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RELATIVE ORIENTATION IN MOUNTAINOUS TERRAIN, VAN DER WEELE 147 
y2 4- Z2 i 
sin p" 4 (X —b) cos " Ç Ax 
XY S ( Y2 + Z2 : i Y 
=, 7 Ag = LUE eos o' + X sin ¢’ Y An + Ab, mz Ab + 
( 3 2 y2+22 |l ; (X — b)Y 
z i X cosq'— - 7. sin q Ç An’ — — TZ A? + 
( Y? 4- Z2 i y 
+ l T cos o" 4- (X — b) sing" Y Am” -— À b d 7 Ab," — 
A: 
( 
and, rearranging this formula, we get: 
XY Y2 {22 
=Py= "7 (Ae! me dip} == Z (Ao' . cos 9’ + Ax' . sin 9' — Ao" eos o"—Ax" sing") — 
YS i —4Ao' .sing' 4 Ax' .cos q' 
Ta Zt Ib, — b. Ag" — Ab, y T F Ao" . sin o" — dx” . cos e 
/ 
F (Ab, —b.sing".Ao" t b.cosq" . Ax" — Ab") 
which may be simplified to: 
XY Y2 + Z2 Y 
=P = [A* — 7 AB* — Z ICH X.AD* AE | 
where: |A* — Ag'— Aq" | 
|B* — cos (4o' — Ao") t sin o (Ax' t Ax") .O ILI) 
AC* — Ab, —Ab," — b. Ag" 
1D* cos 9 ( 1x’ — 1x”) — sin q ( fw’ 4 Aw”) 
and: 1E* 1d5,/— 4b,” + b.singp.4w” +b.cosg. Ax" | 
provided that q' — —«q^", or, in other words, assuming symmetrical convergence. 
This formula is identical in form to formula (IL.2), for vertical photographs and 
there is a corresponding identity in the solutions of the orientation problem. 
For mountainous terrain, as before, the pseudo element AB*, must be determined 
first, and the constructions or computations, treated in Section II, can be used here in 
an almost identical way. For normal angle photography, with a convergence of — 15 gr., 
the principal points will nearly coincide, in the centre of the model. In this point, the 
influence of the two rotations, x, will be practically zero, so that it offers a good pos- 
sibility of separating the x rotations from b, and o. 
If we have chosen the positions of the wing points symmetrically, so that Y/Z — 
the elimination of //p and Ab, offers no difficulty. For the remaining three elements, 
two combinations of choises are possible; w, x and b,, or c, x', and x”. (Where no index 
is written, the named element of either projector may be used.) The first combination 
(vo, x and b,) can easily be solved in the cross-section through the principal point, where 
x has no influence, and the separation of « and b, is exactly the same as for vertical 
photography except that the coefficient of Aw is multiplied by cos ¢. This multiplication 
has, however, no influence on the overcorrection factor. 
The second combination (c, x' and x") offers the possibility of correcting for w in 
the central point of the model. The difference (4x" — 4x”), can be corrected in one of the 
nadir points, and the remaining parallaxes in the four corners of the model should then 
be equal, and of the same sign, for flat terrain, while they will be different for moun- 
tainous terrain, due to the fact that the relevant term is: —k.Z.sing (dx + Ax”). 
+ Lk,