Last week, we saw how, starting in the late 1600s, astronomers published almanacs of predictable celestial events, in particular the eclipses of Jupiter's four bright ("Galilean") moons, allowing travelers anywhere in the world to compare their local time with almanac time, thus giving them their longitudes. Let's see how that worked in real life, especially in North America.

Within a few years of publication, cartographers used Cassini's Connaisance de Temps to redraw the map of Europe, which was mostly unchanged since Roman times. On seeing the new map (see illustration), the French king is supposed to have complained that his mapmakers had stripped more land from France than in all the wars fought by all his predecessors. Not to be outdone by the Paris Observatory, which had published Cassini's tables, the Royal Observatory in Britain began issuing its own Nautical Almanac in 1766, stating that its predictions for eclipses of the Galilean moons "are well known to afford the readiest and ... best method of settling the longitudes of places at land."

Which is fine if you have a decent 40-power telescope to fix the exact time of immersion (disappearance behind Jupiter) or emersion (reappearance) of one of the Galilean moons. Alexander Mackenzie, who in 1793 became the first white explorer to complete an east-west traverse of the American continent, schlepped a heavy London-made brass telescope. Upon reaching Dean Channel on the coast of (what is now) British Columbia and having determined local noon with a sextant (and setting his watch accordingly), that night he was able to time emersions of Ganymede and Io with his telescope. He thus determined his longitude by comparing his timing with "Greenwich time" of the same events listed in his Nautical Almanac.

In an accident of history, Mackenzie just missed meeting Capt. George Vancouver, who had explored Dean Channel just six weeks earlier. Vancouver, a skilled navigator, used both marine chronometers and "lunar distances" to determine longitudes. (The latter is another celestial navigation trick, using a sextant to measure the angle the moon makes with a bright star and comparing this with what is predicted in an almanac.) Vancouver determined the latitudes and longitudes of prominent features along the Pacific Coast, including Cape Disappointment on the north side of the mouth of the Columbia River, near where Meriwether Lewis and William Clark wintered 12 years later, 1804-1805.

Lewis and Clark were army men, not trained surveyors, and their attempts at fixing locations along their route were mostly unsuccessful. Clark's map (published in 1814, a full eight years after their return) was anchored not on data obtained during the expedition, but on three previously known points: their starting point, St. Louis; the approximate midway point, Fort Mandan, the location of which had been fixed by professional surveyor David Thompson in 1797 using lunar distances; and Cape Disappointment. Clark mapped the rest by dead reckoning, which explains, for instance, his 50 percent overestimate of the width of the Rocky Mountains.

Today my iPhone receives GPS data from satellites 12,000 miles overhead, giving — almost instantly — my location to within about 25 feet. What would those doughty navigators of old have given for such convenience?