which is introduced for simplicity's sake is the assumption that the longitudinal
tilts 9° and y are not correlated with the other orientation elements *).
The matrix of weight- and correlation-numbers then will be:
Q boi | bxi | byi | by'i 1 | by
boi | Aı | Ae | As Fo | eT
bu | As | A» | As -— y=
by | As | As | 3 ve —
boi. 7! t | m | — Ar As
Pi | — | — | — | As Ar
Table 1.
The angular elements, expressed in radians, have been multiplied by the base
b in order to get quantities of the same dimension as the linear element by.
The quantities A,, A», etc. depend mainly on the type of survey (focal length,
flying height, overlap, etc.), the triangulation instrument and the observer. They
are to be determined by executing a certain number of orientations of a single
pair of photographs, which is considered representative for the area in question.
b. Weight symbol of f;. ?)
Relative orientation may be and generally will be carried out while the base
has only an arbitrary, approximate length. After that the model 7, +1 obtained
is set to the scale of the preceding model by adjusting the provisional base
(bi--1) to make the provisional height (zi) of the scale transfer point equal to the
height zi of the same point in the preceding model; in a formula:
: bi 1 Ta $ (zi) 7 Zi
lim. (bi+1) zi ) == i ! (b; + 1)> bi +1
whence:
bi+ . bi - Zi
fs E: — ]im. S TT
Application of the law of propagation of errors to this formula gives:
Jit d Ou
Q B, = bi . Zi Q;; Zi Qz |
or approximately:
Mec
QE; Qo Qe (19)
Evidently the accuracy of fi is dependent on the accuracy of zi and zi,
which in turn depends on the accuracy of the height measurement and the relative
orientation of both pairs i—1,i and i,;+1 involved:
9
Z7 72 :
Qu mt > Q yi pt "p. Qui PR Q 2;
27 72 ;
Qu” b Qo, — b Op + Qr,
^) This does not mean that every method of relative orientation would have that property;
we merely suppose that it occurs so often in practice that it is worthwhile to develop a
theory on the assumption.
5) The Appendix III gives a definition of weight symbols.
8
