Figure 12-5.—Slope reduction using difference in elevation. electro-optical   systems,   however,   have   the   EDM transmitter built into the theodolite. In this way, the vertical  angle  and  the  slope  distance  can  be  observed simultaneously. In some of these models, there is a vertical  offset  between  the  electrical  center  of  the transmitter and the optical center of the theodolite. Also, the height of the EDM reflector may not be at the same height as the target used to observe the vertical angle. For these conditions, you still need to consider these vertical offsets in the reamer described above. Slope Reduction Using the Difference in Elevation Between End Points Now let’s refer to figure 12-5 to see how to reduce a  slope  distance  using  the  difference  in  elevation between  two  stations. In figure 12-5, the EDM transmitter is located at station A and has an h.i. equal to AD. The  reflector,  at station B, has an h.i. equal to BE. The ground elevations at A and B are  known  and  the  difference  between  these elevations  is  designated  &-B.  To  reduce  the  slope distance,   s, you  first  determine  the  difference  in elevation between  D and E. This can be done using the following  equation: In other words, &  =  &-B  –  h.i.  of  EDM  +  h.i.  of reflector. Now, looking again at figure 12-5, you see that  CDE is a right triangle; therefore, since the slope distance was observed and recorded using the EDM, and having calculated  A_DE,  the  horizontal  distance,  CD, can  be simply  determined  using  the  Pythagorean  theorem. ELECTRONIC  POSITIONING SYSTEMS Three classes of modern positioning systems are used to determine positions on the surface of the earth. Two of the classes are the  initial positioning systems and the doppler positioning systems.  The initial positioning  systems  require  experience  with  navi- gational systems on board aircraft, and the doppler systems  deal  with  signals  received  from  satellites.  Both systems  are  beyond  the  scope  of  our  discussions; however,  the  doppler  positioning  systems  will  be discussed briefly at the EA1 level in part 2 of this TRAMAN. The third class of positioning systems is the electronic positioning systems. Electronic  positioning  systems  consist  of  specially designed   short-to-medium   range   EDMs   that   are attached to, or built into, a theodolite and can be used to determine distances and directions from a single setup of  the  instrument.  Although  many  different  electronic positioning systems are manufactured, each individual instrument is classed into one of three general groups as follows: 1. Combined theodolite and EDM.  Instruments within   this   group   consists   of   an   optical-reading repeating  or  direction  theodolite  with  an  attached  EDM transmitter  that  can  be  removed  for  independent  use  of the  theodolite. 2. Computerized  theodolite  and  EDM.  The instruments in this group are similar to those within the combined theodolite and EDM group but have built-in electronic  computers. 3. Electronic tachometers. The equipment in this integrated, digitized, electronic systems consist of a digitized   theodolite,   microprocessor,   and   EDM transmitter  incorporated  into  one  instrument.  The instruments in this group also can be equipped with solid-state memory and magnetic tape or punched- paper-tape storage units for storage of data. The above systems can be applied to nearly any type of  surveying  that  is  discussed  in  this  or  the  EA3 TRAMAN; however, for the normal day-to-day work that the EA surveyor performs, you will have little need for these types of instruments since most of the surveys you  perform  require  only  lower-order  precision.  When its  use  is  justified,  however,  an  electronic  tachometer is available as augment equipment for the Naval Mobile Construction Battalions. The equipment consists of an electronic  digitized  theodolite,  an  EDM  unit,  a microprocessor, a keyboard and display register, and a data storage unit. By inputting certain controlling data, 12-5