Trig ScalesTrig scales were in use almost as early as the logarithmic scales. Trig scales went through various inventions and improvements. Let us review the progress.
|
Early slide rules were so called "Mannheim" type, which had A =B, C= D scales on front side and =S(sin), L(log), T(tan)= on rear of the slide. S scale is referenced to A/B scales and graduated in degree/ minutes. Since A scale has two cycles, sin covers a wide range of 35 minutes to 90 degrees. T scale is referenced at C/D scale and covers 6 degrees to 45 degrees.
![]() Exhibit 1. Trig sacles for K&E 4053-3 Why this asymmetry? One explanation is that, when the slide is reversed so that trig scales are on the front side, S and T scales are opposit A and D scales, respectively. This enables direct reading of trig values on A or D scales.
Besides, scales used for calculations were mainly A and B scals in early days. A/B scales were prefered bacause "over scales" happen less frequently. |
There is yet another variant to the Hemmi's SI/TI scales. It is on a Hemmi's Wat-time economy rule and the earlier model of 2664. The scales are designated as SI1, SI2, TI1 and TI2.
![]() Exhibit 5. Hemmi SI1, SI2, TI1, TI2 scales (Click above to view full range image. ) SI1 and TI1 are the regular inverted trig scales covering 6 degrees and up. SI2 and TI2 cover angles less than 6 degrees, very much the same way the ST scales do. But why two saparate scales? To get more accuracy on values near 6 degrees? May be. Sin and Tangent values at 5' 45" are about 0.5% apart. There may have been applications requiring better than that. And there is another neat idea built into TI2 scale. The right half of TI2 scale, just about beyond 2 degees, is replaced with the tan scale for between 45 and 70 degrees. So tangent smaller than 2 degrees share the SI2 scale and you get extra range up to 70 degrees for tangent. |