Finally, for the 0.32 foot, look up the latitude for32 feet, which is 30.84 feet. If the latitude for 32 feet is30.84 feet, the latitude for 0.32 foot must be 0.3084 fret,which rounds off at 0.31 foot. The numerical value ofthe latitude then is 698.59 + 0.31 = 698.90 feet. Becausethe line AB bears northeast, the latitude is positive.You get the departure in the same way by using thedeparture column.Finally, you enter the adjusted latitudes and adjusteddepartures in the last two columns. Determine the valuesin each case by applying the correction to the originallatitude or departure. Note that the negative latitudesnow equal the positive latitudes and the negativedepartures equal the positive departures. This indicatesthat the errors of closure have been entirely distributed.With the adjusted latitudes and departures, you cannow adjust the original bearings and distances by themethod called inversing. Inversing simply meanscomputing the bearing and length of a traverse line fromthe latitude and departure. Again the process is one ofsimple triangle solution. Figure 7-16 shows traverse lineAB with the adjusted latitude and departure noted. Todetermine the adjusted angle of bearing, you solve thetriangle AA'B for angle A'AB as follows:The adjusted bearing of AB, then, is N3°42'E. Forthe adjusted distance, solve the triangle for AB asfollows:Figure 7-16.—Adjusted bearing and distance from adjustedlatitude and departure.The adjusted length of AB, then, is 584.22 feet.Plane CoordinatesThe location of a point by plane coordinatesmeansto describe the location of the point in terms of itsdistance north or south and east or west from a point oforigin.Figure 7-17 shows how coordinate distances aremeasured on an axis (called the Y axis) running north tosouth through the point of origin. East to westcoordinates are measured on an X axis running east towest through the point of origin. Values on the Y axisnorth of the point of origin are plus; values south of thepoint of origin are minus. Values on the X axis east ofthe point of origin are plus; values west of the point oforigin are minus.PLANE COORDINATES FROM LATITUDEAND DEPARTURE.— Figure 7-17 also shows therelationship between the plane coordinates of the endstations on a traverse line and the latitude and departureof the line. You can see that the difference between theY coordinate of A and the Y coordinate of B (which is200.00 feet) equals the latitude of AB. Also, you can seethat the difference between the X coordinate of A andthe X coordinate of B (which is 600.00 feet) equals thedeparture of AB. Therefore, if you know the coordinatesof one of the stations in a traverse, you can determinethe coordinates of the others from the latitudes andFigure 7-17.—Location by plane coordinates.7-13

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