TL;DR: The ex-meridian problem has been studied extensively in the history of nautical astronomy as well as the double altitude problem as mentioned in this paper, and many ingenious solutions have been contrived and a diversity of exmeridian tables were constructed, all aimed at facilitating the problem of finding latitude at sea.
Abstract: The method of finding the latitude of a ship at sea from an observation of the Sun or other body near the meridian is practised extensively in the Merchant Navy. The history of the method, which dates from the middle of the eighteenth century, is full of interest: and the ex-meridian problem is almost as celebrated in the history of nautical astronomy as the double altitude problem. Considerable attention was devoted to the ex-meridian problem during the last century—a period which was, in truth, the golden age of astronomical navigation. Many ingenious solutions were contrived and a diversity of ex-meridian tables were constructed, all aimed at facilitating the problem of finding latitude at sea.
TL;DR: In this paper, the error introduced by taking the maximum altitude of a heavenly body for its meridian altitude is not sufficiently great to need correction when it is due to variation of declination alone, as it is then much within the probable errors of observation.
Abstract: IN navigation the error introduced by taking the maximum altitude of a heavenly body for its meridian altitude is not sufficiently great to need correction when it is due to variation of declination alone, as it is then much within the probable errors of observation. When, however, a ship is steaming at a highspeed, the error is considerably increased by the variation of latitude, especially when this is of opposite sign to the variation of declination.