# NavList:

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

**Bowditch Table 9**

**From:**Martin Gardner

**Date:**2002 Apr 11, 07:21 -0700

First things first - I'd like to introduce myself. I'm Martin Gardner, but not _the_ Martin Gardner. That should save some correspondence. I've been lurking with interest for a few weeks. A couple days ago, I was fooling around putting some formulas on my Palm. One of them was the formula to compute table 9 in Bowditch. To review: Table 9 is "Distance by Vertical Angle Measured between Sea Horizon and Top of Object Beyond Sea Horizon". "Angle" runs from -4 minutes (a puzzle in itself) to +30 degrees; "Difference in feet between height of object and height of eye of observer" runs from 25 feet to 2000 feet The formula given in my 1981 Bowditch is Distance = sqrt ( ((tan A)/0.0002419)**2 + (H-h)/0.7349 - (tan A)/0.002419 ) I plugged this into my calculator and got hopelessly wrong results. Naturally I figured I'd keyed wrong, and checked and checked. (Maybe I did key wrong......but damned if I can find it) Then I looked more closely: (1) I do match table 9 for A=0 - so I keyed the middle of the three terms correctly. (2) An Ocean Navigator reference page on navigation repeats this formula, but in their case both of the ...2419 constants have three leading zeros, contrary to my Bowditch. (3) The current online Bowditch leaves the third term outside the sqrt - probably a typesetting error. I tried these variations of the formula without success. More serious: as I read the formula, we are taking the sqrt of three terms of the form A**2 + B - A Which will get larger with increasing A (if A is > 1 - which is true for angles over 1 minute) So the formula, as I understand it, is going the wrong way - producing larger distances for increasing angles.... Please help me find my error or -- gasp -- an error in Bowditch. Thanks, Martin Gardner Venice CA