can consequently be regarded as a “mathematical model" and the results of the 
measurements can be controlled by the condition that they shall describe a plane. 
From the discrepancies of this condition a statistical value of the errors of the 
measurements can be computed. Evidently it is desirable to use a great number 
of measured points. Using the three parameters one translation and two rota- 
tions in connection with the determination of the standard error of the measure- 
ments the number of redundant observations will be n—3 where n is the number 
of measured points. 
  
  
  
  
FiG. 2. The distribution of the standard errors of the final elevations within the surface 
to be tested, after orientation of the surface to contain the points 1, 2 and 3. The standard 
error of unit weight of the elevation measurements 1. 
The number of settings in each point must be the same as during ordinary 
practical measurements of surfaces to be determined (for instance three settings). 
The discrepancies between the averages of the settings and the corresponding 
errorless elevations of the surface plate are adjusted according to the method of 
the least squares. The remaining discrepancies after the adjustment are used for a 
statistical determination of the standard error of unit weight of the measurements. 
The procedure is founded upon the differential formula (1). 
4.1. The Procedure 
We assume 7 points in the surface plate to have been measured. The positions 
of the points are defined Ly the co-ordinates x and y in an arbitrary co-ordinate 
system. 
The task is to determine such values of the corrections dhy, dn and dé that 
the square sum of the residual discrepancies in all n points become a minimum. 
For such purposes it is suitable to transform the plane co-ordinates x and y 
into a co-ordinate system, the origin of which is located in the point of gravity of 
the points. This co-ordinate system is denoted X, Y.