I've used modern gunners' quadrants like this in black powder cannon shooting in as follows:
Find flat spot on top of cannon barrel anywhere, doesn't even have to be parallel to bore if it is flat and you can set quadrant on the exact same spot each time.
-Before each shot, put quadrant in place, and adjust the quadrant's arm so the bubble is centered. You don't need to read any numbers with this method, unless you want to do so to create range tables. Put quadrant aside before firing, without changing setting.
-If the shot was "on target" in elevation, when aiming next shot, take quadrant with setting from previous shot, put it in place on the barrel, and adjust only the cannon's elevation so the bubble becomes centered again. As long as cannon shots remain "on target" in elevation, don't change the quadrant setting.
This is advantageous if you shoot cannons without "modern type" sights, or with poor sights, or no sights. It is helpful for firing howitzers, where the higher angles used make sighting over the barrel difficult. For firing blackpowder mortars, find out where the 45-degree setting is, and use that.
If there's no perfectly flat spot on to p of the barrel for the quadrant, you may need to use a straignt piece of metal about a foot or more long that will go down the bore, which you can hold or mount the quadrant on outside the muzzle.
