How was bore/caliber size expressed in the period?

How was bore size expressed in the period?

Short answer is in the number of balls to a pound of lead, which, is the equivalent of "gauge" as is used on most modern shotguns, the exception being the .410, which is .41 caliber - go figure. .75 cal = 11 balls/lb, and .69 cal = 15 balls/lb though these are  usually rounded off to their modern shotgun equivalents of 12 & 16  gauge, respectively. Though the period way would be to refer to it as a 11 bore rather then a 12 gauge. Some of the more common ones (roughly rounded off) are:

 Gauge/Balls/lb              Caliber             Weight/gr.                                    ```                8                     .835                 875 ``` ```               10                    .776                 700 ``` ```               12                    .730                 583 ``` ```               13                    .710                 538 ``` ```               14                    .693                 500 ``` ```               16                    .663                 438 ``` ```               20                    .615                 350 ``` ```               24                    .579                 292 ``` `               28                    .550                 250     `

Knowing that there are 7000 grains in a pound, we can divide 7000 by 28 and see that 28 gauge balls weigh 250 grains each. If we measure one of those balls, we see that it is .550 inches in diameter. In modern usage that is the same as '.55 caliber'. The same relationship holds true for any size bore.

While  "Caliber" was a period term, it was used by artillery as a measure of the relative length of a gun barrel, defined as the length divided by the diameter of the bore. Thus a 50-caliber gun on a warship has a barrel 50 times longer than its bore. Confining the shell within the barrel for a longer time increases the velocity, so guns with a higher caliber usually have a longer range.

I'm not sure when it came to refer to the bore size expressed in hundredths of an inch, which is what it means today.  At least in England the use of bore versus caliber seems to be the norm through the 1850’s at least