Latitude

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Latitude of the Three Forks

While at camp on Camp Island near the Three Forks of the Missouri, Meriwether Lewis took two observations of the sun's noon (meridian) altitude for latitude. He calculated latitudes from these observations and, from them, obtained an average of 45°24'08.5" N. Lewis's average, unfortunately, lies more than 36 miles south of the camp's redetermined latitude of 45°55'44" N (see Table I). The principal reason for this difference stems from Lewis'suse of the wrong index error for his octant.

If Lewis had used an index error of 2°11'40.3"1 instead of 2°40' and an estimated longitude of 111° W when he calculated the latitudes from these observations he should have derived an average latitude for this camp of 45°51'02" N. This latitude, however, still is about 4'42" (5½ miles) too far south of the redetermined latitude for the expedition's camp on Camp Island.

This difference in latitude could have resulted from observational errors that Lewis made, but it is much more likely that the octant, though made of seasoned wood, had warped slightly from the low humidity that is so common to southwestern Montana summers, thereby changing the octant's index error. Lewis should have checked the index error of both octant and sextant regularly because handling, transporting, humidity and temperature can affect the index error of these sensitive instruments.

Table I, Latitude of the Three Forks Camp
Date Lewis, 1805 Recalculated
(This study)
Redetermined latitude
(map evaluation)
1805 July 28 45˚24'54" north 45˚50' 04" north  
1805 July 29 45˚23'23" north 45˚51' 59" north  
Average 45˚24'08.5 north 45˚51' 02" north 45˚55'44"

On Clark's map of 1805, made while at Fort Mandan, two possible "three forks" are shown. The northernmost is at a latitude of about 45°35' N, the other is at 44°19' N. The latitude shown for the Three Forks of the Missouri on the Lewis and Clark map of 1806 is about 45°30' N, on Clark's map of 1810 it is about 45°20' N and on the Lewis and Clark map of 1814 it is 45°10' N.


1. This is the value Lewis recorded in 1804 in his journal entry for July 22 (see Moulton, Journals 2:411) and again in the Fort Clatsop Miscellany (ibid., 6:496). Even though Lewis left no calculations for us to evaluate, by calculating in reverse from the latitude Lewis derived, it is possible to determine the index error he must have used for these calculations. Lewis's calculated latitude for 1805 July 29 = 45°23'23".

  90˚
Zenith [this calculation can be omitted]
45˚23'23"
latitude that Lewis derived
  44˚36'37"
co-latitude,
+ 18˚45'36.7"
declination (Lewis may have used a slightly different value)
  63˚22'13.7"
true altitude of sun’s center
– 00˚15'47.2"
sun’s semidiameter
– 00˚00'04"
parallax
+ 00˚00' 24.5"
refraction
  63˚06'47.0"
apparent altitude
x 2
 
  126˚13'34.0"
double altitude because of artificial horizon
  180˚
 
  53˚47'26"
observed angle + index error
  59˚07'
observed angle
+ 5˚20'34"
octant’s index error
÷ 2
 
+ 2˚40'17"
after rounding = +2˚40' = half index error (correction = -2˚40'). This value of 2˚40' is the (half) octant error that Lewis recorded on April 12 at the mouth of the Little Missouri River and incorrectly used throughout 1805 except at Camp Fortunate.

Funded in part by a grant from the National Park Service, Challenge-Cost Share Program