The Small Calculator

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The small Small Calculator

The reason The Small Calculator is called The Small Calculator isn’t that it is a small calculator; the reason The Small Calculator is called The Small Calculator is that it was invented by Mr. Gilbert Small of Waltham, Massachusetts.
That said (hey, I just had to say it!), one must admit that Mr. Small’s invention is really quite small for a full fledged slide rule, being about 5 cm in diameter and 1 cm thick. It is also original in construction and lovely in form. Hats off to Mr. Small!

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Unlike the more common type of circular slide rule, the Small calculator places its primary pair of logarithmic scales -- the C and D scales used to multiply and divide -- not on its face but around its edge, one scale on each of two stacked discs -- flattened cylinders -- that are connected at their centers to rotate relative to each other. It also has a uniquely shaped cursor that points at these scales and at those on the flat faces of the discs.
The general form factor of two stacked discs is not original to Small, and is seen in an earlier patent from 1900 issued to one Roger W. Conant.

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What makes Small’s design unique, as he stresses in the patent application he'd filed on Feb. 17, 1913, is the convenience with which the device can be held when in use.

Unlike most other slide rules, where there is a stationary “stock” that can be grasped in one hand while the slide and cursor are moved with the other, the Conant design is all moving parts, with no place to hold the tiny device without interfering with its operation -- especially with the motion of the cursor, which extends to the center of the circle, where it is pivoted. Gilbert Small has given his device a much wider hub, and made the cursor attach to a groove outside this hub. This means that the cursor may be rotated freely with one hand without interfering with the thumb or forefinger of the other hand as they grasp the calculator firmly by its wide, stationary hub. Much better human engineering than the original design!

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This calculator packs all the functionality of a basic pocket slide rule. It can multiply and divide, and do square roots, reciprocals, sines and logarithms. It has the scale length -- hence the precision -- of a 15 cm straight slide rule, but fits in a beautiful leather case a mere 6 x 6 x 1.5 cm in size. You can identify the different scales in the image below.

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There are two unusual aspects to this arrangement. One is the set of interpolating index lines marked "L" that the cursor dedicates to the Log scale, which let you read this scale at the side of the cursor rather than in the middle. The other is the linear six-inch scale around the circumference of the back side. The only function I could think of for this is to serve as a ruler -- many slipsticks have measuring rulers on their straight edge. Since this slide rule has no straight edge, Mr. Small may have decided to design it with an exact circumference of six inches, so you can measure distances by rolling it on the surface being measured. If you can think of another use for this scale, let me know!

		Exhibit provenance: I bought this item in one of the Oughtred Society’s wonderful meetings. More info: Here is the original patent granted to Mr. Small in 1918.

The small Small Calculator