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4 — On the most suitable equidistance of contour lines in air surveyed maps. 
  
it is necessary to refer to a fundamental geometric conception as the following 
one may be: 
Contour lines plotted from air photographs are affected in every point by 
an (altimetric) error and principally by an error that arises in tracing contours 
with the plotting apparatus. Naturally from this error of height derives a pla- 
nimetric displacement of the contour line. It is possible to ascertain this displa- 
cement by plotting the same contour line for a second time. As I have already 
explained in an other communication (1) to this Congress — in such cases the 
divergency /; between the two tracings, divided by the distance L; between a 
generic point of the considered contour line and the two adiacent ones must ful- 
fill (at the scale 1:2000) the following double relationship: 
Dd Gus TS 
— A ors aie € = + 
E J/ 0,50 - 120 ig? « 1 [1] 
in which E is the contour interval and x the slope of ground in the conside- 
red point. 
If, maintaining E constant, we take into consideration a zone, where « 
becomes considerably steeper, the second relationship [11 will arise no more. 
In other words, becoming slopes of the ground steeper, the allowable maxi- 
mum error could raise such to surpass the interval between two adiacent con- 
tour lines. In this case it is, of course, possible, that during the plotting opera- 
tion two adiacent contour lines touch one another or even interlace themselves, 
although no fault may be ascribed to the plotting operator. 
In order to avoid this inconvenience, it is necessary to have care of ful- 
filling always the relationship [11; therefore, if a is highly steep, the contour 
interval E must be increased. 
Solving now the [1] referring to E and taking into account that — com- 
patable to what we said above — we should use the smallest possible contour 
interval, E will obviously result little superior to the limit 
E, — 2,64 0,50 + 1,20 tg? [2] 
(1) see my communication to this Congress, entitled: «On the final testing of 
contours in air surveyed maps on large scale» and my former paper: «The 
mean error in plotting contours for air photogrammetric mapping», publi- 
shed in the «Rivista del Catasto e dei Servizi Tecnici Erariali», Rome 1940.