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GILSON  ATLAS  CIRCULAR  SLIDE  RULE
( 8" / 21 cm Diameter )

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S C A L E S    of  the  CIRCULAR SLIDE RULE    >> ATLAS <<    (1931)
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               made by  GILSON SLIDE RULE CO., Stuart, Florida / USA

Front Side with 2 Cursors  ( Long Cursor = LC,  Short Cursor = SC ):

(1) Circular X-Scale       Diameter  =  20 cm     =  8 inch

(2) 1/4 Segment Circular   Radius    =  97 mm     =  3 7/8 inch
        ( labeled "sLOG"     0 .. 05 .. 10 .. 15 ..  .. 95 .. 100 )

(3) Long Spiral X-Scale    Length    =  11 meter  =  35 feet
        ( starts inside  ... ends outside for better resolution !!!)

(4) Circular lgX Scale     Diameter  =  68 mm     =  2 3/4 inch
        ( labeled "cLOG"     0 .. 0.05 .. 0.1 .. 0.15 ..   .. 1.0 )
  
(5) Coils Directory        ( 1 ... 25  )
(6) List of Constants      ( ... e, π, 1/π, ... )

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Back Side with a Single Cursor:

(1) 3 DEGREES Circles   ( 0°/90° .. 30°/60° .. 60°/30° .. 90°/0° )
(2) 3 SIN; COS Circles  ( 0  ...  0.5    ...  0.866  ...  1      )
(3) 3 TAN; COT Circles  ( 0  ...  0.577  ...  1.732  ...  oo     )
(4) Fraction-to-Decimal Conversion Table   (  1/64   ...  63/64  )


R E M A R K S :
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Using the ATLAS Spiral Scale with 25 turns, results may be found to
5 figures. Logarithms of numbers may be found to 5 figures too.  To
conserve space, instead of a parallel Spiral Log Scale with 25 turns
there is only a QUARTER sLOG Scale drawn  ( 1/25 ) / 4  =  0.01
to obtain the last 3 figures of the Logs ...


Calculating the Length of the Spiral in the   A T L A S   Slide Rule
====================================================================
  25 "Rings" ;  Inner Diameter = 75 mm ... 195 mm = Outer Diameter
     Difference = 5 mm  ( Distance about 2.5 mm on each Side )

  L  =  π * 75 + π * 80 +  ...  + π * 185 + π * 190 + π * 195

Is there a better way to calculate this ???                  YES !!!
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(As little K.F.GAUSS found out when he had to add 1 + 2 + ... + 100)

L  =  π * ( 75 + 80 + 85 +  ...  + 135 +  ...   + 185 + 190 + 195 )

                       +------  sum = 270  --------+
                  +-----------  sum = 270  --------------+
             +----------------  sum = 270  --------------------+

L  =  π * ( 12 * 270 + 135 )  =  10602,87       WOW!    = 10.6 METER


How to use the   A T L A S   Slide Rule
====================================================================

MULTIPLICATION Example:  5 * 3  =  15
*************************************
Set the longer cursor LC on 5 and hold it. Set the shorter cursor SC
on 1.  Turn LC ( SC will follow, keeping the angle ) until SC is
over 3.  Read the result under LC.

DIVISION Example:  5 / 3  =  1.666
**********************************
Set the longer cursor LC on 5 and hold it. Set the shorter cursor SC
on 3.  Turn LC ( SC will follow, keeping the angle ) until SC is 
over 1.  Read the result under LC.

Get a MORE PRECISE RESULT using the  11 meter  ( 35 foot )  SPIRAL:
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Example:  22 / 7  =  3.142857    <<==   "true result"

1st Step:  Make the calculation with the X-Scale on the outer ring,
           to get the sequence of the result-figures...
           =  3.14(3)      < 3 digits precise >
           ( and under LC the expected coil number 13 )
           
2nd Step:  Start the calculation again, using the spiral scale
           to get a better result...
           =  3.142(8)     < 4 digits precise >    ( in coil 13 )

LOG Example (1):  lg16  =  1.204119    <<==   "true result"
***********************************

"0" Step:  Because the 16 has 2 digits, set
           =  1.____

1st Step:  Set the longer cursor LC to 16 on the circular X scale.
           Read the result on cLOG scale under LC:  0.20(4)
           =  1.20(4)      < 2 digits precise >

Get a MORE PRECISE RESULT using the 1/4 SEGMENT CIRCULAR  sLOG:
---------------------------------------------------------------

2nd Step:  Set the longer cursor LC to 16 on the SPIRAL SCALE.
           Read the 3rd & 4th DIGITS on sLOG under LC:
           =  ..41(2)      < 2 digits precise >

Combined:  =  1.2041(2)
=======================

LOG Example (2):  lg5  =  0.698970    <<==   "true result"
**********************************

"0" Step:  Because the 5 has 1 digit, set
           =  0.____

1st Step:  Set LC to 5 on the circular X scale.
           Read the result on cLOG scale under LC:  0.69(8)
           =  0.69(8)      < 2 digits precise >

2nd Step:  Set LC to 5.0 on the SPIRAL SCALE.

The sLOG scale is only a 1/4 circle. In this example the location
of the number in the spiral is outside of the direct readability
of the sLOG scale.  Notice, that the COIL-DIRECTORY has STROKE (|),
PERCENT (%) & PLUS (+) MARKS.  These marks refer to the marks on
the outer circle  ( AS PARTS OF THE sLOG SCALE )  where the SC has
to be PLACED. ( Observe the relative LC position in its quadrant ! )

           In this example the hairline is near the (%).  Set SC
           to mark (%) on the outer circle and turn LC  ( SC will
           follow, keeping the angle ) until SC is over (+) on sLOG.
           Read the 3rd & 4th DIGITS on sLOG scale under LC: 
           =  ..89(7)      < 2 digits precise >

Combined:  =  0.6989(7)
=======================

Historical Remarks ...

This famous GILSON circular slide rule was also distributed under
other brand names like DIETZGEN, POST, ...

impressum:
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© C.HAMANN    http://public.beuth-hochschule.de/~hamann     06/08/08