A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
From: Robert Pearson
Date: 2016 Nov 5, 18:59 -0700
Sumner's method for lop solved a "time sight" twice for longitude using 2 different latitudes that differed only by a small amount - Frank suggests 0.1 deg. Plotting the 2 positions and drawing a straight line between them gives us a chord of the circle of position (cop) corresponding to the measured altitude. Marc St Hilaire's intercept method for lop gives us a distance between 2 cops one thru the ap and one corresponding to the measured altitude. With St Hilaire's method we also calculate the azimuth from the ap to draw the tangent to the cop corresponding to the measured altitude at the point where it intersects the azimuth line. Both methods give a good approximation to the same cop.
We also have modified Sumner methods that solve the time sight for longitude and also the azimuth from that position. The resulting lop plotted thru that tangent to the azimuth would also approximate the cop thru the one position found. In fact it would be the same lop found by the St Hilaire method if the ap was the position found by time sight. Lops found by these methods were all called Sumner lines.
Sumner's method came 1st by many years (1837 vs 1875) and if memory serves me well both were used in the US Navy in preference to the time sight for longitude. In the US merchant marine officers preferred the time sight and noon sights to a much greater extent maybe up to WW I even.
To recap: with Sumner we solve 2 spherical triangles for 2 position points but they use the same altitude and declination. With St Hiliare we solve 1 spherical triangle for altitude and azimuth. Both give accurate results for ordinary navigation. Manual calcs using tables/logs vs calculator methods might favor one method over the other or as in the past familiarity and personal preference might also play a role.
I guess what goes around comes around - right Frank.