of the parameters 
of the comparator. In general, the standard deviations of the adjusted x, y 
coordinates will be somewhat smaller than the rms error of closure.