NavList:

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:

On most of his Davis's quadrants [Benjamin] King included a chart of
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°)

The instrument I was mentioning was indeed built by Benjamin King, made in 1755 for Captain George Buckmaster.

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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