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 5º-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.