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of summation veils this impression with the large x-values. In order
residual errors more clearly it is obvious to represent and to eliminate the apparently systematic portion
of errors by a simple algebraic function (carrier function). We have computed these best carrier functions
with all 1200 points and applied polynomials of up to the 10th degree of the following form:
to show the irregular course of the
Y=aux+ax+ax+...+a,xk.
The coefficients of normal equations have been computed on the IBM Computer,
systems have been manually reduced and solved. At first the mean residual discr
sharply with the increasing degree k of the approximation polynomials,
constant in spite of additional terms. The course of the residual, devi
oscillation of a wave length of about 340 and an amplitude of about
lations of a wave length of about 120 with amplitudes of 230, as well a
amplitudes of up to 50. Not even the basic oscillation, occuring three
a polynomial of the 10th degree. This is shown by the f
decreases from a certain degree onward.
whereas the equation
epancy m, decreases
but subsequently remains nearly
ations (see Fig.2) shows a basic
750, furthermore, harmonic oscil-
s a wave length of about 50 with
successive times, can be covered by
act that the mean residual deviation m; hardly
500 1000
m ; gell 1 | l l I l ] l I e
N mi
— 50000 —
—100000 |—
Fig. 1
Two operators have visually checked the curve by means of a graph to find all distinct Un TM
first operator has found an average wave length of 2 Ax = 15 throws (variations between 6 an 3 ) and
an average amplitude of Ay — 155. The corresponding values pertaining to the second opera or a
2Ax —12, throws (variations between 5 and 50) and Ay — 15. Then those points have been select
which became outstanding when the undulations were considered more generously. The Ap d
measured previously have also been used, so that the selection was easier. Thereupon and indepen m y
both the operators have tried to find the points of inflection of the curve. At first a rigorous SOT
has been applied and subsequently the minor undulations neglected. The differences ac S an ed
of the uncertainty. Finally the mean values have been computed. We found that the curve has a sn
of 150 points of inflection. Thus the "average" half of a phase length amounts to about Ax 2 8 values
or 8 stereoscopic models, and the mean amplitude Ay = 17 is about 5 times the mean error of measure-
ment or observation ma. But with both the operators, 25 per cent of all cases exceeded this mean value.
In order to avoid risks we therefore should assume the amplitude to be twice its value. Then it corresponds
to 10 times the mean error of measurement or observation ma. Four values even exceed this limit.
. . . ; ^ o i i i i most
For a quadratic adjustment the section of the curve located between two points of inflection is ae 1
: | ; ; ; ; i s we
favourable. Because of the angular deflections we cannot go beyond these points of inflection, m E
dne ur
Want to exceed the mean error of measurement or observation ma. Conditions are less favourable if o
