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 11

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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 11

[[page#]]7[[/page#]]
or in this case, M=16 .
The column [[underline]]t[[/underline]] gives the value of a single interval as found by dividing each mean difference by its number of intervals. [[underline]]P[[/underline]] [[?is?]] weight of each arithmetic mean has been found using both the arguments 1 / ((E[[subscript]]0[[/subscript]]) squared) and N[[subscript]]v[[/subscript]] . 
The weight of two observations being reciprocally proportional to the squares of their mean errors. [Chauvenit, Method of Least Squares, Art. 24] ; and since a single observation of [[underline]]n[[/underline]] intervals may be considered as having the same error as the mean of [[underline]]n[[/underline]] observations of a unit interval, and as the [[underline]]Measure of Precision[[/underline]] increases as the square root of the number of observations : Therefore the value

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[[page#]]7[[/page#]] or in this case, M=16 . The column [[underline]]t[[/underline]] gives the value of a single interval as found by dividing each mean difference by its number of intervals. [[underline]]P[[/underline]] [[?is?]] weight of each arithmetic mean has been found using both the arguments 1 / ((E[[subscript]]0[[/subscript]]) squared) and N[[subscript]]v[[/subscript]] . The weight of two observations being reciprocally proportional to the squares of their mean errors. [Chauvenit, Method of Least Squares, Art. 24] ; and since a single observation of [[underline]]n[[/underline]] intervals may be considered as having the same error as the mean of [[underline]]n[[/underline]] observations of a unit interval, and as the [[underline]]Measure of Precision[[/underline]] increases as the square root of the number of observations : Therefore the value