DIY History | Transcribe | Scholarship at Iowa | Eccentricity of the Sextant by Frederic Furbish, 1893 | Eccentricity of the Sextant by Frederic Furbish, 1893, Page 85

Transcribe
Translate

Eccentricity of the Sextant by Frederic Furbish, 1893

Eccentricity of the Sextant by Frederic Furbish, 1893, Page 85

[page][illegible][/page]

     Expressed in full (5) is
     h[subscript]0[/subscript] = h + ((cos φ cos δ)/(sin(φ - δ)))m - ((cos φ cos δ)/(sin(φ - δ)))[superscript]2[/superscript] cot (φ - δ)n   --
The following special applications of the formula may be found useful for reference. 
     For the direct position of the sextant, 

(∝) Star South of zenith; i.e. δ<φ
h[subscript]0[/subscript] = h + ((cos φ cos δ)/(sin(φ - δ)))m - ((cos φ cos δ)/(sin(φ - δ)))[superscript]2[/superscript] cot(φ - δ)n

(β) Star North of zenith; i.e. δ>φ ,
h[subscript]0[/subscript] = h - ((cos φ cos δ)/(sin(φ - δ)))m + ((cos φ cos δ)/(sin(φ - δ)))[superscript]2[/superscript] cot(φ - δ)n

     For the Reverse position of the sextant,

(∝) Star South of zenith; i.e. δ<φ
h[subscript]0[/subscript] = h - ((cos φ cos δ)/(sin(φ - δ)))m + ((cos φ cos δ)/(sin(φ - δ)))[superscript]2[/superscript] cot(φ - δ)n ,

(β) Star North of zenith; i.e. δ>φ ,
h[subscript]0[/subscript] = h + ((cos φ cos δ)/(sin(φ - δ)))m - ((cos φ cos δ)/(sin(φ - δ)))[superscript]2[/superscript] cot(φ - δ)n

     For lower culmination

(∝) h[subscript]0[/subscript] = h - ((cos φ cos δ)/(sin(φ - δ)))m - ((cos φ cos δ)/(sin(φ - δ)))[superscript]2[/superscript] cot(φ - δ)n

Saving...

[page][illegible][/page] Expressed in full (5) is h[subscript]0[/subscript] = h + ((cos φ cos δ)/(sin(φ - δ)))m - ((cos φ cos δ)/(sin(φ - δ)))[superscript]2[/superscript] cot (φ - δ)n -- The following special applications of the formula may be found useful for reference. For the direct position of the sextant, (∝) Star South of zenith; i.e. δ<φ h[subscript]0[/subscript] = h + ((cos φ cos δ)/(sin(φ - δ)))m - ((cos φ cos δ)/(sin(φ - δ)))[superscript]2[/superscript] cot(φ - δ)n (β) Star North of zenith; i.e. δ>φ , h[subscript]0[/subscript] = h - ((cos φ cos δ)/(sin(φ - δ)))m + ((cos φ cos δ)/(sin(φ - δ)))[superscript]2[/superscript] cot(φ - δ)n For the Reverse position of the sextant, (∝) Star South of zenith; i.e. δ<φ h[subscript]0[/subscript] = h - ((cos φ cos δ)/(sin(φ - δ)))m + ((cos φ cos δ)/(sin(φ - δ)))[superscript]2[/superscript] cot(φ - δ)n , (β) Star North of zenith; i.e. δ>φ , h[subscript]0[/subscript] = h + ((cos φ cos δ)/(sin(φ - δ)))m - ((cos φ cos δ)/(sin(φ - δ)))[superscript]2[/superscript] cot(φ - δ)n For lower culmination (∝) h[subscript]0[/subscript] = h - ((cos φ cos δ)/(sin(φ - δ)))m - ((cos φ cos δ)/(sin(φ - δ)))[superscript]2[/superscript] cot(φ - δ)n