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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Bowditch Table 15
From: Bill B
Date: 2005 Jan 26, 19:44 -0500

```George wrote:

> In fact, working on those simplifying assumptions, the "simple
> trigonometry" would be to use
>
> distance in feet = height in feet / tan angle
>
> or distance in miles = height in feet / (6080 tan angle)
>
> or (as near as dammit) for 106 ft height at a mile distant you will see an
> angle of 1 degree. Smaller angle, then proportionately bigger distance.

> But then, to follow that text directly with the formula for Table 15,
> without further comment, is just crazy. Because that formula DOES allow for
> the fact that the Earth isn't flat, and it DOES allow for refraction!
> That's its whole point.

In reading Jim's quote from chapter 22, it indeed looked like the
explanations for table 15 and table 16 somehow been mixed together, but did
not have time to explore it in depth so deleted that paragraph from my
>
> In my edition, such problems are assisted by using table 41, "distance by
> vertical angle; measured between waterline at object and top of object".
> Does the newer edition carry that table, perhaps with a different number?

Not sure I understand.  For your table 41 is the whole object visible down
to where it meets the body of water?  If so, this is table 16 in the 1995
edition.

There are three tables in the 1995 edition for finding distance by vertical
angle.

Table 15, where one can see the top but not the water/base and knows the
objects height above sea level.  Angle measured from top to visible horizon.

Table 16, where one can see the top and the base/waterline and know the
height above waterline.  Angle measured from the top to base/sea level.
This is the one that claims to use geometry, flat earth, etc.  No mention of
subtracting dip in the explanation.

Table 17, where one does NOT know the height of the object but can see the
base/waterline intersection and horizon beyond it (above the intersection of
course).  Angle is measured from horizon to base/waterline.  Again no
mention of dip correction but height of eye is accounted for when entering
the table.  It is an odd table, as the instructions claim one should enter
the table with "the height of eye of the observed in nautical miles,"
corrected sextant angle, and the output is in yards.  Just to certain you
don't miss the "nautical mile" reference, it is italicized.  Ah, but the
legend on actual table calls for "Height of eye above the sea level, in
feet."  Go figure!!

Bill

```
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