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

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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 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.

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[[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.