segments  of  each  of  the  six  scales.  Each  of  the six  scales  is  designated  by  a  number  representing the number of graduations that particular scale has  to  the  linear  inch.  On  the  10  scale,  for example, there are 10 graduations to the inch; on the 50 scale there are 50. You can see that the 50 scale   has   50   graduations   in   the   same   space occupied  by  10  on  the  10  scale.  This  space  is 1 linear inch. To  determine  the  actual  number  of  gradu- ations  represented  by  a  numeral  on  the  engineer’s scale, multiply the numeral by 10. On the 50 scale, for  instance,  the  numeral  2  indicates  2  x  10,  or 20 graduations from the 0. On the 10 scale, the numeral 11 indicates 11 x 10, or 110 graduations from the 0. Note that the 10 scale is numbered every   major   graduation,   while   the   50   scale is   numbered   every   other   graduation.   Other scales on the engineer’s scale are the 20, 30, 40, and 60. Because  it  is  decimally  divided,  the  engineer’s scale can be used to scale dimensions down to any scale in which the first figure in the ratio is 1 in. and  the  other  is  10,  or  a  multiple  of  10. Suppose,  for  example,  that  you  wanted  to scale  a  dimension  of  150  mi  down  to  a  scale of   1   in.   =   60   mi.   You   would   use   the   60 scale,   allowing   the   interval   between   adjacent graduations  to  represent  1  mi.  To  measure off  150  mi  to  scale  on  the  60  scale,  you  would measure  off  2.5  in.,   which  falls  on  the  15th major   graduation. Suppose now that you want to scale a dimen- sion of 6,500 ft down to a scale of 1 in. = 1,000 ft. The second figure in the ratio is a multiple of 10  times  a  multiple  of  10.  You  would  therefore use  the  10  scale,  allowing  the  interval  between adjacent graduations on the scale to represent 100 ft,  in  which  case  the  interval  between  adjacent numerals on the scale would indicate 1,000 ft. To measure  off  6,500  ft,  you  would  simply  lay  off from  0  to  6.5  on  the  scale. To  use  the  engineer’s  scale  for  scaling to  scales  that  are  expressed  fractionally,  you must   be   able   to   determine   the   fractional equivalent  of  each  of  the  scales.  For  any  scale, this equivalent is simply 1 over the total number of   graduations   on   the   scale,   or   1   over   the product  of  the  scale  number  times  12,  which comes to the same thing. Applying this rule, the fractional expressions of each of the scales is as follows: 10  scale  =  1/120 20  scale  =  1/240 30  scale  =  1/360 40  scale  =  1/480 50  scale  =  1/600 60  scale  =  1/720 Suppose  you  wanted  to  scale  50  ft  down  to a scale of 1/120. The 10 scale gives you this scale; you  would  therefore  use  the  10  scale,  allowing  the space between graduations to represent 1 ft, and measuring off 5 (for 50 ft). The line on your paper would  be  5  in.  long,  representing  a  line  on  the object itself that is 120 in. x 5 in., or 600 in., or 50  ft  long. Similarly,  if  you  wanted  to  scale  50  ft  down to  a  scale  of  1/600,  you  would  use  the  50  scale and measure off 5 for 50 ft. In this case, the line on your paper would be 1 in. long, representing a line on the object itself that is 1 x 600, or 600 in.,  or  50  ft  long. When it is not required that the drawing be made  to  a  specified  scale—that  is,  when  the dimensions  of  lines  on  the  drawing  are  not required   to   bear   a   specified   ratio   to   the dimensions of lines on the object itself—the most convenient scale on the engineer’s scale is used. Suppose, for example, that you want to draw the outline of a 360-ft by 800-ft rectangular field on an  8-in,  by  10  1/2-in.  sheet  of  paper  with  no specific  scale  prescribed.  All  you  want  to  do  is reduce  the  representation  of  the  object  to  one  that will  fit  the  dimensions  of  the  paper.  You  could use  the  10  scale,  allowing  the  interval  between adjacent  graduations  to  represent  10  ft.  In this  case,  the  numerals  on  the  scale,  instead of representing 10, 20, and so on, will represent 100,  200,  and  so  on.  To  measure  off  360  ft  to scale,  you  should  measure  from  0  to  the  6th graduation beyond the numeral 3. For 800 ft you should  measure  from  0  to  the  numeral  8. Because  you  allowed  the  interval  between adjacent   graduations   to   represent   10   ft,   and because the 10 scale has 10 graduations to the in., the scale of your drawing would be 1 in. = 100 ft, or  1/1,200. 2-20