"
Hmmm... Never heard of using chalk.
I would think it would degrade the accuracy since it has finite thickness, unlike Prussian Blue, which can be squished very thin.
You definitely do not want to scrape anything against the cylinder square surface, nor rotate the square while in contact with the work.
Cylinder squares are self-calibrating, like levels. Set up a reference, with two points of contact near the bottom, horizontally separated, and a sensitive dial indicator near the top. Simply rotate the square to several different positions and make sure the DI readings are identical. If not, the bottom end is out of square.
You can check for taper at the same time, although that problem is extremely unlikely.
The square that you got is of the more desirable type, with one end square and one end angled.
The curved lines around the surface indicated deviation from true square, calibrated
in .0002" increments (I think), when the angled end is on the surface plate.
For books I would suggest
Inspection and Gaging by Kennedy, Hoffman, and Bond. Industrial Press, New York.
I have the sixth edition, from 1987, ISBN 0-8311-1149-6"
From...https://www.practicalmachinist.com/forum/threads/brown-sharpe-558-cylindrical-square.241840/
Edit:
Even better. Youtube video....