1. Submitted By: Mon Alfred B. Cabia Submitted To: Roberto Cabrera

3. Latitude  The latitude of a line is its projection onto the reference meridian or a north-south line.  Latitude is sometimes referred to as northings or southings.  Latitudes of lines with northerly bearings are designated as being north (N) or positive (+); those in a southerly direction are designated as south or negative.  The departure of a line is its projection onto the reference parallel or an east west line.  Departures are east (E) or positive (+) for having a easterly bearings and west (W) or negative (-) for lines having westerly bearings. departures

4.  The algebraic sign of latitude and departures are thus assigned on the basis of the direction of the bearing angles. Noted: Latitude and departure are simply the x and y components of a line in a rectangular grid system, as commonly used in mathematics.

5.  From the geometry of the given figure given, it is easily seen that the magnitude of the latitude is the product of its length by cosine of its bearing angle,  The corresponding departure is numerically equal to the length of the line multiplied by the sine of its bearing angle. The horizontal length of a line is designated by d and its angle by α.

6. When the direction of a line is given in terms of azimuth from north, the proper signs of the latitudes and departures are automatically generated in the calculator or electronic digital computer. The common error committed in traverse computations is to enter a latitude or departure with a wrong sign, or to enter a latitude in a column designated for departure and vice versa. The following equations may be obtained for lines AB, CD, GH, and EF.

8.  There is no such thing as mathematically perfect survey.  Small error in both distance and angles will always be present even in closed traverses observed using instruments and methods of high precision. In all probability a surveyed closed traverse would not satisfy the geometric requirements of a closed polygon. Until adjustments are made to these observed quantities it will always be expected that the traverse will not mathematically close.  When a closed traverse is plotted on paper the survey must close on the starting point.  The closure must be effected not only graphically but also mathematically.  For a closed traverse, this simply means that the algebraic sum of the north and south latitudes should be zero, and the algebraic sum of the east and west departures should also be zero. Error Of Closure

9.  The difference between the north and south latitudes, designated here as C L, is called the closure in latitudes, It indicates how much the traverse computations fail to close in a north-south direction.  The difference between the east and west departures, designated here as C D is referred to as the closure in departure and it indicates how far the closure misses in an east-west direction.  The values of C L and C D assume the sign which is obtained by adding algebraically all latitudes and all departures respectively.

10.  The linear error of closure (LEC) is usually a short line of unknown length and direction connecting the initial and final station of the traverse.  It is approximately determined by plotting the traverse to scale, or more exactly by computing the hypotenuse of a right triangle whose sides are the closure in latitudes and the closure in departures, respectively. This quantity reflects the algebraic sum of all the accumulated errors of measurement both in angles and distances when running the traverse. The length of the linear error of closure and the angle that this line makes with the meridian is determined by the following equations. Linear error of closure (LEC)

11.  If the linear error of closure is excessive, it indicates that a mistake has been committed during the field measurement or in plotting and computing the traverse data.  The first step then would be to check all the calculations to make sure that the mistakes is not in the calculations themselves. The field work should either be checked or repeated is after a recomputation the error of closure still does not come within the excepted limits.  The linear error of closure does not indicate the precision of the measurement until it is compared with the total length of the traverse. A convenient and more useful measure of precision is defied by ratio of the linear error of closure to the perimeter or total length of traverse. This is usually expressed as a fraction whose numerator is unity and denominator rounded off to the nearest multiple of 100, as1/5000. Such a fraction states that the error of the survey is one part in 5,000 parts, thus RP = LEC/D Where: RP = relative precision LEC = linear error of closure D = total length or perimeter of the traverse RP, should be expressed in the same unit of linear measure.

14. TRAVERSE ADJUSTMENT  The procedure of computing the linear error of closure and applying corrections to the individual latitudes and departures for the purpose of providing a mathematically closed figure is referred to as traverse adjustment.  It is necessary that the traverse is geometrically consistent before coordinates or areas are determined, or prior to determining the location of the lines from the traverse stations.  When a traverse adjustment is undertaken it must be borne in mind that the adjustment to the latitudes and departure will slightly alter the length and direction of the measured sides of the traverse. Also, the adjustment should only involve small or allowable errors which must be within the range of the precision specified for the survey.

15. TRAVERSE ADJUSTMENT  It is not possible to determine the true magnitude of the errors in angular and linear measurements for a traverse. However, in surveying practice it is reasonably fair to assume that errors are gradually accumulated and corrections can be applied accordingly if conditions surrounding the field measurements have been uniform.  There are some surveys where traverse adjustment is not required, particularly when the latitudes and departures are to be used only in plotting the positions of the stations on a map and when the error of closure is too small to be portrayed and when the error of closure is too small to be portrayed to scale. Also, in some instances a rough combination of traverse adjustment is employed instead of exact mathematical application of only one method.

16. TRAVERSE ADJUSTMENT  There are different rules and methods used in adjusting a traverse. Some are performed graphically and other analytically. Each of which will produce a closed figure. These methods of adjustment are usually classified as either rigorous or approximate.  The least squares methods provides the most rigorous adjustment  The arbitrary method the compass rule the transit rule and the Crandall method are all approximate methods of traverse adjustment.