EUGEN DIETZGEN CO., Chicago, Illinois / USA SN = 110443 (1950) ************************************************************************ SCALES of the » MANIPHASE MULTIPLEX VECTOR LOG LOG « Model 1735 ======================================================================== Front Side [ inverse / RED ] Back Side ======================================================================== L lgX [LL0] [exp(-0.001X) .. exp(-0.01X) .. exp(-0.1X)] LL1 exp(0.01X) [LL00] [exp(-0.1X) .. exp(-1X) .. exp(-10X)] DF πX A X2 ------------------------------------------------------------------------ CF πX B X2 [CIF] [1/πX] T tan(0.1X) ; [cot(0.1X)] [CI] [1/X] ST arc(0.01X) C X S sin(0.1X) ; [cos(0.1X)] ------------------------------------------------------------------------ D X D X LL3 exp(X) Th TanH(0.1X) <0.1 .. 3> LL2 exp(0.1X) Sh2 SinH(X) <0.85 .. 3> Sh1 SinH(0.1X) <0.1 .. 0.9> R E M A R K S : ======================================================================== [LL0] & [LL00] are keyed to A ( !!! ) ; LL1, LL2 & LL3 are keyed to D This » VECTOR LOG LOG « is made of mahogany with scales on celluloid veneer. It came in a brown leather case with a double-sided cardboard in it: CONVERSION TABLES on one side, MATHEMATICAL FORMULAS on the other. 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 = CosH2(X) - SinH2(X) CosH(X) = SinH(X) / TanH(X) = sqrt( 1 + SinH2(X) ) = H(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. Historical Remarks ... This "DIETZGEN" is made by KEUFFEL & ESSER. Scales on front are the same as K&E Model 4080-3. But the back side is different: The TRIGONOMETRIC SCALES are DECIMAL and the lower body has the HYPERBOLIC SCALES instead. The CURSOR ( with blocks made from sheet metal ) is a "DIETZGEN"-Patent. impressum: ************************************************************************ © C.HAMANN http://public.BHT-Berlin.de/hamann 01/01/10 |