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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
% ris EIN A: -— »
Fig. 6: A part of the map of Central Switzerland by J. J.
Clausner created on the basis of Pfyffer's measurements. The
map is overlaid with residuals on identical points (red lines).
(1) (2) (3) (4)
1:11'700 470 m
vifars - IRC
ds 208 ELU so ann sn
eae 1:11200 sb. 111m
D "PE, '
Ses ns | 1244700 -0.65* 387m
nap 0 7 1:249'200 north-oriented 528m
Central Sw.
P Lu i 1:36'000 15.29° 191 m
ap 1:33'300 south-oriented 117m
Rengg area
Map of 178 1:125'200 15.62° 408 m
Clausner 1:123'200 south-oriented 483 m
(1) Number of identical points
(2) Scale in coordinate directions
(3) Orientation (or westerly declination, see Fig. 9)
(4) Sigma a posteriori in coordinate directions
Table 1: Results of coordinate transformations with weighted
observations: metric parameters of Pfyffer's Relief and related
maps.
3. RECONSTRUCTION OF PFYFFER'S SURVEYING
AND RELIEF CONSTRUCTING PROCEDURES
F. L. Pfyffer was a passionate surveyor who spent years
performing measurements in the alpine terrain, sometimes with
a couple of assistants, but mostly on his own. Although he was
a self-educated practitioner, he could build on experiences
gained during his four decades' career in the French military
service which gave him an opportunity to learn modern
surveying methods, to get in touch with reputed scientists and
instrument makers and to find access to the scientific literature.
Back in Switzerland, he decided to present his mountainous
homeland in the most natural and understandable form, in the
form of a topographic relief. He was aware of the inaccuracy of
existing maps of the region and around 1750 he met the
challenge to newly map almost 3:500 km? at a large scale,
including a novelty at that time, the height measurements all
over the country.
3.1 Triangulation and detailed surveying
On the basis of Pfyffer's letters (Pfyffer, 1761) to the famous
Swiss scientist Micheli Du Crest (1690-1766) it is known now
that Pfyffer defined a mesh of large triangles which he surveyed
precisely by triangulation. Later on, he densified this primary
network by detailed field measurements, using the
superordinate triangulation points for forward intersection. The
calculated relief accuracy (Table 1) and the more or less
homogeneous relief distortions over the whole mapped area
(Fig. 3) confirm that the triangulation with its basic principle
"from superordinate to subordinate" must have been applied.
On the other hand, the accuracy analysis supplies evidence that
Pfyffer evaluated his measurements mostly graphically in
combination with simple formulas of planar trigonometry
instead of adopting more accurate, purely numerical methods
under consideration of the curved Earth surface.
Being aware that the requisite for a precise triangulation is a
baseline few kilometres long measured with great care, Pfyffer
was particularly concerned with the appropriate methods for
direct distance measurements. He regularly checked the length
of his metal bars and chains (having respectable dimensions
from 15 to 120 French feet corresponding to 4.9 and 39 m)
along the side of a marmoreal quadrate which he considered to
be perfectly shaped. After a long search in mountainous Central
Switzerland, Pfyffer finally found a suitable, possibly flat area
for the baseline measurements. Then he measured shorter
distances in a zigzag manner as well as the corresponding
angles and hence he determined the searched baseline length
(Fig. 7). With a careful procedure Pfyffer tried to eliminate the
impact of systematic errors. Thus, he always laid his chains or
bars along a strained cord in order to keep the desired
measurement direction and he considered the influence of
sloped terrain by a successive horizontal arrangement of the
instruments. During the survey for his relief Pfyffer measured
several different baselines; only in summer 1761 he mentions
about 6 of them. The reason for such excessive measurements
was probably the quality control, which was for Pfyffer of great
importance.
p
e —— em diede
us itt oe = —
- 5 ea, 4
ia Mouse dies ae dy
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Fig.7: The triangulation sketch of F. L. Pfyffer, found in one of
his letters to Micheli Du Crest. The long dotted zigzag line in
the upper part was measured using metal chains. Out of these
direct measurements Pfyffer determined the length of the
baseline MN to 2832 French toises (around 5.5 km).
Before starting angle measurements for the triangulation,
Pfyffer had made himself familiar with the territory to be
surveyed. During the reconnaissance he checked the
reciprocative lines of sight and assigned the future signals and
stations. However, as he complains several times in his letters,
