sed 
of 
ck 
(8) [N+W - N(N44)7! K/]1826-W& - N (Qui !(e-We) 
involving only elements of orientation as unknowns. The crucial consideration 
in the formation of the reduced system is that by virtue of the block dia- 
gonality of N+W in (1), the required inversion of N+W (a 3nx3n matrix) 
reduces to the inversion of n, 3x3 matrices, the fi; +#;. As shown in Brown 
(1958), by exploiting this fact one can develop the following algorithm for 
the formation of the reduced normal equations. In terms of the submatrices 
generated by the jth point in equation (5), the following five auxiliaries 
are set up 
0 N eee 0 — N, = Ce, 
(9) N; = y 4 ’ N, = . 3 , C4 i « 
0 0 . N, , N, , Cay 
(10) N; = 2 N 5 Cy = S Cy 
= 151 
In terms of these and the quantities Wa, £j the following secondary auxiliaries 
are evaluated 
SN A INT 
Q; (N; *W;) N 
R.. = N- > 
(11) J 07 
Sagen N;-R; 
= = I qoo d.. 
cj * €3-05 (cj-W;e;) 
As the S and c matrices are generated for each point, in turn, they are 
added to the sums of their antecedents to produce ultimately the quantities 
an 
I 
GERMANS 
(12) 
ol 
Ct ot ur FTC, 
The desired reduced system of normal equations (8) is then given by 
„5-