A Text book On the Method of Least Squares

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X, Observed^.
Computed^.
V, 1786.5 -63.5 +S°.42 5°.28 + 0.14 1810.5 -39-5 4-77 5-25 — 0.48 1824.5 -25-5 5-75 5.60 + 0.15 1829.0 — 21.0 6.05 5-76 + 0.29 1859.6 + 9-6 7.29 7-34 — 0.05 1867.6 + 17-6 7.82 7.84 — 0.02 1879.6 + 29.6 8-57 8-59 — 0.02 The sum of the squares of these residuals is 0.36, and hence, by (32), • = 0.6745 V -^ = 0.19, '^ 7 — 3 which gives the probable error of a single computed value if the observations be regarded as exact, or the probable error of an observation if the law
...expressed in the empirical formula be regarded as exact.
* See the numerous valuable papers by Schott, in the Reports of the United States Coast and Geodetic Survey, the latest of which is in the Report for 1882, pp. 211-276. The above formula for the declination is the one there adopted, as giving the best value of the period m.
138 INDEPENDENT OBSERVATIONS.
VII.
III. Lastly, consider the deduction of a formula to represent certain experiments, made by Darcy and Bazin, on the flow of water in a rectangular wooden trough lined with cement.


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