Burrard wrote he felt it was a mistake to have barrels of different length fitted to the same gun as Barrel Flip would cause them to hit to a different point "Vertically". He did not confine this to sub-bores but was speaking primarily of the 12 gauge, which was at the time of his writing "THE" gauge in the UK.
This I believe was not what Joe was speaking of. Perhaps the best term here would simply be Barrel Displacement. As I read through these posts I believe we are all pretty well in agreement that the barrels are moving during the load's travel down the bore, otherwise there would be an unacceptable amount of crossfire, as the barrels whether straight or bent do converge.
Now let me Speculate a bit. I believe it is a False Assumption to believe that the barrels of every given length, every weight of gun & every load fired has to end with the same degree of convergence. Maybe I am misinterpreting here Mike but I seem to be getting the feeling you are saying this has to be so. I have gone back & re-read your link to the Parker Board. Let me say this as kindly as I can, but I can see absolutely nothing there other than the speculation that barrels of different lengths having the same breech spacing & still touching at the muzzle "Must" have been bent so the last section of the barrels at the muzzle would have the same convergence. This is as far as I can see an unproven hypothesis.
In studying the history of barrel making one finds their configurations were Set, well back in the Welded barrel era. At this point a barrel was generally made to be round at any point, though contoured down its length. Metal for the flats was welded on. It was also found that flats needed to be put on the mating surfaces of the breech ends of the two barrels to bring their centers closer together, else they would indeed crossfire. Of all the barrels I have ever checked this on I still find that the web between the two barrels is not equal to twice the the wall thickness at the extreme breech end of the barrels, thus Gunmakers are still building to essentially the same criteria. All the writings I have seen would indicate that standard practice was to make the barrels as straight as humanly possible & to set them at a converging angle, no doubt worked out over time by trial & error. The "Very" limited amount of barrels which I have personally checked show that "Those" barrels were indeed made in this fashion.


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