K e slide rule dating
The slide carries two identical scales, wasting one interface. The Soho rule shown here is a beautiful exemplar, having been made by the renowned Gravet-Lenoir workshop in Paris near the middle of the 19th century.
The reason for the odd scale arrangement on the Soho rule is that unless the scales on the slide were identical, there would be no way to move across the slide from the top to the bottom scales.
The first slide rule, constructed by William Oughtred in 1622, essentially put two Gunter scales next to each other, so that distances along the scale could be added directly by sliding the scales against each other.
This idea remained for three centuries at the heart of every slide rule made.
The variety of calculations required ran into a problem: to calculate (multiply or divide) or convert between different quantities one needs to move from a number on one scale to the number at the equivalent point on another scale.
This required the two scales to touch each other, so the equivalent points could be pinpointed accurately.
One couldnt, however, multiply with the greater accuracy that the single-cycle scale would allow were there a matching one sliding above it, on the slide, which is curiously lacking.
The logarithmic calculating function used the narrow slide in one of its legs (For more, see this article).
Another standard form factor was used extensively in Ullage rules, which were used to calculate the excise tax on alcoholic beverages based on alcohol content and liquid depth in barrels of various shapes.
they used fixed scales on a wooden rule that allowed distances to be measured and added using a pair of dividers.
This "Gunter's Rule" was the original device introduced by Edmund Gunter in 1620, which remained in use for some two centuries.
To do that, youd need a cursor, a sliding member that traces a perfect perpendicular line across the rule. Who invented the Cursor (or, as it was sometimes called, Index, indicator, or Runner) is debatable.