Figure 7-11.—Graphic solution of a closed traverse by latitudeand departure.Figure 7-11 is a graphic demonstration of the factthat, in a closed traverse, the algebraic sum of the plusand minus latitudes is zero; and the algebraic sum of theplus and minus departures is zero. The plus latitude ofCA is equal in length to the sum of the two minuslatitudes of AB and BC; the minus departure of BC isequal in length to the sum of the two plus departures ofCA and AB.LINEAR ERROR OF CLOSURE.— In practice,as you will learn, the sum of the north latitudes usuallydiffers from the sum of the south latitudes. Thedifference is called the error of closure in latitude.Similarly, the sum of the east departures usually differsfrom the sum of the west departures. The difference iscalled error of closure in departure.From the error of closure in latitude and the error ofclosure in departure, you can determine the linear errorof closure. This is the horizontal linear distance betweenthe location of the end of the last traverse line (ascomputed from the measured angles and distances) andthe actual point of beginning of the closed traverse.For example, you come up with an error of closurein latitude of 5.23 feet and an error of closure indeparture of 3.18 feet. These two linear intervals formthe sides of a right triangle. The length of the hypotenuseof this triangle constitutes the linear error of closure inthe traverse. By the Pythagorean theorem, the length ofthe hypotenuse equals approximately 6.12 feet. Supposethe total length of the traverse was 12,000.00 feet. Thenyour ratio of linear error of closure would be6.12:12,000.00, which approximately equates to1:2,000.CLOSING A TRAVERSE.— You close or balancea traverse by distributing the linear error of closure (onewithin the allowable maximum, of course) over thetraverse. There are several methods of doing this, butthe one most generally applied is based on the so-calledcompass rule. By this rule you adjust the latitude anddeparture of each traverse line as follows:1. Correction in latitude equals the linear error ofclosure in latitude times the length of the traverse linedivided by the total length of traverse.2. Correction in departure equals the linear error ofclosure in departure times the length of the traverse linedivided by the total length of traverse.Figure 7-12 shows a closed traverse with bearingsand distances notes. Figure 7-13 shows the computationof the latitudes and departures for this traverse enteredon the type of form that is commonly used for thispurpose. As you can see, the error in latitude is +0.33foot, and the error in departure is +2.24 feet. The linearerror of closure, then, isThe total length of the traverse is 2614.85 feet; therefore,the ratio of error of closure is 2.26:2614.85, or about1:1157.We will assume that this ratio is within the allowablemaximum. Proceed now to adjust the latitudes anddepartures by the compass rule. Set down the latitudesand departures on a form like the one shown in figure7-14 with the error of closure in latitude at the foot ofthe latitudes column and the error of closure in departureat the foot of the departures column.Figure 7-12.—Closed traverse by bearings and distances.7-10