 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 Jim McCavitt. I'm a supervisory land surveyor with the branching cadastral survey, Bureau of Land Management. I've worked for the BLM since 1976. I'm also a licensed land surveyor in California, having passed the 1984 exam. I'd like to welcome you to unit 12 of the Caltrans LS LSIT video training course. Course, the United States Public Land Survey System. Since I'll be referring to the United States Public Land Survey System throughout this course, from this point on, I'll shorten it to the letters PLSS. In preparing for this course, I reviewed previous LS exam questions about the PLSS. The questions focused on three primary aspects of the PLSS, which a licensed land surveyor is likely to become involved with. The topics are the dependent resurvey, the restoration of lost corners, and the subdivision of sections. If you are familiar with the basic principles in these three areas of the PLSS, then you should be able to correctly answer the PLSS questions on the previous exams. The questions generally do not involve complex, tricky, or unusual situations. This course, then, is designed to present the principles of dependent resurveys and the basic procedures used in restoring lost corners and subdividing sections. Prior to the presentations on these three topics, though, I'll discuss the background information necessary to understand them. I want to start with a short history of the PLSS. The authority for starting the PLSS was provided by the land ordinance of 1785. This ordinance provided for the systematic survey and monumentation of federal lands into a rectangular system with townships and sections. The state of Ohio served as a testing ground for this new type of boundary surveys. Changes were made in the method based on the early experiences in Ohio. The major concepts of our present day system were largely in place by 1805, with mostly minor refinements being made from time to time thereafter. The intent of the system was to survey and monument the western lands prior to the federal government's patenting the lands to its citizens. The rectangular system provided standardized parcels of land interrelated by reference to townships and initial points. Simple output part descriptions, dividing sections into halves and force ad infinitum, were all that were necessary to describe with certainty a parcel of land. The general land office, or GLO, was created by Congress in 1812 and was given jurisdiction over all matters concerning the survey and sale of the federal lands. In 1946, the GLO was combined with the grazing service and became the Bureau of Land Management. The BLM, as successor to the GLO, still has responsibility for the survey and resurvey of federal lands. The surveys in California were initiated in 1851, shortly after statehood. Most of the original surveys were made under the contract system. Under this system, the GLO contracted with private individuals to complete the required surveys. Millions of acres of federal lands were surveyed under the system by good, bad, and indifferent surveyors. A 1910 act of Congress, however, directed that the surveys and resurveyors of the federal lands were to be made by such competent surveyors as the Secretary of the Interior may select. This new system of making the surveys is called the direct system. It effectively abolished the contract system. CA White, in his history of the rectangular survey system, states that most of the easy surveying had been done, so not even the deputy surveyors themselves were sorry to see the contract method go. In the early days of the PLSS, instructions were issued to field surveyors which specified the method of survey and accuracies expected. It gradually became evident that a consolidation of officially authorized surveying procedures was needed. On March 3rd, 1851, the Oregon manual entitled, Instructions to the Survey General of Oregon, being a manual for field operations, was issued. Supplies to this manual were also issued to the Survey General of California, so it was immediately applicable to California as well. The 1855 manual of surveying instructions and expansion of the Oregon manual with a few improvements was issued on February 22nd, 1855. Subsequent manuals were issued in 1881, 1890, 1894, 1902, 1930, 1947, and 1973, each slightly improving the PLSS in both accuracy and uniformity. The current manual of 1973 summarizes itself in section one dash one as describing how cadastral surveys of the public lands are made in conformance to statutory law and its judicial interpretation. What I want to stress about the different manuals is that the BLM GLO surveys were and are established in accordance with the manual enforced as of the date of the survey. To properly execute a retracement or resurvey today of older PLSS surveys, it is a must to have an understanding of the methods and procedures used to execute these older surveys. This understanding can be gained from the manuals enforced at the time of this original survey. At a minimum for the PLSS portion of the LS test, your library should contain the manual of surveying instructions 1973. The official record of BLM GLO surveys usually consists of a set of field notes and a plat. The field notes are the official written record of the survey. They identify and describe the lines and corners of the survey and procedures by which they were established or reestablished. The plat is the drawing which represents the lines surveyed or resurveyed, showing the direction and length of each line. The plat furnishes the basic data for the description of all areas within a township. This is a typical plat showing township five south, range five west, not Dabla meridian. The other township plats, like this one, were often composites of several different surveys. Colored lines were often used to distinguish between the surveys. Unfortunately, these colored lines reproduced as shades of gray, which are usually not distinguishable. If you should ever need to determine the color of certain lines, the BLM should be contacted for help. When lands are patented, the plat's field notes and marks of the survey become a part of the patent and control as far as boundaries are concerned. If evidence of a corner monumented by a prior survey cannot be recovered, the field notes and plat provide the basis for restoration of a lost corner. All the original California field notes and plats in existence at the time were destroyed by the fire which resulted from the April 18th, 1906, San Francisco earthquake. The rectangular plats were replaced by copies of the duplicate plats which were on file in Washington DC. The field notes were replaced from one or a combination of the following. The triplicate set on file in the GLO land office, a transcribed copy of the duplicate set on file in Washington, and copies of unknown origin. The copies of unknown origin were most likely obtained from state or county sources. These multiple copies occasionally result in discrepancies between plats and notes, different versions of the plats, and different versions of the notes. In order to resolve these conflicts, it is important to know which generation or version you have. The survey record staff of the California BLM office can help you distinguish between the different generations of field notes and plats. The address and phone number of this office are 2,800 Cottage Way, room E 2807, Sacramento, California 95825. The phone number for this office is area code 916-978-4779. Copies from microfiche to the plats and field notes for BLM GLO surveys in California are available for purchase from this office. The measurement data reported on GLO BLM survey plats and in field notes are bearings and distances. The distances by law are horizontal measurements reported in chains based on the US survey foot at actual ground distance. One chain is equal to 66 feet. Partial chain measurements are made in links. The chain contains 100 links with one link being equivalent to 7.920 inches. 80 chains is equivalent to one mile. The chain unit was devised so that 10 square chains would be equivalent to one acre. A measurement shown on a plat as 80.121 chains is equivalent to 80 chains and 12.1 links. For the direction of lines, the 1973 manual at section 217 states that the direction of each line of the public land surveys is determined with reference to the true meridian as defined by the axis of the Earth's rotation. Section 219 further states that current practice is to determine true azimuth by one of the following methods. The first is direct observation of the sun, Polaris, or other stars. The second is observations with a solar attachment. The third is the turning of angles from triangulation stations of the horizontal control network. Historically, though, many of the early PLSS surveys were made with a magnetic compass. The use of the compass was partially abolished by the 1890 manual, which stated that the survey of all principal base and meridians, standard parallels and guide meridians, and township lines must be made with an instrument operating independently of the magnetic needle. The 1890 manual further stated that where the needle can be relied on, however, the ordinary compass, if provided with a revolving compass box and variation arc, may be used in subdividing and meandering. The 1894 manual completely abolished the use of the magnetic compass by stating the surveys of the public lands in the United States, embracing the establishment of baselines, principal meridians, standard parallels, meander lines, and the subdivision of townships will be made with instruments provided with the accessories necessary to determine the direction with reference to the true meridian independently of the magnetic needle. In the PLSS, lines which are surveyed due east or west are curved lines of latitude. Other than on a meridional line, a straight line in the PLSS, surveyed by flopping the scope of an instrument and subsequent setups to establish straight line points, is a line of constantly changing bearing. The graphic now on the screen illustrates how dramatic this effect can be. This particular example is at a latitude of 45 degrees, 34.5 minutes north. Beginning at a point on the left side of the screen, two lines six miles long are surveyed. The top line is surveyed on a bearing of east on a true parallel of latitude. Due to the shape of the earth, this is a curved line. The bottom line is a straight line with an initial bearing of east. After one mile, the straight line is one length south of the due east line. After two miles, four lengths south. After six miles, the bearing of the line is south 89 degrees, 54.7 minutes east, a little over five minutes different, and is 37 lengths southerly of the curved line. The divergence between the two lines is dependent on the latitude of the lines. The further north you go, the differences become greater. The further south you go, the differences become less. For resurveys being made today, you need to be aware that all lines of the PLSS, except for subdivision of section lines and meridional lines, are curved lines. Three methods for correcting for the curvature of the PLSS lines are presented in the 1973 manual in sections 276, 77, and 78. These are the solar transit method, the tangent method, and the secant method. Nowadays, with calculators and computers readily available, these methods are seldom used. Instead, curvature corrections for each traverse leg are computed, which are then applied to the bearing of the traverse leg. These curvature corrections are dependent upon the departure and mean geographic latitude of each course. This method allows you to determine your position directly without having to offset from a tangent or secant line or using a solar attachment. The PLSS, like other branches within the surveying profession, has many unique terms unto itself. Understanding the meanings of these terms is important for taking the exam and even more important for later as a practicing professional land surveyor. At this time, I'd like to define some of the terms, which will be used later in this course, and that you should be familiar with. An adequate part is a portion of a section made by subdividing the section into halves and quarters. A law does not consider an adequate part. When dividing a section into halves and quarters by federal law, area is not a consideration. The surveying procedures determine the parts. A resurvey will almost always reveal differences in acreages and halves or quarters of a section. This differs from California state law, where a one-half is defined as one-half of the area of a whole. As a professional land surveyor, you will have to make the determination of whether federal or state rules apply. A standard corner is a senior corner on a standard parallel or baseline. A closing corner is a corner established where a survey line intersects a previously fixed boundary at a point between corners. The position of a closing corner is located by law at the actual point of intersection without regard to its monument and position. A witness corner is a monument and survey point usually on a line of the survey and near a corner. It is established only in situations where it is impractical to occupy the side of a corner. As an example, a witness corner would be set on one of the lines leading to the true corner position when the true corner position falls on the face of a steep cliff. A patent is a document by which the United States conveys legal title to a portion of the federal lands. The term lot is currently used in the PLSS to describe a subdivision of a section which is not described as an adequate part of the section but is instead designated by number. A lot may be regular or irregular in shape. Its acreage varies from that of a normal 40 acre adequate part. An example of the correct terminology to use in describing a lot is lot two of section 14, township Four North range Four East, not Davao Meridian. The system for numbering lots within a section is similar to that for numbering sections. You start in the northeast part of the section and sequentially number westerly to the north quarter tier of the section. Then drop subtly to the next lower quarter tier of the section and proceed easterly to the east boundary. Then drop subtly to the next quarter tier of the section and proceed westerly to the west boundary. Then drop again and proceed easterly through the bottom quarter tier of the section. In the 1800s, some lots were referenced to a township instead of a section. To describe ranchos, Indian reservations, mineral surveys, and other non-rectangular surveys. Today similar parcels would be designated as tracks instead of lots. Surveyors outside the BLM often refer to PLSS lots as government lots in order to distinguish them from lots on a subdivision map filed in a county. A tract is a modern term used to describe an area at large within a township. More specifically, it is a parcel of land which lies in more than one section or that cannot be completely identified as a part of a section. Tracks are numbered with the next highest unused number or unused section or track number for a township as in track 37 of township four north, range four east, not Dabba or Meridian. A bearing tree is a corner accessory. The bearing and distance to the tree are measured from the position of the monument and recorded in the field notes. The bearing tree is usually blazed and inscribed with marks designated in the corner position. The marks remain as long as the tree is sound. Eventually the tree heals over, usually leaving an identifiable scar. When necessary to secure proof of the position of a corner, the overgrowth can be removed to reveal scribing. Removing the overgrowth inflicts severe injury on a tree and should only be done as a last resort to conclusively prove the position of a corner. I have with me an example of overgrowth removed about 1940 from a bearing tree scribed in 1867. The reverse scribe marks in R1WS8 are readily identifiable. The blazed portion was about four inches into the tree. A parenthetical distance is an implied survey plat measurement. They are used to indicate the position of unmonumented points on a line shown on an official plat. Parentheses are used where the distance is not supplied by the field notes, indicating that the distance was not measured on the ground. Most of these terms will be re-emphasized later in this course. Now let's move on to the general scheme or framework used for the PLSS in California. Knowledge of the scheme is essential in determining the precedence or importance of the lines and monuments of the original surveys. The surveys in California were started using the instructions set forth in the 1851 Oregon manual and then replaced by the 1855 manual. The methods provided for the surveys in the 1855 manual differed in some respects from those provided in the 1851 Oregon manual. The general scheme I'm going to present is that which is based on the 1855 manual under which most of the control lines in California were surveyed. After presenting the entire scheme, I'll discuss the primary differences between the surveys executed under the 1851 Oregon manual and those executed under the 1855 manual. The PLSS surveys were started from initial points. California has three initial points. The Mount Diablo initial point was established in 1851 and is located about 30 miles Easterly of San Francisco. The San Bernardino initial point was established in 1852 and is located about 70 miles Easterly of Los Angeles. The final California initial point, the Humboldt, was established in 1853 and is located about 25 miles southerly of Eureka. Principal meridians were extended north and south from these initial points. Regular quarter section and section corners were established and monumented ultimately at intervals of 40 chains and township corners at 480 chains or six miles. Baselines were extended east and west from the initial points. Standard quarter section and section corners were established and monumented alternately at intervals of 40 chains and standard township corners at intervals of 480 chains. Because of the shape of the earth, meridional or north-south lines converge together as they extend toward the poles. This is illustrated by the graphic now on the screen. To adjust for the shortening of the east-west lines due to convergence, latitudinal correction lines called standard parallels are run at specified distances northally and southerly of the initial points. This graphic shows the distance northally and southerly of the initial points to the standard parallels as 24 miles each. This is the current specification for the 1973 manual. In California, correction lines are every 30 miles northally and every 24 miles southerly of the baseline. Oddly, these distances are opposite of those specified by the 1851 Oregon manual and the 1855 manual. Both manuals required correction lines 24 miles northally and 30 miles southerly of the baselines. Standard quarter section and section corners were established on standard parallels and monument it alternately at intervals of 40 chains and standard township corners at 480 chains or six miles. The principal meridian, baseline and standard parallels form the controlling lines for the further division into townships and sections. The manual of 1881 required the running of guide meridians placed at intervals of 24 miles east and west on the principal meridian. The guide meridians are extended north from a baseline or standard parallel to a closing corner on the next standard parallel to the north. By 1881, however, most of the primary control for the surveys in California have been established. Therefore, guide meridians were not used to integrate extent here. The primary difference between the range lines surveyed most of California and guide meridians is that guide meridians are double measured. The intent of the 1881 manual was to have the surveyed baselines and standard parallels and principal meridian and guide meridians form quadrangles to confine errors resulting from convergence of meridians and inaccuracies and measurements. After the primary control lines were established, the public lands were subdivided into townships about six miles square. A township is uniquely identified by number based on the position north or south of the baseline and east or west of the principal meridian. The highlighted township shown is identified as township two south, range two west. The township exteriors were surveyed through a quadrangle successively and ranges the townships, whenever practical, beginning with the townships on the south. An example of the order in which township lines were supposed to be surveyed is as follows. Starting at the southwest corner of township one north, range one west, the meridiana boundary, or range line, was surveyed from south to north on a true meridian. Quarter section and section corners were established alternately at 40 chain intervals for a distance of 480 chains where a temporary township corner was established. A random latitudinal line, or township line, was then run east of the principal meridian to a following north or south of the previously established northeast township corner. If the errors were within acceptable limits, the true township line connecting the township corners was computed. Permanent quarter section and section corners were then monumented on the true line at 40 chain intervals. The excess or deficiency in measurement was placed in the westerly half mile of the township line. This procedure of surveying the range line, then the random and true township line, continued northerly to the establishment of the northwest corner of township three north, range one west. The final meridiana line was then run on a true meridian, establishing regular quarter section and section corners at 40 chain intervals until intersecting the standard parallel or baseline where a closing corner was established. This procedure was then repeated for the adjacent range of townships to the west. Once the exterior boundaries of a township were established, the township was normally subdivided into 36 sections of land, one mile square, containing 640 acres each, except along the north and west boundaries where the excess and deficiency in measurement was placed. Each section was given an identifying number according to the scheme shown. The subdivision of a normal township in the sections was initiated on the south boundary at the previously established corner of sections 35 and 36. From this corner, the section line between sections 35 and 36 is surveyed parallel to the east boundary. The one quarter section corner of sections 35 and 36 is set at 40 chains, and the corner of sections 25, 26, 35, and 36 is established at 80 chains. The section line between sections 25 and 36 is then run east on a random line to the northeast corner of section 36 on the range line and then run back westerly on the true line. The one quarter section corner of sections 25 and 36 is established at midway or midpoint along the line. This procedure is continued northerly until section 12 is completed. The section line between sections one and two is then run on a random line to the section corner on the north boundary and finally surveyed southerly on the true line. One quarter section corner of sections one and two is established at 40 chains from the corner of sections one, two, 11, and 12 with the excess or deficiency in measurement being placed in the northerly half mile. If a township closes on a standard parallel to the north, however, the section line between sections one and two is surveyed parallel to the east boundary. A one quarter section corner is established at 40 chains and a closing corner for sections one and two established at the intersection with the standard parallel. The survey of the section lines then continues for the next tiers of sections to the west as just described. The section lines connecting with the west boundary, such as the line between sections 30 and 31, are run west on a random line and then easterly on a true line connecting the section corners. The one quarter section corners are established on the true line, 40 chains exactly from the easterly section corners. All excess or deficiency in measurement is placed in the westerly half mile. The procedure I have just described for the survey of federal lands into townships and sections is a theoretical or ideal procedure. In reality, the lines of the original surveys may not have been run in the prescribed manner. The order of the surveys in California was often determined by settlement or development pressures. The demand for surveys on valuable agricultural, timber and mineral lands greatly influenced the progression of the surveys. Extremely rugged terrain, then thought impossible and impractical to survey, also necessitated departures from the general scheme. Only by acquiring and researching the pertinent field notes and plots of the original surveys can you positively determine how the original surveys were made and determine the precedence of lines for a present day resurvey. California surveys under the Oregon manual between 1851 and 1855 differ from subsequent surveys in three ways. First, the one quarter section corners and section corners established along the baselines were common to the townships both north and south of the baseline. There were no closing corners on the baselines as per the 1855 and subsequent manuals. Second, the standard parallels lying south of the baseline constitute the base for the townships to the south. In other words, the standard corners apply only to the townships and sections south of the standard parallel. Closing corners were established where the township and section lines to the north intersected the standard parallel. This is the reverse of the present practice. Third, for townships south of the baseline, the range lines are run from north to south. Where standard township or section lines intersect meanderable bodies of water, meander corners are established. Navigable bodies of water and other important rivers and lakes were meandered through a township by the original surveyors. A meander line is a traverse of the mean high water line of the body of the water. A meander line is not run to define the boundaries of a parcel. It's purpose is to determine the quantity of land in a parcel. The body of water is the actual boundary line. The original surveyors were required to monument all section and one quarter section corners. When the survey is executed in the 1800s, generally used materials native to the area survey for monumentation, such as a large marked stone and a mound of smaller stones or a marked wooden post and a mound of earth. Not your groove marks were made on a stone or post monuments by the original surveyors to identify the corner. Where possible, corner accessories such as bearing trees were taken. The original surveyors were also required to note all objects and features on and along the survey lines. Trees which were intersected by survey lines were hacked or notched with an axe twice on each side of the tree. These trees are called line trees. Topographical features such as creeks, ravines, ridges, canals, washes and so on are noted. Online objects and features were reported and described in the field notes at measured distances. Two key points which you should remember regarding PLSS surveys are first that the boundaries and subdivisions of the federal lands are unchangeable after the passing of the title by the United States. And second, that the original township section, quarter section and other monuments as physically evident must stand as the two corners of the subdivisions which they were intended to represent and will be given controlling preference over the recorded directions and lengths of the lines. As I mentioned earlier, the excess or deficiency in measurement in a regularly surveyed township is placed along the north or west boundaries of the township. The graphic now on the screen illustrates a normal platting of sections five, six, seven and eight. The usual deficiency in area which results from convergency of the meridians is placed in fractional areas called lots along the west boundary. The surplus or deficiency in area which results from the discrepancy in meridional measurements between the exterior boundaries and the subdivisional lines is placed in fractional lots along the north boundary. Once the public lands were surveyed and the plots created and approved, a parcel of land could be described with certainty. Section 14 will be used to illustrate the nomenclature which is used to describe an adequate part or legal subdivision of a section. The parcel at the top left of the section is described as the northwest one quarter, northwest one quarter of section 14. Immediately below is the parcel described as the southwest one quarter, northwest one quarter of section 14. And below that the parcel described as the northwest one half, southwest one quarter of section 14. Locating adequate part descriptions such as these is often easier if read backwards. For example, the southwest one quarter, northwest one quarter would be pictured first as the northwest one quarter, then as the southwest one quarter of that northwest one quarter. In this illustration, section 14 is made fractional by a lake and two non-equipped parts of a section were created. These two parcels adjoining the lake are described as lot one and lot two of section 14. Subdivision of section corners have been given specific names. If you are given a 16th section corner name or designation, you should be able to quickly visualize the location of that corner in relation to the section. The example shown is of the northwest quarter of a section. The northwest quarter is shown subdivided into quarter quarter or 16th sections. The center quarter of the section shown at the lower right of the screen and abbreviated as C one quarter is normally established at the intersection of straight lines between the opposing one quarter section corners. The 16ths controlling the subdivision of the northwest quarter, the north one 16th, the west one 16th, the center north one 16th, and the center west one 16th are established either midway or in the case of sections that adjoin the northwest boundaries of a township at the proper proportional distance between the pertinent section or one quarter section corners along the line. The northwest one 16th shown in the center of the quarter section and abbreviated as northwest one 16th is usually established at the intersection of straight lines between the opposing controlling one 16th corners. If you're not familiar with these corner designations and their approximate location in a section, you should have used sections 438 and 439 of the 1973 manual. This concludes the background material on the PLSS which I wanted to provide. I'd now like to move on to a PLSS subject which you are very likely to encounter on the LS exam. This subject is the subdivision of sections. Lands were patented or conveyed to individuals from the federal government under various settlement laws, such as the Homestead Act. Under these laws, patents were issued for adequate parts or lots of a section. Private surveyors are now often called upon to determine the boundaries of these patented sectional parts. In most of the original surveys by the GLO, the only boundaries which were surveyed by the federal government were the exterior boundaries of the sections. On the official plat of the surveys though, the federal government's plan for the subdivision of section lines was protracted. This was usually done by showing dashed lines on the plat. These dashed lines do not contain measurements. This graphic shows the protracted lines for a typical platting of sections five, six, seven and eight. Sections shown on the plat containing 640 acres, such as section eight in this graphic were protracted in the quarter sections usually by dashed straight lines connecting opposite one quarter section corners. For a normal section such as this, the boundaries of the quarter-quarter sections were not protracted because such subdivisions are adequate parts of a section and are based on midpoint positions for the 16th corners. Sections five, six and seven contain additional lines protracted on the plat to indicate the boundaries of the lots. This is typical for sections which adjoin the north or west boundaries of a township where the excess or deficiency in measurement was placed. Using the protracted subdivision plan shown on the original plat and the laws and regulations of the federal government, the procedure to use in subdividing a section can be determined. Before a section can be subdivided though, the positions for the corners on the section boundaries have to be located. This includes establishing the positions for the 16th corners if necessary. Once this is done, the section can be subdivided. The procedures to subdivide sections which I'll now discuss are for the first survey of the subdivision of a section. To subdivide a section into quarter sections, the center lines are run from the established one-quarter section corners to the opposite quarter section corners. This is illustrated by the protracted center lines in sections five, six, seven and eight. The point of intersection of the center lines of the section will be the corner common to the four-quarter sections. It is a legal center of the section and as I mentioned earlier, it's called the center one-quarter of the section. The position for the center one-quarter section corner can easily be determined by using a bearing-bearing intersection calculation. To subdivide a quarter section into quarter-quarter sections, the center lines of the quarter section will be run straight between opposing corresponding 16th corners. This principle does apply to the quarter sections along the north and west boundaries of the township, even though it may not appear that way from the protracted lines. For example, in section seven, only the line between lots three and four is protracted. This line is actually the west half of the east-west center line of the southwest quarter. The southeast corner of lot three, which is identical with the northeast corner of lot four, is determined by the intersection of the center lines of the southwest quarter. The point of intersection is the legal center of the southwest quarter and is called the southwest one-sixteenth section corner of section seven. In order to subdivide sections which join the north and west boundaries in the quarter-quarter sections, parenthetical distances usually have to be determined. As we defined earlier, a parenthetical distance is an implied survey plat measurement. As an example of why it's necessary to be able to determine parenthetical distances, let's again focus on the southwest corner of the southwest quarter of section seven. In order to determine the location of the north-south center line, the positions of the west one-sixteenth along the south boundary and the center west one-sixteenth along the east and west center line have to be determined. The west one-sixteenth is not at midpoint between the south quarter and the southwest corner of the section, nor is the center west one-sixteenth at midpoint between the center one-quarter and the west one-quarter. The fractional measurements in the last quarter mile make it necessary to determine the parenthetical distances in order to place the sixteenths at the correct proportions along the lines. A parenthetical distance is not in the field notes which indicates that the distance was not measured on the ground. Parenthetical distances are used to determine where certain points not monumented by the original survey are to be established. They may or may not be shown on a plat. If shown, they are usually in parentheses. If not shown, they are implied by the principles used to lot sections and can be calculated. They are considered as part of the record. Because parenthetical distances were used to calculate the areas of a section, they are also used to protect such areas by means of proportionate measurements to determine the position of the previously unmonumented points. To clear up any confusion about parenthetical distances, let's look at an example. This section is an example of platting along the west boundary of a normally surveyed township. The section is protracted into two 160-acre adequate parts, the northeast and southeast corners of the section, quarters of the section, two 80-acre adequate parts, the east one-half northwest one-quarter and the east one-half southwest one-quarter and along the west boundary, lots one, two, three and four. The lot number is usually stacked above the area in acres of the lot. In this example, lot one contains 42.75 acres and lot two, 42.65 acres. Along the south boundary of this section, normally the only distance measurement given is the overall distance. In this case, 81.20 chains. The implied measurements from east to west are 40 chains to the monumented south one-quarter corner, 20 chains to the unmonumented west one-sixteenth and the remainder along the south boundary of lot four, 21.20 chains. The west one-sixteenth corner along the south boundary of this section would be established using the proportional elements, 20 and 21.20, between the south one-quarter section corner and the southwest section corner. The position of the west one-sixteenth on the north boundary of this section is determined in the same manner. Along the north boundary, the implied measurement for lot one is 21.40 chains. The measurement along the west boundary of the section is 80 chains. The west boundaries of lots one through four are implied to be equidistant or 20 chains each. In a normal original survey, the east boundary of the section is also 80 chains. The east boundaries of lots one through four then are also 20 chains each. Since each of them already on the lines of the lot is 20 chains, an easy way to calculate the north boundary of lot four is to subtract the distance along the south boundary from the acreage. 42.45 minus 21.20 is equal to 21.25 chains along the north boundary of lot four. Similarly, the north boundary of lot three can be computed. 42.55 minus 21.25 equals 21.30 chains. The north boundary of lot two is 42.65 minus 21.30 or 21.35 chains. As a check, the north boundary of lot one is determined in the same manner. 42.75 minus 21.35 matches the remainder distance of 21.40. Although in this case, the distances could have been calculated directly by averaging the remainder distances along the north and south boundaries of the section. It is a good idea to check the areas to make sure of the plotting intent and that there are no computational errors. Once the parenthetical distances have been calculated, the center west one sixteenth can be established along the east and west center line. The center west one sixteenth will be established at proportion between the center one quarter and one quarter corner on the west boundary using the proportional elements 20 and 21.30. Now let's move on to a more difficult section. This is a normally plated section six, being lotted against the north and west boundaries. Although it looks more complicated, the analysis and methods used to calculate parenthetical distances are the same. All excess or deficiency in measurement is placed to the north on a meridional line or to the west on a latitudinal line. Let's look at each of the boundaries of the section and determine the implied measurements. Along the south boundary, the implied measurements from east to west are 40, 20 and 18.40 chains. Along the west boundary, the 80 chains implies that the west boundaries of lots 4, 5, 6 and 7 are 20 chains each. Along the east boundary of the section, the implied measurements from south to north are 40, 20 and 19.06 chains. And along the north boundary of the section, the implied measurements for lots 1, 2 and 3 are 20 chains with the deficiency in measurement of 19.00 chains being placed along the north boundary of lot 4. From this analysis, you can determine that the parenthetical distances along the east and west boundaries of lots 5, 6 and 7 are 20 chains each. Also, you can determine that the parenthetical distances along the north and south boundaries of lots 1, 2 and 3 are 20 chains each. Therefore, to calculate the remaining parenthetical distances of the lots, the same method used in the previous example will work. The north boundaries of lots 7, 6 and 5 can be determined by subtracting the distance from the acreage. For the north boundary of lot 7, 36.95 minus 18.40 equals 18.55 chains. The calculation would continue northward to the north boundary of lot 5, which would equal 18.85 chains. Then you would determine the west boundaries of lots 1, 2 and 3 in a similar manner. For the west boundary of lot 1, take the acreage for lot 1 of 38.35 and subtract the distance of 19.06 along the east boundary of lot 1. This works out to be 19.29 chains. Similarly, for the west boundary of lot 2, 38.82 minus the just calculated 19.29 equals 19.53 chains. And finally for the west boundary of lot 3, 39.29 minus 19.53 equals 19.76 chains. As a check, you should mean the opposing boundaries of lot 4, and then multiply them times each other to get the acreage of lot 4. In this case, the north and south are 19.00 and 18.85 chains respectively, which mean to 18.925 chains. The east and west boundaries of lot 4 are 20 and 19.76 chains, which mean to 19.88 chains. Then multiplying the means of 18.925 and 19.88 gives you 376.2 square chains or 37.62 acres. This checks within a hundredth of the acreage, which is acceptable. When originally calculated, the mean of the north and south boundaries of lot 4 were probably rounded from 18.925 to 18.93 to make the multiplication easier. Using 18.93 for the check, the acreage actually works out to 37.63, which is the same as shown on the graphic. These examples provide you with the basics necessary to analyze and determine parenthetical distances for most normally surveyed sections adjoining the north and west boundaries of a township. Three important rules to remember about parenthetical distances are. Number one, they are considered as part of the official Platt record. Number two, areas shown on the Platt are based on parenthetical measurements. And number three, they must be used to determine the record patent boundaries. Now let's move on to the subdivision of a fractional section. Basically their boundaries are not completed because of an intervening body of water, a senior boundary, or an uncompleted survey. A section is fractional if it cannot be completed because of a private land grant boundary, such as one of the many ranchos in California, or an Indian reservation boundary as shown here. The north and east boundaries of section 4 were terminated at their intersection with a senior Indian reservation boundary. Closing corners were established at the intersection points. As you can see, there is not a north section corner to determine the direction of the north-south center line. Fractional sections may be created against a meandered body of water, as in this example along the Smith River. The north and west one-quarter section corners of section 32 were not set. Fractional sections could also result from uncompleted surveys. In this example, the section lines of sections 8 and 9 could not be completed, most likely due to unsurveyable terrain. On the survey Platt's, acreages and alcove parts of the section are joining the surveyed lines. As an example, the southwest quarter of section 9, totaling 160 acres, was returned to surveyed. The north and east boundaries were not surveyed, and the northeast, southeast, and northwest quarters are not considered surveyed. Since the north and west one-quarter section corners were not established, the section as shown here would be considered fractional. Sections which are not in alignment on opposite sides of meandered rivers are fractional. And for a final example, sections which border large bodies of water are considered fractional. By law, where opposite quarter section corners have not been fixed, the subdivision of sections will be run from the established corners north, south, east, or west, to the boundary or body of water that cause the opposite fractional exterior. The law presumes, section lines are north, south, east, or west. To carry out the spirit of the law, meeting courses for the subdivision of section lines must be adopted, or parallel lines run, as conditions may require. Now shown are two situations where parallel courses would be used to survey the center lines. In a situation on the left of the screen, the section was made fractional, and a normal north boundary does not exist. Therefore, the east-west center line of the section, or the center lines of the quarter sections, would be surveyed parallel to the south boundary of the section. In a situation on the right of the screen, where the section is partially unsurveyed and the north boundary is not yet established, parallelism would be used to determine the courses of the center lines. Meeting courses are necessary to subdivide fractional sections and the two situations now shown. Both situations are similar, and that one of the one quarter section corners is nonexistent, but both portions of the corresponding section lines exist. In the section shown on the left of the screen, the east-west center line would be surveyed on the mean bearing of the north and south boundaries of the section. If the section shown on the right, in the section shown on the right, the north-south center line would be surveyed on the mean bearing of the east and west boundaries of the section. Where two adjacent quarter section corners are nonexistent, the portions of all the exterior boundaries of the section exist. Again, mean courses will be adopted. As far as we've identified situations where mean courses would be adopted to subdivide a section, there are three different ways to calculate a mean course. Conditions found in the fractional section will determine the method used to determine the bearing of the mean course. First is the arithmetic mean. The arithmetic mean is used where opposite section lines are relatively equal in length. As shown in this example, the east and west section lines are about equal in length. Therefore, the center line is surveyed on the arithmetic mean of the bearing of the east and west boundaries of the section. The third type of mean course is the weighted mean. The weighted mean is used where opposite section lines differ greatly in length, as illustrated here. The weighted mean bearing to survey the center line is developed based on the ratio of the links of the two section lines. The third type of mean course is the weighted mean for an uncentered center line situation. An example where this may occur is along the west boundary of a township. As you can see from this example, the north and south center line is not centrally located. In this case, a mean course would be developed based on the ratio of the distances from the east and west section lines to the uncentered center lines. Now let's look at actual calculations necessary to determine the mean courses to run in these three different types of situations. The arithmetic mean would be used in this fractional section situation. Since the east and west boundaries of the section are of about equal length, and the center line is centrally located in the north and south center line. First, determine the difference between the bearings of the west boundary and the bearing of the east boundary, which is 58 minutes. Next, divide the differences by two. The result is 29 minutes, which is the amount to be subtracted from the bearing of the west boundary as shown here. The arithmetic mean bearing to survey the north-south center line is south zero degrees, 09 minutes west. The known position of the north-one quarter corner and runs south zero degrees, 09 minutes west to intersect the south boundary of the fractional section. The weighted mean would be used to determine the east-west center line of the section. Since the north and south boundaries of the section are significantly different in length, the easiest way to determine the weighted mean bearing for the east-west center line is to first break the bearings and distances of each line into latitudes and departures. The latitude of the north line 0.4735 is then added to the latitude of the south line plus 0.1367 to give a total latitude of plus 1.6102. Similarly, the departures are added together to give a sum of plus 93.3678. The total latitude and departure is then converted to polar coordinates, which yields a bearing of north 89 degrees, 00 minutes and 43 seconds east. This is the weighted mean bearing to use for the survey of the east-west center line. The survey of the east-west center line would start at the known position of the west-one-quarter section corner and run on the weighted mean bearing to intersect the east boundary of the fractional section. A weighted mean bearing for an uncentered center line situation is necessary to determine the bearing for the north and south center line of this section. Basically, the mean bearing will be determined by the proportion of the lengths of the south boundary. The first step is to determine the length and departure of the east and west segments of the south boundary and add them together for a total departure of the line. In this case, the departures are given as 40.23 and 7.21, which total 47.44 chains. Next, determine the difference in minutes between the east and west boundaries, which is 66 minutes. A proportion is then set up as follows. The partial departure of 7.21 is divided by the total departure of 47.44 to give a proportion factor which is labeled as K on the graphic. The proportion factor is then multiplied by the difference in bearing of 66 minutes, which yields a result of 10 minutes. The 10 minutes is then subtracted from the bearing of the west boundary, which gives the weighted mean course for the north-south center line of north 0°02 minutes east. As a check, the partial departure of 40.23 is divided by the total departure of 47.44 to multiply times the difference in bearing of 66 minutes, which will yield a result of 56 minutes. The 56 minutes is then subtracted from the bearing of the east boundary to give the same weighted mean of north 0°02 minutes east. The survey of the north-south center line would then start at the south-quarter corner of the section and run north 0°02 minutes east on the weighted mean bearing to intersection with the boundary which made the section fractional. In the preceding cases involving fractional sections, the recommended procedures for subdividing fractional sections have been demonstrated. As a word of caution, when subdividing a fractional section, strong consideration must be given to any existing collateral evidence which was established in good faith. Acceptable collateral evidence would preempt any of the recommended procedures. To conclude this discussion on subdivision of sections, I'd like to remind you that this is a prior to subdividing. Only by doing so can you ensure that you've adopted the correct procedures to subdivide a section. At this point, we're about midway through Unit 12 of the PLSS course. This is a good place for you to stop and review the material discussed so far. So let's take a break. Welcome to the second half of Unit 12 of the Caltrans LS-LSIT video training course. During the second half of this course, we'll be discussing the principles of the Dependent Resurvey, the last corners, and going over several questions from previous LS exams. Now let's start by defining five terms which will need to be understood for subsequent discussions. There is much confusion in the profession about these definitions. To be successful on the exams, you must understand them. Although they are sometimes used as if they were interchangeable, the term corner and monument are not. Synonymous. This is the point determined by the surveying process. A monument is the object or physical structure that marks the corner point. The corners of the PLSS are those points that determine the boundaries of the various subdivisions represented on the plats. Examples are the township corner, the section corner, the one quarter section corner, and the subdivision of section corner. PLSS corners may or may not be monumented. Monuments of the PLSS have included marked trees, marked stones, wooden stakes, and metal post monuments in use today. Accessories such as bearing trees are aids in identifying the corner position. In their broad significance, the accessories are a part of the corner monument. Recovered original monuments are corners of the PLSS. Monuments subsequently set during resurveys or subdivision of section surveys may or may not be PLSS corners. Subsequently set monuments whose positions were established using proper procedures and where the original evidence was not overlooked are corners of the PLSS. If evidence of the original survey monument was overlooked by the resurvey, the resurvey monument would not be the corner. In this latter case, the resurvey monument is just a monument. Because a monument is subsequent to the original survey may not be a PLSS corner, it is extremely important to verify the acceptability of a monument as a PLSS corner. Never use a monument based solely on another survey or statement that it is a corner. Make that determination for yourself. Examine the position and history of a monument to the extent possible. Make sure evidence of the original survey was not overlooked. A professional survey should be skeptical of a monument until it can be determined that the monument is acceptable as the corner. An existing corner is one whose position can be identified by verifying the evidence of the monument or its accessories by reference to the description that is contained in the field notes or where the point can be located by an acceptable supplemental survey record, some physical evidence or testimony. An obliterated corner is one where no trace of the monument or its accessories remain but whose location has been perpetuated or may be recovered beyond reasonable doubt by the acts and testimony of interested landowners, competent surveyors, or other qualified local authorities, or witnesses or by some acceptable record evidence. A lost corner is a point of survey whose position cannot be determined beyond reasonable doubt, either from traces of the original marks or from acceptable evidence or testimony that bears upon the original position and whose location can be restored only by reference to one or more interdependent corners. The terms just defined are commonly used in relation to the PLSS. When a corner, monument, obliterated corner, or lost corner is referred to, you should immediately know what is meant by the term. Now let's discuss resurveys. The subject of resurveys is found in Chapter 6 of the 1973 manual. For the LS exam, Sections 1 through 32 of this chapter should be studied. The discussion on resurveys, which I'm going to present, is based on this chapter of the manual. There are two types of resurveys, the dependent and the independent. An independent resurvey is a new survey which supersedes the prior official survey insofar as the remaining public lands are concerned. Patented lands are not affected as to location. The authority to make independent resurveys of the federal lands rests only with the Bureau of Land Management. Since an independent resurvey is solely the function of the BLM, I will not discuss it now. You should know that independent resurveys exist and look for them when you are researching a project. A dependent resurvey is defined in the 1973 manual at Section 6-4. The section states that a dependent resurvey is a retracement and re-establishment of the lines of the original survey in their true original positions according to the best available evidence of the position of the original corner. As a professional licensed land surveyor, any job you do involving the PLSS will invariably involve dependent resurveying section or township lines. For this reason it is very important to understand what a dependent resurvey is and what it is not. A dependent resurvey is first-array-tracement to identify original corners and other acceptable points of control. Second, it restores lost corners by proportionate measurement in accordance with the record of the original survey. The purpose of a dependent resurvey is not to correct the original survey by determining where a new or exact running of the line would locate a particular corner. It is instead used to determine where the corner was established by the original survey. A properly executed dependent resurvey protects existing rights acquired under the original survey in the matter of location on the earth's surface. An important point to remember is that the boundaries of sections based on the original survey are identical to the boundaries of the same sections based on a properly executed dependent resurvey. The guidance given by the courts in retracing lines of previous surveys is to follow in the footsteps of the original surveyor. It is possible to follow in the footsteps requires knowledge of the procedures and instruments which the original surveyor used to make the surveys. As I mentioned in the first portion of this course, some of this knowledge can be gained from the manual and force as of the date of the survey. The courts have attached major importance to evidence relating to the position of the original corner. The location of the original corners are given much more weight than the record bearings and distances of the lines. Existent original corners are fixed in position and are unchangeable. As a part of the retracement, an exhaustive search must be made for all existing evidence of the PLS Monuments and their accessories. The evidence recovered can be expected to range from that which is inconclusive to that which is unquestionable. The need for corroborative evidence is therefore in direct proportion to the uncertainty of the evidence. The evidence should agree with the record field notes of the survey with allowance for natural changes. Topographic calls made by the original surveyors should be located during the retracement. Topographic calls are often very useful in locating original corners. They also may help prove or disprove questionable corner evidence. For a subject to only one interpretation, topographic calls may fix the position of a missing corner beyond a reasonable doubt. To fix the position of a missing corner, the topographic call should have a questionable interpretation. It should result in a definite locus within a small area and it should not be contradicted by other topographic calls or by evidence of a higher class. Even questionable evidence of the original corner or its accessories substantiated by topographic calls provides a much more defendable corner position than from topographic calls alone. Where questionable topographic calls are the only indication of a corner position is ordinarily better to establish the position by proportionate measurement. After retracing the lines of an original survey and identifying existing original controlling corners, lost corners are then re-established. The Restoration of Lost or Obliterated Corners is discussed in Chapter 5 of the 1973 Manual. For the LS Exam, it is important that this chapter be studied. Again, my discussion on the subject of Restoration of Lost Corners is based on this chapter in the 1973 Manual. On the topic of re-establishing lost corners, I also highly recommend this informative pamphlet of 40 pages. It is titled Restoration of Lost or Obliterated Corners and Subdivision of Sections A Guide for Surveyors. It is issued by the BLM as a supplement to the Manual of Survey and Instructions. I recommend that it be included in your LS Exam Library. The pamphlet discusses the fundamental practices of the two subjects mentioned in the title from the viewpoint of the BLM. The pamphlet can be obtained from the U.S. Government Printing Office whose address is listed in the workbook. For the LS Exam and for the Professional Practicing Surveyor involved in resurveys of the PLSS, it is important to know how the restoration procedures are computed. Even more important though, the professional surveyor must know when the use of a certain restoration procedure is appropriate. For an analogy of the situation, let's look at the medical profession. A doctor is highly educated to know what medicines are available and how they work. More importantly though, the doctor must know when a particular medicine's use is necessary and warranted. Again, I want to stress that you should not only learn how to do the calculations for a restoration procedure, but learn in what situations the restoration procedure is appropriate. The rules for the restoration of lost corners should not be applied until all original and collateral evidence has been developed. Where these means have been exhausted, the surveyor will turn to proportionate measurement. This method of reestablishment harmonizes surveying practice with legal and equitable considerations. Proportionate measurement is always employed to reestablish the position of a lost corner, unless outweighed by conclusive evidence of the original survey. A proportionate measurement is one that gives equal relative weight to all parts of the line. The excess or deficiency between two existing corners is distributed to proportion to the record measurements of the line. In reestablishing lost corners of the PLSS, consideration must be given to the precedence or importance of the lines. The type of proportionate measurement to be employed is dependent on the procedures used to establish the original survey. As I stress in the first half of this video, it is extremely important to acquire and analyze the original survey records to determine how the original survey was established. In general, lost corners on standard parallels are given precedence in the order of reestablishment over lost corners on other township lines. Lost township corners are given precedence over sectioned corners, and lost sectioned corners are reestablished before lost one-quarter sectioned corners. The record measurements to use in any proportionate are from the latest acceptable survey. For example, if the original survey of a township was made in 1875 and subsequent re-surveys were made in 1917 and 1967, the measurements from the 1967 re-survey would ordinarily be used. 1967 measurements are of a higher accuracy than the 1875 and 1917 measurements and are more likely to re-establish the lost corner in its true position. Record measurements to use in proportioning can be made up of a combination of surveys. For example, the lines to the south and east of a lost sectioned corner may have been surveyed in 1867 and the lines to the northwest in 1885. In this instance, both records would be used for the proportional elements. The two most commonly used forms of proportionate measurement are the single and double proportion. Typically, a double proportion is employed to re-establish the lost corner of four townships or a lost corner of four sections. The double proportion is made between the nearest identified corners to the north and south and to the east and west of the lost corner. In the graphic shown, the identified controlling corners are E. The township corner at X has been determined to be lost. The position and latitude, labeled E, to re-establish the lost corner is determined by proportion between corners A and B. The position and departure, labeled F, to re-establish the lost corner is determined by proportion between corners C and D. The re-established position, X, is located at the latitude and departure determined from the double proportion. In a double proportion, a lost corner is re-established on the basis of measurement only, disregarding the record directions. The manual, in section 5-25, states, links of proportioned lines are comparable only when reduced to their cardinal equivalence. What this means is that the latitudes of the record meridional measurements are used and the departures of the record latitudinal measurements. This is an example of a latitudinal line with a record measurement of north 80.07 chains. For a double proportion, the departure of the line is used as the record proportional element. In this case, the departure to use is 79.875 chains. This is an example of a meridional line with record measurements of north 2 degrees east, 80.00 chains. For a double proportion, the latitude of the line is used as the record proportional element. In this case, the departure to use is 89.951 chains. The links of the record lines are broken into latitudes and departures so that lines with bearings varying greatly from cardinal directions are not given excess proportional frontages. Where the record lines are all very close to cardinal directions, it may not make much difference whether you use the latitude or departure of the line. However, using the latitudes and departures is the technically correct procedure to use and where other than cardinal bearings exist will make some difference. Also, if you don't use the latitudes and departures for the record lines on the LS exam question, you should lose points for an incorrect procedure. Let's look at an actual example of a double proportion and work through the numbers. The record measurements shown are from an 1880 survey. The diamonds are the existing controlling corners, with the circle being the lost section corner to be reestablished. The purpose of this proportion is to determine the latitudes of the record meridional lines and the departures of the record latitudinal lines. The latitudes and departures shown will be used to form the record proportional elements. The coordinates shown at each of the controlling corners are the coordinates from the current retracement of the lines. For a meridional line, a proportion is set up as shown. The partial record latitude is to the total record latitude as to the partial latitude L is to the total retracement latitude. Using algebraic procedures, the formula can be manipulated to determine L directly. Similarly, the departure can be determined. The northern coordinate to restore the lost corner is determined as follows. The partial latitude L is first determined by dividing the partial record latitude of 40.00 chains by the total record latitude of 40 plus 40.195 chains or 80.195 chains. The result is multiplied by the current retracement northern between the meridional controlling corners which is 80.00 chains. This provides the latitude north of the subtly controlling corner to restore the lost corner. This latitude is then added to the northern coordinate of the subtly controlling corner which is zero in this case to give the northern coordinate of the reestablished corner which is 39.903. The east end coordinate to restore the lost corner is then determined in a similar manner as shown. The calculated partial departure of 40.121 chains is added to the east end coordinate of the westerly controlling corner in this case zero to give the east end coordinate of the reestablished corner which is 40.121. and 40.121 chains east. In this case these coordinates can then be inverse with the controlling corners to give the bearings of the reestablished lines. In a case where a controlling line extends beyond another lost section corner the additional lost section corner would also have to be reestablished before you could inverse to get the bearing of the section line. As an example, say the nearest controlling corner to the east of the shown reestablished corner had been two miles or two section corners away The additional intermediate section corner would also have to be reestablished by double proportion before the bearing of the section line between them can be determined. A double proportion to determine two or more lost section corner positions is made using essentially the same techniques as discussed earlier. Essentially, a double proportion is two single proportions one in the north-south direction to determine the latitude of the position to reestablish a corner and another in the east-west direction to reestablish a corner. Now let's look at an example of a single proportion. A single proportion is used to determine one or more positions on a line with one continuous record bearing. In this example the diamonds show the controlling section corners and the lost one-quarter section corner of sections 3 and 10 is shown as a circle. The record measurements are north 88 degrees east 80.10 chains. The current retracement measurements are north 87 degrees east 80.57 chains. In a single proportion it is not necessary to break the record measurements into latitudes or departures. The record and measure distances between the controlling monuments are what's important and they are directly comparable. The single proportion is set up similarly to that of the double proportion. The partial record distance of 40.05 chains is divided by the total record distance of 80.10 chains and multiplied by the total measured length of 50.57 chains. The result is 40.285 chains which is the distance from the section corners to the re-established position for the one-quarter section corner. Some township boundaries were not established on one continuous bearing. These are termed irregular exteriors shown as an example of such a situation. The south boundary of the township along sections 34 and 35 was surveyed in 1863. The record bearing of the lines is west. A completion survey of the south boundary was made in 1879 using a random and true line. The record bearing of the south boundary of section 33 is north 88 degrees 14 minutes west. Lost corners along this township line would be re-established using a modified form of single proportionate measurement. In order to restore one or more lost corners on such irregular exteriors a retracement is made between the nearest acceptable corners The retracement determines the direction and length of the closing distance of the measurements of the retracement versus the measurements of the record. In a latitudinal line such as this the position in easting is determined by using an ordinary single proportion of the record and retracement departures. The position in northing is determined using the differences in latitude of the record and retrace measurements. The difference in latitude is distributed to each line between controlling corners in proportion to the length of each course. On meridiano irregular boundaries the position in northing and easting to re-establish a lost corner would be determined in reverse of those for the latitudinal irregular boundaries. This modified single proportion is commonly called an irregular boundary adjustment. It is also applicable to a section line or a township line shown to be irregular by a previous retracement. This discussion on irregular boundaries is intended to make you aware that they exist. Hopefully if an irregular boundary situation is encountered you will be able to identify it and realize that a modified form of single proportion is required. I haven't used any numbers for a step-by-step irregular boundary problem solution. So to clear up any confusion which may exist problem 4 in the workbook for this course involves an irregular boundary. The solution for the irregular boundary is worked out step-by-step. Where a line has not been surveyed in one direction from a lost township or section corner the record distance will be used to the nearest identified corner in the opposite direction. In the example shown the sections to the north have not been surveyed. The position in the northern of the lost corner is determined by the cardinal equivalent of the record distance to the controlling corner to the south. For instance, if the one quarter section corner of sections 35 and 36 is the control to the south and the record measurements are south 40.00 chains then the lost corner will be reestablished to the 0.00 chains and latitude north of the one quarter section corner. The position in the east is determined by single proportioning the record departures between the nearest controlling corners to the east and west of the lost corner. Notice that in this case it is again necessary to use cardinal equivalents of the record east-west measurements. Where lost corner was established from two directions only the record measurements to the nearest existing corners on the two surveyed lines were the record measurements shown as an example where the lines to the north and east of the northeast corner of section 10 were not surveyed. The northeast corner of section 10 is determined to be lost. The position in latitude to reestablish the lost corner is the cardinal equivalent of the record line or lines from the nearest controlling corner to the south. The position in the easting to reestablish the lost corner is the cardinal equivalent from the nearest corner. Where a lost corner was established from one direction only it should be restored at the record bearing in distance from the nearest controlling corner. In the example shown the east one quarter section corner of section 3 is lost. It was established at the terminus of the section line surveyed from the south. If the original southeast corner of section 3 is recovered then the lost one quarter section corner will be reestablished at record bearing in distance from the southeast corner called reestablishment by one point control. The appleville section of the 1973 manual is 5-45. The sufficient lines of the record survey have been retraced to conclude that a consistent difference exists between the record measurements and the current retracement measurements then an index correction should be applied to the record measurement used in reestablishing the corner. This is another example of where a line has been terminated with measurement in one direction only. In this situation the meander corners will ordinarily be restored by record bearing in distance from the nearest controlling corner. Again, an index correction for average error if applicable should be applied. Where lost meander corners were originally established on a line projected across a meanderable body of water it will ordinarily be relocated by single proportionate measurement. In both situations involving meander corners though under favorable conditions it will be restored by treating the shoreline as an identifiable natural feature. In the event of extensive obliteration of the original corners within the locality of the lost meander corner this method may be preferable to one obtained by record bearing in distance or proportionate measurement. A lost closing corner is reestablished on the line closed upon at single proportionate distance between the nearest acceptable corners to the right and left. Shown as an example of a lost closing corner the intersection line was originally closed on the rancid boundary. The position of the closing corner is reestablished by a single proportionate measurement between maples 5 and 5.5 on the rancid boundary. Where monuments set for a closing corner are recovered off the line closed upon they determine the direction of the closing line but do not determine the terminus of the line. The correct position for the terminus of the line is at the intersection of the closing line with the line closed upon. There are examples in the PLSS of monuments which are not necessarily the corner. On this graphic, recovered monuments are shown with diamonds and triangles. On the west boundary of section 3 the closing corner monument is recovered north of the line closed upon. The true point for the closing corner is located on the line between the recovered closing corner monument and the west one quarter corner of section 3 where it intersects the north line of the section. The north half of the westerly section line terminates at the true point for the closing corner. On the east boundary of section 3 the closing corner monument is recovered to the south of the line closed upon. The north half of the eastern section line of section 3 actually extends from the east one quarter corner of section 3 through the recovered closing corner monument to its intersection with the north line of the section. The true point for the closing corner is at this position. Any new monuments for the closing corners will be placed at the point of intersection at the true point of intersection. The recovered offline monument should then be marked AM for amended monument. When an offline original closing corner monument is recovered the recovered original position is used in proportioning to reestablished lost corners or to proportion 16th section or locked corners on the closing section line. Let's look at an example of this. Shown as the original record of the north half of a typical closing section on a standard parallel the parenthetical distances to establish the north one 16th section corner are from the one quarter corner 20 and 18 chains. A resurvey made to locate the position of the north one 16th section corner reveals that the original closing corner monument is actually 37 chains north of the recovered one quarter corner and 18 chains north of the standard parallel. The distance from the one quarter corner to the north one 16th corner is determined by proportioning between the recovered one quarter corner and the recovered original closing corner monument. The partial parenthetical distance of 20.00 chains is divided by the total of the parenthetical distances which is 38.00 chains and the result multiplied by the retracement distance between recovered monuments of 37 chains. The proportionate distance from the one quarter corner to place the north one 16th corner then is 19.474 chains. This would place at north of the standard parallel as shown by the retracement distance to the standard parallel of 19.00 chains. This resurvey reveals that lots one and four shown in the preceding graphic and the north one 16th do not exist. The section line actually terminates at the standard parallel. This is a dramatic example of how the recovered original closing corner is used to position a one 16th section corner. In closing sections the practice in older surveys was not to monument one quarter section corners between the closing section corners. In such cases the one quarter and one 16th section corners of the closing section along the line closed upon will ordinarily be established by proportionate measurement based upon the parenthetical distances. The areas of the lot should confirm the parenthetical distances. In the example shown section five closes on a standard parallel. The one quarter section corner section five only between the closing section corners was not monumented by the original surveys. This position is shown as a half circle on the graphic. If hired by a client to determine the boundaries of lot three section five you will need to determine the positions of the one quarter and west one 16th section corners of section five only on the standard parallel. These corners will be established using single proportionate measurement between the two points for the closing corners closing section corners of section five. The first step then is to determine the true positions of the closing corners. The true positions are as I previously discussed at the intersection of the closing section line with a standard parallel. In a normally surveyed section five the parenthetical distances along the north boundary of lots one through four are all 20.00 chains. Since the north boundaries of the lots are all 20.00 chains a single proportion to determine the position of the one quarter corner therefore the one quarter section corner will be established on the standard parallel at midpoint in departure between the two points for the closing section corners. The west one 16th corner of section five only will be established similarly on the standard parallel at midpoint between the closing section corner to the west and the just determined one quarter corner of section five only. The section can then be subdivided to determine the remaining boundaries of lot three. If this example had been of section six instead of section five then the one quarter corner one quarter section corner of section six only most likely would not have been at midpoint in departure between the closing section corners. This is because of the fractional measurement in a township being placed against the west boundary. The parenthetical distances along the north boundary of lots one through four would need to be determined and the positions of the one quarter and one 16th section corners of section six only established in the right proportion between the closing corners and on the standard parallel. Now let's discuss situations where a recovered witness corner is used as a control to establish a corner or to reestablish a corner. The first step is to closely analyze the plat and field note records of the witness corner. From this analysis make a determination as to whether the witness corner was originally established on the line of the survey or as an offline witness corner. A section corner as is an example of a recovered witness corner was originally established on a section line. A section corner to the west is established by double proportionate measurement if no complications arise using the recovered witness corner as a controlling corner. In this example a witness corner not originally established on the line of the survey is recovered. In this instance the true point for the section corner would be established at record bearing and distance of the witness corner. A definitely identifiable line tree is a monument of the original survey. It is used as a control point in the reestablishment of lost corners by the appropriate method of proportionate measurement. To be acceptable a recovered line tree must be positively identifiable. It also must have been on the true line of the original survey. On latitudinal section lines it was not uncommon for line trees to have been established on the random line instead of the true line of field notes on the random line. Again, the record field notes must be analyzed. In the example shown a positively identifiable line tree is recovered south of a lost section corner. This line tree is used as the control corner to the south for the reestablishment of the lost section corner by double proportionate measurement. The line tree becomes an angle point in the section line. In the graphic now on the screen a positively identifiable line tree is recovered south of a lost one quarter section corner. The line tree is used as the control to the south to reestablish the lost one quarter section corner by single proportionate measurement. Again, the line tree becomes an angle point in the section line. On many township lines and section lines two sets of corners have been established. One set of corners applies to the township to the north and one set applies to the townships to the south. Which corners control depends on how the line was surveyed. There are three common situations. The first situation as shown here is where a single set of corners was established in the survey of a line. Closing corners were later established for the sections on one side of the line. The corners first established are the senior corners and control both the alignment and any proportional measurements along the line. A standard parallel is an example of this first situation. The standard corners are the senior corners of the line. The second situation is where two sets of corners were established by measurement along the line in a single survey. Both sets of corners would have equal status for both alignment and any proportional measurements along the lines. This situation is not common in the PLSS. An example of how this type of situation occurs is on the original survey of a township line where number one, the surveys of the sections to the north and south are to be initiated from the township line because of existing conditions the section corners are to be offset. The third situation is where a set of corners was established for one side of the line during the course of a survey and a second set of corners is established for the other side during a later resurvey. The corners established by the first survey are considered senior and control the direction of the line. If both sets of monuments along the line are recovered a junior corner line offline is treated in the same manner as a closing corner insofar as the alignment of the subject line is concerned. Since the junior corners were established during the resurvey of the line it can be used for control to determine the cardinal equivalent in re-establishing a lost corner along the line by proportionate measurement. The lost corner is then re-established at the proportional cardinal equivalent and on the line controlled by the senior corners. This concludes the discussions on dependent resurveys and corners. In order to demonstrate the principles discussed in this video I've selected a few problems from past LS exams. Let's take a look at the first one. Problem A5 of the 1991 California LS exam was worth 36 points shown as a depiction of the diagram provided in the exam for the problem. The diagram is titled Platte Approved, April 3rd, 1893 The legend which is not shown is that the filled-in circles are found original government monuments. The X is our positions which were searched for but not found. The legend further states that all distances and bearings shown are record. The problem statement says you have been commissioned to survey fractional Section 8, Township 4 South Rain 6 West has shown on the official Platte which was approved on April 3rd, 1893. Your client has requested that all corners be monumented. The first problem requirement is to identify the method and the positions and or monuments you would hold for control to establish six listed corners. The first corner listed to be determined is the southwestern section corner. The first thing to look for in determining the correct procedure to use is whether all four section lines into the corner have been surveyed. In this case they have. Therefore the correct procedure to use in re-establishing the lost section corner is double proportionate measurement. The corners to use for the double proportion are the one-quarter corners to the north, east, south, and west of the lost southwestern corner of Section 8. These corners are the nearest recovered corners in all four directions from the lost position. The second corner to be determined is the northwestern corner of Section 8. From the platte you can see that Section 8 is made fractional because it closes on a senior rancid boundary line. Thus the northwestern corner of Section 8 is the closing corner which in this case is lost. The closing corner would be re-established by single proportioning along the rancho line. The controlling corners for the single proportion are the rancho corners shown to the southeast and northwest of the lost position. The third corner to be determined is the closing subdivision in the section corner of the north-south centerline of the section. To clarify this position on the graphic it's the intersection of the dash north-south centerline and the rancho boundary located just below the H in rancho. In the northeast corner the north-south centerline of the section has to be surveyed. The first thing you should notice is that the section is fractional and that the north-one quarter corner of the section does not exist. This indicates that a mean bearing is to be used to survey the north-south centerline. But what type of mean bearing? Notice that the centerline is centrally located within the section about midway between the east and west lines of the section. Also notice that the east and west lines of the section do not exist. As we discussed earlier in the video an arithmetic mean bearing is the appropriate type to use. The mean bearing of the north-south centerline would then be surveyed from the south-one quarter corner to intersection with the rancho boundary. The intersection point is the closing subdivision of section corner. The fourth corner to be determined is the northeast corner of the section. Since the section is fractional along the north boundary this corner is the closing corner. As shown in the graphic the eastern corner monument was recovered north of the rancho line. The intersection of the rancho boundary and the line between the southeast section corner and the recovered closing corner is the true point for the closing corner. The fifth corner to be determined is the east-one quarter corner of section 8. This position is shown to be lost. The east-one quarter corner is reestablished by single proportioning between the southeast section corner and the recovered original closing corner monument. Remember, recovered original closing corners are used for proportioning along the closing section line. The sixth and last corner the problem asked you to determine is the center-one quarter section corner of section 8. This position is at the intersection of the north-south and east-west centerlines. The east-west centerline is a straight line between the east and west-one quarter corners of the section. The north-south centerline is run from the south-one quarter corner northerly on the arithmetic mean bearing of the east and west lines of the section. The second problem requirement is to cite the governing reference that verifies the method of establishing the corners. The site is either the manual of surveying instructions or the manual supplement, the restoration of lost and obliterated corners and subdivision of sections pamphlet. The third and final problem requirement is to calculate the coordinates for the southwesternly corner of section 8 and show all work. A double proportion is the procedure to use here as determined in the first problem requirement. The controlling corners for the double proportion are the one quarter corners to the north, east, south and west. The coordinates shown on these points are the current retracement coordinates. The first step in the double proportion process is to break down the record bearings and distances into their appropriate cardinal equivalents. The record bearings to the lines to the east, south and west are cardinal, so the actual distances is the departure of those lines. The line to the north is on a bearing of north zero degrees, zero one minutes west, however. The cardinal equivalent of that line is 39.994 chains. The cardinal equivalent of 39.994 is to be used in the north-south portion of the double proportion instead of the distance of 40 chains. Let's step through the determination of the eastern coordinate of the southwest corner. One way to determine the eastern coordinate is as follows. First take the partial departure of the western line, which is 40 chains, and divide it by the total departure of the latitudinal line, which is 80 chains. The result is one-half, which is the record east-west proportional factor. The difference in retracement eastings are the controlling latitudinal corners, which is 7,669.76 feet minus 2,360.00 feet equals 5,309.76 feet is then multiplied by the record proportional factor. This yields a result of 2,654.80 and 154.88 feet of proportional departure, which in this case is then added to the easting of the westerly one-quarter corner. The result is an easting coordinate of 5,014.88 feet for the southwest corner. As you probably noticed, it's okay to use chains for figuring the record proportional factor and feet for measured distances. The northern coordinate is determined in the north-south proportion in a similar manner to that to use the coordinate equivalent of 39.994 chains for the line to the north, though, instead of the 40-chain distance. Now let's discuss another problem. Problem A1 from the 1990 California LS exam was worth 27 points, shown as a portion of an 1860 plaid. The distances are in chains and the basis of bearing is a solar observation. The problem statement is that Rancho Leonardo is shown in part on the plaid dated 1860. The Rancho follows sectional lines, end of statement. Since the Rancho follows sectional lines, we can assume in this problem that the Rancho lines do not have any seniority over any of the other sectional lines. On the screen, the Rancho lines are highlighted. The Rancho lines we'll be determining are denoted as A, B, and C. A is a portion of the south boundary of the section. B is the north and south center line of the southwest corner, southwest one-quarter of the section. And C is the westerly quarter sectional line of the section. The problem requirement is to calculate the bearings and distances of A, B, and C based on the retracement of the section and identify the methods used. To determine the required bearings and distances, it is necessary to determine the positions of the west one-sixteenth section corner on the south boundary of the section and the center west one-sixteenth section corner. The retracement situation, which you are given, is as shown. The squares are recovered original corners. Coordinates were provided on the exam for each recovered corner, but are not shown here. The position of the west one-quarter section corner is established at the record bearing and distance from the recovered bearing tree. What I'm going to present is a step-by-step procedure to use in determining the required lines. This problem is included in the workbook, along with the solution in its entirety. The first step is to calculate the coordinates of the lost corner positions on the exterior boundary of section 14, of which there are two. The southwest corner needs to be reestablished so that the position of the west one-sixteenth section corner on the south boundary of section 14 can be determined. The north one-quarter section corner needs to be reestablished to control the direction of the north-south centerline of the section. Section lines were surveyed in all four directions from the southwest section corner. Therefore, the coordinates of this position will be determined by double proportioning between the controlling corners. The controlling corners for the double proportion are the filled-in squares. Once the coordinates of the southwest corner have been calculated, the north one-quarter corner is determined. The coordinates of the north one-quarter corner are calculated by single proportioning between the northeast and northwest section corners. The filled-in squares represent the controlling corners. With the position of the north one-quarter corner now calculated, the positions of all four one-quarter corners for the section are known. The centerlines of the section can now be determined. The north-south centerline is a straight line between the south and north one-quarter corners. The east-west centerline is a straight line between the east and west one-quarter section corners. The bearings and distances of both centerlines are readily determined by inversing the coordinates of the appropriate one-quarter section corners. The intersection of the two centerlines is the position of the center one-quarter. The position of both needed 16th corners can now be calculated. As shown, in this case, the West 1-16th corner is at midpoint between the South 1-quarter corner and the reestablished Southwest corner. The center West 1-16th is at midpoint between the West 1-quarter corner and the Center 1-quarter and on the East-West centerline. Once the 16th corners have been established, the North-South centerline of the Southwest corner can then be determined. This centerline is a straight line between the two 16ths. The bearing and distance are calculated by inversing the coordinates of the 16th positions. The bearings and distances of the other two lines needed for the problem solution can then be determined by inversing the coordinates between the pertinent corners. Now let's discuss the final problem. Problem B3 from the 1990 exam was worth 16 points. Shown are the two sketches provided by the problem. The top sketch is compiled from GLO Platt and field notes dated July 26, 1879. The lower sketch shows the results of a field survey performed in January 1990. The first problem requirement is to describe how you would reestablish the missing 1-quarter corner monument position. The 1990 survey recovered a black oak tree with scribing. The black oak tree was 12 inches in diameter, larger in 1990 than in 1879. The scribing was found about six inches deep into the tree, which is where you would expect to find it based on the current and record diameters of the tree. Therefore, it is apparent that an original black oak bearing tree was recovered. The answer then is that the 1-quarter corner would be reestablished at record bearing and distance from the recovered bearing tree, which is north, 40 degrees west, 30 lengths. The second problem requirement is to assume that in addition to the recovered black oak, you have found a blazed 18-inch living pine tree without visible scribing near the location called in the record notes for the 18-inch pine bearing tree. Now, how would the missing 1-quarter corner be reestablished? They further ask you to explain your answer. The first thing to do is to examine this new evidence they've given us. The pine tree they ask us to assume found in 1990 is 18 inches. The original field notes called for the pine tree to be 18 inches in 1879. There is no visible scribing in 1990. I believe the answer that the examiners are looking for is that the missing 1-quarter corner would still be reestablished at record bearing and distance from the recovered 24-inch black oak bearing tree. The 18-inch pine tree would be rejected because the 1990 diameter is the same as in 1879, but the tree is still alive and no scribing is visible. Ordinarily, a pine tree usually grows significantly in diameter in 111 years. As a word of caution regarding the 18-inch pine, the original surveyors did make mistakes when writing up field notes. It's possible that the actual diameter measured by the original surveyor was significantly less than reported. You should be certain that the pine recovered by the 1990 survey could not have existed in 1879. If in doubt, the tree should be bored to determine the age based on the rains. As I mentioned at the beginning of this video, past PLSS problems on the LS exam generally do not involve complex, tricky, or unusual situations. Don't be overwhelmed by the entire problem at once. Break a PLSS problem into parts where possible, as we did in the first and second example LS problems, which I presented. Be familiar with PLSS reference books like the manual, so if you need guidance on a particular area, you can quickly look it up. The PLSS topics and procedures discussed in this video should provide a good foundation for the LS test. However, you should not rely solely on this video in your PLSS studies for the exam. The pertinent portions of the 1973 manual, such as chapters 5 and 6, should be read and understood. There are also other advised readings on the PLSS which are mentioned in the workbook. In closing, I wish you success on the exam and in your PLSS related activities.