100 200 
ln’|1,2 =— and [n'as = ~~ 
IV. The corrections for the internal adjustment have to be computed with 
form (5) in which x and 7 are now replaced by the arbitrary values x’ =f to 
and 7° = because the entire calculations are carried out in that system. Ax and 
A y, however, are obtained in millimetres at the scale of observation as the true 
discrepancies have been substituted in formulae (18) and (19). Initially only the 
corrections to the five arbitrary points on each side of the runs are determined 
numerically. 
According to formulae (7) and (18) 
Axi— Axip1 = AXi— (+1) + & 
The index j in formula (18) denotes the number of each of the five points along 
the tie line of run ¢ and run i + 1. The same condition applies to the ordinates 
A y: and A y;+1 and so it is found that the differences of the corrections in stage IV 
for each point must be equal to the ordinates of the parabolae of connection as 
computed in stage II. This provides a check on the calculations of a,b,c, 0,4 
and r for each run. 
Secondly, the corrections to five points on each side of the run may be con- 
sidered adequate to draw correction graphs for both sides in the classical way, and 
the corrections for the points actually observed are obtained by linear interpolation 
between the curves. Where a point has been observed in two runs the means of the 
internally adjusted values form the block co-ordinates ANY. 
V. ‘The block co-ordinates are brought into the geodetic system by means of 
the linear transformation 
E zm a. Xu 5Y--c 
N— —b.X Ha. Y +d 
The final adjustment by elimination of misclosures on ground control follows 
exactly along the lines already discussed in the second paragraph of the theory. It 
is necessary to have a regular disposition of control to facilitate the construction of 
curves for lines of constant Eastings or Northings. 
Whether nine points are indeed sufficient depends on the degree of consistency 
desired between the geodetic framework and the pass points established by photo- 
grammetry. It is emphasized that the figure 9 does not automatically follow from 
the theory of observations as though the observed figure of derived control would 
be determined geometrically by nine points. In fact it is solely based on graphical 
considerations for the construction of parabolae through any desired longitudinal 
section. 
In rigorous adjustments the observations are corrected to satisfy a certain 
number of geometrical conditions inherent to the problem (e.g. the sum of the 
angles in a triangle equals 180° in plane surveying). The semi-graphical method 
developed in this paper is not a rigorous adjustment in that sense. It is better 
defined by saying that it adapts the observed figure by means of transformations to 
circumstances necessary to produce a consistent answer. For instance, the correction 
of the runs to reduce the discrepancies on the tie points is based neither on strict 
geometrical relations nor on the assumption that the actual error propagation is 
exactly parabolic. 
The aim is to process the observations in such a way that the runs are brought 
together within certain accepted limits. The transformation of the 2nd order is 
convenient and also proved by experiments to give the desired effect. If the 
results do not fall within the prescribed limits other formulae of higher order may 
be tried. The overall internal agreement is ensured by the nature of the preliminary 
adjustment.