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Eccentricity of the Sextant by Frederic Furbish, 1893

Eccentricity of the Sextant by Frederic Furbish, 1893, Page 47

The marks both on the Vernier and arc may be rendered much plainer by occasionally rubbing them with a little sweet oil and lamp black.

     The theory of the two classes of Verniers is given in the following equations:--

     For the second class,
Let ([[n?]]) = the number of divisions on the Vernier
([[n?]] - 1) = the number of divisions in the same space on the arc.
d = the value of one division of the arc.
d' = the value of one division of the Vernier.
Then 
(1) [[n?]]d' = ([[n?]] - 1)d
(2) [[n?]]d' = [[n?]]d - d
(3) d = [[n?]]d - [[n?]]d'
(4) d = [[n?]](d - d')
(5) (d / (d - d')) = [[n?]]
From (1) [[we get:...]] 
(6) d' = ((([[n?]] - 1)d) / [[n?]])
From (3) [[we get:...]]
(7) (d - d') = (d / [[n?]]) = least count.

In Pistor and Martins' sextants:
(d - d') = (d/10) = 10"
d = 10'
[[n?]] = (d / (d - d')) = (10' / 10") = 60
([[n?]] - 1) = 59
d' = ((59/60) * d)

     For the first class, substitute ([[n?]] + 1) for ([[n?]] - 1) in the pre-

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The marks both on the Vernier and arc may be rendered much plainer by occasionally rubbing them with a little sweet oil and lamp black. The theory of the two classes of Verniers is given in the following equations:-- For the second class, Let ([[n?]]) = the number of divisions on the Vernier ([[n?]] - 1) = the number of divisions in the same space on the arc. d = the value of one division of the arc. d' = the value of one division of the Vernier. Then (1) [[n?]]d' = ([[n?]] - 1)d (2) [[n?]]d' = [[n?]]d - d (3) d = [[n?]]d - [[n?]]d' (4) d = [[n?]](d - d') (5) (d / (d - d')) = [[n?]] From (1) [[we get:...]] (6) d' = ((([[n?]] - 1)d) / [[n?]]) From (3) [[we get:...]] (7) (d - d') = (d / [[n?]]) = least count. In Pistor and Martins' sextants: (d - d') = (d/10) = 10" d = 10' [[n?]] = (d / (d - d')) = (10' / 10") = 60 ([[n?]] - 1) = 59 d' = ((59/60) * d) For the first class, substitute ([[n?]] + 1) for ([[n?]] - 1) in the pre-