NavList:

Frank wrote

Exactly but bypass the intercept method, and then you don't even need to cheat on azimuth. We only need azimuth if we force ourselves to use the intercept method. But if we're using a calculator, we don't have to do that and can generate our celestial lines of position as "two-point" geometric objects instead of "pont-slope" objects. In fact, you've written about this before, David C. It's a great idea! So "great" that this is one of the key methods that I teach in my "modern celestial navigation" workshops. As for the math, it's the same equation that we know for altitude (which is also identical to the standard great circle equation), arranged a bit differently, and you use it twice to generate longitude from two "assumed" latitudes. No need to learn or puzzle over a separate azimuth equation.

I agree that if you have a calculater  the Sumner chord method is easier than the intercept method. Plotting two lat/lon points (calculated by calculator) and drawing a line between them is IMHO much easier than plotting a point, measuring an angle, drawing and measuring a line and then drawing a second line at right angles. This is a variation on the time sight method except that the result is a position line rather than a longitude that is dependant on an (in)accurate latitude. Also not having to calcuate azimuth eliminates the NSEW to 360 degree confusion.

I believe that  the chord method (two points) was Sumner's original method. The later tangent method (point plus azimith) reduced the amount of computation if tables were available for azimuth.

Do you mention Sumner in your course? Some years ago I remember using the terms Sumner Chord and Sumner Tangent and you commented  that the the terms were unnecessary and created confusion?