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 73

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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 73

[page]68[/page]

Wire inteval [?interval?] of Transit reticule in inches

[table has 3 columns]
X[subscript]0[/subscript] = weighted mean = 0.227in.
====================
A - G     |   delta    |   delta delta
-------------------------------
0.241 in  |  - 0.014  |  0.000196
0.230 in |  - 0.003 |  0.000009
0.225 in |  + 0.002 |  0.000004
0.225 in |  + 0.002 |  0.000004
0.225 in |  + 0.002 |  0.000004
0.225 in |  + 0.002 |  0.000004
0.230 in |  - 0.003 |  0.000009
0.225 in |  + 0.002 |  0.000004
0.230 in |  - 0.003 |  0.000009
0.230 in |  - 0.003 |  0.000009
0.230 in |  - 0.003 |  0.000009
0.227 in | +- 0.000 | 0.000000
0.230 in |  - 0.003 |  0.000009
0.230 in |  - 0.003 |  0.000009
0.230 in |  - 0.003 |  0.000009
0.226 in |  + 0.001 |  0.000001
0.226 in |  + 0.001 |  0.000001
0.227 in | +- 0.000 | 0.000000
0.227 in | +- 0.000 | 0.000000
0.225 in |  + 0.002  |  [?0.?]000004

0.229 in |  - 0.002 |  0.000[?1?0?]04
0.225 in |  + 0.002 |  0.000004
0.225 in |  + 0.002 |  0.000004
0.241 in |  - 0.014   |  0.000196
0.225 in |  + 0.002 |  0.000004
0.225 in |  + 0.002 |  0.000004
0.225 in |  + 0.002 |  0.000004
0.222 in |  + 0.005 |  0.000025
0.225 in |  + 0.002 |  0.000004
0.222 in |  + 0.005 |  0.000025
-------------------------------
   [?]    |  [delta delta] = 0.000607
-------------------------------
[/table]

X[subscript]0[/subscript] The mean of the measurements according to each scale affected with the weight the reciprocal of its mean error squared; and the weighted mean taken.

[?epsilon?][subscript]0[/subscript] = mean error weighted [?means?meas.?]

Then [?epsilon?][subscript]0[/subscript] square root of (0.000607/870) = 0.0008 in.

R[subscript]0[/subscript] = probable error weighted mean.

R[subscript]0[/subscript] = (0.6745)(square root of (0.000607/870)) = 0.00054 in.

For value of inteval [?interval?] see page 65.

Saving...

[page]68[/page] Wire inteval [?interval?] of Transit reticule in inches [table has 3 columns] X[subscript]0[/subscript] = weighted mean = 0.227in. ==================== A - G | delta | delta delta ------------------------------- 0.241 in | - 0.014 | 0.000196 0.230 in | - 0.003 | 0.000009 0.225 in | + 0.002 | 0.000004 0.225 in | + 0.002 | 0.000004 0.225 in | + 0.002 | 0.000004 0.225 in | + 0.002 | 0.000004 0.230 in | - 0.003 | 0.000009 0.225 in | + 0.002 | 0.000004 0.230 in | - 0.003 | 0.000009 0.230 in | - 0.003 | 0.000009 0.230 in | - 0.003 | 0.000009 0.227 in | +- 0.000 | 0.000000 0.230 in | - 0.003 | 0.000009 0.230 in | - 0.003 | 0.000009 0.230 in | - 0.003 | 0.000009 0.226 in | + 0.001 | 0.000001 0.226 in | + 0.001 | 0.000001 0.227 in | +- 0.000 | 0.000000 0.227 in | +- 0.000 | 0.000000 0.225 in | + 0.002 | [?0.?]000004 0.229 in | - 0.002 | 0.000[?1?0?]04 0.225 in | + 0.002 | 0.000004 0.225 in | + 0.002 | 0.000004 0.241 in | - 0.014 | 0.000196 0.225 in | + 0.002 | 0.000004 0.225 in | + 0.002 | 0.000004 0.225 in | + 0.002 | 0.000004 0.222 in | + 0.005 | 0.000025 0.225 in | + 0.002 | 0.000004 0.222 in | + 0.005 | 0.000025 ------------------------------- [?] | [delta delta] = 0.000607 ------------------------------- [/table] X[subscript]0[/subscript] The mean of the measurements according to each scale affected with the weight the reciprocal of its mean error squared; and the weighted mean taken. [?epsilon?][subscript]0[/subscript] = mean error weighted [?means?meas.?] Then [?epsilon?][subscript]0[/subscript] square root of (0.000607/870) = 0.0008 in. R[subscript]0[/subscript] = probable error weighted mean. R[subscript]0[/subscript] = (0.6745)(square root of (0.000607/870)) = 0.00054 in. For value of inteval [?interval?] see page 65.