Observations

Synopsis

This instrument offers the possibility of a tenfold increase in resolution over a 'traditional' spiral design. Given that, it might seem surprising that the calculator didn't become a major contender in the marketplace.

There are some issues with the logarithmic spiral technique that probably were a factor.

The spiral

The main limitation of this Log Spiral is inherent in the logarithmic spiral itself.

The inner turns are much closer together than the outer turns, and this disparity increases with the number of turns.

As with other spiral scales to increase the scale resolution, the number of turns must increase. Also, you need a bigger Log Spiral than an Archimedean spiral to have the same overall scale length, or conversely, if two spirals have the same diameter and the same number of turns, the traditional spiral will be longer. In the cases I've tried it looks like the Vernier capability more than compensates for that difference.

At any rate, what this means is we need to make the calculator larger we would need with a traditional spiral design, to avoid excessively small separation between the first turns. I have a 25 turn version below side by side with a Gilson Binary that shows this.

Vernier limitations

It should be apparent that the Spiral vernier is harder to use near the centre of the spiral. They begin to curl inward, and are closer together in the centre, and also intersecting the Spiral at a sharper angle towards the center. Coupled with the fact that the turns are closer as well, it's basically tough to take a reading.

George Macdonald was completely aware of these problems and attempted to address it in his patent.

He proposed several mechanisms to keep the instrument readable, including:

1. Removing leading digits from the numbers on the disk. Macdonald added an extra scale on the Vernier cursor that allowed you to infer the leading digits.

2. Writing the numbers horizontally (perpendicular to the line of the spiral, rather than parallel with it)

3. Replacing tick marks with dots.

4. Extending the Vernier to the opposite side of the cursor in large turn spirals, which allows for even and odd coil numbers to be separated. He also doubled (halved?) the log scale to fit 2 cycles on the outer circle.

Manufacturing costs

I reckon that this would be an expensive calculator, particularly if you were chasing the high-precision market. The framed vernier and index that Macdonald describes includes 3 locking mechanisms, various techniques to allow for maintaining precise alignment, and for the really long scale versions, mechanisms to provide for fine adjustments.