Scale is a line. Each point of a scale represents a real number. This number is sometimes called 'the name' of this point. Some points are marked with ticks and some ticks carry numeric and symbolic labels thus helping user to determine the name of the point. Distance between 2 ticks is choosen that way to allow linear approximation for points between them.
The formula that represents the distance from the begining of the
scale to a point with name x is often caled "formula of a scale".
Thus D scale has formula
What cursor essentially does, it finds the point on one scale that is on the same distance from the scale beginning as point on another scale.
It is the toughest and the most important skill required for using slide rule.
Generally this document does not give rules to determine digit count. This topic is widely discussed in numerous slide rule manuals.
What constitutes "easy for human" depends a lot on a specific human in question. It can be (in the order of increasing difficulty):
These steps are considered elementary though they can lead to big errors.
The most often occuring relationship is equality. In this case operation becomes "find such position of the cursor that it marks the same numbers for two given scales".
This type of search is used to calculate square roots without A or CI scale and also to calculate cubic roots without K scale. See (R. Manely site).
Input values of algorithm usualy get names u, v, w, t etc. Constants get names a, b, c etc. Values that should be found or intermediate values get names x, y, etc. Constants present on the scales denoted with their quoted names: 'pi', 'c1', 'rho'
Number followed by scale name represents point on the scale where this number is located.
Index does not necessarily means "left edge" or "right edge", since sometimes scales have extensions that extend beyond index. Example would be LL scales, S scale, ST scale etc.
Informally, index of a stock scale is number that is aligned with 1 or 10 on scale D and index of a slide scale is number that is aligned with 1 or 10 on scale C.
There are two kinds of moving elements -- points on the scales located on the slide and cursor. Arrow points from moving entity to its position. Example: [1CI->| means "move left index of CI scale to cursor position".