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ŠUMARSKI LIST 5-6/1958 str. 68     <-- 68 -->        PDF

In the Croatian text the simple hypsometers and their features (see Fig. 1) are
described. There is also described Eić´s modification (see Fig 2) having a handle with
the Cardan joint, thanks to wich it can have a longer rule (50 cm).


However, the text also presents a description of the sources of systematic errors
(Flury 14], Levaković [9], Petrini [11]), without taking into consideration the sources
of errors not directly connected with the hypsometer such as the lean of tree, eccentricity
of the tree top etc. (Chaturvedi [1], Todorović [16]).


The error due to the hyperbolic scale on Christen rule has also been investigated.
If the height of a tree is measured several times, and assuming that the errors
of lines of sight on the rule are normally distributed around the point on the rule
corresponding to the true value of the measured height, then the heights read off


— will not be distributed normally any more, so that the arithmetical mean of these
readings will differ from the true height. It has been found that this difference
amounts approximately to A =-0"2H ,/H and consequently insignificart, if we take
into consideration that crH is less than 1 meter.
Random errors have been tested experimentally The experiment was laid out
in such a manner as to exclude all systematic errors and such errors as are involved
by other factors not directly connected with the hypsometer (as for instance the
lean od the tree, eccentricity of the tree top etc.).


From a high point (steeple of Zagreb Cathedral) a measuring tape was let down
with a signal attached to it which made it possible to ascertain the exact relative
height of the signal above the staff bottom. The height of the signal was messured
by Christen hypsometers of an ordinary standard design (1953-with 4 measurers),
and with Eić´s modification of this instrument (1956-with 6 measurers). The differences
between the measured height (X) and the true height (H) i. e. A =X — H,
were grouped — into classes of 2 m and 1 m width respectively — according to the
true height. The arithmetical mean A and the standard deviation aA were computed
for each class (see Tables 1 and 2). The values of c>A were plotted on a logarithmic
paper as ordinates, and the H — values as abscissas respectively, whereby a
graph (see Fig. 8)* was obtained showing clearly that the data plotted might be
adjusted with a straight line having a slope of ca. b = 1. The values of the regression
coefficient b were also computed by the method of least squares for each observer
separately, and the values of the results obtained equally amounted to approximately
b = 1 (see Tab. 3).


If we assume that b = 1, i. e. that the equation reads


log o-A = a + b . log H = a + log H


o-A = 10« . H = A . H


(the coefficients a and A being also computed — see Tab. 3) we may arrive at the
conclusion that random errors occurring in the measurements carried out with
Christen hypsometer have a standard deviation


o-A = aH = 1,5 ~ 2,0 VoH


This value is considerably less than 6%, as indicated by Tischendorf [5]. It is
also smaller than the experimental data obtained by Stoffels [13] and [14] and that
because Stoffels measured the standing trees in the forest where along with the
accuracy of the hypsometer also other influences played a certain part (e. g. eccentricity
ot the tree top, lean of the tree etc).


The results of our measurements are also out of harmony with the theory of
errors of Christen and Hub hypsometers as established by Tischendorf and Stoffels.
After Tischendorf´s formula, and approximately after Stoffels´ formula too, the slope
of the regression straight line on the logarithmec paper ought to be b = 2 (i. e. the
standard deviation of the height random error should be proportional to the square


* Fig. 8 (see pagge 206) — Graphical representation of the interdependence of O// and H on logarithmic
paper. The full dots indicate the results of measurements performed in 1953, wlihe the
empty ones stand for the measurements carried out in 1956. In the polygon are connected the
points belonging to the observers D and H. As visible, the data are parallel with the straight
line of a slope b=l.