The Flat Earth Society Strikes Again!
Plane surveying, which assumes that the Earth is flat, is the most commonly practised form of surveying. It consists primarily of locating the positions of features on the ground (or fairly close to it). This is achieved, in the first instance, by a combination of angular and linear measurement. Linear measurement is therefore at the foundation of surveying, which is at the foundation of the geomatics and geodetic science disciplines. It is this process of measuring things on the ground which is fundamental to later, fancier measurement systems. All of photogrammetry comes to nothing unless we can ascertain its results with respect to what is really on the ground. GPS is worthless if the base stations' locations are not known and receivers can't be tested against ground values. Mapping and GIS require the ability to check data in the database against what's on the ground.
If the area that you are covering with your survey is less than about 250 km2 (about 95 sq. miles), the assumption of a flat arth is valid for most standards of measurement in 2-D. Larger areas cause the systematic errors caused by the flat Earth assumption to become apparent in your measurements. Such errors are classical systematic errors, as they are caused by using an inappropriate model of the measurement process. They can be corrected by using the appropriate model.

Basic Surveying Rules
There are a large number of procedures which you should try to follow as closely as possible. However, most of these are variants of the following four basic rules.

1. Always work from the whole to the part, i.e. think about the whole thing before you attack the detailed parts, or put in your control before you do your detail work.
2. Always carry out independent checks. You breach this rule at your considerable peril! In today's litigatious society, it's like swimming in shark-infested waters after a quick dip in some fresh bullock's blood.
3. Work to a constant and appropriate standard of accuracy and precision. Being too accurate and precise tends to cost time and money, but being of too low a standard is professional suicide.
4. Systematically record all detail. It may seem like a lot of work at the time, but when you suddenly realize that something has gone wrong later on, it may save your hide. However, don't carry this rule to excess. Photographs are cheap, quick and easy insurance!

Origins of Linear Measurements
In many cases, the objects of interest do not lie along a single straight line. If this were the case, we could simply measure the distances to objects along the line and making a map would be quite simple. But a 1-D world would be rather boring. For more details on such worlds, read Edwin Abbott's classic book of the late 19th Century (1884), Flatland. [SEL
Compact Stacks, Stacks and 3-day Reserve QA699 A3, as well as other branch libraries.] In order to pick up detail in an area, one method is by what is sometimes called chaining with detail surveying. Chaining is one term for the process of measuring distance with some type of tape or band, and reflects the historical use of an actual `chain'. The `chain' was originally made from wrought iron and was developed in the 17th Century. The slightly more modern Gunter's Chain was developed with heavy wire links last century. The chain was made up of 100 links and was one chain long: 66 feet, 22 yards, 20·1168 meters. You can still find surveys made in some parts of the US that were made in chains, especially in rural areas. This was the US Government standard unit for survey measurements until fairly recently. The chain, while robust and easy to repair, was of limited accuracy, owing to the very large number of wear points, the tendency to stretch, and the ease with which mud could get into the links. It was gradually replaced with the tape or band.

A Bit of History
If we go back about 3-4 millennia or so, we find that surveyors used ropes for linear measurement. Surveyors were hard at work in Babylon and the settlements of the Tigris and Euphrates Rivers, where a great deal of work went into irrigation between the two great rivers. (As it happens, the conventions of degrees, minutes and seconds and 360 degrees in a circle
are Babylonian creations.) In Egypt, surveying had reached a high standard with the need for annual re-surveying of land after the annual Nile flood, as well as for the construction of the pyramids and other major public works. Surveying in the Ancient Greek world reached a high point, especially in Egypt, that was not equaled for many centuries. The influence of the
formalism of geometry, codified by Euclid in about 200 BC, shows that surveying, mathematics and geometry were very closely bound for the Greeks, whose mathematics were very much influenced by geometry, and whose geometry had very practical applications.
Most of the equipment, methods and theory of the Greek surveyors were too complicated for the Romans, who like present-day engineers, preferred simple methods wherever possible. The Romans used a lot of chain surveying and preferred building straight roads. Roman surveyors were good at working with levels, however. Since the Romans, there has been much refinement of equipment and techniques over the centuries, but the development of radically new ways to deal with the problem of detail surveying had to wait for the development of the tacheometer and the total station. A significant amount of information about the historical aspects of surveying is covered in the GS560 course, History of Surveying.

Chain Surveying
The basic idea is that we proceed across the countryside, measuring with a chain or similar piece of equipment and recording distances to features of interest as we go. Some features will not lie on the line of measurement, and we can pick up the location of these points in a number of ways. These include using tie lines, offsets, and if using an angle measuring instrument, bearing and distance (radiation) or intersection. This is a discussion of this in Chapter 2 of the text, together with some examples of how you do it and how you record it. For most chain surveying, we use tie lines and offsets, with offsets being most common.

Tie lines
Tie lines are run from points on the chain line whose chainage (distance along the line, also called running distance
(RD) in some circumstances) is known. The length of the tie lines are measured, and the side of the line on which they were made is established. For plotting, you need a pair of compasses, or suitable means to convert the data to an offset.

Offsets
Offsets are measured by a crew member standing on the line, and with an optical square (a right angle prism, or other device to turn a right angle) moving until the point of interest is exactly at right angles to the line. The chainage of this point is noted, and the distance from the line to the item of interest is measured. This measurement is the offset distance. For plotting, place a scale along the line where the chain was run, and use it to find the correct running distances. Then use a smaller scale at right angles to the first, and with its zero at the chaining line, to plot the point measured. When one is measuring a distance greater than one length of the chain or tape, it is necessary to mark where the end of the tape comes, so that the next person can find it. Such marking must be sufficiently clear that it can be found, and the point of transfer must be fine enough to allow the carrying of the distance to within 1-2 mm. To achieve this, a mark must be left for the rear chainman to locate.

Traditionally, this mark has been a chaining arrow or pin. This is a piece of wire with a loop in one end and a point at the other, which is pushed into the ground. The point to which the measurement is made is generally the middle of the wire at ground level. The advantage of the arrow is that it is about a foot long and colored red and white, making it easy to find inlong grass. It is harder to use on concrete, but handy for other marking, such as making a scratch. Note that making a powerful scratch with a plumbob tip often leads to the tip breaking off, leaving the threaded piece inside!

Other strategies for a marker include nails placed into the ground (the center of the head is the measurement point), scratches placed on hard surfaces (in general two lines at right angles, with the apex being the measurement point), or some obvious object placed so that the measurement point cannot be missed, preferably driven into the ground to hold the marker
firmly. When marking the end point, it is often a good idea to clear a little space on the ground (a kick mark is good) and in difficult situations, leave a more obvious guide, such as a small tripod of sticks in long grass. Grass can also be trampled around the point, to aid location. If you are working along the edge of a road, a kick mark with some dirt on the asphalt is a good marker. You can also use chalk, crayon or spray paint to help locate a marker. Naturally, it is best if these types of landscaping are done before the mark is measured and placed.

Ranging
Distances between points are best measured in a straight line. With undulating terrain, this is not possible, as far as the vertical dimension is concerned. But one can ensure that there is minimal deviation from the horizontal line. If one is chaining across the landscape, one should have a target at which to aim, such as some kind of sighting mark at the end of the line. Each time the chain is moved on, the back chainman stands at the mark placed by the front chainman, sights the target at the other end of the line, and brings the front chainman onto line. If there are obstructions to ranging in points, one can use other things to help.

It sometimes happens that you cannot see one end of a line from the other. How can you range the line? The simple answer is to station a person on each end of the line and two people in between, such that each person at the ends can see both people in the middle. You begin with one end placing both middle people in line and on the approximate line. When this has been done, the person at the other end will probably see the middle people anywhere but in a straight line, so they move the middle person nearest their end onto the line between their location and that of the further person in the middle. The person at the first end then moves the person nearest them onto the line with further person in the middle. This process continues until the middle people are on a straight line with both ends, at which time all four points will be on the one line. This process can take a little time, but it is very effective.

Obstacles to Measurement
If you cannot see the far end of the line, but will be able to measure to it, you can range in using the iterative approach discussed above. If the obstruction is something like a hill or hole, however, and the previous method is not applicable, you can lay off a random line that misses the obstacle, measure an offset to the objective, and locate it that way. Sometimes you can have obstacles to measurement, such as a building or a river. It is possible to construct parallel lines, with measured offsets, to go around the obstruction. This works well with buildings. For rivers, you can construct similar triangles and deduce the distances across the river. If you can see the line, you can line in range poles down to the water's edge,
and so miss nothing on the land. Sometimes you have a situation where you can't see around the obstacle, and you can't
measure over it either. In this case you can construct an offset line and carry the measurements along this. You may need offset lines on two sides of the obstacle, in order to collect detail on both sides of it.

Chaining as a major source of topographic detail is declining today, if it hasn't largely disappeared. Modern survey equipment means that the drudgery of computations is reduced, as are complex measurements to overcome limitations in being able to tape directly. The total station and the calculator mean that you will rarely have to use this method of collecting detail. However, the basic idea of collecting data along a line or section is extremely common and popular in surveying and other circles, so you will see other data collection exercises that work in the same kind of way, but with different names. For example, most data concerning roads, pipelines and other linear features is line-based and stored in a compatible manner to
the above discussion. Linear construction plans are based on this same set of ideas. The processes of measuring cross-sections and longitudinal sections in construction work is approached in exactly this kind of way, as is the resulting design, which is often based on the same approach.

The Measurement Procedure
When taping or chaining across the countryside, there are a number of things that need to be done. Given that you have the correct equipment with you, you should measure the temperature (and do it at intervals during the course of the measurements) and ensure that you can apply the correct tension with a spring balance. With each length of tape used, you should ensure that the ends are at the same level, or that you can measure the slope between the end points of that section of tape. You should also note the amount of tape in catenary, the amount supported, and the number of bays. The corrections and corrected distances must be written into the field book, so you should allow sufficient room for them.

Cut Tapes and Add Tapes
Tapes tend to come in two types. Add tapes have a zero point on the tape, and when the tape is used, the whole meters or feet are measured in the body of the tape, while the finer parts are measured in the additional part of the tape, then added to the large reading. For some common tapes, the entire tape may be marked down to millimeters, even to lengths of 50m or 100m or more. These are the types of tapes that you buy at a hardware store, such as self-retracting box tapes or pocket tapes. With these tapes, the distance can be measured directly. With cut tapes, the finer marks are in the first part of the tape, so that when an even distance is held at the back end of the tape, the person reading the front measures the distance back from this overall distance to the mark, The small reading is then subtracted (or cut) from the overall reading. You need to have your wits about you when using this type of tape! As subtraction is more error-prone than simple addition, you may consider that add tapes are a safer bet, and most of the world tends to agree. Cut tapes are popular in the US, but in very few other parts of the world, where add tapes are used, or tapes that are finely marked along their entire length. Which tape you prefer to use
depends upon you, but always check that you are using the right kind of tape.

Detail Pick-up
If you wish to pick up the extent of an irregular object, perhaps a meandering stream, it is often best to run a chaining line beside the object, measure offsets to the object, together with the distances to the offset point. This will enable you to plot the location of the irregular object. You will have to make some judgments as to how much detail you pick up, based around how frequently you measure the offsets. This will tend to be a function of the accuracy with which you intend to determine the area or plot the object. As most geographical phenomena can be shown to have a fractal nature in their boundaries, there are almost no limits to the fineness of the measurements and the level of detail that can be obtained. However, the question must always be addressed in terms of both the requirements of the job and the costs involved. An additional consideration may be the area that you compute for the object. For a purely graphical solution, a planimeter is a good approach. In GS410 we look at a range of methods for computing areas, and assess which are suitable for various circumstances. We will also consider their accuracy and precision. Today, the picking up of irregular boundaries and objects is one of the few remaining areas
of traditional chain surveying still in regular use.

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