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
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 multi-talented friend Nancy Shaw ( see her "5D-art.net" WebSite ) found the
explanation: »CIRCLE« Scales refers to T R U E L E N G T H of the CIRCUM-
FERENCE PART, and NOT to its SECANT ...
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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