42 
In formulae (6) 81-2 was substituted for (bı — ba) + 2|n|1,2. (p1 + p=). Having 
determined ßı_2, etc., in an earlier stage and fi, etc., from (10) the following set 
is obtained to solve b, bs, etc. 
b, — b» = 1-2» — 2]nl1,2- (P1 + P2) 
ba — ba — ».a — 2|nlz.s. CP» 9 P3) 
: HTS (14) 
bo -— b, - Buin ses 219], —1, n° {Pn—1 + Pn) 
bebo ED : 
By continuation : 
gi — qir1 = Kicag» t 2l, i21. (64-041) for i— 125m. . (12) 
X97 0 
and 
€ — C617 yicaen — Inl, igi (di d- di1) for ln bes (13) 
Xci =0 
and 
"—ri4i-—p-aen o Inlé ét a+ (Di + Diqr) for = lon. - (14) 
37; T 
'To each set of equations an extra one is added, viz. the sum of the parameters — 0 
to which the same considerations apply as given for a. Together from (9) to (14) 
there are 6 X n linear equations from which » X 6 parameters of internal adjust- 
ment can be solved (viz. a, b, c and f, q, r for each run) 
Using (5) as a general formula, the corrections Ax and Ay for all points in 
each run can now be computed, taking the appropriate values of the parameters in 
each case. It will then be found that the adjusted co-ordinates x, and xe, etc, will 
be very nearly the same for corresponding points. 
Aíter taking the mean, one set of co-ordinate values is obtained for every 
point which can be designated as the block co-ordinates X and Y. 
2. The final adjustment to ground control 
At this stage internal agreement has been obtained, i.e. all the strips have been 
subjected to a transformation of the second degree to make them fit together. The 
next condition which should be satisfied to make the adjustment complete, is that 
each strip and thus the entire block should be fitted to ground control. Assuming 
that this can also be done by a transformation of the second degree, and bearing in 
mind that the internal agreement as reached before should not be disturbed, it is 
found that the parameters of the total adjustment can only differ from those of 
the first stage by constant quantities. 
Thus the total correction for x in run 7 for example, is 
Ax, a. x? + bi.x + Ci —n(2Pi-4 + qi) 
in which a; = a; + Ka; 5, — b; 4- K»; etc. 
The condition of internal agreement remains satisfied because 
A — dii — Gi he K, rer ll 1 TT Kı — dij — dj.1 — 94— (i--1)» etc. 
The sum of the parameters Xa; — Xa 4- n.K, — 0 4- n.K, 
Sb; == 3b; + n.K, = 0 4 n.K» 
etc. 
In other words, if in the first stage the right-hand members of the last equation 
of group (9) had been given the value n.K, (a quantity to be determined from 
ground control) and likewise for the other parameters, the adjustment would be 
finished in the first stage. Conversely it can be said that by giving the last equation 
in the groups (9) to (14) the value zero, an additional correction is required of 
the form: 
A Xi E a? op Ky.x -—p K. — 2(2K,.« E Ky) l (15 
An=K AK, fpEDSHR4GKe44E) 1^ 707 3)