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 15

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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 15

[[page#]]11[[/page#]]
In measuring 18.71 / 100 of a revolution of the azimuth screw the probable error is 0.063 of a graduation, then, as from the nature of the quantity under consideration, it may be treated as a linear function, the probable error of one revolution would be expressed by 

.063 : [[?E?]] :: [[square root of:]] .1871 : 1

[[?E?]] = .063 / [[square root of:]] .1871 = 
[[?+- 0.145?]] graduation

Therefore the value of one revolution of the azimuth screw = 5.345 +- 0.007 intervals of the transit reticule. One wire interval of the transit reticule 
= 5[[superscript]]s[[/superscript]].422+-[[superscript]]s[[/superscript]] .005 [see page 29]

Then, [[? 5,345 ?]] intervals would 
= 28[[superscript]]s[[/superscript]],979+-0[[superscript]]s[[/superscript]].02 = 7' - 14".685 +- 0".3 arc
This last probable error is found from formula
R[[superscript]][[?s?]][[/superscript]] = (((dX / dx) squared)(r squared)) + (((dX/d(x[[subscript]]1[[/subscript]])) squared)(r squared)) +  in probable error for X in function expressed by X = [[integral sign]] (x x[[subscript]]1[[/subscript]] x[[subscript]]2[[/subscript]] . . . ) [Churnvent, Art. 22.]

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[[page#]]11[[/page#]] In measuring 18.71 / 100 of a revolution of the azimuth screw the probable error is 0.063 of a graduation, then, as from the nature of the quantity under consideration, it may be treated as a linear function, the probable error of one revolution would be expressed by .063 : [[?E?]] :: [[square root of:]] .1871 : 1 [[?E?]] = .063 / [[square root of:]] .1871 = [[?+- 0.145?]] graduation Therefore the value of one revolution of the azimuth screw = 5.345 +- 0.007 intervals of the transit reticule. One wire interval of the transit reticule = 5[[superscript]]s[[/superscript]].422+-[[superscript]]s[[/superscript]] .005 [see page 29] Then, [[? 5,345 ?]] intervals would = 28[[superscript]]s[[/superscript]],979+-0[[superscript]]s[[/superscript]].02 = 7' - 14".685 +- 0".3 arc This last probable error is found from formula R[[superscript]][[?s?]][[/superscript]] = (((dX / dx) squared)(r squared)) + (((dX/d(x[[subscript]]1[[/subscript]])) squared)(r squared)) + in probable error for X in function expressed by X = [[integral sign]] (x x[[subscript]]1[[/subscript]] x[[subscript]]2[[/subscript]] . . . ) [Churnvent, Art. 22.]