Thanks to all who have replied, and to Bill for starting this thread.
After staring at the (few) labeled sample segments and illustrations available until cross-eyed

, I believe Parker offered BOTH Bernard I and Bernard II barrels.
IF there are very distinct "roses" in the pattern, I think we can safely call it Bernard II
The "rough forged tubes" were ordered matched, paired and wired together, and the pattern is difficult to read when "rough forged". Parker Bros. obviously knew what they were ordering, but the subtle differences in the batches supplied by the Belgian makers would not be unexpected.
I could still be wrong, but have changed these documents to reflect that opinion
https://docs.google.com/document/d/1...YvzD18i3c/edit
http://www.picturetrail.com/sfx/album/view/17227428
http://www.picturetrail.com/sfx/album/view/19025099