If you are unfamiliar with what a vernier is, the internet has a lot of tutorials on them (one example here). Vernier calipers are being replaced by their digital counterparts, but still exist.
This calculator has 2 scales, a log mantissa scale and the spiral scale of numbers.
The vernier cursor (my name for it) has verniers for both scales.
The vernier for the spiral scale of numbers is a set of curved lines that curve inward as they approach the scale origin. They intersect the log spiral coils and you read them based on which coil you are interested in.
The vernier for the log mantissa scale is formed in an arc and is read against the circular mantissa scale.
The patent discusses options for exploiting the precision that verniers offer. According to the inventor, up to 2 additional significant digits could be extracted from a Log Spiral calculator (at best, I believe this would be a 50 x improvement, not 100).
In the sample I placed on these pages, I used a 19/20 vernier for the log scale, and a 9/10 vernier for the spiral, as these add 1 decimal point to what's shown on the scales.
The vernier cursor also has markings along the cursor line, called the coil index.
The coil index had two functions.
The function was that it provides the first 1 or 2 digits of the log mantissa scale (depends on the number of turns).
The second purpose was to help find which turn the answer for a computation lies on,
During a computation, one kept a running tally of which turn each intermediate result fell on; this was used to figure out which coil that the answer is on. Every time the running tally exceeded the total number of turns, you subtracted the total number of turns (to reset to 1). The resulting number was the turn that the computation was on.