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Heights and Distances

We'll probably never know with any certainty how to interpret Clark's phrase, "Spirit leavels &c.," and it really doesn't matter. All that matters is that he "took the hight with as much accuracy as possible." We may interpret that literally.

--Joseph Mussulman; 11/03

1. "It is called the Rule of Three from having three numbers given to find a fourth but more properly, the Rule of Proportion, because by it we find a fourth number proportional to three given numbers: and because of the necessary and extensive use of it, it is called the Golden Rule." s.v. Proportion: "When two quantities &are compared, the former term is called the antecedent and the latter the consequent....Thus the ratio of...two numbers in geometrical proportion, is found by dividing the antecedent by the consequent, and the quotient is the exponent or denominator of the ratio." Owen's Dictionary, Rule of Three.

2. Jefferson had recommended to Lewis that he take a theodolite, with which both horizontal and vertical angles could be measured. However, Andrew Ellicott and Robert Patterson, Lewis's mentors on such matters, advised against it on the grounds that the instrument was too fragile to be dependable. Instead, Lewis took an octant. Donald Jackson, Letters of the Lewis and Clark Expediton, with Related Documents, 1783-1854 (2nd ed., 2 vols., Champaign: University of Illinois Press, 1975), 1:48.

3. Owen's Dictionary, s.v. Trigonometry: "Case II. The angles and one of the legs given, to find the hypothenuse. Example: In the triangle ABC, (ibid. no 4.) suppose AB 124, and the angle A 34°, 20 .; consequently the angle C 55°, 40 . required the hypothenuse AC, in the same parts with AB. &Geometrically, & the hypothenuse, AC, is found, by taking its length in your compasses, and applying that to the same line of equal parts from which AB was taken."

4. Ibid.: "Case III. The angles and hypothenuse given, to find either of the legs. Example: In the triangle ABC, &suppose the hypothenuse AC = 146, and the angle A = 36°14 .; consequently the angle C = 53° 35 .; required the leg AB. &Geometrically: draw the line AB at pleasure, and make the angle BAC equal to 36°, 25 .; then take AC equal to 146 from any line equal parts; lastly, from the point C, let fall the perpendicular CB, on the line AB. So the triangle is constructed, and AB may be measured from the line of equal parts."

Funded in part by a grant from the Montana Cultural Trust.

From Discovering Lewis & Clark ®, http://www.lewis-clark.org © 1998-2014
by The Lewis and Clark Fort Mandan Foundation, Washburn, North Dakota.
Journal excerpts are from The Journals of the Lewis and Clark Expedition, edited by Gary E. Moulton
13 vols. (Lincoln: University of Nebraska Press, 1983-2001)