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Re: Table on Davis Quadrant
From: Nicolàs de Hilster
Date: 2007 Sep 22, 17:43 +0200
From: Nicolàs de Hilster
Date: 2007 Sep 22, 17:43 +0200
My archives are better than I imagined as they contained the answer to
my own question:
The article Davis' Quadrants in America by Deborah Jean Warner in Rittenhouse (1988) shows the same table on page 36. About it she writes:
Nicolàs
Nicolàs de Hilster wrote:
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The article Davis' Quadrants in America by Deborah Jean Warner in Rittenhouse (1988) shows the same table on page 36. About it she writes:
On most of his Davis's quadrants [Benjamin] King included a chart ofThe instrument I was mentioning was indeed built by Benjamin King, made in 1755 for Captain George Buckmaster.
latitude and departure for every 1/4 point, up to 4 points, on the back
of the 30° arc. This chart was a simplified version of one that would
have been available in most navigational texts of the period. With the
chart and a glance at his compass, a navigator could easily know the
relation between his distance in a north-south direction and his
distance in an east-west direction. (360° = 32 points, so 4 points =
45°)
Nicolàs
Nicolàs de Hilster wrote:
Dear group,
last week I got in contact with an owner of a Davis Quadrant. On the back of the large arc the following table is inscribed:
L
D
L
D
L
D
L
D
¼
100
5
1¼
97
24
2¼
90
43
3¼
80
60
½
99
10
1½
96
29
2½
88
47
3½
77
63
¾
99
15
1¾
94
34
2¾
86
51
3¾
74
67
1
98
20
2
92
38
3
83
56
4
71
71
In simplified form we could change this into:
L D 0.25 100 5 0.50 99 10 0.75 99 15 1.00 98 20 1.25 97 24 1.50 96 29 1.75 94 34 2.00 92 38 2.25 90 43 2.50 88 47 2.75 86 51 3.00 83 56 3.25 80 60 3.50 77 63 3.75 74 67 4.00 71 71
The table lacks an entry for 0.00, which would most probably have read L=100 and D=0. The figures in columns L and D can also be calculated using simple math:
L=COS(a*b)*100
D=SIN(a*b)*100
In above formulae 'a' stands for the value in the first column (so 0.25, 0.50, 0.75 etc) and 'b' is a constant. Using the least squares method I was able to calculate 'b' as 11.266, so the formulae used were:
L=COS(a*11.266)*100
D=SIN(a*11.266)*100
Question that remains is: what use was this table to a navigator?
Anyone any idea?
best regards,
Nicolàs
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