45.132X Figure 2-22.-Proportional dividers. bar called a beam. The slide-mounted attachments can be locked in any desired position on the beam. Thus, a beam compass can be used to draw circles of any radius up to the length of the beam. With one  or  more  beam  extensions,  the  length  of  the radius of a beam compass ranges from about 18 in.  to  70  in. PROPORTIONAL  DIVIDERS PROPORTIONAL  DIVIDERS  (fig.  2-22)  are used  for  transferring  measurements  from  one scale to another. This capability is necessary when drawings  are  to  be  made  to  a  larger  or  smaller scale.  They  can  also  be  used  to  divide  lines  or circles into equal parts. Proportional  dividers  consist  of  two  legs  of equal   length,   pointed   at   each   end,   and   held together  by  a  movable  pivot.  By  varying  the position of the pivot, you can adjust the lengths of the legs on opposite sides of the pivot so that the  ratio  between  them  is  equal  to  the  ratio between  two  scales.  Therefore,  a  distance  spanned by  the  points  of  one  set  of  legs  has  the  same relation to the distance spanned by the points of the other set as one scale has to the other. On  the  proportional  dividers,  a  thumb  nut moves the pivot in a rack-and-gear arrangement. When  the  desired  setting  is  reached,  a  thumb-nut clamp  on  the  opposite  side  of  the  instrument  locks the  pivot  in  place.  A  scale  and  vernier  are provided on one leg to facilitate accurate setting. On  less  expensive  models,  the  movable  pivot  is not on a rack and gear, and there is no vernier. The dividers may be set by reference to the table of settings that is furnished with each pair; they will accommodate varying ranges of scales from 1:1 to 1:10. However, it is better not to depend entirely  on  the  table  of  settings.  You  can  check the  adjustment  by  drawing  lines  representing  the desired proportionate lengths, and then applying the  points  of  the  instrument  to  them  in  turn until, by trial and error, the correct adjustment is reached. To divide a line into equal parts, set the divider to a ratio of 1 to the number of parts desired on the  scale  marked  Lines.  For  instance,  to  divide a line into three parts, set the scale at 3. Measure off the length with points of the longer end. The span  of  the  points  at  the  opposite  ends  will  be equal  to  one-third  the  measured  length.  To  use proportional  dividers  to  transfer  measurements from feet to meters, draw a line 1 unit long and another line 3.28 units long and set the dividers by  trial  and  error  accordingly. Some proportional dividers have an extra scale for use in getting circular proportions. The scale marked  Circle  indicates  the  setting  for  dividing the  circumference  into  equal  parts. The  points  of  the  dividers  are  of  hardened steel,  and  if  they  are  handled  carefully,  these points  will  retain  their  sharpness  during  long use. If they are damaged, they may be sharpened and the table of settings will still be usable, but the  scale  on  the  instrument  will  no  longer  be accurate. SCALES In  one  sense,  the  term  scale  means  the succession  of  graduations  on  any  graduated standard  of  linear  measurement,  such  as  the graduations on a steel tape or a thermometer. In another  sense,  when  we  refer  to  the  “scale  of  a drawing,”   the term means the ratio between the dimensions  of  the  graphic  representation  of  an object  and  the  corresponding  dimensions  of  the object  itself. Suppose,  for  example,  that  the  top  of  a rectangular  box  measures  6  in.  by  12  in.  If  you draw a 6-in. by 12-in. rectangle on the paper, the dimensions of the drawing would be the same as those  of  the  object.  The  drawing  would,  therefore, be  a  full-scale  drawing.  This  scale  could  be expressed fractionally as 1/1, or it could be given as  1  in.  =  1  in. Suppose  that  instead  of  making  a  full-scale drawing,   you   decided   to   make   a   half-scale drawing.  You  should  then  draw  a  3-in.  by  6-in. rectangle  on  the  paper.  This  scale  could  be 2-16