The correlation numbers become 
1 
Qdhın "e 552,058) 
Qdh,£ — 0, 113449) 
Que = 0. n (20) 
According to (8) we find 
13 317 p, x 
Q aM corii Bcorr. À 8 sat 2m 4a {21} 
According to (9) we find 
M 3x y! X 
Oni inal FE 8 + sat 2:3 4a vin (22) 
The standard error of the final elevations are, according to (10), 
> 11 3x' y! x 
nno rez) $25. (23) 
This expression can easily be presented graphically for a certain value of so. 
Temporarily we assume s, = |. 
‘ 3 243 . 
A minimum = ip is found for x = 4 and y = 0. 
The distribution of the standard error over the surface is demonstrated in Figure 
2 for $0 = M 
It is further of interest to determine the mean square value of the errors over 
the entire surface 2a x 2a. This can be done mathematically in the following well 
known way: 
= 1 x=a y-u 11 3x? y? x 
M ii d) (Te use . ve £230) 
After integration we find M = 1:3 5, ... (24a) 
4. DETERMINATION OF THE STANDARD ERROR OF UNIT WEIGHT OF THE BASIC 
MEASUREMENTS 
For the determination of the final accuracy in a certain case according to Fig. 2 
the standard error of unit weight of the basic measurements is evidently of the 
greatest importance. 
The standard error of unit weight cannot be determined from repeated measure- 
ments or settings only but has to be determined from discrepancies in suitable 
conditions, which have to be as rigid as possible. The best way is to use the measur- 
ing device for measurements of a surface with accurately known shape (for instance 
a high precision surface plate) and under similar conditions as those which are 
valid for the practical application to surfaces, the shape of which shall be deter- 
mined. 
We assume that a surface plate is available, the flatness of which is so high 
that it can be regarded as exactly flat, at least in comparison with the accuracy of 
the measuring gauge. If the plate is sufficiently large, one part of it can be mea- 
sured while the measuring gauge is supported by another part. The surface plate 
269