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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:**George Huxtable

**Date:**2005 Jan 25, 14:00 +0000

It seems that we're not yet finished with the Bowditch Table 15 (Table 9 in my earlier edition) I transcribed into emailese, writing A instead of Alpha, the expression in my edition (1981 vol 2) of Bowditch as- d = sqr { (tan A / .0002419 )^2 + ((H-h) / .7349) - (tan A / .002419) } in which d is the distance in nautical miles, A is the corrected vertical angle, H is the height of the top of the object above sea level in feet, and h is the height of the observer above sea level in feet. The constants .0002419 and 0.7349 are parameters which characterise the effect of terrestrial refraction. Is the expression and the text the same in later editions? Somebody please state, for my benefit, the expression for d as given in a more recent edition. I wrote- To me, it seems a bit suspicious that that text refers to "The constants .0002419 and 0.7349", although a third, and different, constant of .002419 also appears to be used in the expression. Is that a misprint, I wonder? But it seems me there's more wrong with the expression I quoted above than a simple matter of the number of decimal places in a constant term. When the angle =0, then the expression gives the same results as does the table, but the two seem quite inconsistent in the way they vary with the angle. I've no reason to believe that the numbers in the table are wrong (on the other hand, no reason to be certain that they are correct). But the numbers in Table 9 and the expression in the text for Table 9 are quite inconsistent. Just to check that my Table 9 and the later Table 15 are the same, here are two spot values to compare- angle = 0', H-h = 100 ft., distance 11.7 miles angle = 1 deg 50', H-h = 450 ft., distance = 2.3 miles Does Table 15 give those same values? It strikes me that this must be a common problem in surveying, the angular elevation, above the true horizontal, of some object at a certain distance that's at a certain height above the observer, and the solution must be well-known. Otherwise, someone will just have to deduce it from first principles. George. ================================================================ contact George Huxtable by email at george@huxtable.u-net.com, by phone at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ================================================================