15 
to bring the X axis in the vertical plane that contains the dihedral edge, and another for 
an i-angle around the Y axis in order to bring the Z axis vertical. The m angle is perfectly 
identifiable. 
In the survey of objects having linear development whose form is bound to the 
direction of the vertical (suspended structures or trajectories) it will be possible in some 
cases to prearrange the take in a manner so that the profile plane of the take dihedral 
results vertical and co-incident with the launching plane or with that in which the suspension 
points of the structures lie, which will permit by a simple rotation of the system about 
the Y axis, to horizontalize the plotted model my means of a carthesian transformation 
of the coordinates. 
b) Benefits of the intrinsical reference system. 
The selection of the intrinsical reference trine X YZ bound to the take dihedral presents 
the following advantages in plotting operations of spatial lines by numerical method: 
1st. Simplicity and universality of the plotting formulae for any absolute or reciprocal 
orientation of the take arrangement adopted, so long that it converges in the limits 
of use of the homolog-comparator. 
2nd. It is possible by the intrinsical trine reference of the take dihedral to keep account 
of the influence of the earth’s curvature in the same setting parameters of the take 
arrangements, thereby avoiding the necessity of modifying plotting formulae, which 
therefore acquire universality in respect to the earth curvature. 
3rd. Simplicity and practicality in the operations of measuring the photographic coor- 
dinates of the single points to be plotted; in fact, these can be measured in the 
homolog-comparator without modifying the orientation of the frames of the 
perspectives that already has served for the identification of the homologs. 
IV. INSTRUMENTAL SCHEME OF THE HOMOLOG-COMPARATOR. 
a) Genesis of the scheme. 
- : , 
The scheme of the homolog-comparator mechanically translates the reduced homo- 
graphic frame of the take dihedral developed in plane at faces closed, one of which results 
translated in the same plane in respect to the other, and according to the axis of the 
idc 
projectivity of a constant segment called undoubling, in all manners analogous to that 
which characterizes the instrumental scheme of every virtual model photogrammetrical 
plotter (disjointed parallelogram of Zeiss). 
To form an idea, it is enough to consider Fig. 9 that shows the various phases of the 
instrumental scheme. Beginning in fact with the representation of the projective frame 
of the take dihedral developed open-faced, with the two frames of the perspectives arranged 
symmetrically in respect to the edge of the dihedral and the nuclear points N, and N, 
(Fig. 9a). 
Let us now imagine to overturn the right face of the dihedral rotating it about the 
edge, which is the projectivity axis; thereby obtaining the projective representation at 
closed faces, upon which the principal points of the photographic frames will result 
superimposed (Fig. 9b), since the abscissi of the united fulerum F are equal. Let us now 
imagine to translate, along the axis of the projectivity, one of the faces of the dihedral, 
for example the same face which has rotated with the respective photographic frame 
together with the respective nuclear point, with all its bundle of nuclear beams, in respect 
to the other face, and by such a quantity that the two frames no longer result super- 
imposed, but sufficiently distant so as not to disturb each other also when mechanically 
made to hold the plates. The instrumental scheme thereby obtained obviates also to the 
drawbacks of reciprocal encumberance of the frames in the direction of the r fulerums 
abscissi, as shown in the above mentioned Fig. 7.