10 
h 
Tp (— cos g (2' sin x 4- y' cos x)} de + 
a 
+ 37 dh + 
h 
+ pi {— (x? — y'?) cos o sin x eos x — x'y' cos q cos 2 x + 
+ csin p (x' sin * + y' eos x)} do + 
+ D {x (sin? x + sin? o cos? x) 4- z'y' cos? g sin 2 x + 
+ y"? (cos? » + sin? p sin? x) + € sin 2 9 (z' eos x — y' sin x) 
+ c? cos? q } do + 
h 
c De {an + 92) sin ¢ + € cos  (x" cos x — y' sin x)} dx (13) 
2. The photography case 
In this case the coordinates x’y' are expressed as function of the 
coordinates x y and the elements of orientation of the two coordinate 
systems. Also here different sequences of the rotations can be taken 
into account. We will, however, concentrate upon the sequence g, c, x. 
According to HALLERT 1954—55 the fundamental expressions are 
for this case: 
€ {x (cos p COS x — sin @ sin w sin x) — y cos w sin x — h (sin q cos x + cos q sin w sin x)} 
x = — 2 es ey 
x sin © cos w — y sin w + h cos q cos w 
  
€ {a (eos g sin x 4- sin y sin c cos x) + y cos w cos * — h (sin @ sin x — cos ¢ sin « eos x)) 
y! um _ —" : v 
x sin o cos o — 3 sin e + h cos q cos o 
With the notations N,, N,, for the numerators of the expressions (14) 
and (15) respectively and D for the denominator we find the complete 
differential formulae as follows: 
14) 
(15)