DIY History | Transcribe | Scholarship at Iowa | Eccentricity of the Sextant by Frederic Furbish, 1893 | Eccentricity of the Sextant by Frederic Furbish, 1893, Page 117

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Eccentricity of the Sextant by Frederic Furbish, 1893

Eccentricity of the Sextant by Frederic Furbish, 1893, Page 117

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These equations have the form, - 
     (1) [aa]x' + [ab]y' + [ac]z' + [an] = 0.
(2) [ab]x' + [bb]y' + [bc]z' + [bn] = 0.
(3) [ac]x' + [ac]y' + [cc]z' + [cn] = 0.
Turning to our table of squares we find the quantities [aa], [ab], etc. and substitute them in the brackets.
[aa] = 4.61455
[ab] = 0.82071
[ac] = 3.43949
[bb] = 0.25288
[bc] = 0.69512
[cc] = 2.64902
[an] = -0.00115
[bn] = -0.00022
[cn] = -0.00094
hence the normals become,
(1) 4.61455x' + 0.82071y' + 3.43949z - 0.00115 = 0.

(2) 0.82071x' + 0.25288y' + 0.69512z - 0.00022 = 0.

(3) 3.43949x' + 0.69512y' + 2.64902z - 0.00094 = 0.

     [underlined]Solution of the normal equations.[/underlined]
Professor Comstock in his book on the "Method of Least Squares" presents the following scheme for the solution of the normal equations which has proven very satisfactory.-

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[page][illegible][/page] These equations have the form, - (1) [aa]x' + [ab]y' + [ac]z' + [an] = 0. (2) [ab]x' + [bb]y' + [bc]z' + [bn] = 0. (3) [ac]x' + [ac]y' + [cc]z' + [cn] = 0. Turning to our table of squares we find the quantities [aa], [ab], etc. and substitute them in the brackets. [aa] = 4.61455 [ab] = 0.82071 [ac] = 3.43949 [bb] = 0.25288 [bc] = 0.69512 [cc] = 2.64902 [an] = -0.00115 [bn] = -0.00022 [cn] = -0.00094 hence the normals become, (1) 4.61455x' + 0.82071y' + 3.43949z - 0.00115 = 0. (2) 0.82071x' + 0.25288y' + 0.69512z - 0.00022 = 0. (3) 3.43949x' + 0.69512y' + 2.64902z - 0.00094 = 0. [underlined]Solution of the normal equations.[/underlined] Professor Comstock in his book on the "Method of Least Squares" presents the following scheme for the solution of the normal equations which has proven very satisfactory.-