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KEUFFEL & ESSER   4083-3   ( 10" / 25 cm Scales )



KEUFFEL & ESSER, New York / USA           SN = 098614             (1940)
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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       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

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)

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 ...
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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:
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© C.HAMANN      http://public.beuth-hochschule.de/~hamann       08/18/14