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

[[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

[[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