But, in practice, trying to shoot for a higher degree of accuracy is advantageous if it does not affect the  proper  progress  of  the  work.  The  following criteria   should   be   observed   in   fourth-order leveling: 1.  All  lines  are  to  start  from,  and  close  on, previously established BMs of the third or fourth order  of  accuracy. 2.  Maximum  sight  distance  is  about  500  ft. Rod  readings  are  read  to  hundredths  of  a  foot. BS  and  FS  distances  are  roughly  balanced  only when lines of great lengths are run, either uphill or downhill. TPs are taken on solid or any well- defined,  firm  objects. The instrument commonly used in third- and fourth-order  leveling  is  the  engineer’s  level  and the  Philadelphia  rod.  Always  check  the  proper adjustments  of  the  instrument  before  using  it. Order of Precision The  precision  of  a  level  run  is  usually prescribed  in  terms  of  a  maximum  error  of closure.  This  is  obtained  by  multiplying  a constant  factor  by  the  square  root  of  the  length of  the  run  in  miles  or  in  kilometers,  depending upon the system of measurement being used. The Federal   Bureau   of   Surveying   and   Mapping specifies certain requirements and the maximum closing errors, such as those shown in table 14-1. You  may  refer  to  this  standard  if  the  order  of precision is not specified for a particular survey project. Calculating Error of Closure A level run that begins at a particular BM and is carried back again to the same BM is called a level  loop.  A  run  that  does  not  close  on  the initial BM is called a level line. A level line closes on another BM; but when a level line is carried back to its origin, it becomes a level loop. Usually, a  level  line  is  carried  back  to  the  initial  BM  to determine  the  error  of  closure. Error  of  closure  is  simply  the  difference between the known elevation of the initial BM and the  elevation  of  the  same  (BM)  as  computed  in the level run. The   error   of   closure   that   can   be   allowed depends on the precision required (first, second, or  third  order).  The  permissible  (or  allowable) error of closure in accuracy leveling is expressed in  terms  of  a  coefficient  and  the  square  root  of the  horizontal  length  of  the  actual  route  over which  the  leveling  was  done. Most differential leveling (plane surveying) is third-order   work.   In   third-order   leveling,   the closure  is  usually  made  on  surveys  of  higher accuracy  without  doubling  back  to  the  old  BM at the original starting point of the level circuit. The  length  of  the  level  circuit,  therefore,  is  the actual distance leveled. For third-order leveling, the  allowable  error  is  as  follows: By  adding  the  sight  distances  in  the  sixth  and seventh  columns  of  the  differential  level  circuit shown in figure 14-14, you will find that the length of the level circuit is 2,140 ft. The length in miles is 2140  +  5280  =  0.405. The  allowable  error  of  closure  is Since the actual error is only 0.015 ft, the results are  sufficiently  accurate. First-  and  second-order  levels  usually  close  on themselves. The leveling party runs a line of levels from  an  old  BM  or  station  to  the  new  BM  or station, and then doubles back to the old BM for closure. The actual distance leveled is twice the length  of  the  level  circuit. For second-order leveling, the allowable error is First-order leveling is still more precise. The allowable  error  cannot  be  greater  than MISTAKES   AND   ERRORS IN  LEVELING As explained in an earlier chapter, the terms mistakes  and  errors  are   NOT   synonymous   in surveying. Leveling   operations,   like   other   survey measurements, are susceptible to both. Mistakes can  be  avoided  by  a  well-arranged  system  of operation  and  by  constant  alertness  by  the  survey party members. Checking, as described in some of  the  operations,  will  eliminate  many  possible 14-22