Substituting in (1) we obtain 
C/C, — (sin coss 4. (b'/f) (L cosy + sin A) 
by : or. ; 
/ T (cos ^ — L sins — in’ sin | wt old) 
Equating (4) and‘ (4) and neglecting third and higher order terms 
we obtain 
| C, « of bb | 
5 tlg Eg Ÿ cos ÿ — } v7 sin 27... ga (5) 
X 
= | tilt (inclination of air base — }tip + 1p | 
Numerically, ^ hardly exceeds one or two minutes with modern 
aerial photography. In mountainous regions, however, & may become 
appreciable it either principal point falls on a point of extreme elevation 
or depression. When (b' — b)/b' is 20% in the presence of 2° tilt 
the contribution of the relief term is about 36° when b’ = 100 m/m and 
f = 150 m/m. It can however be brought down to a negligible quantity 
by a swing. | 
We may therefore proceed to follow up the consequences of choosing 
the axes to yield zero A : 
1) With A = o the matrix of transformation reduces to 
| I — (1 — cos ®) sin’p (1 — cos?) sing cos — sin®sing ) 
(1 — cos) sing cos 1 — (1—cos®) costó sindcosg }--- (6). 
| — sin? sing sing cos ¢ — cos 8 
which reflects the symmetrical disposition of the reference systems with 
respect to the plane containing the camera axes. 
2) Under the circumstance all the points on the line 
y - Xx tang ; Z}= 01 +0 (5) 
emanating from the principal point of the right hand picture and lying in 
its own plane will retain their coordinates under the transformation from 
the P (x, y, z) system to the P (£,7,5")- 
The proof may be started from the property that any affine trans- 
formation leaves unaltered either one or three directions. A point on any 
of these directions which has the coordinates x,y’, z' will have the