5 
-(1-23)3-2(1-2)? (1-coss) * (x -A) [1— coss)? 4 sin2# | 
- (1 -3) ( (1-3)? - 2 (1-3) (1 - cos) 4 (1 — coss)? 4- sin?o- | 
Since 
4 (1 —cos®)? — 4 i (1 — cos 8)? + sin? 9} 
is definitely negative it follows that A = 1 is the only real root. 
3. Want of Correspondence along the Invariant Direction 
and the direction of Tilt. 
In the derivation of the expressions giving the want af correspon- 
dence along and at right angles to the invariant direction it was assumed 
that the x axis in the left hand picture lies on the principal-point base; 
whereas the x axis in the right hand picture is swung about its principal 
point to equalize the azimuths. 
  
  
Omitting an appreciable amount of algebra, the ratio of the want 
of correspondence at a point on the invariant direction (i) to its radial 
distance turns out to be 
Py. fPx—b tie Cr... 
==); - cos. w, T (Px sin g— Py cos #) d t 5) 4 c; (9) 
r 
  
X 
The cdrresponding ratio at a point on the direction of tilt (t) 
is 
  
  
P | fPx-b p : 
C, 
(e + €) +0 … … (19) 
where, z 
tan 7 
Wo = f . , 
I — — tang sin d 
b 
C 
Z 
€: = } 52 > sing. @ (C../Cx)3 c; = #(C,/C,) — 1€? sing, 
X 
e = (f/b) e^ (1 4 Lo sing) - 8(C, ? sing 
References 
(1) A. M. Wassef, Photogrammetria, 1953-1954, No. 2. 
(2) A.M. Wassef, Photogrammetria, 1955-1956, No. 2. 
(3) A.M. Wassef, Photogrammetria, 1957-1958, No. 3.