EUGEN DIETZGEN CO., Chicago, Illinois / USA      SN = 110443      (1950)
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SCALES  of  the   » MANIPHASE MULTIPLEX VECTOR LOG LOG «      Model 1735
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Front Side                   [ inverse / RED ]                 Back Side
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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 
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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)]
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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 :
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[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:
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© C.HAMANN         http://public.BHT-Berlin.de/hamann           01/01/10