GM MacDonald Logarithmic Spiral Calculator

Here is a rare example of a Spiral slide rule using a logarithmic spiral rather than an Archimedian spiral. I am pretty sure this calculator never was manufactured.

The patent US 2426362 can be found on the International Slide Rule Museum.

The inventor's full name was George Marsden MacDonald.

This instrument has 2 scales on a disk, a logarithmic spiral of numbers, and a circular line of logarithms. It has one cursor, and an index ring (which is not used for setting or reading numbers).

The cursor does not use a center post for the cursor or ring. Instead, the cursor is held by a casing that is analogous to a framed cursor on a traditional slide rule. The most interesting feature is that the cursor as 2 sets of verniers, one for the circular line of logarithms, and the other (appears as a set of curved radial lines) is for the spiral. The verniers give 1 or 2 extra digits of precision and are the principal advantage that this invention brings.

The index ring has a single pointer and is housed between the cursor casing and the disk, held in place by the cursor.

The cursor and index ring move freely, and independently from each other and the disk; the instrument required locking mechanisms to allow computations to take place. The index needed to be locked to the disk during some parts of computations, and to the cursor in other parts.

The patent offers a number of ways to implement the underlying concept, e.g., different sizes/number of turns, different ways to lock the cursors, and of course different levels of precision, and calibration. One was in a 9.5 inch 50 turn model that MacDonald claimed capable of 6 digits precision.