Comments

"Mannheim," "Rietz," "Darmstadt," and "Stadia"

The words "Mannheim," "Rietz," "Darmstadt," and "Stadia" denote specific arrangements of calculating scales:
Mannheim: A slide rule with scales A [B, C] D and [S, L, T].  (The original Mannheim slide rule had only A [B, C] D scales but common usage includes trigonometric and common logarithm scales.)
Improved Mannheim Scales: A slide rule with scales A [B, CI, C] D, K and [S, L, T].  On both Mannheim and Improved Mannheim rules, angles between 0º-34’ and 90^o are set on the S scale and their sines read from the A/B scales.  (But note that Hemmi used Rietz S scales on all their Mannheim and improved Mannheim slide rules from about 1940 until about 1955.)
Rietz Scales: K, A [B, C] D, L and [S, S&T, T].  Rietz rules may also have a CI scale.  Angles between 5^o44' and 90^o are set on the S scale and their sines read from the C/D scales.  Angles between 0º-34’ and 5º-44’ are set on the S&T scale and their sines and tangents (which are essentially equal to each other) read from the C/D scales.
Darmstadt Scales: L, K, A [B, CI, C] D, COS, Sin, Tg and [LL1, LL2, LL3].  The Sin scale is in degrees and gives the angle whose sine is shown on the D scale.  Similarly, the Tg scale give the angle whose tangent is shown on the D scale.
Stadia Scales: For surveyors.  Click here for explanation of stadia scales.
 

Gauge Marks

The gauge marks most frequently appearing are
pi  = 3.14,
C² = 4/pi = 1.27,
C = SQRT(4/pi) = 1.128,
Hp = 0.736 kW/hp (French/metric) or 0.746 kW/hp (British/American).
 

Horsepower

“Electro” and some other slide rules are constructed to provide automatic conversion between watts and horsepower.  Originally the conversion factor was 746 watts = 1 hp, but starting about 1930, France and other countries changed to a “metric” horsepower of 736 watts, leaving the United States and Great Britain as the principal countries still using the old, 746-watt, horsepower.  After the early 1930s, all rules where the comments mention “hp” were available in separate British/US and French/metric versions.  From the early 1930s to the early 1950s the different versions had different gauge marks, different cursors, and a different knife-edge arrangement for reading scales in the gutter.  By the middle 50s Hemmi had eliminated the gauge marks and knife edge and the only difference between the French/metric versions and the British/US versions was in the spacing of hairlines on the cursor.

The existence of separate French/metric and British/US hp versions means that there are many possible variants of slide rules with hp gauge marks or cursors.  For example, Hemmi model 80 came in single- (80/1) and triple- (80/3) hairline versions, both with two definitions of horsepower and each of those available with at least two different sets of measuring scales on the top and bottom edges.  There must be at least eight different variants of the Hemmi model 80 slide rule.
 

Cursor Hairlines

Whenever a cursor has multiple hairlines, this catalog attempts to give the spacing between the hairlines.  To understand the notation used consider a hypothetical cursor with two hairlines spaced such that when the left hairline is set to 1.000 on the A scale the right hairline is over 2.00 on the A scale.  If this hypothetical cursor were to be reset to put the left hairline on 2.50 on the A scale, the right hairline would be on 5.00.  Or set the left hairline on 4.12 and the right hairline will be on 8.24.  In every case the number under the right hairline will be twice the number under the left hairline.  The spacing between the lines on this hypothetical cursor would be indicated by the notation {A: 2}.

A common spacing for 3-line cursors is {A: hp, C²}.  This notation indicates that the space between the left and center hairlines corresponds to a ratio of 0.736 kW/hp (or 0.746 kW/hp, depending upon which definition of horsepower was in use in the country where the slide rule was originally sold) and the space between the center and right hairline corresponds to a ratio of 1.27, where 1.27 = 4/pi = "C^2", measured on the A scale.

Another example: “{D: hp-C, C}” indicates that the space between the center and right hairline corresponds to a ratio of C = SQRT(4/pi) = 1.128 and the space between the left and right (not center) hairlines is 0.736kW/hp or 0.746kW/hp -- both measured on the D scale.