9 
opening towards 180°, or by carrying to extremes the asymmetry of the take azimuth 
of the ground arrangement 1). 
Then by adopting a scale of representation proportioned to the dimension of greater 
topographic order (as is necessarily imposed by the practical exigencies of encumberance) 
generally there would result an excessive reduction of the dimension of the frames and of 
the images brought by them. This, whenever should it be possible to execute by photographic 
means while respecting the orthoscopy. Therefore the impossibility to obtain from them 
the accuracy that instead the photographic resolution can and must give. 
This difficulty can and must be overcome by eliminating from our representation of 
the take upon the dihedral, the dimensions of topographic order of magnitude in order, 
instead, to proportion the scale of the representation to the possibility offered by the photo- 
graphic resolution without overcoming the practical encumberance limits. 
This elimination is without doubt possible only in the very particular case of nil 
staggering 2) thanks to a scale reduction of the (d, + u,) and (d, + u,) distances. But 
this reduction became universally possible by imposing a contraction to the entire 
representation of the dihedral so as to bring into coincidence two particular character- 
istic points of the take’s reciprocal angle orientation: the nuclear fulerums, which will 
be treated in the next chapter. 
II. INVARIANCY OF THE NUCLEAR FULCRUMS AND REDUCED 
REPRESENTATION. 
a) Definitions, (Fig. 5). 
Let us again take the take dihedral (not as yet developed in plane) with the frames 
and the nuclear points in place. Among the infinite nuclear planes there is one, and only 
one, that intersects the bisector plane of the take dihedral according to a line normal 
to its edge: we shall call it for short the master nuclear plane. 
It is easy to demonstrate that the two nuclear beams corresponding between themselves, 
according to which the master nuclear plane intersects the faces of the dihedral, form 
equal and supplementary angles with the edge of this, consequently at open developed 
dihedral the homologous nuclear beams coincide with themselves in a single line which 
is the united beam of the nuclear plane projectivity. 
The intersections of this united nuclear beam with the lowered perpendiculars of the 
principal points on the edge of the dihedral, are points that enjoy particular proprieties. 
Therefore their ordinates are always nil. Their abscissi then, counted, as are the ordinates, 
in the respective system of orthogonal photographic reference with the y parallel to dihedral 
edge, are invariable in respect to the reciprocal spatial orientation of the parameters 
1, d,, d,, and they depend instead solely on the 2 y opening of the dihedral and from the 
principal distance f. More precisely the said abscissi are worth: r = = f ctg. y. 
In other words, by either changing the staggering or the distinces d, and d,, the 
united nuclear beam of the projectivity always remains “pivoted” in the two beforesaid 
particular points and for that reason have been in short called the fulerwms of nuclear 
projectivity. They are therefore characteristic only of the angular reciprocal position of 
the two takes and not of the spatial position. 
On the strength of this, we can then make translate the two frames of the two 
1) It would be illusive to take recourse to the representation of the take dihedral with 
positive frames instead of with negative frames. It is true that the abscissae of the nuclear 
points would incline towards value r instead of inclining to the infinite. Obviously with 
the abscissa inclined to r, we go towards forms of indetermination. 
2) When the staggering 1 becomes nil, in fact, it causes the coincidence of the united nuclear 
beam with the joining line of the two principal points of the frames, thereby causing the 
annulent of the two nuclear point ordinates,