The co-ordinates of an arbitrary point arc evidently 
une, ....(29) 
n 
GLb 
Y= o. 3, 25) 
The expression (1), written as a correction equation, evidently becomes 
dh = — dh, — Xdn — Yd£. a +26) 
Since there are n — 3 redundant measurements each individual dh must be corrected 
with a small quantity v in order to make the expression (26) valid for all observa- 
tions. Hence 
dh+v = — dh, — Xd, — Yd£ MN FE 
or 
v —dh,— Xd — Yd£ — dh.. 
For the n points we have the equations 
V1 = — dh, — X,dn— Y, dE — dh,, 
4 ^l. "uec. erit e) t)» Miele eon , 
On = —dh,— X,do — Y,d£ — dh,. 
Such values of dh,, dz and dé shall now be determined that the square sum [vv] 
becomes a minimum. From this condition we find the normal equations 
n dhy +[X]dn +[ Y]d€ +[dh] =0 
[LX]dhg + [X X]dn + [X Y] dé + [Xdh] = 0, oon(29) 
[Y]dh,- [X Y] d - [Y Y]d£ - [Ydh] = 0. 
But [X] = [Y] = 0 because the co-ordinates are expressed in the system of the 
point of gravity. Hence 
ndh, — — [dh], 
[XX]dn + [XY]dE€ = — [Xdh], +» 30) 
[XY]an +[YY]dé = — [Ydh]. 
From the solution of this equation system the corrections dh, etc. can be 
determined which make the square sum of the residual discrepancies a minimum. 
In this connection the corrections are of less importance since we are interested 
primarily in the expression for the square sum [vv]. 
Using well known procedures we find 
[dA]? [XX] [Ydh 4- [Y Y] LXdh? — 2LX Y] LXdh] [ Ydh] 
[vv] ^ [dhdh] - —-— DX YY] -DXYT ation M) 
50.28) 
The standard error of unit weight of the measurements is then determined as 
Je) 
The standard error of the standard error of unit weight is 
So 
$0 = 20-3 
271