DIY History | Transcribe | Scholarship at Iowa | Eccentricity of the Sextant by Frederic Furbish, 1893 | Eccentricity of the Sextant by Frederic Furbish, 1893, Page 81

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Eccentricity of the Sextant by Frederic Furbish, 1893

Eccentricity of the Sextant by Frederic Furbish, 1893, Page 81

we get the true value of the altitude. The explanation of the theory is as follows. -
[image of top hemisphere with labels]

Let h = AS' = the observed altitude of the star S' corresponding to the hour angle t. Let DES' = circle parallel to the horizon ABC. S'S" = path of star from point of observation S' to S" the position on the meridian. BS" = h[subscript]0[/subscript] = altitude of star on meridian. Z[subscript]0[/subscript] = S"Z = Zenith distance of star on meridian = 90° - h[subscript]0[/subscript] [= or - ?] φ - δ , S'Z = 90° - h , ZP = 90° - φ , angle ZPS = t.

     In the delta ZPS' by fundamental formula (Formula 8 [Greene?] P.7) we have (1) sin h = sin δ sin φ + cos δ cos φ cos t. Write for cos t its value 1 - 2 sin[superscript]2[/superscript] (1/2) t and (1) becomes cos Z = sin h = sin δ sin φ + cos δ cos φ (1 - sin[superscript]2[/superscript] (1/2) t)

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we get the true value of the altitude. The explanation of the theory is as follows. - [image of top hemisphere with labels] Let h = AS' = the observed altitude of the star S' corresponding to the hour angle t. Let DES' = circle parallel to the horizon ABC. S'S" = path of star from point of observation S' to S" the position on the meridian. BS" = h[subscript]0[/subscript] = altitude of star on meridian. Z[subscript]0[/subscript] = S"Z = Zenith distance of star on meridian = 90° - h[subscript]0[/subscript] [= or - ?] φ - δ , S'Z = 90° - h , ZP = 90° - φ , angle ZPS = t. In the delta ZPS' by fundamental formula (Formula 8 [Greene?] P.7) we have (1) sin h = sin δ sin φ + cos δ cos φ cos t. Write for cos t its value 1 - 2 sin[superscript]2[/superscript] (1/2) t and (1) becomes cos Z = sin h = sin δ sin φ + cos δ cos φ (1 - sin[superscript]2[/superscript] (1/2) t)