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 ) ******************************************************************************** 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 ... 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 : ================================================================================ 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 PART ONE = A DIFFERENT APPROACH = HAFF Model 195aE ... Back to the ENGINEERING TOOLS Main Page impressum: ******************************************************************************** © C.HAMANN http://public.BHT-Berlin.de/hamann (*) 12/13/14 ```