I suspect the strength of the engagement between the tape and sprocket
wasn't a primary consideration, as the sprocket drove only the
plotting mechanism. Does an easy-to-index factor of 360 such as 12, 24
or 36 make sense as the number of sprocket pins?

A sprocket of 11.459" diameter would revolve once per 3' of band
travel. It might have 24 pins spaced 1.500" apart, or 36 at 1.000". A
7.639" diameter sprocket would correspond to 2'.

The fusee and the frame suggest that a tower (turret) clock maker
built it, so a 30 tooth sprocket is possible.
http://www.model-engineer.co.uk/foru...s.asp?th=75826

This shows a clock built on a similar frame:
https://en.wikipedia.org/wiki/Turret...k_movement.png
-jsw



Associated pages to that pic of the gauge
http://trigtools.co.uk/data/2GLMain_24.htm
http://trigtools.co.uk/data/2GLMain_25.htm

Looks like an exploration of the background to the Cary & Porter company
as to any clockmaking connection.

Same company tide gauges , but the models using the troublesome
counterbalance going down the stilling well, and no metal tape
(ignore what I was saying on there about slippage in the traverse area,
moved on from that)
https://www.ordnancesurvey.co.uk/blo...-our-antiques/

going by the B&W graphic , the original model, not the one in coloured
pic ,
was one of these earlier fusee, and perforated tape suspension models
http://www.tandfonline.com/doi/pdf/1...9.2015.1121175

Busy today, but i'll try pixel counting on those "trigtools "
" images.
The pulleys ,rather than gear wheels, have a reinforcement flange on the
inside of torque/tension bearing flange, so the tape is quite recessed
into those pulley rims .