Hempenius, Makaroviê, Van der Weele, Tests of Restitution Instruments 
2. Combined effect of the backlash, elastic deformations, time lag effects or their electrical 
equivalents in the: 
a. mechanism, for scanning the photograph: r, 
b. mechanism for scanning the projection, its connections to the lower gimbal joint 
of the space rod, and to the plotting device: t, 
c. transmission to the tracing style, inclusive the gear box (in orthog. coordinato- 
graphs) or the pole (in pantographs): T 
Some of the disturbances have continuous effects in the output (e.g. elasticity, vibra 
tions, time lag effects), while the others cause discontinuouties (e.g. backlash, dry friction 
etc.). 
The elastic deformations are the combined effect of the nature of the input (forcing 
function), elasticity, the moving masses, the consequent accelerations, and some other 
parameters of the system. Dynamic signals applied to an elastic mass result in vibrations. 
However, they are damped by the friction forces to a great extent. 
The above disturbances can be combined into three principal groups. Their effect in 
the output depends on the scale parameters (see (3) and (4)) of the plotting system. 
a. Group 8, containing the disturbances with a constant level in the photo plane. Their 
effect on the output is proportional to the ratio of the map scale to photo scale VW. 
b. Group d with disturbances which have a constant level in the projection. Their effect 
on the output is proportional to the ratio of the map scale to projection scale W. 
c. Group D, involving the disturbances, originating in the plotting device. 
They have a constant level in the output itself. 
The effect of all mentioned disturbances in the actual working conditions (production 
of maps) has a stochastical character in the output. Their sources are practically 
uncorrelated. The total effect is obtained by combining the Gaussian distributions of in 
dividual distortions. When doing this for each of the three principal groups, we obtain: 
<5 2 = A 2 + t 2 , d 2 = l 2 + t 2 and D 2 = L 2 + T 2 
The cumulative summation of disturbances throughout the system follows different 
laws for the stochastical (A, l, L) and systematic (see sect. III. 5) disturbances (r,t,T). 
Some effects (e.g. due to the backlash and elastic deformations) accumulate in the output 
according to their linear summation: 
R = VW t +Wt+T 
(3) 
Disturbances, such as elastic deformations, may not have strictly linear effects pro 
portional to V or W. In such cases the assumed mathematical process-simulating model may 
be regarded as a simplified assumption, which approximates the process. This is in general 
permissible; if necessary a more consistent simulation of the actual process can be set up. 
The subgroups A, l and L contàin random effects only. They are practically independent 
from each other and have normal statistical distributions. Their cumulative sum is: 
M 2 = (VW) 2 A 2 + W 2 l 2 4- L 2 
The coefficients V and W are the scale parameters: 
V = s p : s m = Z : c, W = s m : s c and VW = s p : s c , 
(4) 
where s p , s m and s c are the scale numbers of the photo (s p ), projection (s m ) and the map 
scale (s c ), while Z and c are the projection and the principal distance respectively. 
The unknowns r, t, T and X', l, L can be determined from at least three equations for 
each of the two combinations. For this purpose the scale parameters V and W are selected 
following: 
(5)