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 72

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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 72

[page]67[/page]

Wire inteval [?interval?] of transit reticule in inches.

[table 1 has 3 columns]
Scale (1/40) in.
====================
A - G   |   delta   |   delta delta
-------------------------------
0.241 in | -0.0124  | 0.00015376
0.230in | -0.0014 | 0.00000196
0.225in | +0.0036 | 0.00001296
0.225in | +0.0036 | 0.00001296
0.225in | +0.0036 | 0.00001296
0.225in | +0.0036 | 0.00001296
0.230in | -0.0014 | 0.00000196
0.225in | +0.0036 | 0.00001296
0.230in | -0.0014 | 0.00000196
0.230in | -0.0014 | 0.00000196
-------------------------------
0.2286  |      [?]    | [delta delta] = [?0.?]00022640
-------------------------------
[/table 1]

[table 2 has 3 columns]
[?Scale?] (1/50) in.
====================
A - G    |    delta   |   delta delta
-------------------------------
0.230   | -0.0034in | 0.00001024
0.227   | -0.0002   | 0.00000004
0.220   | +0.0068   | 0.00004624
0.230   | -0.0032   | 0.00001024
0.230   | -0.0032   | 0.00001024
0.226   | +0.0008   | 0.00000064
0.226   | +0.0008   | 0.00000064
0.227   | -0.0002   | 0.00000004
0.227   | -0.0002   | 0.00000004
0.225   | +0.0018   | 0.00000324
-------------------------------
0.2268  |      [?]     | [delta delta] = [?0?].00008160
-------------------------------
[/table 2]

[table 3 has 3 columns]
[?Scale?] (1/60) in.
====================
A - G     |   delta       |   delta delta
-------------------------------
0.229in | -0.0026in | 0.00000676
0.225    | +0.0014   | 0.00000196
0.225    | +0.0014   | 0.00000196
0.241    | -0.0146   | 0.00021316
0.225    | +0.0014   | 0.00000196
0.225    | +0.0014   | 0.00000196
0.225    | +0.0014   | 0.00000196
0.222    | +0.0044   | 0.00001936
0.225    | +0.0014   | 0.00000196
0.222    | +0.0044   | 0.00001936
-------------------------------
0.2264   |      [?]     | [delta delta] = [?0?].00027040
-------------------------------
[/table 3]

[?epsilon?][subscript]1[/subscript] = mean error on scale 50 [?to an?] inch

[?epsilon?][subscript]2[/subscript] = " " " " [ditto for mean error on scale] 60 " [ditto for [?to an?] inch]

[?epsilon?][subscript]3[/subscript] = " " " " [ditto for mean error on scale] 40 " [ditto for [?to an?] inch]

then [?epsilon?][subscript]1[/subscript] = square root of (0.00008160/90) = +-0.00[?3?5?] inch (0.6745)

[?epsilon?][subscript]2[/subscript] = square root of (0.00027040/90) = +- 0.0054 " [ditto for inch] (0.6745)

[?epsilon?][subscript]3[/subscript] = square root of ([?0.?]00022640/90) = +- 0.005 " [ditto for inch] (0.6745)

The measure of precision varying as the square of the mean error: the above results show the scale of 50 to a more accurate than [strikethrough]then[/strikethrough] the others in the ratio of 25:9

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[page]67[/page] Wire inteval [?interval?] of transit reticule in inches. [table 1 has 3 columns] Scale (1/40) in. ==================== A - G | delta | delta delta ------------------------------- 0.241 in | -0.0124 | 0.00015376 0.230in | -0.0014 | 0.00000196 0.225in | +0.0036 | 0.00001296 0.225in | +0.0036 | 0.00001296 0.225in | +0.0036 | 0.00001296 0.225in | +0.0036 | 0.00001296 0.230in | -0.0014 | 0.00000196 0.225in | +0.0036 | 0.00001296 0.230in | -0.0014 | 0.00000196 0.230in | -0.0014 | 0.00000196 ------------------------------- 0.2286 | [?] | [delta delta] = [?0.?]00022640 ------------------------------- [/table 1] [table 2 has 3 columns] [?Scale?] (1/50) in. ==================== A - G | delta | delta delta ------------------------------- 0.230 | -0.0034in | 0.00001024 0.227 | -0.0002 | 0.00000004 0.220 | +0.0068 | 0.00004624 0.230 | -0.0032 | 0.00001024 0.230 | -0.0032 | 0.00001024 0.226 | +0.0008 | 0.00000064 0.226 | +0.0008 | 0.00000064 0.227 | -0.0002 | 0.00000004 0.227 | -0.0002 | 0.00000004 0.225 | +0.0018 | 0.00000324 ------------------------------- 0.2268 | [?] | [delta delta] = [?0?].00008160 ------------------------------- [/table 2] [table 3 has 3 columns] [?Scale?] (1/60) in. ==================== A - G | delta | delta delta ------------------------------- 0.229in | -0.0026in | 0.00000676 0.225 | +0.0014 | 0.00000196 0.225 | +0.0014 | 0.00000196 0.241 | -0.0146 | 0.00021316 0.225 | +0.0014 | 0.00000196 0.225 | +0.0014 | 0.00000196 0.225 | +0.0014 | 0.00000196 0.222 | +0.0044 | 0.00001936 0.225 | +0.0014 | 0.00000196 0.222 | +0.0044 | 0.00001936 ------------------------------- 0.2264 | [?] | [delta delta] = [?0?].00027040 ------------------------------- [/table 3] [?epsilon?][subscript]1[/subscript] = mean error on scale 50 [?to an?] inch [?epsilon?][subscript]2[/subscript] = " " " " [ditto for mean error on scale] 60 " [ditto for [?to an?] inch] [?epsilon?][subscript]3[/subscript] = " " " " [ditto for mean error on scale] 40 " [ditto for [?to an?] inch] then [?epsilon?][subscript]1[/subscript] = square root of (0.00008160/90) = +-0.00[?3?5?] inch (0.6745) [?epsilon?][subscript]2[/subscript] = square root of (0.00027040/90) = +- 0.0054 " [ditto for inch] (0.6745) [?epsilon?][subscript]3[/subscript] = square root of ([?0.?]00022640/90) = +- 0.005 " [ditto for inch] (0.6745) The measure of precision varying as the square of the mean error: the above results show the scale of 50 to a more accurate than [strikethrough]then[/strikethrough] the others in the ratio of 25:9