NavList:

Sir William Thomson ("On the Determination of a Ship's Place from Observations of Altitude," The Nautical Magazine, April 1871) says,

"The ingenious and excellent idea of calculating the longitude from two different assumed latitudes with one altitude, marking off on a chart the points thus found, drawing a line through them, and concluding that the ship was somewhere on that line at the time of the observation, is due to Captain T. H. Sumner. It is now well known to practical navigators."

Instead of reducing a sight twice with different assumed latitudes, Thomson says the same result may be obtained from one assumed latitude and an azimuth. But that would involve about as much work.

"It has occurred to me, however, that by dividing the problem into the solution of two right angled triangles, it may be practically worked out so as to give the ship's place as accurately as it can be deduced from the observations, without any calculation at all, by the aid of a table of the solution of the 8,100 right angled spherical triangles of which the legs are integral numbers of degrees."

https://archive.org/details/the-nautical-magazine-1871/page/n223/mode/1up?view=theater

Thomson's method is mentioned in Bowditch (1984 p. 587):
"A table of only nine pages by Sir William Thomson, better known as Lord Kelvin, was published in London in 1876 to provide a solution for the longitude. This very thin volume, called 'Tables for Facilitating Sumner's Method at Sea,' contains the first known solution by dividing the navigational triangle into two right triangles... Although the tables are among the shortest of the various methods, their manipulation is difficult."

--
Paul Hirose
sofajpl.com