required number of full tape lengths. Theremaining partial tape length is then laid off bysetting the rear chainman’s plumb bob at theappropriate tape graduation.Making Tape CorrectionsA 100-ft tape should, in theory, indicateexactly 100.00 ft when it is in fact measuring100.00 ft. However, a tape supported only at theends has a sag in it, so when it indicates 100.00ft, actually the distance measured is less. Even atape supported throughout on a flat surface canbe slightly longer under tension than it is withouttension. Also, a tape will be longer when it iswarm than when it is cold.CALIBRATING A TAPE.— All tapes aregraduated under controlled conditions of tempera-ture and tension. When they are taken to the field,these conditions change. The tape, regardless ofthe material used to make it, will be either tooshort or too long. For low accuracy surveys, theamount of error is too small to be considered. Asaccuracy requirements increase, variations causedby the temperature and sag must be computed andused to correct the measured distance. In thehigher orders of accuracy, the original graduationis checked for accuracy or calibrated at intervalsagainst a standard distance. This standard isusually two points, a tape length apart, that havebeen set and marked using a more precise tapeor a tape already checked. The standard may bejust the precise or checked tape (known as the kingor master tape). This tape is kept in a safe locationand is not used for making field measurements,but only to check the accuracy of the field tapes.For the highest orders of accuracy, the tapes aresent to the National Bureau of Standards, U.S.Department of Commerce, Washington, DC,20234, for standardization under exact conditionsof tension, temperature, and points of support.A tape standardization certificate is issued foreach tape, showing the amount of error under thedifferent support conditions and the coefficientof expansion. The certificate (or a copy) is keptwith each tape. For field operations, the tapes arecombined in sets; one is selected as the king tape,while the others are used as field tapes.The standard tension for a tape supportedthroughout is 10 lb, and the standard temperatureis 68°F. Standard length is, simply, the nominallength of the tape. A 100-ft tape, for example,at a temperature of 68°F, supported throughout,and subject to a tension of 10 lb, should indicate100 ft when it is measuring exactly 100 ft.To CALIBRATE a 100-ft tape means todetermine the exact distance it is actuallymeasuring when it indicates 100 ft, while beingsupported throughout, at a temperature of 68°Fand under a tension of 10 lb.In addition to the National Bureau ofStandards, many state and municipal authoritiesprovide standardizing service.RECOGNIZING TAPE OR STANDARDERROR.— Suppose now that you send a 100-fttape to the Bureau of Standards to be calibrated;the bureau will return a certificate with the tape.Assume that the certificate states that when thetape, supported throughout at a temperature of68°F, and under a tension of 10 lb, indicates 100ft, it actually measures 100.003 ft on the standardtape. The tape, then, has a STANDARD ERROR(also called TAPE ERROR) of 0.003 ft for every100 ft it measures. This tape “reads short.”Depending on the order of precision of the survey,you may have to apply this as a correction tomeasurements made with this particular tape.CORRECTING FOR STANDARD ERROR.–Whether you add or subtract the standard errordepends upon the direction of the error. The tapein the above example indicates a distance that isshorter than it actually measures; in other words,when you use this tape to lay off a distance of100 ft, the line is actually 100.003 ft.The decision to add or subtract the errordepends upon whether you are measuring todetermine the distance between two points or toset a point at a given distance from another.Assume first that you’re measuring thedistance between two given points, and thedistance as indicated by the tape is 362.73 ft. First,what is the total tape error? Obviously, it is 0.003times the number of tape lengths. In this case, it is0.003 x 3.6273 = 0.0108819 ft,which rounds off to 0.01 ft.The next question is: Do you add this totalcorrection to, or subtract it from, the recordeddistance of 362.73 ft? Well, if you remember thatthe tape reads short, you will realize thereasonable thing to do is ADD the total standarderror to the recorded distance. The correctdistance between the two points, then, is 362.74 ft.Suppose now that with the same tape, you areto set a point 362.73 ft away from another point.12-16