0 + 00 and 2 + 50. The distances AB and AD canbe computed by ratio and proportion, as follows:These distances are laid off on the random linefrom point A toward station 0 + 00. Theinstrumentman then occupies points B and D;turns the same angle, 108°00´, that he measuredat point A; and establishes points C and E on linesfrom points B and D through the stations beingsought. The dist antes are computed by similartriangles as follows:TYING IN A POINTDetermining the horizontal location of a pointor points with reference to a station, or twostations, on a traverse line is commonly termedTYING IN THE POINT. Various methods usedin the process are presented in the next severalparagraphs.Locating Points by Swing OffsetsThe SWING OFFSET is usedpoints close to the control linesfor locating(fig. 13-21).Measurement of a swing offset distance providesan accurate determination of the perpendicularFigure 13-21.-Swing offset method of locating points.Figure 13-22.-Perpendicular offsets.distance from the control line to the point beinglocated. The swing offset is somewhat similar tothe range tie (explained later), but as a rule,requires no angle measurement. To determine theswing offset distance, a chainman holds the zeromark of the tape at a corner of the structure whileanother chainman swings an arc with thegraduated end of the tape at the transit line AB.When the shortest reading on the graduated endof the tape is observed, the swing offset or perpen-dicular distance to the control line is obtained atpoints a or b. In addition, the horizontal distancesbetween the instrument stations (A and B) andthe swing offset points (a and b) maybe measuredand marked. A tie distance and angle a or @ maybe measured from either instrument station to thecorner of the structure to serve as a check.Locating Points by Perpendicular OffsetsThe method of PERPENDICULAR OFF-SETS from a control line (fig. 13-22) is similarto swing offsets. This method is more suitablethan the swing offset method for locating detailsof irregular objects, such as stream banks andwinding roads. The control line is established closeto the irregular line to be located, and perpen-dicular offsets, aa´, bb´, cc´, and so on, aremeasured to define the irregular shape. When theoffset distances are short, the 90° angles areusually estimated; but when the distances areseveral hundred feet long, the angles should belaid off with an instrument. The distances to theoffset points from a to i are measured along thecontrol line.Locating Points by Range TiesA point’s location can also be determined bymeans of a RANGE TIE, using an angle and a13-18