 Welcome to Caltrans LSIT LS exam preparation course. One aid in your preparation for California licensure examinations. A word of caution, don't use this course as your only preparation. Devise and follow a regular schedule of study which begins months before the test. Work many problems in each area, not just those in this course's workbook, but problems from other sources as well. This course is funded by Caltrans, but you and I owe a profound thanks to others, the courses instructors from the academic community, the private sector, other public agencies, and from Caltrans as well. We wish you well in your study toward becoming a member of California's professional land surveying community. Hello, my name is Bill Jackson. I'm an associate land surveyor for department of water resources in Sacramento. I want to welcome you to unit six of the Caltrans video training course. Carol Leong and I will be presenting this video unit on leveling. We will be introducing the basic concepts, equipment, and methods used in leveling. This course will serve to introduce leveling to those of you who have not had much experience running levels, and for those of you who are well experienced in leveling, it will serve to reinforce what you are already familiar with and help guide you into those areas that might need additional study for taking the LSIT and LS exams. Hi, I'm Carol Leong, and I too am an associate land surveyor with the department of water resources, and I want to welcome you to this video on leveling. Leveling, the surveying procedure of vertical measurements, the measurement of differences in elevation. The first thing in learning any subject requires an understanding of the basics, knowing the definitions of the terms used. Our first topic we will be discussing is the basic concepts of leveling. The basic concepts of leveling are detailed in the following illustration from your workbook. The first concept is datum. To measure any distance, you must start from a selected reference plane, datum, or surface with a known or assumed elevation. This is usually mean sea level based on 1929 information. The next one is level line, a line that is parallel with the selected datum. Since datums are based on measurements of a curved Earth's surface, the level line is curved also. Vertical line, a line that follows the center of gravity, plumb bob line at the point of observation. Next is horizontal line, a line that is perpendicular to the vertical line passing through the point of observation. An important concept to remember is that a level line and a horizontal line are not the same. A level line is curved parallel to the datum and the horizontal line is straight at right angles to the vertical line at the point of observation. Next is elevation. It is the vertical position above or below the selected datum. Next is benchmark. That is a permanently fixed point with a known elevation. And last, orthometric correction. Because the Earth is not a perfect sphere, the effects of gravity and centrifugal force vary somewhat at higher elevations. This variation must be corrected on long level runs, made in a generally north-south direction at higher elevations. A discussion of this correction is given in chapter five of the Caltrans manual. You should make a point of familiarizing yourself with the concept of orthometric correction. It was part of a question in a recent LS exam. The orthometric correction is just one of several corrections you should know. Here's Bill to explain the need for correcting curvature and refraction. Thanks, Carol, for your explanation of the basic concepts of leveling. As Carol pointed out, a level line is parallel with a reference datum. The level line is curved and follows a curvature of the reference datum, deviating from the horizontal sight line. Because of this deviation from the horizontal, a curvature correction must be considered on long level sightings. As can be seen in the illustration, the greater the length of the sighting, the more the level line deviates from the horizontal line. The more the two lines depart from one another, the greater the curvature correction will be. Another correction that must be considered along with curvature is refraction. When light passes through the atmosphere, it bends slightly causing an object to appear higher than its actual location. Again, in the illustration, we can see the actual line of sight is lower than the horizontal line by the difference labeled r. This difference is a refraction correction. Because both curvature and refraction affect sightings at the same time, the two corrections can be combined. The combined effect of curvature and refraction is calculated by the formula c plus r equals 0.021 k squared. C is equal to the curvature correction, r equals the refraction correction, and k is the distance in thousands of feet squared. An example for k would be that if the level line was 2,000 feet long, then k would be 2 squared or equal to 4. Applying this correction to various sighting distances, we can calculate the combined effects of curvature and refraction. The table in your workbook shows correction values for various distances. It is interesting to note that a sight distance of 700 feet results in only 100th correction in elevation. A level sighting would have to be longer than 500 feet before an actual correction for curvature and refraction would be a major consideration in elevation calculations. It can be seen from the table that the relationship between curvature and refraction and sight distance is not a direct ratio. Because the formula for curvature and refraction is exponential, the correction for curvature and refraction increases exponentially, not proportionally, as the sight distances increases. Although curvature and refraction must be considered for accurate level work, the effects of curvature and refraction can be eliminated. The most common method used to eliminate the effects of curvature and refraction is to balance the length of the four sides and back sides for each sighting. Example, if we took the 700 foot sight distance from the table, the correction for curvature and refraction would be minus 0.01 hundredths of a foot for our back sight. The curvature and refraction correction would lower the back sight rod reading by 100th of a foot. If we took a four-sight reading on an equal 700 feet away, the correction for curvature, excuse me, the correction for curvature and refraction would then be the same minus 0.01 hundredths of a foot as a back sight. The four-sight rod reading would also be lowered by the same 0.01 hundredths of a foot, thus canceling the effect of the curvature and refraction on the setup. We will discuss this method of leveling in more detail shortly. Now, Carol will introduce the three methods of vertical measurement leveling we'll be covering. The three leveling methods we will be covering are direct vertical measurement leveling, trigometric leveling, and differential leveling. The first topic, direct vertical measurement leveling, is according to the Caltrans manual chapter five, direct vertical measurement is the direct reading of elevations or vertical distances. Values are not mathematically manipulated except to apply corrections and adjustments. Another direct method to be discussed is altimetry is also known as barometric leveling. It uses altimeters that display the elevation based on the variation in atmospheric pressures at different altitudes. Because the atmospheric pressure varies daily, the use of altimetry for other than very rough approximations is not encouraged, useful for preliminary surveys. Then we have direct elevation rods. With the use of a pendulum level and special rods known as linker rods, elevations can be read directly on selected points. This is a common method used in construction surveying. This method is also good for determining elevations in moderate terrain, but is not accurate enough for control work. Bill will demonstrate the use of a linker rod. This is a linker rod, as Carol referred to it, a direct reading rod. The interesting thing about this rod is that it's two-part construction. It has a wood section in the front that slides over the back section, and in the front section has a tape that rotates around the first portion. Now this tape is 10 feet long, and the interesting thing about this tape is that instead of reading zero at the X and then going one, two, three, four, and feet, it starts zero at the X, and it goes one, two, three feet downwards so the tape is backwards. Now what this does is it facilitates setting an elevation in the rod, so when the instrument sets up and reads the elevation on this rod, set on the benchmark, the instrument man can tell the rod person what the elevation is. Let's say, for example, that the rod reading is 109 feet and in one-tenth. So when the line of sight was down here, this tape would be rotated to read 910 right here on this tape. And once that is read, it can be locked in position with this little lock on the side of the rod. When that is locked in position, now when the front portion moves, the tape doesn't move, so that elevation is always locked into the rod at that point. So when you pick the rod up and you move it to another position and set it down, even though it might not be at the same elevation as the benchmark, you can then directly read the elevation on the rod. For example, if you took the rod and you set it on a point that was higher than the original benchmark, that would raise the rod, which means that the elevation should be higher. So if the line of sight was at 910 here and you raised the rod, which means that the elevation should be higher. So if you're reading at say a half a foot higher, then you'd be reading at 950 instead of the 911 that you started with. And likewise, if you set the rod on a point that was lower than the starting benchmark, then the rod be further down from the line of sight and you'd be reading higher, which means that you'd be reading a lower elevation. And this is one example of a direct reading rod called the linker rod. Thanks, Bill, for that explanation on the linker rod. The next direct vertical measurement is lasers. With the advent of laser technology, it is possible to measure elevations with the use of lasers and special leveling rods. With this method, it is used frequently in construction projects and in agriculture to locate contours. The next method is global positioning system, GPS. It does not measure elevations directly in relation to a datum with accuracies good enough for survey work. The system measures ellipsoid heights very accurately and could be used to measure relative differences in the elevation of points with elevation, with known elevations or otherwise. In the past, there had been very few questions on direct vertical measurement asked on the LSIT exam and none on the LS exam. But you should still be familiar with these, especially with the concept of GPS. It is likely that it will be used to form a question or answer for problems in future exams. Our second method of leveling is trigonometric leveling. This is an indirect vertical measurement method that determines the difference in elevation between two points by trigonometric means. Vertical differences in elevations are computed from slope distances, vertical angle measurements and the instrument and prism heights. The most common uses of trigonometric levels are determining elevations on distant remote points or where there is considerable differences in elevation between points. Topographic surveys where points are inaccessible by normal leveling methods such as crossing rivers and highways and it can be very useful for control surveys or small scale photo control such as one inch equals 200 feet. And it can also be used in place of differential leveling. The most convenient method used today for trigonometric leveling is with the use of a total station and prism pole. But depending upon the accuracy required, a theodolite and rod employing stadia can be used. The following illustration details the basic concepts of trigonometric leveling. A total station is referenced to a point of known elevation, a benchmark, such as point A in the illustration. Or it can be set up over a point with a previously determined elevation. The total station is then cited on a rod and prism at a remote point such as point B. To calculate the elevation of the sided point, the vertical angle to the center of the prism is read from the total station and the slope distance is measured. Knowing the height of the instrument and the height of the prism, the elevation of point B can be calculated. As an example, a total station is set up at 5.25 over a point with a known elevation of 100 feet. The prism is set at 6.41 feet over a point where the elevation is to be determined. The zenith angle is measured at 86 degrees 49 minutes 29 seconds. The zenith angle is measured from zero degrees being directly overhead of the instrument. The slope distance is measured at 1,486.71 feet. What is the elevation of point B? The elevation of B is equal to the elevation of A, 100 feet, plus the HI of the instrument, 5.25 feet, plus the cosine of the zenith angle, 86 degrees, 49 minutes, 29 seconds, times the slope distance of 1,486.71 feet minus the HI of the prism, 6.41 feet, and that minus the correction for curvature and refraction, 0.021 times 1.486 squared to equal 181.14 feet for point B. Notice in this example, the correction for curvature and refraction about minus 0.05 feet must be included. With this type of leveling, the balancing of forward and backward sightings or simultaneous trigonometric leveling will eliminate the need for correcting for curvature and refraction. Simultaneous trigonometric leveling is the same as the example given above, except two instruments are used to shoot the distances and angles at the same time from both ends of the lines being determined. This method of trigonometric leveling eliminates the problem of changing atmospheric conditions. Bill will now continue with our third method of vertical measurement leveling, differential leveling. Our third method of vertical measurement leveling is differential leveling. Differential leveling is a process of measuring the differences, the differentials, and elevation between any two points by spirit leveling. Differential leveling is broken down into different levels of accuracies known as orders. These orders are first, second, and third order. And first and second order, the orders are further broken down into class one and two. The highest order of accuracy being first order, class one, and the least accurate being third order. We will present a more detailed discussion of these accuracies later on. The equipment used in differential leveling is in third order work, pendulum type automatic levels. These automatic levels with glass prisms hung on wires to eliminate errors caused by mislevelling the instrument. The illustration on the screen shows the internal construction of these levels. If you notice in your illustration, the shaded areas represent the glass prisms that are built into the level. These glass prisms are all hung on wires. So if the level is out of adjustment or out of level just a little bit, when you sight through the level, these prisms correct for that adjustment. And level the sighting up, so the level can be out of adjustment or out of level just a little bit, and you can still read accurately. The rods used in third order work are generally Philadelphia type rods graduated in feet, or single construction rods graduated in yards or meters. Carol has a Zeiss level and a Philly rod to show us now. This is a Zeiss Ni2 level. It is a typical pendulum level normally used with Philadelphia rods. It has an eyepiece with an objective lens and focus and adjustment. There are three level screws used in leveling the instrument. There is a bubble level used to level the instrument more precisely. The Philly rod is a two-piece wooden rod with graduation marks in feet, tints, and hundreds. Unextended, it can be read to a height of seven feet. For heights greater than seven feet, the additional section can be raised and clamped in place. In first order work, the level is used to highly accurate micrometer type pendulum levels such as a Zeiss Ni1 and single construction enviroyard or meter rods. Carol has an Ni1 level and first order rod to show us. This is a Zeiss Ni1 pendulum level. It looks and functions the same as the level that was previously shown. With an exception, there is an addition of a micrometer with an eyepiece. The micrometer and eyepiece is an auxiliary device to provide the measurement of very small increments. With a first order level rod, the increments can be read to two 10,000ths of a meter. This is a first order leveling rod, also known as an Envar leveling rod and meter rod. This one is aluminum with an Envar tape with graduation marks and meters. Envar is a metal alloy that resists expansion and contraction due to temperature fluctuations. Springs are attached to maintain a constant tension and stability. The rod has a hard metal foot and sets up on a heavy metal boot. Once placed on the boot with the use of the bubble level attached to the back of the rod, the legs adjust and clamp to maintain the rod on a stable vertical plane. These rods are made in matched calibrated sets. Thank you Carol for your help in demonstrating that equipment. Chapter two, section eight of the CalTrans manual gives a good detailed discussion of the equipment used in differential leveling. The methods used in differential leveling are illustrated in your workbook and can be seen on the screen now. The level is set up some distance from a benchmark and the direction the level run is to proceed. A benchmark is a permanent point with a known elevation such as BMA. The rod is placed on the benchmark and a backside reading is taken with the level. This reading is added to the elevation of the benchmark which gives the elevation of the level. In this case, 100 feet plus 10.63 feet equals the height of the instrument or 110.63 feet. The rod is then moved forward if possible and equal distance to the backside and placed on an intermediate turning point. This level is turned, the level is turned and a reading is taken again on the rod at the foresight turning point. This foresight reading is then subtracted from the HI of the instrument to give the elevation of the turning point. In our example, this would be 110.63 feet minus 1.15 feet equals an elevation of 109.48 feet for the new point. The level is then moved ahead and set up at some convenient point. The distance from the rod to the new setup point, the backside distance should equal the distance to the next point ahead where the rod will be placed, that is the next foresight turning point. After the instrument is set up and leveled, a backside reading is then taken on the rod at the previous turning point. This backside reading is then added to the elevation of the turning point. The sum of the backside reading and the elevation of the turning point gives a new HI for the level at the new setup. In our example, this would be 109.48 feet. The elevation of the turning point plus 9.92, the reading on the rod at the turning point equals 119.40 feet, the elevation of the level at the new setup point. This process is then repeated until the level run is tied into a point of known elevation or is looped back to end on the beginning benchmark. Closing the level run back on itself is called a closed loop level run. Closing the level run on a point of known elevation other than the beginning benchmark is called an open level run. It is open because it does not close back on the beginning point. Closing the level run gives a means by which the level run can be checked to determine any random errors in the run. These errors can then be eliminated by several different methods we will be discussing later. Another aspect of differential leveling is profile leveling. Profile levels are basically the same as differential leveling except several foresights are taken on predetermined points before the level is moved ahead to the next setup. For example, if a differential level run was used to run along the centerline of a road to be constructed, it would be necessary to determine the elevation along the centerline stations to calculate the cuts and fills for the new road. This would be done by intermediate foresight readings on as many centerline stations as possible from one level setup. Without moving the level ahead, these intermediate foresight readings would be subtracted from the HI of the level to give the elevation of each station along the road centerline. An essential part of differential leveling is taking good understandable fill notes. Several methods of taking differential level notes are used in surveying. Different methods are used depending on what level of accuracy is desired and the procedures of your organization. It is important to understand how level notes are written. The computations made with level notes have appeared on several LS exams and LSIT exams. In one LS exam, the applicants were actually required to reproduce notes in the test booklet to show they knew how to take and reduce level notes. The following illustration demonstrates several methods used in taking fill notes. Our first example of level notes shows a differential profile level note using a Philadelphia-type foot rod. Notice the notes are taken going up the page. Taking notes going up the page simplifies retracing the level run in the field. To interpret these notes, start with the elevation 407.535 at the bottom right corner of the example. The first plus shot or backside reading is 6.995. This plus shot is added to the starting elevation of 407.535 to give us the elevation of the level, or HI, as 414.530. The first foresight reading or minus shot, 4.765, is then subtracted from the calculated elevation of the level of 414.530. So 414.530 minus the foresight of 4.765 gives us the elevation of the turning point as 409.765 feet. This procedure is repeated until the last elevation of 412.005 for the closing bench is checked against the known elevation for the point of 412.011. This comparison tells us the level run does not close on the known elevation for the benchmark by a difference of 6,000ths of a foot. This error is distributed throughout the level loop to close the elevation run on the bench with a difference of zero. Our next example of level notes illustrates differential level notes for three-wire levels using a foot rod. Through three-wire levels is a method used to obtain higher accuracies than normal differential level procedures. In our example, the first set of back-site readings represents the readings on the rod for the top, middle, and bottom cross-airs of the level scope when siding the rod. 8.266 is the top cross-air reading. 8.105 is the middle cross-air reading, and 7.940 is the bottom cross-air reading. The number 161 is the interval difference between the top and middle cross-airs. So if you subtracted 8.105, the middle cross-air from the top cross-air of 8.266, the difference is 161. The number 165 is the interval difference between the middle and bottom cross-airs. So if you subtracted 7.940, the bottom cross-air from 8.105, the middle cross-air, the number would be 165. The number 8.1037 equals the mean of the three readings and is used as the plus shot or the back-site reading for your notes. 326 is the sum of the two intervals, 161 plus 165 between the cross-airs. This is added to the sum of the next back-site interval. The total for the second back-site is in 7.59, as shown in the example in your workbook. In three-wire levels, there is a maximum amount allowed for the difference between the top interval, 161, in our example, and the bottom interval, 165. The maximum allowance for the difference between the top interval and the bottom interval is determined by the standards of accuracy for vertical control. A more detailed discussion of these standards will follow shortly. In our example, the difference between the top and bottom intervals is 161 minus 165 or 4,000ths of a foot. 4,000ths is generally acceptable for a maximum difference in third-order work, but not for second-order levels. The four-site readings for the three cross-airs are treated the same way. The mean of the four-site is then subtracted from the instrument height, just as in normal differential level runs. If the level run closes back on the same benchmark it started from, then the algebraic sum of the means for the back sites, the plus shots, and the sum of the means for the four sites, the minus shots, should total zero for the level run to close. If the level run closes on a different benchmark than the beginning bench, then the differences between the sum of the back sites, the plus shots, and the sum of the four sites, the minus shots, is algebraically added to the elevation of the beginning benchmark to determine the elevation of the ending benchmark. The calculated elevation should be the same as the known elevation of the ending benchmark. Any misclosure in the closed loop run or the open loop run must be distributed throughout the level run. We will be discussing adjusting level runs later. Another method for taking three-wire differential level notes is shown in your workbook using a meter rod. In this example, the notes are going down the page. Notice the three-wire level notes for a meter rod are taken just like they were for the foot rod. The reference on the notes to the back of the rod means a foot graduation tape on the back of the rod is shot as a check on the readings for the front of the rod. Knowing that one meter is equal to 3.28083 feet. In our example, we can easily see that 2.3650 meters is then 7.76 feet. From this check on the back of the rod, we know the mean for the readings on the front of the rod 2.3650 meters has been made without error. We have given you a few examples of acceptable level notes. You may find in your professional surveying career that some surveys prefer to take level notes differently than what we have presented. It is not uncommon to see different methods of taking filled notes. The important factor to remember in taking filled notes is that they must be legible, accurate, and understandable, and fully detail exactly what you did in your fieldwork. Presented the different methods of recording level notes ends our discussion on the basic concepts of leveling. We presented the three methods of leveling, direct vertical measurement, trigonometric leveling, and differential leveling. These three methods are used throughout the surveying profession. To round out our understanding of leveling, there are a couple of special leveling concepts that need to be understood. The first special concept we need to understand is pegging a level. Carol will explain how this is accomplished. Before any type of level run is attempted, it is important that the level be in a proper adjustment. The method commonly used to adjust a pendulum type level is called pegging a level. Here is an illustration showing one method used in pegging a level. The level is set up at point one, midway between two points, approximately 200 feet apart. By setting the instrument midway between two points, we can balance the backside and foresight, eliminating instrument error. For the backside reading, the rod can be set on a point of known or assumed elevation. In our example, the backside point is A. With the level at point one, the backside reading BS one is taken on the rod at point A. This backside is added to the elevation of point A to give the height of the instrument at point one. The level is turned and the foresight reading FS one is taken on the rod at point B. This foresight is subtracted from the level elevation to give the elevation of point B. The level is then moved and set up at point two, a short distance from the backside point A. The second setup should be where the backside point A and the foresight point B can be observed with minimal turning of the level. By setting the level a short distance from A, the foresight and backside are intentionally unbalanced. The unbalanced sight distances will exaggerate any error in the mechanical workings of the instrument. Another backside reading BS two is taken on the rod at point A, the point nearest the level. This gives a new elevation for the instrument height at setup point two. Another foresight reading FS two is then taken on the rod at point B. This foresight rod reading establishes a new elevation for point B. We now have two elevations for the same point. Any difference in the two elevations is the result of misalignment of the instrument crosshairs. This mechanical error must be adjusted out of the instrument by actually moving the crosshairs in the level scope up or down to make the foresight FS two yield the same elevation for point B as FS one, thus eliminating the error. As an example, the following illustration details the computations used in paging a level. Assuming an elevation of 100 feet for point A with a backside reading of 5.10 feet makes the HI 105.10 feet. Reading a foresight of 4.96 feet and subtracting that from the HI gives an elevation of 100.14 feet for point B. After moving the level, the new backside reading is 5.51 feet with an HI of 105.51 feet. Then subtracting the foresight reading of 5.35 feet, the elevation of point B is 100.16 feet. Note that there is a difference of two 100s of a foot when comparing the two elevations for point B. This error is a result of the crosshairs in the level being misaligned. The error of plus 0.02 must now be removed from the level by mechanically moving the level crosshairs up 200s to read 5.37 on the rod. The new reading on the rod will yield the correct elevation for point B. After the level has been adjusted, it is strongly recommended that the peg test be run a second time as a check on the adjustment. Another correction that should be considered in the adjustment of pendulum type levels is the culmination error. The culmination error is the slight variance that exists between the centerline of the level scope and the actual centerline of the crosshairs that cannot be eliminated by adjustment. If this error is known for a particular level, it should be considered and corrected on higher order level runs. A good discussion of the culmination error is given in chapter five, section three of the Caltrans manual. In taking your LS or LSIT exam, you should be aware of the culmination correction. It has appeared on previous LS and LSIT exams. Now, Bill will tell us another special leveling procedure. Your workbook shows a general method used to accurately transfer elevations across rivers, canyons, and similar obstacles, or when the back sides and fore sides in a level run cannot be balanced. This method is reciprocal leveling. The illustration shows the obstacles to be crossed as a river. The obstacle could also be a freeway or a canyon. Reciprocal levels can also be used to transfer elevations between floors and high rise buildings. In our example, the level is set up at point number one. A back side is taken on the rod placed on BM number one. A fore side is then taken on the rod placed on BM two. The difference in elevation between BM number one and BM number two is determined by differential leveling. It is customary to take several back site and fore side readings at setup number one and averaging the shots. It is also recommended to use two rods. Two rods, one at BM number one and one at BM number two, will eliminate any delay in moving a single rod. Atmospheric conditions could change during the time it might take to transfer one rod from the first benchmark across the obstacle to the second benchmark. Atmospheric changes do affect instruments and rod readings. The level then is transported across the obstacle to setup number two. A back side is then taken on BM number one. The level is rotated and a fore side is taken on the rod at BM number two. Again, it is preferable to take several shots and average them. Now you have two differences in elevations taken from two different setups. The average of the two differences in elevations is determined and used to determine the elevation for BM number two. Another area of leveling that has been tested on past LS and LSIT exams is the classification of accuracy standards and adjustments for vertical control. The table in your workbook shows the classification of accuracies for vertical control. The table specifies minimal observation methods, maximum site distances, maximum number of setups, and the maximum allowable misclosures for first, second, and third order levels. A closed reading of the tables reveals a lot of specific information that should be considered before determining the accuracy required for a level run. For example, the requirements for a second order class two level run are a minimum of three wire levels with a closing error no greater than 8 times the square root of D millimeters. D equals the shortest length of a section one way in three wire level runs in kilometers. And remember, a kilometer is 3,280.83 feet, and there are 304.80 millimeters per foot. If a level run is 3,280.83 feet or one kilometer long in one direction, the maximum misclosure allowed would then be 8 millimeters or 0.026 feet. If the closure is greater than 0.026 feet, it would not qualify for second order class two. If you wanted to run levels to qualify for first order class two, you would have to use a first order level with a micrometer readings, as we demonstrated earlier, and only have a misclosure of 0.013 feet or 13,000ths of a foot in 3,280.83 feet or in one kilometer. It is very important that you familiarize yourself with these standards and how to apply them to specific level runs. You should plan on studying this area further by using any of the resources in the bibliography at the end of the chapter in your workbook. After the accuracy standards have been determined and applied, it finally comes down to what do you do with the error in your level runs. There are three methods of adjustments that are generally used to adjust level runs. These methods are the length of line method, number of turning points method, and least squares method. Here we have an example of a level run. This level run has four legs of various lengths. The closing error is plus 0.05 feet. To distribute the error of this run, the elevation for each of the four TBMs would be adjusted down to make the run close flat on BMB. This adjustment can be done by one of the three methods. In the length of line method, each leg would be adjusted based on the ratio of each leg to the total length of the run. For leg one of the run, the adjustment would be 300 feet is to 2,000 feet, as the adjustment is to 0.05 feet, or the error of the total run. In this case, that correction is minus 0.0075 feet or about 1-hundredths of a foot. The elevation of TBM number one would be lowered by this amount. Each of the subsequent legs would then also be adjusted similarly, accumulating the adjustment through the remaining turning points. The last leg would get the full correction of 0.05 feet to close the leg flat on the ending benchmark. To distribute the same error by the number of turning points method, the error is evenly distributed among the turning points. In this example, we'd have the error of 500ths of a foot divided by 4 equals minus 0.0125 feet per turn. Turning point number one of our example would then be adjusted by 0.0125 feet. Turning point number two would be minus 0.025 feet. And turning point number three would be minus 0.375 feet. And so on through the remaining turns to close flat on the benchmark. In the least squares method, adjusting lever ones by least squares adjustment is beyond the scope of this presentation. We encourage you to study this method in the Surveying Handbook by Minneken Brinker, reference at the end of the chapter in the workbook. Carol and I have covered the basic concepts, methods, and corrections for the three main areas of leveling. We have refreshed your memory on Pagina level, accuracy standards, and adjustment routines. To further reinforce what we have presented, we encourage you to consult the references at the end of the chapter in the workbook. Work the sample exam questions at the end of the chapter, many of which have been taken from past LS and LSIT exams. Remember, there is no substitute for good study habits, hard work, and a strong willingness to succeed. Good luck in your endeavor to become part of the professional land surveying community.