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I'm reading "Finding North America - Longitude by Wire" by Richard Stachurski which chronicles the formation of the U.S. Coast Survey, 1832, and the creating of the first set of accurate costal charts. Thanks to John Howard for mentioning this book, it’s a good read.

The survey team faced an interesting celestial navigation problem - how to find the LATITUDE of important grid triangulation points used as references when creating charts.

I was quite surprised in the method they used to determine refraction and the accuracy they claimed.

Ferdinand Hassler, the survey leader, used theodolites to measure star altitudes at meridian passage. Although almanacs published star declinations, they were not trusted.

Andrew Talcott, a West Point engineer graduate, developed a technique using the zenith distances of two stars culminating within a short time of each other and on opposite sides of the observer's zenith.

Quoting from the text:

"Talcott reasoned that if refraction error grew larger as the zenith angle became greater, it made sense to use stars close to the zenith. Even better, the surveyor could use pairs of stars, S and S' that crossed the meridian, one to the south of his zenith and one to the north, and measure only the small zenith distance between them, z-z'. The latitude then is equal to one-half of the sum of the declinations, d+d', added to one-half of the distance z-z'. ... the correction for refraction is very small, being the difference merely between the two refractions on either side of the zenith.  For a pair of stars with zenith distances out to thirty-five degree and z-z' equal to twenty-four seconds of arc, the refraction correction was a minuscule 0.31 seconds of arc. Combined with improvements to the meridian telescopes used to make the observation, the Harrebow-Tallcot [1] method produced latitude results accurate to 0.1 second of arc, or ten feet."

Ed Popko

[1] Although Talcott's method was considered unique at the time, it was actually invented a hundred years earlier in 1730 by astronomer Peder Harrebow but lost to history or considered unimportant at the time. Today, this technique is called the Horrebow-Talcott Method. See also
Wikipedia, Peder Horrebow, en.wikipedia.org/wiki/Peder_Horrebow