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 14

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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 14

[[page#]]10[[/page#]]
Let E[[subscript]]1[[/subscript]] = mean error of single arithmetic mean = +-0.41 = [[?unclear? square root of {[delta delta]} / (n-1) ...ooorrr...  square root of {[delta delta] / (n-1)} ?]]

R[[subscript]]1[[/subscript]] = Probable error of single arithmetic mean = .6745 E[[subscript]]1[[/subscript]] = +- 0.276

E[[subscript]]0[[/subscript]] = mean error of weighted mean of series of observations = [[?unclear? square root of {[delta delta]} / n(n-1) ...ooorrr...  square root of {[delta delta] / n(n-1)} ?]] = +-0.094

R[[subscript]]0[[/subscript]] probable error of weighted mean of series of observations = .6745 E[[subscript]]0[[/subscript]] = +- 0.063

The weighted mean was found [page 21] to be 18.71  in one interval of transit reticule corresponds to (18.71+-0.063) / 100 revolutions of azimuth screw. 

"The squares of probable errors are directly as the length of lines," [Merriman, Method of Least Squares, Art. 91.] in the probable error in the measurement of a linear function increases as the square root of the function.

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[[page#]]10[[/page#]] Let E[[subscript]]1[[/subscript]] = mean error of single arithmetic mean = +-0.41 = [[?unclear? square root of {[delta delta]} / (n-1) ...ooorrr... square root of {[delta delta] / (n-1)} ?]] R[[subscript]]1[[/subscript]] = Probable error of single arithmetic mean = .6745 E[[subscript]]1[[/subscript]] = +- 0.276 E[[subscript]]0[[/subscript]] = mean error of weighted mean of series of observations = [[?unclear? square root of {[delta delta]} / n(n-1) ...ooorrr... square root of {[delta delta] / n(n-1)} ?]] = +-0.094 R[[subscript]]0[[/subscript]] probable error of weighted mean of series of observations = .6745 E[[subscript]]0[[/subscript]] = +- 0.063 The weighted mean was found [page 21] to be 18.71 in one interval of transit reticule corresponds to (18.71+-0.063) / 100 revolutions of azimuth screw. "The squares of probable errors are directly as the length of lines," [Merriman, Method of Least Squares, Art. 91.] in the probable error in the measurement of a linear function increases as the square root of the function.