counterclockwise   angles.   The   slope   of   the numerals  in  the  vernier  to  be  used  corresponds to  the  slope  of  the  numerals  in  the  circle  being read.  Care  must  be  taken  to  use  the  correct vernier.  In  figure  11-11,  view  E,  the  circle  is graduated  to  half  degrees,  or  30  min.  On  this vernier,  30  divisions  are  equal  in  length  to  29 divisions on the circle. The least reading of this vernier is 30 min divided by 30 divisions, or 1 min. The index (fig. 11-11, view E) is seen to lie between 342°30´ and 343°. In the left vernier, graduation Number  5  is  seen  to  coincide  with  a  circle graduation.  Then,  the  clockwise  reading  of  this circle  is  342°30´  plus  05´,  or  342°35´.  When  the right  vernier  is  used  in  the  same  way,  the counterclockwise  reading  of  the  circle  is  17°00´ plus  25´,  or  17°25´.  In figure 11-11, view F, the circle is graduated in 15-min divisions and each half of the double vernier contains 45 divisions. The least reading on this vernier is 20 sec. The clockwise  reading  of  the  circle  and  vernier  is 351°30´plus   05´40"   or   351°35´40".   The counterclockwise  reading  is  8°15´  plus  9´20",  or 8°24´20". THEODOLITE A  theodolite  is  essentially  a  transit  of  high precision.   Theodolites   come   in   different   sizes and  weights  and  from  different  manufacturers. Although  theodolites  may  differ  in  appearance, they are basically alike in their essential parts and operation.  Some  of  the  models  currently  available for  use  in  the  military  are  WILD  (Herrbrugg), BRUNSON, K&E, (Keuffel & Esser), and PATH theodolites. To  give  you  an  idea  of  how  a  theodolite  differs from a transit, we will discuss some of the most commonly  used  theodolites  in  the  U.S.  Armed Forces. One-Minute Theodolite The  1-min  directional  theodolite  is  essentially a  directional  type  of  instrument.  This  type  of instrument  can  be  used,  however,  to  observe horizontal  and  vertical  angles,  as  a  transit does. The  theodolite  shown  in  figure  11-12  is  a compact,  lightweight,  dustproof,  optical  reading instrument. The scales read directly to the nearest minute or 0.2 mil and are illuminated by either natural or artificial light. The main or essential parts  of  this  type  of  theodolite  are  discussed  in the next several paragraphs. HORIZONTAL MOTION.—  Located on the lower portion of the alidade, and adjacent to each other,  are  the  horizontal  motion  clamp  and tangent screw used for moving the theodolite in azimuth. Located on the horizontal circle casting is a horizontal circle clamp that fastens the circle to the alidade. When this horizontal (repeating) circle  clamp  is  in  the  lever-down  position,  the horizontal  circle  turns  with  the  telescope.  With the  circle  clamp  in  the  lever-up  position,  the circle  is  unclamped  and  the  telescope  turns independently.   This   combination   permits   use of  the  theodolite  as  a  REPEATING  INSTRU- MENT.  To  use  the  theodolite  as  a  DIREC- TIONAL  TYPE  OF  INSTRUMENT,  you  should use the circle clamp only to set the initial reading. You should set an initial reading of 0°30´ on the plates when a direct and reverse (D/R) pointing is  required.  This  will  minimize  the  possibility of  ending  the  D/R  pointing  with  a  negative value. VERTICAL   MOTION.—   Located  on  the standard  opposite  the  vertical  circle  are  the  vertical motion  clamp  and  tangent  screw.  The  tangent screw  is  located  on  the  lower  left  and  at  right angles to the clamp. The telescope can be rotated in the vertical plane completely around the axis (360°). LEVELS.— The level vials on a theodolite are the circular, the plate, the vertical circle, and the telescope   level.   The   CIRCULAR   LEVEL   is located on the tribrach of the instrument and is used  to  roughly  level  the  instrument.  The  PLATE LEVEL,  located  between  the  two  standards,  is used  for  leveling  the  instrument  in  the  horizontal plane.  The  VERTICAL  CIRCLE  LEVEL  (verti- cal  collimation)  vial  is  often  referred  to  as a split bubble. This level vial is completely built in,  adjacent  to  the  vertical  circle,  and  viewed through a prism and 45⁰ mirror system from the eyepiece end of the telescope. This results in the viewing of one-half of each end of the bubble at the same time. Leveling consists of bringing the two  halves  together  into  exact  coincidence,  as 11-20