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Eccentricity of the Sextant by Frederic Furbish, 1893

Eccentricity of the Sextant by Frederic Furbish, 1893, Page 76

[page][illegible][/page]

gives x + (1 - cos (1/2)∝') (ρ/[i or l?]) sin θ + sin (1/2)∝'
(ρ/[i or l?]) cos θ = ((Π/2) + δ + [b or 6?])) - (1/2)∝' .   (2)

     Letting 
          1 - cos (1/2)∝' = A
          sin (1/2)∝' = B
          ((Π/2) + δ + [b or 6?]) - (1/2)∝' = C   (3)
          (ρ/[i or l?]) sin θ = y
          (ρ/[i or l?]) cos θ = z

equation (2) may be written 

x + Ay + Bz = C   (4)

A series of equations such as (4) one of which may be found for each star observed, will, upon reduction by the method of least squares, give thet values of the unknown constants x, y and z.

     Having obtained y and z
tan θ = (y/z) , and (ρ/[i or l?]) = (square root of (y squared)) + (z squared) .

     The values ε corresponding to any values of x' may now be computed by equation (1) which, by means of equation (3) becomes ε = 2(1 - cos (1/2)∝i)y

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[page][illegible][/page] gives x + (1 - cos (1/2)∝') (ρ/[i or l?]) sin θ + sin (1/2)∝' (ρ/[i or l?]) cos θ = ((Π/2) + δ + [b or 6?])) - (1/2)∝' . (2) Letting 1 - cos (1/2)∝' = A sin (1/2)∝' = B ((Π/2) + δ + [b or 6?]) - (1/2)∝' = C (3) (ρ/[i or l?]) sin θ = y (ρ/[i or l?]) cos θ = z equation (2) may be written x + Ay + Bz = C (4) A series of equations such as (4) one of which may be found for each star observed, will, upon reduction by the method of least squares, give thet values of the unknown constants x, y and z. Having obtained y and z tan θ = (y/z) , and (ρ/[i or l?]) = (square root of (y squared)) + (z squared) . The values ε corresponding to any values of x' may now be computed by equation (1) which, by means of equation (3) becomes ε = 2(1 - cos (1/2)∝i)y