Widths of the Columbia and Ki-moo-e-nim (Snake) Rivers
Measured the width of the Columbia River, from the point across to a point of view is S22°W; from the point up the Columbia to a point of view is N84°W, 148 poles, thence across to the 1st point of view is S28Ω°E. Measured the width of the Ki moo e nim River, from the point across to an object on the opposite side is N41Ω°E; from the point up the river is N8°E, 82 poles, thence across to the point of view is N79°E. Distance across the Columbia is 960-3/4 yards water Distance across the Ki moo e nim 575 yards water.
–William Clark, 18 October 1805
In the morning of October 18, 1805, while Lewis and an assistant were taking celestial observations, Clark and several others were taking measurements to determine the width of the Columbia and Snake rivers near their junction. Clark used triangulation, and his method was relatively straightforward.
Survey Instruments – Two instruments were needed to make the surveys for river width: a circumferentor (six-inch-diameter surveying compass) and a two-pole chain (a measuring device 33-foot long, composed of 50 chain links, each 7.92 inches long).
The Survey – Clark, having already chosen the junction point of the rivers as his starting point (call it "A") from which to begin his survey, examined both rivers upstream from the junction. He needed to make sure the shorelines were straight enough and long enough to provide good baselines1 for the triangulation. He then looked for a conspicuous landmark such as a large rock or distinctive tree upstream on the opposite side of the Columbia ("B") and another upstream along the Snake ("D"). While the men, with the two-pole chain, measured the distances between "A" and "B" (148 poles) and "A" and "D" (82 poles), Clark set up and carefully leveled his surveying compass on the point ("A"). From "A" Clark shot the magnetic bearing (South 22° West) to a prominent object ("C") on or close to the far shore of the Columbia River, then shot a bearing upstream along the base line (North 84° West) to "B". After recoding the bearing he had observed, he moved his surveying compass to "B" and shot the bearing (South 28Ω° East) across the river to "C" and recorded that bearing and that of the distance of the base line. That done, the surveying part of the operation for the Columbia River was complete.
Plotting instruments – 1) a ruler to draw straight lines and measure line lengths and 2) a protractor to mark off the angles that he had measured.
This is how Clark might have proceeded to determine the rivers' widths:
Clark used his ruler and plotted the base line for the Columbia River at a convenient scale.2 Then, setting the center mark of his protractor over "A" and aligning the protractor so that the mark for N84°W fell on the extension of the line through "B", he marked off the magnetic bearing he had shot from "A" to "C" (S22°W) and drew a line from "A" through that mark. He then placed the center mark of the protractor over "B" and aligned the protractor so the base line going back through "A" fell along the mark for S84°E. He then marked off a bearing of S28Ω°E and drew a line from "B" through that mark. The intersection of the lines from "A" and "B" marked the location of "C" on the opposite shore. With his ruler, Clark then measured the shortest distance between the base line and "C", then converted that measurement to actual distance. In doing so he obtained the river's width without getting his feet wet.
Actually, the surveying operations at the mouth of Snake River were a little more involved than outlined above. Clark also had designated a point ("D") on the shore upstream along the Snake River to be the end of a second base line, and the men also measured the distance from "A" to "D" with the two-pole chain. Clark, before moving to "B" also shot a bearing from "A" to "D" and to "E" (a point on the far shore of the Snake River). After shooting the bearing to "C" from "B", Clark moved his surveying compass to "D" and shot a bearing to "E" on the far shore of the Snake River. He then plotted his survey of the Snake River's width in the same manner as he did for the Columbia River.
In triangulation where precision is not critical, using a ruler and protractor is a convenient means of determining the approximate distance to an object not easily reached. For precise work, such as in Geodetic Triangulation, trigonometry is used. By trigonometry, the width of the rivers (from Clark's survey data) are:
Depending upon the scale of the plot Clark made, the widths that he derived by scale and protractor easily should have been within plus or minus 2 poles (33 feet) of the actual distance. Yet, he recorded a width of 960 yards for the Columbia and 575 yards for the Snake. It is interesting to note that the distances that Ordway, Gass and Whitehouse recorded in their journals from Clark's data, 860 yards and 475 yards, are more nearly correct when compared to the widths derived by trigonometry. Did Clark miscopy his own work?
1. For best results the baseline should not be significantly shorter than the estimated width or distance to be measured.
2. For example: Suppose Clark had only a ruler marked off in sixteenths of an inch. To obtain a measuring precision of no worse than plus or minus 2 poles, he could have plotted his survey at a scale as small as 1 inch = 40 poles ( inch = 10 poles, inch = 5 poles, inch = 2Ω poles, and, by eye to 1 poles). His plotted base line from "A" to "B", then, would have been just a little longer than 3 inches.
3. name="note3u"> The bearing that Clark shot from D across the Snake River to E does not make a right angle with the river's width (shortest distance). By measurement, the width (using Clark's data) is more nearly 70 poles (385 yards).
Funded in part by a grant from the National Park Service's Challenge Cost Share Program