Note that Kenny said the gun was from the 1880s. If it was proofed prior to 1887 then the 13 marks could indicate a bore diameter from 0.710" up to just under 0.729". The 13/1 size (.719") was not used prior to 1887. In this case, it would be immaterial as the current size is between 13 & 13/1 anyway, in proof either way it goes.

By the proof marks, you can tell whether it was proofed under 1887 rules or earlier ones.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra