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respect to the triangulator-reading, a comparison of both readings
provides us with a mean to determine the errors from the above
mentioned two sources. They were computed as follows
The mean value of the readings of both verniers be/^,, the cor
responding reading of the theodolite be ty
A value for the orientation-difference of both circles is found from
C<P {<f P V i
The differences v cp o cp are caused bv errors in the
n
readings and errors in the graduation. Since a direction in the radial-
triangulator is always determined as the mean value of the readings in
two positions of the plate-carrier, the resulting errors iv cp in these
directions are computed from:
ZU y (V cp Vcp+zoo)-
The mean error may be computed from
m 2 - \WV wf\
1 n i
mx is consequently the mean error in a direction caused by the sum
of the errors in graduation and reading.
If the graduation-errors have a systematical character, the analytical
function for them can be determined by interpreting the values w
as observations for this function. In general the function for gradua
tion-errors can be represented by
x y <7, sin cp l\ cos cp a 2 sin 2 cp b2 cos 2 cp a3 sin 30+ etc.
Since always the mean value of two opposite readings is used, the
systematical graduation-error in this mean value is
X (x cp X cp 200)
Since x"1 sin© bx coscp a2 sin 2 cp
-f b 2 cos 2 cp a3 sin 3 cp ....etc.
is x a2 sin 2 cp l>2 cos 2 cp ax sin 401 bx cos 4 cp>
From the observations Wcp the coefficients a2, b2, 04 and b± were
computed and from the differences wcp x the mean square error in
Wcp, caused by the readings of the verniers only, could be derived.
Calling this mean error nu2, we have
The results are, with respect to the six circles that were examined,
condensed in table II.
From this table it is evident that the mean error, due to the reading
of the verniers is ca 0,20 cgr. Likewise is it obvious that the circles
on the instrument from manufacture De Koningh supply only a small
contribution to the total mean error since for these instruments the
average values of and w2 are respectively: 0,21 and 0,18 cgr. With
