at 
: tO 
| on 3? 
Co» 
nal 
NOW 
18 
the 
at 
by 
Helmert shows in his direct Solution, which seems suited for our problem, 
that it is only necessary to add to the normal equation system the corre- 
sponding conditional equations and to restore the quadratic form of the equation 
system by introducing for each added conditional equation an unknown aux 
Assuming the observational equations 
1liary . 
Vi EE toy tem gf 
À à l 
Vo = asx *tbytez- b, ! 
= —- 2 (42) 
Vs a" + bzy + GB £y 
v = a, X + b * ea 7 f£, 
and the conditional equations 
O = p. + p,x +p y 
2 
2 (43) 
0 = 4, + ax + 077 
We obtain from (12) the corresponding normal equations: 
[aa] X + [ab] y + [ac] Z- [a] = 0 
font + fini! y + [hd a [bd]. =p (44) 
[ac] X + [cb] yt [cc] Zz = [c4] = 0 
This system is being enlarged by adding the conditional equations (43) ; into 
the following form: 
En : 0 
[aa] X + [ax] y + [ac] z + P,k, + ak, 
[ab] x + [nd y + [bc] z + Pak, °c = m = 0 
[ac] P [cb] y+ [eel =+ . à ask, - [e2] = 0 (45) 
p,X + Doy e e a + Po = 0 
qx . + qz . « v qo * 0 
The presence of zeros in some of the diagonal terms must be taken into 
consideration when the system (45) is being inverted. 
55