8 
c 
dœ = — dx y + dx 2 — dx 3 + dx 4 ) 
Aa 
(13) 
The minimized sum of the squares of the residuals is 
M = 0* 2 ] + [dz 2 ] 
[i/x] 2 + [i/z] 2 Nl 1+ N; 
(dx x — dx 2 + dx 3 — dx 4 f + (dz t — dz 2 + dz 3 — dz A ) 2 
(14) 
The standard error of unit weight can then be determined from 
Sn — 
[>] ] \vv\ 
8^6~I ~Y 
(15) 
The determination of the standard error of unit weight is rather weak because 
only 2 redundant measurements (degrees of freedom) are present. The classical 
concept of the standard error of the standard error becomes in this case 
s S o = ^° = 0 - 505 o (16) 
In order to determine more reliable values of the standard error of unit 
weight, more redundant observations must be used. 
The weight and correlation numbers of the corrections, by definition and 
directly from expressions (8) through (13) are: 
1 4 2 
1 C C 
Qx oX o = Qzozo=- 2 + ^ + ^2 
(17) 
c 2 
Qcc= s? 
(18) 
1 
(19) 
c 2 
Q 99 Qchd 4^4 
(20) 
c(a z + c 2 ) 
0 =0 = 
^xq (p x^zqco 4^4 
(21) 
The weight coefficient matrix or the variance-covariance matrix can be 
formed, if necessary, from the expressions (17) through (21).