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

[[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.

[[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.