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In the Monthly Notices of the Royal Astronomical Society, April 1857,
W. H. Simms writes at the conclusion of his article on sextant corrections:

"A traveller on land treating the sextant in the manner above described
ought very readily to obtain his latitude to the nearest second of arc:
and if the results of his lunar distances be subsequently corrected for
the errors in the tabular elements of the moon's place, his longitudes
will probably be in most instances much within ten seconds of time from
the truth."

That seems optimistic to me, but make up your own mind:

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?journal=MNRAS&year=%3f%3f%3f%3f&volume=..17&letter=.&db_key=PRE&page_ind=175&plate_select=NO&data_type=GIF&type=SCREEN_GIF&classic=YES

Looking at the Monthly Notices in the 1850s I see many articles on
chronometers, lunars, etc. There's even a proposal for what today we
would call a bubble sextant.

http://adsabs.harvard.edu/journals_service.html

Select the desired periodical in the list, and enter the volume number
in the box above. If you leave the other boxes (page number etc.) empty,
a table of contents for that volume will appear, from which you can
select articles.

Often an excessive number of thumbnail images appear. With a slow
connection it's better to turn browser graphics off, and right click on
on images to view them.

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