By far the most common observations were the daily measurements that are found in the journals of Lewis and Clark as "Course...Time...Distance... Remaks. & refurncs." These were intended to be used as the early 19th century equivalent of the guide book from AAA, that tells you how to get from place to place, what sights you're going to see on the way, where to lay up at night, and where to get a good chicken-fried steak.
Course referred to the direction the expedition was traveling, stated as a compass bearing between two points. To obtain this bearing, or "azimuth," the captains used one of the pocket compasses or else the larger surveyor's compass (circumferentor) to get direction from one reference point to another—from the point of a bluff along the Missouri's north side, for example, to the tip of a prominent sandbar on the south side of the river (reference points were always identified in the journals). Their compasses registered magnetic north rather than geographic north and their readings had to be adjusted for the difference or "declination." They understood the errors that would creep in as they moved from east to west across the continent and continually adjusted the declination of their compasses to insure accuracy of readings.
Compass Bearing: Azimuth
The word "azimuth" comes from an Arabic form of a Latin word meaning "way" or "path." In the illustration, "N 49° E" is an azimuth indicating a compass bearing or direction of 49° east of north (or 41° north of east). "S 70° W" indicates a bearing or direction of 70° west of south (or 20° south of west). Lewis and Clark gave their compass bearings in terms of quadrants or quarters of the compass: 90° from north to east, 90° from east to south, 90° from south to west, and 90° from west back to north. Today, azimuths are often stated in terms of 360°, the full circle of the compass rather than quadrants. A modern statement of the azimuth of "S 70° W" would be 250°; degrees are always counted in a clockwise direction from compass north.
This instrument was normally mounted on the end of a staff that could be rested on the ground. The compass housing and the cross piece with the vertical metal "sights" on either end rotate. To take a bearing, Lewis or Clark would rotate the cross piece and upright sights while looking through the holes for a fixed visible point. When that fixed point was found, the bearing or azimuth between it and the observer could be read from the compass dial.
The variations between magnetic north and "true" or geographic north have been understood for several hundred years. As early as 1585, a Portuguese map showed "isogonic lines" or lines indicating the declination or difference between north as it appeared on a compass and north as a direction of the geographic grid system.
The English scientist Edmund Halley (for whom the first comet to be recognized as such was named), drew a map of the world in 1702, showing isogonic lines for the entire planet and enabling explorers everywhere to correct their compasses for the difference between magnetic and true north.
The great English explorer, Captain James Cook, was the first to use compass declination widely in his mapping of the islands and coasts of the Pacific Ocean. Magnetic poles shift over time, and magnetic north in 1804-1806 was different from today.
Time, stated in hours and minutes, was the time required to get from the reference point used to establish the beginning of a course azimuth to the reference point marking the end of that particular compass bearing. Time was established precisely by chronometer—as long as the captains remembered to keep it wound. Because they did forget to wind it regularly there were frequent occasions when travel time was an estimate. But living as close as they did to the natural world, while still having a temporal frame of reference that included hours and minutes and seconds, reasonably accurate time estimates would have been less of a problem for them than for the native peoples who possessed few or no short-term time concepts, or for us latter-day folks who are not only more divorced from nature but have relied for so long on the watches strapped to our wrists that we find it difficult to evaluate time any other way. Still, most of the temporal observations of Lewis and Clark were obtained by timepiece—the chronometer that cost more than all the rest of their "mathematical instruments" combined.
William Clark's Compass
This is the actual compass, with a paper dial (note the tear across the dial), carried by William Clark on the Expedition. The compass is in a hinged box that can be closed to protect the compass face and is small enough to be carried in a large pocket. The compass ring showing degrees on the outside of the dial can be rotated to adjust the instrument for declination.
From the standpoint of navigation, the chronometer was one of the most important inventions of the 18th century. While this instrument looks a little elaborate for rough fieldwork, it performed well as long as it was kept wound. Note that the dial is calibrated in 12-hour increments rather than the 24-hour Greenwich Mean Time system used today for locational calculations. Much of modern naval terminology stems from the earliest nautical uses of the chronometer. The ship's bell, by which time was noted, was struck at specific intervals ("eight bells" denoted the passage of four hours), a level of accuracy not possible prior to the chronometer. And "watches," or the positions of responsibility for maintaining the ship's course during four-hour intervals, were also regulated bv the new device.
If the distance between reference points A (for example, the upstream tip of a prominent sand bar) and B (the top of a river bluff) is known, and the angles x and y can be read from compass bearings between B and C (a tall tree on the opposite side of the river) and A and C, then lines can be drawn from A to C and B to C completing a triangle with one known leg (AB) and two legs (BC and AC) that can be estimated with a high degree of accuracy.
This estimation can be done by "scaling." If line AB is 1 mile long in the real world and 10 inches long on the diagram, then the map scale is 0.1 inches to 1 mile; the distance from B to C can be determined by measuring the distance on the diagram and multiplying by the scale (if the diagram distance BC is 6 inches, then real world distance is 6 miles). There are also mechanical ways that the distance estimates could be arrived at, using draftsman's dividers or a similar instrument. The points of the divider could be set 1/10 of an inch apart to represent the diagram scale and the dividers could then be "walked" along line BC to determine its length.
Distance was expressed between the same two points used to derive course and time. This was normally given in miles but occasionally in yards or rods. These measurements were obtained either by pacing a course between two points or by estimating distances. Estimations are relatively easy for people having long familiarity with their environment, their own travel paces and their mode of transport. They walked about as often as they rode and this allowed them to judge both time and distances much more accurately than we can while driving a car at speeds that may vary widely (from 15 miles per hour in a school zone to 75 mph on an interstate highway).
Their sense of time and distance was more precise than ours because their survival so often depended on it and because they moved across the landscape in very different ways than we do. Throughout the expedition, the captains were reasonably accurate in their measurement of distance. They accomplished this with good guesswork, enlisted men to do the grunt work of pacing out courses, fairly sophisticated instruments and mathematical calculations, and careful attention to detail.
The reference points that made up the bulk of the notations in the Journals were often given as follows: "…a pt. on L.S. high Land psd. the head of an Isd. above is a large Sand bar on L.S.". This identifies a high point of land on the larboard side of the boat ("L.S."), just beyond ("psd." = "passed") the upper portion or "head" of an island ("Isd.") on the left. Normally, the captains used "larboard" and "starboard" to mean the left and right side of the boat.
Occasionally, they referred to the left or right banks of the river but this did not necessarily mean the bank on the left or right side of the boat. For river travelers in the early nineteenth century, the convention was to name the banks of a stream based on the direction in which the stream was flowing. For a stream flowing from the north, then, the right bank was the west bank, on the right hand side of someone traveling south down the river.
For Lewis and Clark, on their upstream journey, the left and right banks of the Missouri were to the right and the left respectively of the boat. In other words, the right bank of the Missouri (to Lewis and Clark) was the bank on their left as they proceeded upstream, on their right as they proceeded downstream. Those who followed immediately after Lewis and Clark were much less confused than we are about this system and the "references" material was among the most useful parts of the written record of the Expedition
Remarks, or reference observations, were comments on the widths of the Missouri and the creeks and smaller rivers that entered it, the heights of bluffs or hills along the river, and–most common and most important–the identification of the reference points upon which the compass bearing/distance/direction information was based. Jefferson's directive to Lewis had included the order to note "all remarkeable points on the river, & especially at the mouths of rivers, at rapids, at islands, & other places & objects distinguished by such natural marks & characters of a durable kind, as that they may with certainty be recognised hereafter" and the captains were faithful to these instructions.