Measuring the Falls of the Missouri

Rainbow Falls--Lewis's "handsom Falls"--late in a season of unusually low water

Rainbow falls dry

How did Clark manage to measure the heights of the falls with such precision that he could say one was "26 feet 5 inches," another "14 feet 7 inches," a third "47 feet 8 inches," and declare the "great pitch" to be 87 feet and three-quarters of an inch?

He did not specify exactly where he measured each fall. If there was any bedrock visible along the brink, that may have determined his point of reference, for it would be higher than the water level on the date of the observation. If all the rock was covered, he must have measured from the surface of the water at the brink. Nor can we know where or how he delineated the bottom of any fall, obscured as it was by foam and spray.

On Monday, June 17, 1805, Clark and five of his men, including Alexander Willard, John Colter, and perhaps Joseph Field, began the survey by hiking southeast up Portage Creek, then southwest through the "open roleing Prarie" past the heads of two ravines, then turning northeast toward the river, striking it at the mouth of the "Deep Ravine" near the "Rapids of 13 feet descent." (See Clark's map).

Here, he noted, the river is "narrow & Confined in perpindicular clifts of 170 feet," while "from the tops of those Clifts the Countrey rises with a Steep assent for about 250 feet more." They "proceeded up the river passing a Succession of rapids & Cascades to the Falls, which we had herd for Several miles makeing a dedly Sound."

Circumferentor, or Surveyor's Compass

Use cursor to rotate and open compass cover. Drawing and animation by Bob Gilman.

Measuring the falls could be dangerous work. "I in assendending the Clifts to take the hith of the [grand] fall was near Slipping into the water, at which place I must have been Sucked under in an instant, and with deficuelty and great risque I assended again, and decended the Clift lower down (but few places Can be descended to the river) and took the hight with as much accuracy as possible with a Spirit Leavels &c." Those last five words contain the only clue Clark left as to the method by which he took his measurements. No more was necessary, in fact, for as an experienced surveyor in Kentucky and the Old Northwest, he was conversant with a variety of methods and instruments suitable for his purpose. For some insights into what those might have been, we need only look to their traveling library, and to Robert Gibson's Theory and Practice, the leading contemporary book on surveying.

Sextant with Nonius

Click and move the cursor slowly left or right to rotate the image. The nonius, with the "microscope" or reading lens that Lewis directed to be added, is on the lower end of the index arm.3
Drawing and animation by Bob Gilman.

The captains had with them an encyclopedic reference work known as Owen's Dictionary, which contained an article on "Heights & Distances" describing six methods of measuring inaccessible vertical objects, each employing basic trigonometry.1 Thus, Clark only needed to determine one or two angles, plus the length of a baseline between himself and the fall to be measured. See the procedures Clark may have followed, as illustrated in Owen's Dictionary.

Clark's "&c." may have referred to any of several instruments at hand with which he could have observed the necessary angle(s)2: 1) The circumferentor, or surveyor's compass, with its glass cover removed, could be turned on one side. With a plummet, or plumb bob, suspended from its center by a thread or horsehair, and the sights aimed at the top of the fall, the angle between that point and the base of the fall could be read on the compass. 2) The circular protractor with index arm, which he employed in drawing maps, could have been used in a similar fashion. 3) The sextant that the captains used for making celestial observations was fitted with a magnifier with which angles could be measured on the "nonius" down to 7.5 seconds of arc. Given a clearly-defined top and bottom to a fall, the measurement could have been accurate to within a fraction of an inch. Gibson's Theory and Practice of Surveying recommended this as "most to be depended on."5 4) The "Spirit Leavels" on the circumferentor in horizontal position, would have been used to determine an observation point on the riverbank that would be level with the bottom of the fall, and from which the baseline would be measured. 5) The two-pole surveyor's chain would have been used to measure the baseline.

If Clark's knowledge of basic trigonometry was too limited to solve equations such as those in the Dictionary article, he could have plotted the observed angles on paper using the plane table, which he evidently employed in map-making.6 He could then have measured the heights at scale. His protractor to would also serve to plot the triangles to scale.

Still, we must acknowledge Clark's statement that while climbing the "clift" to measure the Great Fall he slipped and nearly fell to his death in the river. A view of that cliff, which is on the far side of the river in this photo (the original waterfall is below the spillway), suggests the sympathetic rejoinder, "No wonder!"

Rainbow falls
The Great Fall, with springtime high water pouring over the spillway of Ryan Dam.

The author appreciates assistance from Donald Ebbutt, Professional Land Surveyor; member, Montana Association of Registered Land Surveyors, and Surveyor's Historical Society; and Bill O'Keefe, formerly superintendent of Montana Power Company dams on the Missouri River.

1. A New and Complete Dictionary of Arts and Sciences; comprehending all the branches of useful knowledge, with accurate descriptions as well of the various Machines, instruments, tools, figures, and schemes necessary for illustrating them, as of the classes, kinds, preparations, and uses of natural productions, whether animals, vegetables, minerals, fossils, or fluids. . . . The whole extracted from the best authors in all languages, by a Society of Gentlemen. 8 parts in 4 vols. ( London: Printed for W. Owen, 1754-1755). The edition referenced here is in the Special Collections Library at Lewis and Clark College, Portland, Oregon. We are indebted to archivist Doug Erickson and assistant archivist Jeremy Skinner for their cooperation.

2. See Silvio A. Bedini, "The Scientific Instruments of the Lewis and Clark Expedition," in James P. Ronda, ed., Voyages of Discovery: Essays on the Lewis and Clark Expedition (Helena: Montana Historical Society Press, 1998), 143-65.

3. Jackson, Letters, 1:82; Moulton, Journals, 2:410-411.

4. Robert Gibson, The Theory and Practice of Surveying (New York: Evert Duyckinck, 1821), 180-187. Collection of Donald Ebbutt, Missoula, Montana. Gibson's first book, Treatise of Practical Surveying, was published in Dublin in 1738. The first American version (Philadelphia, 1785) and subsequent editions, served as the basic text in the art of land and marine surveying until the middle of the nineteenth century.

5. Ibid., 190-195.

6. "A plane table is an oblong of oak, or other wood, about 15 inches long, and 12 broad; they are generally composed of 3 boards, which are easily taken asunder, or put together, for the convenience of carriage. There is a box frame, with 6 joints in it, to take off and put on as occasion serves; it keeps the table together, and is likewise of use to keep down a sheet of paper, which is put thereon. The outside of the frame is divided into inches and tenths, which serve for ruling parallels or squares on the paper [evidently used by Clark in drawing many of his maps, as seen in Moulton, Atlas, passim]. . . . The inside of the frame is divided into 360 degrees, which, though unequal on it, yet are the degrees of a circle produced from its center, or centre of the table, where there is a small hole. The degrees are subdivided as small as their distance will admit; at every tenth degree are two numbers, one the number of degrees, the other its complement to 360." Gibson, 176-177.