DIY History | Transcribe | Scholarship at Iowa | Eccentricity of the Sextant by Frederic Furbish, 1893 | Eccentricity of the Sextant by Frederic Furbish, 1893, Page 75

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Eccentricity of the Sextant by Frederic Furbish, 1893

Eccentricity of the Sextant by Frederic Furbish, 1893, Page 75

[page]68[/page]

or sin COC' : P : : sin θ : l
or since COC' is small, - 
COC' = (P/[l or i?]) sin θ. In Δ CPC'. - 
sin CPC' : CC' : : sin PC'C : PC or
sin CPC' : P : : sin ((1/2)∝' - θ) : l .
or since CPC' is small CPC' = (P/[l or i?]) sin ((1/2)∝' - θ) = (P/[l or i?])(sin (1/2)∝' cos θ - cos (1/2) ∝' sin θ)
     We should note that the angles COC' and CPC' are thus given in circular measure.
     Hence in circular measure :- 
ε = ∝ - ∝' = 2 (P/[l or i?])(sin θ + sin (1/2) ∝' cos θ - cos (1/2) ∝' sin θ) or (1/2) ε = (1/2) ∝ - (1/2) ∝' = (1 - cos (1/2) ∝') (P/[l or i?]) sin θ + sin (1/2)∝' (P/[l or i?]) cos θ    (1)
which is our fundamental equation.
     If the angles measured are the meridian altitudes of stars of known declinations, then for the [underlined]artificial horizon[/underlined] :-   ∝ = Π - 2x + 2 δ + [26?] using circular measure.
     Substituting this value of ∝ in (1)

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[page]68[/page] or sin COC' : P : : sin θ : l or since COC' is small, - COC' = (P/[l or i?]) sin θ. In Δ CPC'. - sin CPC' : CC' : : sin PC'C : PC or sin CPC' : P : : sin ((1/2)∝' - θ) : l . or since CPC' is small CPC' = (P/[l or i?]) sin ((1/2)∝' - θ) = (P/[l or i?])(sin (1/2)∝' cos θ - cos (1/2) ∝' sin θ) We should note that the angles COC' and CPC' are thus given in circular measure. Hence in circular measure :- ε = ∝ - ∝' = 2 (P/[l or i?])(sin θ + sin (1/2) ∝' cos θ - cos (1/2) ∝' sin θ) or (1/2) ε = (1/2) ∝ - (1/2) ∝' = (1 - cos (1/2) ∝') (P/[l or i?]) sin θ + sin (1/2)∝' (P/[l or i?]) cos θ (1) which is our fundamental equation. If the angles measured are the meridian altitudes of stars of known declinations, then for the [underlined]artificial horizon[/underlined] :- ∝ = Π - 2x + 2 δ + [26?] using circular measure. Substituting this value of ∝ in (1)