The standard deviation in one measurement from 7 settings is obtained as 
FACON 
s e 
The standard deviation of the average is obtained as 
^ [wv] 
n= J (25) 
In order to increase the setting accuracy the number of settings and readings 
evidently can be increased. But the setting accuracy is not representative for the 
real accuracy of the measurements since the individual settings in each point are 
mutually correlated with respect to certain sources of errors. A more reliable 
and objective method for a statistical determination of the real accuracy of the 
measurements (the standard error of unit weight of the basic measurements) will 
be demonstrated below. 
  
  
43 
P 
t rp 
dh, / 
/ 
A eux pen 2 +1 > x 
/ d$ 
/ 
Ya 
dn / 
+2 / 
/ 
Fic. 1. The surface the flatness of which is to be tested, and the elements of orientation. 
For the further computations we assume the measured elevations h,, ha, …, 1, 
(Ameasurea) AS averages of a certain number of settings in each point. All averages 
are assumed to be of equal accuracy (to be affected by the same standard error so) 
2. THE COMPUTATIONS 
First the elevation errors are computed as dh = Ameasured — Agiven. AS Agiven We 
use a preliminary /t5esurea Of an arbitrary point, which consequently is subtracted 
from all Ameasurea IN all points. The elevation errors dh now consist of three types 
of errors viz.: 
1. Elevation errors due to lacking parallelism between the plane 1-2-3 and 
the control plane (the surface plate). 
2. Elevation errors due to the errors of the measurements of A, — h,. 
3. Elevation errors due to the deviations of the surface from the plane 1-2-3. 
The errors under point 1 are of systematic character and can be interpreted 
as depending upon one translation and two rotations of the plane 1-2-3. 
The errors under point 2 are assumed to be of accidental character and can 
be expressed statistically by their mean square value (the standard error of unit 
weight of the measurements). According to the central limit theorem these errors 
can be regarded as being at least approximately normally distributed. The errors 
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