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 13

[[page#]]9[[/page#]]
The same value of E[[subscript]]v[[/subscript]] would obtain, had each observation been affected by the square root of its weight and the mean error determined as before from formula
E[[subscript]]v[[/subscript]] = [[?unclear? square root of {[delta delta]} / n(n-1) ...ooorrr... square root of {[delta delta] / n(n-1)} ?]]
The products (square root of P)(t) are shown in the column as designated and their sum [(square root of P)(t)] found ; also the sum of the square roots of the weights, [(square root of P)] . X[[subscript]]0[[/subscript]] = [(square root of P)(t)] / [(square root of P)] represents the weighted mean.
Upon page 22 is given the values of [[underline]]t[[/underline]] and the residuals and their squares found between [[underline]]t[[/underline]] and [[underline]]X[[/underline]][[subscript]]0[[/subscript]] : from which has been found the mean and probable errors of the arithmetic mean and also the source for the weighted mean of the observations.

[[page#]]9[[/page#]]
The same value of E[[subscript]]v[[/subscript]] would obtain, had each observation been affected by the square root of its weight and the mean error determined as before from formula
E[[subscript]]v[[/subscript]] = [[?unclear? square root of {[delta delta]} / n(n-1) ...ooorrr... square root of {[delta delta] / n(n-1)} ?]]
The products (square root of P)(t) are shown in the column as designated and their sum [(square root of P)(t)] found ; also the sum of the square roots of the weights, [(square root of P)] . X[[subscript]]0[[/subscript]] = [(square root of P)(t)] / [(square root of P)] represents the weighted mean.
Upon page 22 is given the values of [[underline]]t[[/underline]] and the residuals and their squares found between [[underline]]t[[/underline]] and [[underline]]X[[/underline]][[subscript]]0[[/subscript]] : from which has been found the mean and probable errors of the arithmetic mean and also the source for the weighted mean of the observations.