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 10

Transcribe
Translate

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 10

[[page#]]6[[/page#]]
to give the arithmetic mean.
The sum of the squares of the residuals is given and designated [delta delta]

Upon page 21 has been tabulated the arithmetic mean of the various differences. In the column marked No. is shown the number of single intervals that correspond to the mean following it: the interval D[[subscript]]1[[/subscript]] to D[[subscript]]2[[/subscript]] being a single interval, D[[subscript]]5[[/subscript]] to E[[subscript]]1[[/subscript]] a double interval and A to B six intervals, and thus for all.

Next to the mean difference is given the sum of the squares of the residuals. E[[subscript]][[?0 or v?]][[/subscript]] is the mean error of the arithmetic mean of the observed set of differences. The formula for E[[subscript]][[?0 or v?]][[/subscript]], is E[[subscript]][[?0 or v?]][[/subscript]] = [[? square root of {[delta delta] divided by m(m-1)} ...ooorrr... (square root of {[delta delta]}) divided by m(m-1) ?]] , m designating the number of observations.

Saving...

[[page#]]6[[/page#]] to give the arithmetic mean. The sum of the squares of the residuals is given and designated [delta delta] Upon page 21 has been tabulated the arithmetic mean of the various differences. In the column marked No. is shown the number of single intervals that correspond to the mean following it: the interval D[[subscript]]1[[/subscript]] to D[[subscript]]2[[/subscript]] being a single interval, D[[subscript]]5[[/subscript]] to E[[subscript]]1[[/subscript]] a double interval and A to B six intervals, and thus for all. Next to the mean difference is given the sum of the squares of the residuals. E[[subscript]][[?0 or v?]][[/subscript]] is the mean error of the arithmetic mean of the observed set of differences. The formula for E[[subscript]][[?0 or v?]][[/subscript]], is E[[subscript]][[?0 or v?]][[/subscript]] = [[? square root of {[delta delta] divided by m(m-1)} ...ooorrr... (square root of {[delta delta]}) divided by m(m-1) ?]] , m designating the number of observations.