**Keying of S Scale**

The S (sine) scale
is treated in two substantially different ways on slide rules. In the
“Rietz” arrangement of trig scales (S, S&T, T), angles between 0º-34’ and
5º-44’ are set on the S&T scale and the value of the sine of
the angle is
read from the C/D scales with the knowledge that it lies in the range
0.01 to 0.1--e.g., sin(4º) =0.0697. Larger angles, in the range 5^{º}-44'
to 90º, are set on the S scale and the value of their sines read from
the same C/D scales as before but this time with the knowledge that the
value lies
in the range 0.1 to 1. In other words, the angle 4º is the same distance from the end
of the S&T scale as its sine, 0.0697, is from the end of the C and D scales and
the angle 40º is the same distance from the end
of the S scale
as its sine, 0.643, is from the end of the same C and D scales. This is
true for all rules that have an S&T scale.

There is no S&T scale in the “Mannheim” arrangement (S, L, T) of trig scales; all angles from 0 degrees 34 minutes to 90 degrees are set on the S scale and the value of their sines (range: 0.01 to 1.0) are read from the A/B scales.

Thus, there are two different ways to set up the sine scale: Rietz (keyed to C/D) and Mannheim (keyed to A/B). Slide rules with [S, L, T] scales usually use the Mannheim sine scale but several Hemmi slide rules, made between WWII and 1955, with [S, L, T] scales used the Rietz sine scale. After 1955 these rules switched back to "Mannheim" sine scales. (Got that? Some Hemmi Mannheim rules used "Rietz" sine scales.) The catalogue notes which style is used on closed body rules with [S, L, T] on the back of the slide.