HOW  A  PROPORTIONAL  DIVIDER  WORKS  -  PART   TWO
A  DIFFERENT  WAY  TO  INTERPRET  »CIRCLES«-SCALE

BOWEN MODEL 770 / U.S.C.E. ( #29 )


THE   B O W E N   PROPORTIONAL DIVIDER   Model 770  ( #29 )  8" long    ( 1940 )
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U.S.C.E. (= US Army Corps of Engineers )   /  J.H.WEIL & CO., Philadelphia / USA

PURPOSE ( and different approach ) see the  HAFF Model 195aE ...

USAGE: With closed legs loosen the SCREW. Move the axle up or down to the SCALE-
MARK  of your choice.  Tighten the  SCREW.  Open the  LEGS,  sample the original
distance with ONE SIDE - the OPPOSITE SIDE will be in the desired PROPORTION.

There are 2 SCALE-MARKS:

  o  In  »LINES«  the sampled  DISTANCES  are set in proportion.

  o  In  »CIRCLES«  when its  D I A M E T E R  IS TAKEN AS THE SAMPLE,
     the  OPPOSITE SIDE should cut the circumference in equal PARTS - BUT !!!

Knowing how the German HAFF works, this »CIRCLES«-Scale is different:

     LIN. = 2   =/=   6 CIRC.   ( NOT-EQ. ! Radius divides a circle in 6 parts )

My friend NANCY found an explanation:
»CIRCLES« Scale refers to   T R U E   L E N G T H  of the CIRCUMFERENCE PART,
and NOT to its SECANT ...

     

     F O R M U L A :       CIRCPART  =  π * DIAMETER / N

... What is the PURPOSE / GRAPHICAL APPLICATION of it ?    A N   E X A M P L E :
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Designing a COGWHEEL ( German = "ZahnRad" ) for restoring a calculator, I looked
in my  BACHMANN & FORBERG / » TECHNISCHES ZEICHNEN « / Teubner (1966), p.137/138

     
     

A closer look to the BOWEN-Scales ...

     

      LIN. = π  ==  10 CIRC.    ==>>   U = 2πR    ====>>   Conclusion ...

Setting the  BOWEN  on  N = NUMBER  of "TEETH".  Measure  t = DISTANCE  with the
SMALL SIDE,  than  the  OTHER SIDE  shows  Dk = DIAMETER  of  the  "KOPF-KREIS".
Setting the  BOWEN  on  N/2 = NUMBER/2  of "TEETH".  Measure  t = DISTANCE  with
the  SMALL SIDE,  than the OTHER SIDE  shows  Rk = RADIUS  of the  "KOPF-KREIS".

      In general:  N/2 ==>> D/2 ;   N/4 ==>> D/4 ;   ...   N/n ==>> D/n

                     Have a look at the HAFF Model 195aE ...
impressum:
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© C.HAMANN           http://public.beuth-hochschule.de/~hamann          10/24/14