Talcott's career was as a military and civil engineer building forts, roads and railroads both in the States and Mexico. He started the 1824 construction of Fort Adams in Newport, Rhode Island. In 1833 he extended a previously invented method of finding latitudinal direction. He rediscovered the method to determine a place's latitude from the stars, a method originally invented by the Danish astronomer Peder Horrebow. On further developing Horrebow's method, it subsequently came to be known as the "Horrebow-Talcott Method". The so-called Horrebow-Talcott method fixed latitude "by observing differences of zenith distances of stars culminating within a short time of each other, and at nearly the same altitude, on opposite sides of the zenith."