Probable error of clise
tion -On he assituation
' pute
tre ahve Tabe umishes
3
be the severaly
observation is the same for every pair of stars, a comparison of the "estuts all means for determining its mean value from all the pairs, thus. Let differences for any pair between the several results for latitude from that pair (of which there have been n observations) and the mean result from that pair; and let such differences or residuals be similarly taken out for all of the pairs which have been observed more than once; and let V be the sum of the squares of all these residuals, N the total number of determinations, M the total number of 'pairs observed more than once, and Q (.6745) the factor for reduction of mean to probable errors. Then e,
the probable error of observation, is found by the formula,
1
V
Q2
N-M
.455
N-M
..(6)
Table III, below, exhibits the steps of the process for determining V.
TABLE III.
TO FIND THE PROBABLE ERROR OF OBSERVATION.
No. of pair
Stars of the pair; B. A. C. Nos.
Seconds of latitude
Means
V
#
#!
Г
9.55
0.68
.4624
9.54
0.69
.4761.
745-786
10.48
10,23
0.25
.0625
11.18
0.95
.9025
10.41
0.13
.0324
13.59
0.54
.2916
872-901
12.26
13.05
0.79
.6241
13.31
0.26
.0676
3
502-518
13.97
13.39
0.65
.4225
1
999-1052
14.55
14.05
0.50
.2500
14.20
0.15
.0225
10.66
0.28
.0781
10
5
1097-1138
9.27
10.38
1.11
1.2321
11.22
0.84
.7056
12.27
0.70
.4900
6
574-628
11.57
10.87
0.70
.4900
12.56
0.03
.0009
1045-1052
11.82
12.53
0.71.
.5041
13.22
0.69
.4761
11.97
0.22
.0484***
.1326-1346
12.19
12.41
0.22
.0484
13.37
0.08
.0064
9
1391-1408
13.29
13.22
0.07
.0019
10
1408-1437
11.70
10.57
0.28
.0784
11
1726-1778
9.74
10.29
0.55
.3025
10.56
0.27
.0729
9.21
0.63
.3969
12
1937-1876
9.17
9.84
0.67
.4489
11.14
1.30
1.6900
13.75
0.59
.3481
13
510- 574
13.16
12.57
0.59
.3481
11.12
0.04
.0016-
14
1377-1444
11.16
11.20
0.04
.0016
13.15
0.03
.0009
15
1420-1444
13.12
13.09
0 03
.0009
13.24
0.12
.0144,
16
1602-1687
14.90
13.36
1.54
2.3716
11.93
1.43
2.0449
9.83
0.03
17
1958-2001
9.86
9.89
0.03
.0009
00094€
18
1408-1432
11.70
1
12.72
0.23
.0529
19
1893-1900
12.49
12.26
0.23
.0529***
20
1990-2082
13.47
Page 120
Page 121
Probable error of clise
tion -On he assituation
' pute
tre ahve Tabe umishes
3
be the severaly
observation is the same for every pair of stars, a comparison of the "estuts all means for determining its inean value from all the pairs, thus. Let differences for any pair between the several results for latitude from that pair (of which there have been n observations) and the mean result from that pair; and let such differences or residuals be similarly taken out for all of the pairs which have been observed more than once; and let V be the sun of the squares of all these residuals, N the total number of determinations, M the total number of 'pairs observed more than once, and Q (.6745) the factor for reduction of mean to probable errors. Then e,
the probable error of observation, is found by the formula,
1
حمد
V
Q2
N-M
.455
N-M
..(6)
Table III, below, exhibits the steps of the process for determining V.
TABLE III.
TO FIND THE PROBABLE ERROR OF OBSERVATION.
No. of pair
Stars of the pair; B. A. C. Nos.
Seconds of latitude
Means
V
#
#!
Г
9.55
0.68
.4624
9.54
0.69
.4761.
745-786
10.48
10,23
0.25
.0625
11.18
0.95
.9025
10.41
0.13
.0324
13.59
0.54
.2916
872-901
12.26
13.05
0.79
.6241
13.31
0.26
.0676
3
502-518
13.97
13.39
0.65
4225
1
999-1052
14.55
14.05
0.50
.2500
14.20
0.15
.0225
10.66
0.28
.0781
10
5
1097-1138
9.27
10.38
1.11
1.2321
11.22
0.84
.7056
12.27
0.70
.4900
6
574-628
11.57
10.87
0.70
.4900
12.56
0.03
.0009
1045-1052
11.82
12.53
0.71.
.5041
13.22
0.69
.4761
11.97
0.22
.0484***
.1326-1346
12.19
12.41
0.22
.0484
13.37
0.08
.0064
9
1391-1408
13.29
13.22
0.07
.0019
10
1408-1437
11.70
10.57
0.28
.0784
11
1726-1778
9.74
10.29
0.55
.3025
10.56
0.27
.0729
9.21
0.63
.3969
12
1937-1876
9.17
9.84
0.67
.4489
11.14
1.30
1.6900
13.75
0.59
.3481
13
510- 574
13.16
12.57
0.59
.3481
11.12
0.04
.0016-
14
1377-1444
11.16
11.20
0.04
.0016
13.15
0.03
.0009
15
1420-1444
13.12
13.09
0 03
.0009
13.24
0.12
0144,
16
1602-1687
14.90
13.36
1.54
2.3716
11.93
1.43
2.0449
9.83
0.03
17
1958-2001
9.86
9.89
0.03
.0009
00094€
18
1408-1432
11.70
1
12.72
0.23
تشير
.0529
19
1893-1900
12.49
12.26
0.23
.0529***
20
1990-2082
13.47
Page 120Page 121
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