C and D Scales

Two of the most basic and important scales are the C and D scales.  The C scale is a fundamental scale on the slide and the D scales is identical but is on the body. The C and D scales are also called single-decade logarithmic scales. (One thing that has perturbed me is the names C and D.  Some of the other scales are simply letters representing the function.  Perhaps there was some musical input into this name ... Who knows!)

Notice that with this slide rule both the left and right indices are marked by a 1.  On some slide rules, the right index is marked as 10.  The C and D scales are mainly use in conjunction with each other to perform the operations of multiplication and division.

A and B Scales

The A and B scales are also identical, A being on the body and B on the slide.  These scales are used with the C and D scales to calculate squares and square roots.

The A and B scales are both double-decade logarithmic scales.  You will notice that the scale is repeated twice and there are three indices on each and that the first decade also has π marked for convenience  On this scale, both indices are marked with a 1, whereas on others they may be marked as 1 and 10.

K Scale

The K scales is a triple-decade logarithmic scale and is used to calculate cubes and cube roots.  There are four indices on this scale.

On this slide rule, all indices are marked with a 1, whereas on others they may be marked as 1, 10, 100 and 1000.

Both  CI and DI are single-decade scales and represent the inverses of the C and D scales, so both of these scales can find reciprocals and also aid in quicker operations of multiplication and division.  CI is on the slide and DI is on the body.  Some slide rules do not have a DI scale.

The CI and DI scales both have two indices like the C and D.  On this slide you will notice that there are less-than symbols.  These are on some slides to remind the user that the scale is read from right to left.  On other slide rules the indices are marked as 10 and 1. The CI and DI scales may also be marked in another color.

The L scale is a single-decade linear scale that is used to calculate the logarithm of a number using the base of 10.  This scale is linear (equally spaced graduations) since it forms the basis of the slide rule operation itself.

The indices of this scale are represented as 0's. On some slide rules, they are represented as 0 and 1 or 1 and 1.0.

The S scale allows the user to calculate the sine of an angle in the range of 5.7° to 90°.  It also allows the calculation of cosines by using the complement property,

cosθ° = sin(90° - θ°)

The S scale may appear on the slide or the body.

On this slide rule, the right-hand number is sine and the left-hand number is cosine.  Some other slide rules only have the angles for sine marked.

The T scale is used to calculate the tangent of angle in the range of 5.7° to 45°.  It can also be used to determine cotangents by using the complement property,

cotθ° = tan(90° - θ°)

Referring to above graphic, tangent values are on the right and cotangent values are on the left.  Some other slides rules only have the angles for tangent marked.  On some slides angles from 45° to 84.5° are marked and their values read from the CI scale.  This can also be done using the standard T by calculating the complement and reading the CI scale.

The ST scale allows us to calculate and use the sine or tangent of angles in the range 0.57° to 5.7°.  This scale is based on the property that for small values of θ°,

sinθ° ≈ tanθ°