STADIA INTERVAL.— As you look at a stadia rod through a transit telescope, the stadia hairs seem to intercept an interval on the rod. The distance on the rod between the apparent positions of the two stadia hairs is the stadia interval  or stadia  reading. Usually,  you  determine  stadia  intervals  by  sighting the lower stadia hair at a convenient foot mark and then observing the position of the upper stadia hair; for example, the lower hair might be sighted on the 2.00 foot mark and the upper hair might be in line with 6.37. By subtracting, we have the stadia reading (6.37  -2.00  =  4.37). It may happen that the stadia reading is more than the length of the rod. By using the middle hair, you may observe a half-interval and multiply it by 2 to get the stadia reading. STADIA  CONSTANT.—  Light  rays  that  pass through the lens (objective) of a telescope come together at a point called the principal focus of the lens. Then these light rays continue in straight-line paths, as shown in figure 8-3. The  distance  between  the  principal  focus  and  the center of the lens is called the focal length(f)  of the lens. For any particular lens, the focal length does not change. If  you  divide  the  focal  length  by  the  distance  between the stadia hairs  (i), you get a number known as the  stadia constant (k). Sometimes the stadia constant is called the stadia factor or stadia interval factor. A convenient value to use for the stadia constant is 100. Stadia hairs usually are spaced so that the interval between them will make the stadia constant equal to 100. STADIA  DISTANCE.—  The distance from the principal focus to the stadia rod is called the stadia distance. As shown in figure 8-3, this distance (d) is Figure 8-3.—Light rays converge at principal focus of a lens. equal to the stadia constant  (k) times the stadia reading (s). INSTRUMENT  CONSTANT.—   The  distance from the center of the instrument to the principal focus is the instrument constant. Usually, this constant is determined by the manufacturer of the instrument. You should find it stated on the inside of the instrument box. Externally  focusing  telescopes  are  manufactured  so that the instrument constant may be considered equal to 1.  For  internally  focusing  telescopes,  though,  the objective in the telescope is so near the center of the instrument  that  the  instrument  constant  may  be considered  as  zero.  This,  as  you  will  learn  in  the following  discussion  of  stadia  reduction  formulas,  is  a distinct advantage of internally focusing telescopes. Most modem instruments are equipped with internally focusing  telescopes. STADIA  REDUCTION  FORMULAS.—  In  stadia work  we  are  concerned  with  finding  two  values  as follows: (1) the horizontal distance from the center of the instrument to the stadia rod and (2) the vertical distance, or difference in elevation, between the center of the instrument and middle-hair reading on the rod. To obtain these values, you must use stadia reduction formulas. Stadia Formula for Horizontal Sights.— For a horizontal sight, the distance that we need to determine is the horizontal distance between the center of the instrument and the stadia rod. This distance is found by adding the stadia distance to the instrument constant as follows: Write ks for the stadia distance and  (f + c) for  the instrument  constant.  Then  the  formula  for  computing horizontal distances when the sights are horizontal becomes  the  following: Where: h = k = s = f + c    = f   = c = horizontal  distance  from  the  center  of  the instrument to a vertical stadia rod stadia constant, usually 100 stadia  interval instrument  constant  (zero  for  internally focusing telescopes; approximately 1 foot for  externally  focusing  telescopes) focal lengths of the lens distance from the center of the instrument to the center of the lens 8-4