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

**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 reply. But you are spot on George. What a proof reader! > > 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