"N_Cook" wrote in message
news
More interesting than the other stuff i should have been doing.

From 24 inch circumference of the recording drum I make the key data
for that top image 0.0868 inches per pixel, vertical and horizontal,
as circular wheels. The clocks were 10 day , allowing 7 days of
continuous recording on one sheet of paper, much overlapping of
about 19 tide cycles, before having to change paper and re-synching.
Hence accurately inferred diameter dimension there.
I reckon, from 20 foot of tide range, 7 turns of tape ,then from the
following, 1 1/3 inches wide and 0.083 inches ,probably 5/64 inch,
thick tape.
The spigotted pulley , the measurement-active bearing face , between
11.08 in and 11.13 in diameter.
So for a jump between 2 and 2.5 inches, if perforations spacing 0.75
in between centres, then 46 spigots and jumped 3, 2.25 inches,
pulley diameter 10.98 in.
If 1 inch spacing, 35 spigots, jumped 2 , or 2 inches, pulley diam
11.14 in
If 1.25 in spacing ,28 spigots, jumped 2 or 2.5 inches, diam 11.14
in
If 4/3 inch spacing , 26 spigots, jump of 1 or 2 is outside the 2
to 2.5 inch range, but if so, then pulley 11.03 in diam .
...

It's easier to space the holes in the tape at some arbitrary
non-integer distance than to divide the wheel by an odd number, unless
the maker already has the correct index plate. 24 is particularly
easy.

This is a modern example of a classic design. I have an indexer that
may date from the 1880's.
https://www.amazon.com/BS-0-Dividing.../dp/B013ZDX6XQ
-jsw