required  number  of  full  tape  lengths.  The remaining partial tape length is then laid off by setting  the  rear  chainman’s  plumb  bob  at  the appropriate  tape  graduation. Making Tape Corrections A  100-ft  tape  should,  in  theory,  indicate exactly  100.00  ft  when  it  is  in  fact  measuring 100.00 ft. However, a tape supported only at the ends has a sag in it, so when it indicates 100.00 ft, actually the distance measured is less. Even a tape supported throughout on a flat surface can be  slightly  longer  under  tension  than  it  is  without tension.  Also,  a  tape  will  be  longer  when  it  is warm  than  when  it  is  cold. CALIBRATING  A  TAPE.—   All  tapes  are graduated  under  controlled  conditions  of  tempera- ture and tension. When they are taken to the field, these conditions change. The tape, regardless of the  material  used  to  make  it,  will  be  either  too short or too long. For low accuracy surveys, the amount of error is too small to be considered. As accuracy  requirements  increase,  variations  caused by the temperature and sag must be computed and used  to  correct  the  measured  distance.  In  the higher  orders  of  accuracy,  the  original  graduation is checked for accuracy or calibrated at intervals against  a  standard  distance.  This  standard  is usually  two  points,  a  tape  length  apart,  that  have been set and marked using a more precise tape or a tape already checked. The standard may be just the precise or checked tape (known as the king or master tape). This tape is kept in a safe location and 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 are sent  to  the  National  Bureau  of  Standards,  U.S. Department  of  Commerce,  Washington,  DC, 20234,  for  standardization  under  exact  conditions of  tension,  temperature,  and  points  of  support. A  tape  standardization  certificate  is  issued  for each tape, showing the amount of error under the different  support  conditions  and  the  coefficient of  expansion.  The  certificate  (or  a  copy)  is  kept with  each  tape.  For  field  operations,  the  tapes  are combined  in  sets;  one  is  selected  as  the  king  tape, while the others are used as field tapes. The  standard  tension  for  a  tape  supported throughout is 10 lb, and the standard temperature is 68°F. Standard length is, simply, the nominal length  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 indicate 100 ft when it is measuring exactly 100 ft. To  CALIBRATE  a  100-ft  tape  means  to determine   the   exact   distance   it   is   actually measuring when it indicates 100 ft, while being supported throughout, at a temperature of 68°F and  under  a  tension  of  10  lb. In   addition   to   the   National   Bureau   of Standards, many state and municipal authorities provide  standardizing  service. RECOGNIZING   TAPE   OR   STANDARD ERROR.—  Suppose now that you send a 100-ft tape to the Bureau of Standards to be calibrated; the bureau will return a certificate with the tape. Assume that the certificate states that when the tape,  supported  throughout  at  a  temperature  of 68°F, and under a tension of 10 lb, indicates 100 ft, it actually measures 100.003 ft on the standard tape. The tape, then, has a STANDARD ERROR (also called TAPE ERROR) of 0.003 ft for every 100   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  to measurements made with this particular tape. CORRECTING FOR STANDARD ERROR.– Whether you add or subtract the standard error depends upon the direction of the error. The tape in the above example indicates a distance that is shorter  than  it  actually  measures;  in  other  words, when  you  use  this  tape  to  lay  off  a  distance  of 100  ft,  the  line  is  actually  100.003  ft. The  decision  to  add  or  subtract  the  error depends  upon  whether  you  are  measuring  to determine the distance between two points or to set  a  point  at  a  given  distance  from  another. Assume   first   that   you’re   measuring   the distance  between  two  given  points,  and  the distance as indicated by the tape is 362.73 ft. First, what is the total tape error? Obviously, it is 0.003 times the number of tape lengths. In this case, it is 0.003  x  3.6273  =  0.0108819  ft, which  rounds  off  to  0.01  ft. The  next  question  is:  Do  you  add  this  total correction  to,  or  subtract  it  from,  the  recorded distance of 362.73 ft? Well, if you remember that the  tape  reads  short,  you  will  realize  the reasonable thing to do is ADD the total standard error   to   the   recorded   distance.   The   correct distance between the two points, then, is 362.74 ft. Suppose now that with the same tape, you are to set a point 362.73 ft away from another point. 12-16