IO 
PIERO BENCINI 
square errors of the coordinates, and finally to calculate the geographic coordinates 
and the convergence of meridians (longitude is referred to the meridian whose value 
is fed into the computer at the starting of calculations). 
Ann. n° 3 shows the results of the calculations for the net in question. It con 
sists of the following six diagrams : 
— Diagram n° i : T — t corrections. For each station point, in the order it 
is entered the computer, we give the reference number of the collimated point and 
the value of the T — t correction calculated, given in sexagesimal seconds. 
— Diagram n° 2 : coordinates. For each adjusted point we show the pro 
visional coordinates entered the calculation, the computed corrections and the 
adjusted coordinates. All values are given in metres ; figures showing thousands 
of km are separated by one space from the remainder of the coordinate. The points 
are listed in the progressive order of their reference numbers. 
— Diagram n° 3 : Adjusted trig stations. For each station point, in the 
same order as that shown in the diagram for T — t corrections, we show in the 
first line the value of the orientation constant of the station (i. e. the value to be 
added to the directions to obtain the grid azimuths) given in degrees, minutes and sec 
onds. The successive lines each contain : the reference number of the collimated 
point, the observed direction, corrected for the T — t correction, the calculated 
adjustment correction, given in seconds, the adjusted direction, the adjusted grid 
azimuth, the side length on the projection plane and that on the ellipsoid. The val 
ues of angles are given in degrees, minutes and seconds, and lenghts are given in 
metres. The adjusted elements have been rounded to o",i because, as the calcula 
tion is effected in single precision (i. e. with eight significant digits) this is the 
actually obtainable approximation. 
— Diagram n° 4 : distances. For every distance fed into the calculation we 
indicate the reference numbers of the extremes, the measured distance value, cor 
rected by the scale factor to reduce it to the projection plane, the adjustment cor 
rection and the adjusted distance value. 
— Diagram n° 5 : mean square errors. We show the mean square error of 
the weight unit, given as a mere number, as the known terms of the observation 
equations are a-dimensional (radians for the angular equations, lenght ratios for 
the distance equations). This is followed by a table of the mean square coordinate 
errors, which have been calculated by inverting the matrix of the normal system : 
calling m 0 the mean square error of the weight unit and an the term of the main 
diagonal of the inverted matrix, the mean square error of the f th unknown quantity 
is given by the relation : 
Wi = ± V5T, m 0 
The mean square errors are given in metres : in fact, all coefficients of the 
normal system have the dimensions of lengths raised to — 2 power, so that the 
coefficients of the inverse matrix have the dimentions of lengths raised to + 2 
power.