The Toise-Metre Problem in the Struve Arc
by Vitali Kaptüg
Key words: standard, conversion, change, evidence, GPS.
The Toise-Metre Problem (TMP) in the Struve arc is similar to that
in other European triangulations based on various national pre-metric
length standards. It has occurred much later than the arc measurement
had been completed (1852) owing to the new International Metre (IM)
standard brought into service since 1889.
To use the former results the related standards were to go through
special investigations in terms of the IM. Particular attention had to
be given to the possibility of geometrical change during the elapsed
2. The Arc Length Standards
The fundamental standard of the Struve arc was his double-toise bar
of iron denoted as "N". Made in 1827 it was determined in
terms of lines of the Toise of Peru by W. Struve himself. It is
precisely the Toise of Peru which is the unit of the arc results
published by Struve. The transported standards used in the expeditions
were: N (up to 1846), its two copies P and R, and K. Tenner's standard
T. The "family tree" of the bar N included a large number of
interconnected "end" and "line" copies extensively
used in 1847-1928. Five members of the "family", N included,
have been compared with some European standards in 1847-1902. Some of
these links can be traced up to the IM standards. Besides, the bar N
was in 1893 directly certificated in terms of the IM at the BIPM.
3. The Problem
During 1894-1905 the toise-to-metre Conversion Coefficient (CC) for
the Struve Arc was determined within the range [1.949057,…1.949073]
by various means based on one or another evidence. Thus the TMP was
the problem of choice. The most reliable value was considered 1.949067
independently by Wassiliew 1905, Helmert 1906 and Zhongolovich 1956.
Common to them was an assumption of the invariability of the bar N
between 1827 and 1893. It is the matter of importance that every
circumstantial evidence gave lower values, within the left third of
the above range.
4. New Evidence
Two Swedish sources are studied (Lindhagen 1863, Jäderin 1915)
which have never been considered with respect to the TMP. They submit
reliable evidence that the 1893 BIPM certification of N is hardly
valid for the Struve times as the bar has lengthened by 24 microns (6
ppm) in between 1862 and 1899. Besides, Wassiliew 1907 has rejected
the temperature correction made in 1893 and advocated the longer (by 3
ppm) value of the metric length of the bar. All this new evidence give
reason to restrict the range of CC dispersion to its lower values
which would manifest significantly better accordance with the
mentioned indirect derivations.
The reduction of the traditional value of the CC would make us
change to some extent our evaluations of the accuracy of the two
Struve arc segments (Kaptüg et al 1996). In the northern segment the
discrepancy between the GPS and Struve results would approach the
3-sigma limit (20 ppm) whilst in the southern one it would not exceed
the 1-sigma level (4 ppm).
Department of Mathematical Geography
Russian Geographical Society
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