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2 - SYNTHETIC MEASUREMENT OF ACCURACY OF A BLOCK: PRINCIPLE 
The research directed toward a solution to the above posed question seemed 
important to us, principally in the case of the 20 experimental tests of this investigation. 
After having studied and tried different ways, we chose the following principle. 
In order to be more clear, we shall give first its description followed by its justification. 
a) Given a control point of the block and an established circular area around 
it, of diameter D, we computed the arithmetical mean of the residual errors (separately 
for each coordinate) for the points contained in that area including the central point. 
b) We computed the difference between the error of the central point of the 
area and the mean computed as in a). 
c) We repeated the computations a) and b) for all the control points contained 
in the block. 
The mean values (which we shall indicate by M) of the errors obtained by a) 
are influenced by the effects only of the oscillations and irregularities of the errors 
whose amplitude is appreciably larger than the diameter D of the chosen circle. 
Therefore, once we establish the value of D, the behaviour of the mean errors obtained 
in this way will reflect the overall behaviour of the errors in the block, without the 
irregularities due to local reasons. 
On the contrary, the values of the differences, that we shall indicate by A, obtained 
by the computation b) are to be ascribed almost totally to the local irregularities 
or to errors of measure of the single point depurated of the error due to oscillations 
of large amplitude. 
In this way, the two fundamental elements characterizing a block are isolated. 
In order to pass from these analytical data to their synthesis, one can follow the normal 
statistical principles. Therefore, the following computations will be carried out: 
d) computation of the general mean M m of the mean values M over all the 
points of the block, separately for each coordinate; 
e) computation of the variance a 2 m of the mean values M over all the points 
of the block, separately for each coordinate; 
/) computation of the mean square value m 2 A of the differences A over all 
the points of the block, separately for each coordinate. 
The value of the mean M m shows evidently the presence of asymmetries of the 
errors. 
The value of the variance a 2 rn represents a statistical index of the dispersion around 
the mean of those errors having slow variations and wide oscillations. 
Finally, the value of m 2 A represents a statistical index of the local oscillations 
of the errors from the general average behaviour. 
Therefore, M m , a 2 w , m 2 A solve the posed question and give synthetic information 
on the most significant qualities of a block. 
This method of synthetic measuring of the accuracy of a block is not free from 
inconveniences. First of all, there is a particularly critical aspect in the arbitrary 
choice of the diameter D of the area around the point. By varying this diameter, 
the values of the three indices would also vary. 
Moreover, the computation of the means M supposes a uniform distribution of