Longitude by Patterson's Formula

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Longitude Observation of October 3, 1805, for Clearwater Canoe Camp

Patterson's Problem 5, 2nd Example1

table of 20 enumerated calculation steps

The following procedure departs from Patterson's method and uses linear regression to find the Greenwich Apparent Time for the True Distance:

table with 6 steps of calculations

Did the captains really make a first-rate observation here, or was it just luck that the longitude calculated from it comes so close to the actual of 116°19'46" West? The other Lunar Distances produced longitudes that were much too far east: that on September 30 with the sun produced a longitude of 115° 46' West, and that on October 6 with Altair produced a longitude of 114°49'. For the second Lunar Distance observation on October 6 the captains identified their target star as Aldebaran, but it was some other star.


1. Thomas Jefferson asked Robert Patterson (1743-1824), professor of mathematics at the University of Pennsylvania, to help Lewis develop his skills in making celestial observations. Jefferson wrote to Patterson on May 2, 1803: "He [Lewis] has been for some time qualifying himself for taking observations of longitude & latitude to fix the geographical points of the line he will pass over, but little means are possessed here [in Washington City] of doing that; and it is the particular part in which you could give him valuable instruction, & he will receive it thankfully & employ it usefully." For the benefit of his pupil, Patterson wrote an instruction manual that is now known as the Astronomy Notebook. Donald Jackson, Letters of the Lewis and Clark Expedition with Related Documents, 1783-1854 (2 vols., Urbana: University of Illinois Press: 1978), 1:21, 28-31.

Funded in part by the Idaho Governor's Lewis and Clark Trail Committee