Measuring Heights
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, 17 June 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.”
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.”
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.
The captains had with them an encyclopedic reference work known as Owen’s Dictionary, which contained an article on Owen’s Heights and Distances describing six methods of measuring inaccessible vertical objects, each employing basic trigonometry.[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 … Continue reading 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.
Other Instruments
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!”
Clark’s “&c.” may have referred to any of several instruments at hand with which he could have observed the necessary angle(s):[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: … Continue reading
- 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.
- The circular protractor with index arm, which he employed in drawing maps, could have been used in a similar fashion.
- 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.”[3]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 … Continue reading
- 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.
- The two-pole surveyor’s chain would have been used to measure the baseline. (See below)
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.[4]“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 … Continue reading He could then have measured the heights at scale. His protractor would also serve to plot the triangles to scale.
First Impressions
Clark’s Measurements[5]The journalists referred to it by several names—”great Fall,” “grand Fall,” and “great Cateract.” On U.S. Geological Survey maps today it is labeled … Continue reading
To read Clark’s journal, point to the image.
Missouri Historical Society.
The remark on the upper right side of Clark’s sketch, “This rivine is 2 inches higher up,” meant that the north ravine was actually 200 yards upriver from the location where he showed it—an arbitrary space-saving decision. That “umbrello” that Clark lost in the flash flood (line 14) is discussed in Clark’s Umbrella. Another critical loss suffered in that incident is revealed in “Pomp’s Bier was a Bar”. The omission of figures for the longitude, at lower right, was deliberate. The captains made numerous celestial observations to acquire the data from which was to have calculated the longitude after their return, but that work was never completed.
Clark recounted his first impression of the Great Fall including its height and widths on 17 June, but whether he would have had time to take the measurements on that day is not known.
we proceeded up the river passing a Sucession of rapids &Cascades to the Falls, which we had herd for Several miles makeing a dedly Sound, I beheld those Cateracts with astonishment the whole of the water of this great river Confined in a Channel of 280 yards and pitching over a rock of 97 feet 3/4 of an [inch], from the foot of the falls arrises a Continued mist which is extended for 150 yds. down &to near the top of the Clifts on L Sd. the river below is Confined a narrow Chanl. of 93 yards haveing a Small bottom of timber on the Stard Side which is definded by a rock, rangeing Cross wise the river a little below the shoot, a short distance below this Cataract a large rock divides the stream, I in assendending the Clifts to take the hith of the 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 accuricy as possible with a Spirit Leavels &c.
River Widths
In 1853 the Stevens Railroad Survey’s engineers measured the distance from the Mississippi River to the Great Fall at 2445 miles, and the fall’s height at 76 feet.[6]Isaac. I. Stevens (1818-1852), Narrative and final reports of explorations and surveys to ascertain the most practicable and economical route for a railroad from the Mississippi river to the Pacific … Continue reading The correct latitude is 47° 30′ North; the longitude is 111° 18′ West.
The geometric procedure Clark used to measure the widths of rivers is illustrated in Snake-Columbia Confluence Observations Other ways of making measurements of heights, besides the one Clark said he used, are illustrated in Owens Heights and Distances.
Surveying the Portage Route
Proceeding up the south side of the Missouri on 17 June, Clark conducted a route survey[7]There were three types of surveys common in Lewis and Clark’s time. The oldest, dating from the beginnings of civilization, was the land survey, by which property lines were fixed and land … Continue reading of the falls, rapids, cascades and ravines from the lower portage camp to the upper falls (Black Eagle) and beyond, using a circumferentor (surveyor’s compass) to determine bearings or directions, and a two-pole chain as a measuring unit. His five-man survey party included two chainmen and perhaps a stakeman, a rear flagman, and a record-keeper with a notebook and a pencil.
S. 9° E | 286 | poles to the enterence of portage river 55 yds. wide at 80 poles a rapid of 4 feet, the Computed decent of the water above is 4 feet together makes | 8 |
S 10° W | 270 | Po: from the enterances of portage River up the Lard. Side of the Missouri. the Computed distance the water in this distance is about 10 feet | 10 |
S 10° E | 160 | P. do [ditto] do do do do Decent of | 6 |
South | 240 | Po. do do do do Computed decent of | 18 |
S. 81° W. | 400 |
Po. do do do do Computed decent of[:] passing a deep Small rivene in this Course |
13 |
S 15° W | 160 | Poles the decent of the water within which distance is about five feet river inclosed in rocks | 5 |
S. 75° W | 80 | Poles to the enterance of a Steep rivene at which there is a fall of 3 feet which aded to the probably decent of the water in that distance 2 feet makes | 5 |
N. 82° W | 340 | Poles to the Grand Cataract of 87 feet ¾ of an inch. Computed decent of water in the distance 6 feet. The river at this Cataract 280 yards wide and just below 93 yards wide total[8]The foregoing is the beginning of one of two different sets of survey notes by Clark for the Great Falls of the Missouri. The next course takes him directly to the river. Moulton, 4:310-17, 417n. | 93¾ |
Clark’s Surveying Method
The surveyor’s chain was called Gunter’s, after its inventor, the English mathematician and astronomer Edmund Gunter (1581-1626).[9]Gunter made significant contributions to trigonometry, and perfeted the quadrant. http://www-history.mcs.st-and.ac.uk/Biographies/Gunter.html (accessed June 2015). The length of the chain is 33 feet, or two poles (also called rods or perches) of 16½ feet each. It consists of 50 links separated from one another by three rings. The length of a link, from the center of one connecting ring to the next, is 7.92 inches. Tally tags having one, two, three or four notches divide the chain into five sections, for convenience in measuring distances of less than a full chain. Gunter’s chain served as the basic surveying instrument for three hundred years, until it was replaced in the early 20th century by the steel tape and later in the same century by the Global Positioning System.[10]Gunter’s chain, with its parcel of awkwardly divisible standards of measurement—chain, pole, yard, foot, and inch—also embedded the English statute mile into the very soil and … Continue reading
Clark used the circumferentor to “shoot” a line from the beginning of his survey to the first visible landmark, or object, the mouth of Portage Creek. He might have sent a stakeman to the landmark with a pole, such as an espontoon, to hold erect as a reference point that the circumferentor sights could be aimed on. (Clark paused here to measure the width of the creek with the circumferentor. For that procedure, see Owens Heights and Distances) While the hinder chainman held one end of the chain at the starting point, or station, the fore chainman carried the other end of the chain straight toward the first object. When the chain was fully extended and pulled taught, the hinder chainman signalled the fore chainman to move to his right or left until the chain was precisely on the line between the station and the object. The fore chainman then dropped a plummet (plumb bob), or else a rock, from the handle of the chain, and inserted in the ground at that point one of the ten iron marking pegs he carried.[11]The process is described in detail in Robert Gibson, The Theory and Practice of Surveying; Containing All the Instructions Requesite for the Skilful Pratice of this Art. (New-York: Evert Duyckinck, … Continue reading
The two chainmen then walked straight toward the first object until the hinder man arrived at the first peg, stopping there until the chain was pulled tight, the alignment was checked by Clark with the circumferentor, and a peg marking the fore end of the chain was driven into the ground. The hinder man pulled up the first peg, the two chainmen moved ahead, and the process was repeated until the hinder man had all ten pegs in hand, indicating they had measured ten chains, or twenty poles (330 feet), in a perfectly straight line along the compass bearing Clark had established with the circumferentor. The crew continued similarly until they reach the first object .in this case the mouth of Portage Creek, or a marker of some sort held there to guide them.
All gradients were measured horizontally, rather than on the angle of the grade. To do this, the hinder chainman dropped a plummet from the handle of the chain, and raised his end until the chain and the plummet line formed a right angle. The fore chainman lowered his end if necessary. If the grade was too steep to be measured with the full two-pole chain, they measured the distance in links between the hinder man’s end, as high as he could hold the chain, to the point where it intersected the grade. They then finished out the chain length horizontally from that station point.
There is no identifiable object at the close of any of the next six courses, so it may be presumed Clark sent the stakeman upstream to the next bend. After the stake was observed, and its compass bearing recorded, the whole procedure was repeated, and so on for each course. A rear flagman may have remained at the beginning of each course to serve as a reference point until the next object was reached.
In the brief example cited above, the crew has repeated the chaining steps 968 times on eight different compass bearings, totalling a little over six miles. The complete survey reached 4,747 poles in 22 courses, totalling 14¾ miles and 27 poles (445½ feet). Clark estimated the total descent of the riverbed in that distance at 360 feet, 2¾ inches.
The same process was employed to survey the route for the portage around the falls, which consisted of six courses in 17¾ miles plus 46 poles (759 feet).
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.
Notes
↑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. |
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↑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 | 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. |
↑4 | “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. |
↑5 | The journalists referred to it by several names—”great Fall,” “grand Fall,” and “great Cateract.” On U.S. Geological Survey maps today it is labeled “Big Fall.” The journalists were ambivalent toward “fall” versus “falls,” but “cateract” and “cascade” were always singular. |
↑6 | Isaac. I. Stevens (1818-1852), Narrative and final reports of explorations and surveys to ascertain the most practicable and economical route for a railroad from the Mississippi river to the Pacific Ocean. . . . made under the direction of the secretary of war in 1853-1855. |
↑7 | There were three types of surveys common in Lewis and Clark’s time. The oldest, dating from the beginnings of civilization, was the land survey, by which property lines were fixed and land areas calculated, to facilitate the identification of real property for ownership, sale, or purchase. The cadastral survey fixed the boundaries of municipalities, as well as state and federal jurisdictions, chiefly as the bases for taxation. The route survey was used for siting and constructing roads—and later, railroads, highways, irrigation ditches, levees and transmission lines. During the nineteenth century, topographic, hydrographic, and mine survey techniques evolved, followed in the twentieth century by aerial surveys. |
↑8 | The foregoing is the beginning of one of two different sets of survey notes by Clark for the Great Falls of the Missouri. The next course takes him directly to the river. Moulton, 4:310-17, 417n. |
↑9 | Gunter made significant contributions to trigonometry, and perfeted the quadrant. http://www-history.mcs.st-and.ac.uk/Biographies/Gunter.html (accessed June 2015). |
↑10 | Gunter’s chain, with its parcel of awkwardly divisible standards of measurement—chain, pole, yard, foot, and inch—also embedded the English statute mile into the very soil and substance of the United States as a nation, despite Thomas Jefferson‘s arduous but futile efforts to establish the metric system. Andro Linklater, Measuring America: How an Untamed Wilderness shaped the United States and Fulfilled the Promise of Democracy (New York: Walker & Company, 2002), 102-116. |
↑11 | The process is described in detail in Robert Gibson, The Theory and Practice of Surveying; Containing All the Instructions Requesite for the Skilful Pratice of this Art. (New-York: Evert Duyckinck, 1821), 145-62. Collection of Donald Ebbutt. |
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- The Lewis and Clark Expedition: Day by Day by Gary E. Moulton (University of Nebraska Press, 2018). The story in prose, 14 May 1804–23 September 1806.
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