100 + 28 degrees are not harder to mark than 64, and then aim 0 and 100 properly. :-/
What would be the process to do that? To aim 0 and 100 properly, you'd need a tool to calculate a 100:28 (25:7) ratio on an arbitrary distance, wouldn't you?
One can build such a tool, but it's not a doubled-over piece of string.
Make marks on the thermometer at 0 and 100 degrees C, then project light from a candle to a wall to see these marks with say 5x magnification. Now project marks from the 128 mark ruler to the same wall and align marks from both, then place marks on the thermometer with 5x better accuracy.
A candle is an exceptionally unstable light source. The flame continually moves location as it burns. Any air currents in the room will disturb it and cause flame shadows to be cast. Adding magnification will just make this all worse.
Henry Cavindish used them to measure G. I used lasers and never got even an order of magnitude closer.
His measurement apparatus was designed to eliminate air currents was it not? He also had a torsion balance and a vernier to make measurements of the /relative/ changes induced in the apparatus.
I don't see how you're going to use this system to effect repeatable markings on glass tubes.
These problems are easy to solve in practice: just put the candle into a lantern.
Try it: it's easy. Use a flashlight from your phone instead of a candle, then project light to a wall, then put your palm in the front of the light.
Sounds doable, but again, you're comparing that approach to:
- get some string
- measure a length between your low and high points
- fold it in half
- make a mark at the halfway point of the string
- fold it in half again, etc.
No candles, projection, transparent or slotted ruler, wall, or carefully moving one's hand back and forth under projected magnification needed. Just some string.
Surely you can simply use a ruler and rotate it away from the parallel to achieve any arbitrary scale, right?
If you happen to have a good ruler (again, 1720s... Those also cost money or time to make). A ruler and a T-square would work. But still, it's more complicated and requires a lot more bench to secure things in place at angles than folding a piece of string in half.
Well... Yeah. It costs money and/or time to make things. That's as much true now as it was back then, but I don't think a ruler would have been particularly difficult to make, even with 18th century technology.