DIY History | Transcribe | Scholarship at Iowa | Theory of least squares applied to the problems arising in our observatory by Arthur George Smith, 1895 | Theory of Least Squares Applied to the Problems Arising in our Observatory by Arthur George Smith, 1895, Page 66

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Theory of least squares applied to the problems arising in our observatory by Arthur George Smith, 1895

Theory of Least Squares Applied to the Problems Arising in our Observatory by Arthur George Smith, 1895, Page 66

[page]61[/page]

[first table: 2 notes at beginning and then 8 columns]

[?epsilon?][subscript]0[/subscript] = mean error

P = (1/{([?epsilon?][subscript]0[/subscript])[superscript]2[/superscript]}) * (No.)

[column 1]
Wire
--------------
[?]
A
B
C[subscript]3[/subscript]
D[subscript]3[/subscript]
E[subscript]3[/subscript]
F
G
--------------
[?]
[?]
--------------

[column 2]
Interval
--------------
[?mark?]
  97.628
  65.132
  32.449
+  0.019
- 32.547
- 65.121
- 97.524
--------------
[?]
[?]
--------------

[column 3]
[delta delta]
--------------
[?]
5.006594
3.139631
3.273097
3.791[?0?]72
3.256059
5.314123
5.0879[?0?]7
--------------
[?]
[?]
--------------

[column 4]
No.
--------------
[?]
3
2
1
0
1
2
3
--------------
[?]
[?]
--------------

[column 5]
[?epsilon?][subscript]0[/subscript]
--------------
[?mark?]
+- 0.004
+- 0.003
+- 0.003
+- 0.003
+- 0.003
+- 0.004
+- 0.004
--------------
[?]
[?]
--------------

[column 6]
i
--------------
[?mark?]
  32.543
  32.566
  32.449
+ 0.019
  32.547
  32.560
  32.508
--------------
[?]
[?]
--------------

[column 7]
square root of P
--------------
[?]
3(square root of 3)
4(square root of 2)
4(square root of 1)
[?4(square root of 0)?]
4(square root of 1)
3(square root of 2)
3(square root of 3)
--------------
[?]
[square root of P] = 28.25
--------------

[column 8]
(square root of P) * i
--------------
[?mark?]
168.898
183.672
129.796
[?0?]
130.188
137.729
168.716
--------------
[?mark?]
918.999
--------------
[/first table]

[second table: 1 note at beginning and then 3 columns]

X[subscript]0[/subscript] = weighted mean = [?mark above?]32.531

[column 1]
i
--------------
[?mark?]
32.543
32.566
32.449
[?]
32.547
32.560
32.508
--------------
[?]
--------------

[column 2]
[delta]
--------------
[?]
-  0.012
-  0.035
+ 0.082
[?]
-  0.016
-  0.029
+ 0.023
--------------
[?]
--------------

[column 3]
[delta delta]
--------------
[?]
0.000144
0.001225
0.006724
[?]
0.000256
0.000841
0.000529
--------------
[delta delta] = 0.009719
--------------
[/second table]

[?epsilon?][subscript]0[/subscript] = mean error general mean

R[subscript]0[/subscript] = provable error " " [ditto for general mean]

[?epsilon?][subscript]0[/subscript] = {square root of (0.004719/[?2?]0)} = [?mark above?] +- 0.018

R[subscript]0[/subscript] = 0.6745 [?epsilon?][subscript]0[/subscript] = 0.012

Interval [?from?] D[subscript]1[/subscript] - D[subscript]2[/subscript] = [?mark above?]5.422 +- [?mark above?]0.005

[See page 10]

Saving...

[page]61[/page] [first table: 2 notes at beginning and then 8 columns] [?epsilon?][subscript]0[/subscript] = mean error P = (1/{([?epsilon?][subscript]0[/subscript])[superscript]2[/superscript]}) * (No.) [column 1] Wire -------------- [?] A B C[subscript]3[/subscript] D[subscript]3[/subscript] E[subscript]3[/subscript] F G -------------- [?] [?] -------------- [column 2] Interval -------------- [?mark?] 97.628 65.132 32.449 + 0.019 - 32.547 - 65.121 - 97.524 -------------- [?] [?] -------------- [column 3] [delta delta] -------------- [?] 5.006594 3.139631 3.273097 3.791[?0?]72 3.256059 5.314123 5.0879[?0?]7 -------------- [?] [?] -------------- [column 4] No. -------------- [?] 3 2 1 0 1 2 3 -------------- [?] [?] -------------- [column 5] [?epsilon?][subscript]0[/subscript] -------------- [?mark?] +- 0.004 +- 0.003 +- 0.003 +- 0.003 +- 0.003 +- 0.004 +- 0.004 -------------- [?] [?] -------------- [column 6] i -------------- [?mark?] 32.543 32.566 32.449 + 0.019 32.547 32.560 32.508 -------------- [?] [?] -------------- [column 7] square root of P -------------- [?] 3(square root of 3) 4(square root of 2) 4(square root of 1) [?4(square root of 0)?] 4(square root of 1) 3(square root of 2) 3(square root of 3) -------------- [?] [square root of P] = 28.25 -------------- [column 8] (square root of P) * i -------------- [?mark?] 168.898 183.672 129.796 [?0?] 130.188 137.729 168.716 -------------- [?mark?] 918.999 -------------- [/first table] [second table: 1 note at beginning and then 3 columns] X[subscript]0[/subscript] = weighted mean = [?mark above?]32.531 [column 1] i -------------- [?mark?] 32.543 32.566 32.449 [?] 32.547 32.560 32.508 -------------- [?] -------------- [column 2] [delta] -------------- [?] - 0.012 - 0.035 + 0.082 [?] - 0.016 - 0.029 + 0.023 -------------- [?] -------------- [column 3] [delta delta] -------------- [?] 0.000144 0.001225 0.006724 [?] 0.000256 0.000841 0.000529 -------------- [delta delta] = 0.009719 -------------- [/second table] [?epsilon?][subscript]0[/subscript] = mean error general mean R[subscript]0[/subscript] = provable error " " [ditto for general mean] [?epsilon?][subscript]0[/subscript] = {square root of (0.004719/[?2?]0)} = [?mark above?] +- 0.018 R[subscript]0[/subscript] = 0.6745 [?epsilon?][subscript]0[/subscript] = 0.012 Interval [?from?] D[subscript]1[/subscript] - D[subscript]2[/subscript] = [?mark above?]5.422 +- [?mark above?]0.005 [See page 10]