HEMMI SLIDE RULE CO. LTD., Tokyo / Japan (1971) ******************************************************************** S C A L E S of the Bamboo-Based HEMMI / ODELCO Model » 255D « ==================================================================== Front Side [ inverse / RED ] Back Side ==================================================================== L lgX Sh1 SinH(0.1X) K X^{3} Sh2 SinH(X) Th TanH(X) DF πX A X^{2} -------------------------------------------------------------------- CF πX B X^{2} [CIF] [1/πX] TI2 [tan(X)]; tan(0.1X) TI1 [tan(0.1X)]; tan(X) [CI] [1/X] SI [sin(0.1X)]; cos(0.1X) C X C X -------------------------------------------------------------------- D X D X LL3 exp(X) [DI] [1/X] LL2 exp(0.1X) Χ (=Chi) Radians LL1 exp(0.01X) Θ (=Theta) Degrees R E M A R K S : ==================================================================== The reciprocal SI, TI1 or TI2 refer to the reciprocal CI(DI) scales: Black Numbers on TI1/2-Scale refer to RED Results on CI/DI-Scale RED Numbers on TI1/2-Scale refer to BLACK Results on C/D-Scale Black Numbers on SI-Scale refer to RED Results on CI/DI-Scale RED Numbers on SI-Scale refer to RED Results on CI/DI-Scale Example: 12 * sin(34°) = 6.71 -------- Set sin(34°) opposit to 12 on D scale (="division" operation) and read the result on D scale under the right "1" of the slider. The DEFINITIVE FORMS for the HYPERBOLIC FUNCTIONS are: ------------------------------------------------------ CosH(X) = ( exp(+X) + exp(-X) ) / 2 <== this is the "Chain Line" SinH(X) = ( exp(+X) - exp(-X) ) / 2 ( eg. suspension bridge ) TanH(X) = SinH(X) / CosH(X) exp(X) = SinH(X) + CosH(X) 1 = CosH^{2}(X) - SinH^{2}(X) CosH(X) = sqrt( 1 + SinH^{2}(X) ) = SinH(X) / TanH(X) Using the Hyperbolic Functions: Start with value on the Sh scales ==>> reading SinH on D scale, start with value on the D scale ==>> reading ArcSinH on Sh. Start with value on the Th scale ==>> reading TanH on D scale, start with value on the D scale ==>> reading ArcTanH on Th. Example: CosH(0.345) = SinH(_) / TanH(_) = 1.060 -------- Set the left "1" of the slider under TanH(0.345). Move the hairline to SinH(0.345) and read the result on C (!) scale. YES! It's clever: This C scale is the "difference" SinH(_) - TanH(_) and - because of log. scales - represents the quotient of its values. This famous slide rule came in a brown leather case together with an instruction booklet. The ODELCO logo (only on the slide rule's front, right on top) refer to the distributor of HEMMI in the Philippines. HEMMI introduced a year code, starts with 1950 = "A" ... and the month code starts with January = "A" ... This slide rule has the code "YI", means it is made in Sept. 1974. Historical Remarks ... impressum: ******************************************************************** © C.HAMANN http://public.beuth-hochschule.de/~hamann 12/25/06 |