12 
ally symmetrical !) when, in its reduced representation on the take dihedral, the photo- 
graphic frames result symmetrical and the respective nuclear points in respect to the axes 
of homology. It is easy to demonstrate that, with the exception of possible cases of com- 
pensation, that such an intrinsical symmetry is verified when the ground take responds 
to the following conditions (classic convergent ground arrangement) : 
— take azimuth symmetrical in respect to the azimuth normal to that of the take base; 
(that is to say a, a, = 180°); 
— nil difference of heights between the two take stations (h — 0); 
— elevation angle the same as that of the take axis in the horizontal plane, (s = 8). 
Renouncing to the symmetry of the two swings there can however exist in the dihedral 
cases of intrinsical symmetry, when on the reduced projection frame the nuclear points 
are symmetric with respect to the axis of homology. 
The above conditions geometrically result in the co-planarity of the take axes (e — o), 
and beside in the equidistance of the principal points of the dihedral of the edges 
(d, = d,). 
2nd. On the photographic frames of a take arrangement, two zones projectively cor- 
respond, when each nuclear beam that traverses one zone, has its homologous nuclear 
beam that traverses the other zone. There follows that for the survey of a spatial object, 
independently from the consideration of the width of the take fields of the single photo- 
cameras, it is a necessary condition the there exist on two photographic frames two 
zones that projectively correspond to each other. The condition is not sufficient, but it 
offers a measure of the possible use for a given arrangement of the two photographic 
frames which in ideal conditions should correspond totally projectively. 
It is easy to demonstrate that while in the take arrangements at parallel axes (normal 
or oblique, see Fig. 13 and 14) the two frames always totally projectively correspond 
to each other, in those at axes non-parallel (converging or askew) this total correspondence 
only happens in the very particular case of intrinsical symmetry. When the symmetry of 
the frame swings falls short, the projective correspondence is practically complete. 
In every other arrangement in which, because of asymmetry of the take azimuth, or 
because of difference of heights of the stations, or because of differences in the elevations 
of the take axes, there should be intrinsical asymmetry, the photographic take frames 
correspond only partially in zones of these. In these cases there results the convenience 
to ascertain beforehand the entity of the before said corresponding zones, which can be 
done most quickly with the homolog-comparator according to the parameters of the pro- 
jective representation of the take, as results from Fig. 4 and from the Fig. 9d. 
The corresponding zones on the two frames are, in fact comprised among the nuclear 
beams limiting the sectors of the two bundles of rays which correspond to each other, 
each bundle passing through one of the frames. 
The necessary condition of the zones correspondence on the two frames, sets practical 
limits of employ to the three factors of take asymmetry, inside of which the limits of 
performance of the homolog-comparator are practically contained. 
III. INTRINSICAL REFERENCE SYSTEM OF PLOTTING. 
a) Definitions. 
When a ground take stereophotogrammetrical arrangement is, in a most general 
way, removed from the normal one (complanary plates and horizontal base) also in the 
survey of objects having simply linear development, the analytical plotting in the reference 
to a horizontalized trine could present some difficulty in the execution of the numerical 
1) The conventional term “symmetrical” (not intrinsically) remains only for those ar- 
rangements where a, + a, = 180°.