while we have the relation: 
Ll + Mm, + Non, +... = 9, = constant. 
We then obtain /,, m,, n,...., from 
—_+K LD, =0 
h 
m 
K.M, =0 
Mm, 
Ny 
EN SD 
A 
where : 
pa Ny 
Lm +M mm + Nm, ae 
With this (3) becomes 
7 
Ss 
Rand 
Lm +M md Nm, Bat 
If we define the weight of the observation equation by: 
isa minimum . (4) 
Sots iar = : = > oa 
Lm, le de Mm, + ANG My een 
then (4) is reduced to 
+ 9, 4,° is a minimum, 
and the equations for the determination of x, y, z....: become: 
Zig, An, —0 
= 9; ys 7, = 9 
= 9; Z, ien: 0 
or: 
[og XX Je + [gp XV ly + [op XZ ]e...- + [op XP] = 0] 
(pV¥X}e+l9Y¥V¥wity¥Ze...-+ fo ¥FI=% . (6) 
[ZN Jo + [9ZV + [ZZ Je. HEE] = 0 
where, according to the usual notation : 
GAN = 9, Xt 9, XP +. Pa 
ANT Ho, AE +9 XY gan VY; 
if n stands for the number of observations. 
We hence arrive at this very simple result, that from the equations 
oe ay ee ee 
Ar le ee 
reduced to the linear form, the normal equations are deduced in the 
same way as when the quantities /,, #,.... are directly derived 
