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.
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.
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.
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.