The probable error of a single pointing (PEs) is measured for a single telescope with a variety of targets. This investigation shows that, although some change in PEs with distance does occur, the distribution of PEs as a function of distance can usually be neglected and a value of 0.62 second assigned as a practical average. The values of PEs for an indoor target usually show a small variation from one experienced observer to another, and from right to left eye of the same observer. There is also a measurable systematic difference in pointing between the right and left eyes of the same observer. In outdoor pointing a long period error or drift is usually superposed upon the short period errors.
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Average PE, for all authors except Pelzer PEs, found here
0.52
0.62
S. Stampfer, “Über die Genauigkeit des Visierens bei Winkel-messungen,” Jahrbücher des k. k. polytechischen Instituts in Wien (1934), Vol. 18, p. 231.
F. Hartner, Handbuch der niederen Geodäsie (Wien, 1856), p. 102.
C. M. v. Bauernfeind, Elements des Vermessungskunde (Stuttgart, 1879), Vol. I, p. 110.
Ch. A. Vogler, Lehrbuch der Praktischen Geometrie (Braunschweig, 1885), Vol. I. p. 81.
R. Wagner, “Über die mit dem Reichbachschen Distanzmesser erreichbare Genauigkeit und einige Erörterungen über die Fehlerursachen desselben,” Zeits. f. Vermessungswesen 49 (1886).
J. Adamczik, Compendium der Geodäsie (Leipzig und Wien, 1901). p. 58.
H. Hohenner, Geodäsie (Leipzig und Berlin, 1910), p. 27.
F. Hartner, J. Wastler, and E. Dolezal, Hand- und Lehrbuch der niederen Geodäsie (Wien, 1910), Vol. I, p. 255.
E. Hammer, Lehrbuch der elementaren praktischen Geometrie (Leipzig und Berlin, 1911), Vol. I, p. 270.
Klauser-Lohn, Lehrbuch der Vermessungskunde (Wien, 1912), p. 20.
M. Näbauer, Gruitdzüge der Geodäsie (Leipzig und Berlin, 1915), p. 90.
A. Noetzli, “Untersuchung die Genauigkeit des Zielens mit Fernrohren,” Zeits. f. Instrumentenkunde 35, 65 and 89 (1915).
Fr. Klempau, “Über die Beziehungen zwischen Winkel-, Nonien-, und Zielgenauigkeit,” Allgemeine Vermessungs-Nachrichten 317 (1923).
Wandhoff and F. Kögler, Taschenbuch für Berg—und Hüttenleute (Berlin, 1924), p. 771.
K. Lüdemann, “Grundlagen für den Voranschlag der Genauigkeits-leistung von einigen Theodoliten bei der Kleindreieckmessung und bei feinen Zugmessungen,” Zeits. f. Instrumentenkunde 44, 558 (1924).
Steinschläger, “Untersuchung eines 8-cm—Schraubenmikroscop-Theodolites,” Allgemeine Vermessungs—Nachrichten 445 (1925).
See reference 8 in text.
P. Werkmeister, Geodätische Instrumente (Leipzig, 1940), Vol. I, p. 22.
Tables (11)
Table I
Probable error for a single observation (PEs) for indoor pointing with target in the focal plane of a collimator.
Aperture
Filter
n
PEs seconds
27.5
K − 3
50
0.24
A
50
.23
B
50
.22
C
50
.42
21.4
K − 3
50
0.21
A
50
.19
B
50
.21
40
K − 3
100
0.24
27.5
K − 3
50
.24
21.4
K − 3
50
.21
15
K − 3
50
.22
10
K − 3
50
.27
6.8
K − 3
50
.28
Total number of independent observations 700 Average PEs = 0.244 second.
Table II
Description of targets.
Name
Range meters
Nature of target
Collimator
3
Vertical wire in focal plane of collimator.
Radio
100
Vertical metal column.
Tilden
323
Six-foot vertical vent pipe two inches in width painted white.
Sedgwick
445
Six-foot vertical vent pipe two inches in width painted white.
Broadmoor
703
Ball-tipped finial.
Ordway
905
Six-foot vertical wooden strip
inches in width, painted white, fastened to brick wall.
Klingle
1153
Six-foot vertical wooden strip six inches in width painted red and white,
inch strip down center.
Swank
1399
Vertical narrow finial.
Majestic
2722
Vertical pipe painted white.
Baptist
3000
Finial on spire.
Unity
3080
Finial on spire.
Howard
4505
Finial on spire.
Clock
4779
Narrow window on clock tower.
Trinity
5533
Gold cross on dome.
Capitol
7554
Vertical member attached to dome.
Bradbury
13,623
Supporting column of water tank.
Table III
Values of PEs for 6 sets of 50 observations each, considered 10 at a time, made by observer W.
Time
10-group number
PEs seconds
Pp
PEs 50-set
Pp
1
2
3
4
5
6
6–14–14
1
0.58
±0.09
1:00 p.m.
2
.34
.05
3
.44
.07
0.45
±0.03
4
.44
.07
5
.47
.07
6–16–44
6
.46
.07
3:00 p.m.
7
.57
.09
8
.65
.10
.51
.04
9
.44
.07
10
.45
.07
6–17–44
11
.61
.10
8:50 a.m.
12
.52
.08
13
.53
.08
.56
.04
14
.64
.10
15
.48
.08
7–1–44
16
.59
.09
1:00 p.m.
17
.72
.11
18
.75
.12
.67
.05
19
.81
.13
20
.48
.08
8–17–44
21
.82
.13
2:20 p.m.
22
.77
.12
23
.52
.08
.63
.04
24
.75
.12
25
.29
.05
8–18–44
26
.45
.07
2:50 p.m.
27
.58
.09
28
.59
.09
.69
.05
29
1.18
.19
30
.65
.10
Av. 0.58
.02
Table IV
Probable error of a single pointing for each o two observers with distant targets.
Target
Range meters
Observer W
Observer B
Average
PEs
n
PEs
n
PEs
n
Collimator
2
0.24
700
0.24
700
Radio
100
0.45
50
.45
50
Tilden
323
.46
100
.42
150
.44
250
Sedgwick
445
.36
200
.50
200
.43
400
Broadmoor
703
.57
300
.57
300
Ordway
905
.61
300
.44
100
.57
400
Klingle
1153
.60
200
.57
100
.59
300
Swank
1399
.58
300
.58
200
.58
500
Majestic
2722
.51
150
.52
100
.51
250
Baptist
3000
.73
200
.73
200
Unity
3080
.75
600
.67
200
.73
800
Howard
4505
.90
50
.72
50
.81
100
Clock
4779
.66
500
.71
150
.67
650
Trinity
5553
.65
200
.65
200
Capitol
7554
.92
100
.69
100
.80
200
Bradbury
13,624
.86
50
.97
50
.92
100
Average
0.64
2750
0.60
950
0.62
4700
Table V
Probable error of a single telescope pointing as a function of distance.
Target
Distance meters
n
PEs
Pp seconds
O − C1 seconds
O − C2 seconds
O seconds
C1 seconds
C2 seconds
Collimator
2
600
0.25
0.26
0.41
±0.01
−0.01
−0.16
Radio
100
50
.45
.40
.45
.03
.05
.00
Tilden
323
250
.44
.47
.49
.01
−.03
−.05
Sedgwick
445
400
.43
.49
.50
.01
−.06
−.07
Broadmoor
703
300
.57
.52
.53
.02
.05
.04
Ordway
905
400
.57
.54
.54
.02
.03
.03
Klingle
1153
300
.59
.57
.56
.02
.02
.03
Swank
1399
500
.58
.59
.57
.01
−.01
.01
Majestic
2722
250
.51
.66
.64
.02
−.15
−.13
Baptist
3000
200
.73
.67
.65
.03
.06
.08
Unity
3080
800
.73
.67
.65
.01
.06
.08
Howard
4505
100
.81
.72
.70
.04
.09
.11
Clock
4779
650
.67
.73
.71
.01
−.06
−.04
Trinity
5533
200
.65
.75
.74
.02
−.10
−.09
Capitol
7554
200
.80
.79
.79
.03
.01
.01
Bradbury
13,624
100
.92
.89
.92
.05
.03
.00
O is the value derived from observations. C1 = 0.064d1/4 + 0.19 second, and C2 = 0.0044d1/4 + 0.41 second.
Table VI
Consistency of observations for each of two observers with distant targets.
Target
Range meters
Observer W
Observer B
〈PEs〉Av second
〈PEm〉Av second
second
second
〈PEs〉Av second
〈PEm〉Av second
second
second
Radio
100
0.45
0.14
0.86
0.72
Tilden
323
0.49
0.15
0.14
−0.01
.42
.13
.62
.49
Sedgwick
445
.36
.11
.16
.05
.50
.16
.63
.47
Broadmoor
703
.57
.18
.70
.52
Ordway
905
.62
.20
.29
.09
.44
.14
.50
.36
Klingle
1153
.62
.20
.30
.10
.57
.18
.42
.24
Swank
1399
.55
.17
.31
.14
.58
.18
.42
.24
Majestic
2722
.51
.16
.16
.00
.52
.16
.21
.05
Baptist
3000
.73
.23
.59
.36
Unity
3080
.75
.24
.34
.10
.67
.21
.63
.42
Howard
4505
.90
.28
.30
.02
.72
.23
.45
.22
Clock
4779
.67
.21
.42
.21
.71
.22
.53
.31
Trinity
5533
.65
.21
.40
.19
Capitol
7554
.92
.29
.31
.02
.69
.22
.54
.32
Bradbury
13,624
.86
.27
.37
.10
Average
.66
.12
.29
.08
.58
.18
.55
.36
Table VII
Values obtained by observer B arranged in chronological order. Each run contains 50 observations.
Average PE, for all authors except Pelzer PEs, found here
0.52
0.62
S. Stampfer, “Über die Genauigkeit des Visierens bei Winkel-messungen,” Jahrbücher des k. k. polytechischen Instituts in Wien (1934), Vol. 18, p. 231.
F. Hartner, Handbuch der niederen Geodäsie (Wien, 1856), p. 102.
C. M. v. Bauernfeind, Elements des Vermessungskunde (Stuttgart, 1879), Vol. I, p. 110.
Ch. A. Vogler, Lehrbuch der Praktischen Geometrie (Braunschweig, 1885), Vol. I. p. 81.
R. Wagner, “Über die mit dem Reichbachschen Distanzmesser erreichbare Genauigkeit und einige Erörterungen über die Fehlerursachen desselben,” Zeits. f. Vermessungswesen 49 (1886).
J. Adamczik, Compendium der Geodäsie (Leipzig und Wien, 1901). p. 58.
H. Hohenner, Geodäsie (Leipzig und Berlin, 1910), p. 27.
F. Hartner, J. Wastler, and E. Dolezal, Hand- und Lehrbuch der niederen Geodäsie (Wien, 1910), Vol. I, p. 255.
E. Hammer, Lehrbuch der elementaren praktischen Geometrie (Leipzig und Berlin, 1911), Vol. I, p. 270.
Klauser-Lohn, Lehrbuch der Vermessungskunde (Wien, 1912), p. 20.
M. Näbauer, Gruitdzüge der Geodäsie (Leipzig und Berlin, 1915), p. 90.
A. Noetzli, “Untersuchung die Genauigkeit des Zielens mit Fernrohren,” Zeits. f. Instrumentenkunde 35, 65 and 89 (1915).
Fr. Klempau, “Über die Beziehungen zwischen Winkel-, Nonien-, und Zielgenauigkeit,” Allgemeine Vermessungs-Nachrichten 317 (1923).
Wandhoff and F. Kögler, Taschenbuch für Berg—und Hüttenleute (Berlin, 1924), p. 771.
K. Lüdemann, “Grundlagen für den Voranschlag der Genauigkeits-leistung von einigen Theodoliten bei der Kleindreieckmessung und bei feinen Zugmessungen,” Zeits. f. Instrumentenkunde 44, 558 (1924).
Steinschläger, “Untersuchung eines 8-cm—Schraubenmikroscop-Theodolites,” Allgemeine Vermessungs—Nachrichten 445 (1925).
See reference 8 in text.
P. Werkmeister, Geodätische Instrumente (Leipzig, 1940), Vol. I, p. 22.