KEUFFEL & ESSER, New York / USA SN = 098614 (1940) ************************************************************************ S C A L E S of the » H Y P E R L O G DUPLEX « Model 4083-3 ======================================================================== 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 X^{2} ------------------------------------------------------------------------ CF πX B X^{2} [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 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) 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. The scales are identical to DIETZGEN-1735 ... The SR came in a brown plastic case with missing flap. This model is made of mahogany with scales on celluloid veneer. The CURSOR-BLOCKS, made of CELLULOID where detoriated ... ... and had to be replaced by home-made PVC ones. Same "CELLULOID DISEASE" happened also (e.g.) to the DIETZGEN 1732 ... ************************************************************************ Celluloid, first produced in 1872, was the 1st used plastic world wide. It consists of a mix of cellulose nitrate & camphor. The plasticizer camphor is given off over time and the nitrate breaks up under the influence of oxygen & moisture and transforms to nitric acid. Both effects destroy the material - and the acid is the reason why the metal of frame and spring get brittle & rusty. Historical Remarks ... impressum: ************************************************************************ © C.HAMANN http://public.beuth-hochschule.de/~hamann 08/18/14 |