Bach mouthpieces use a Morse taper: 0.05208" (1.322832 mm) rise per inch length.
Conn Remington mouthpieces, which were manufactured in Elkhart IN in the 1970's and supplied with Conn 8H, 88H, 60H 62H, 70H-73H and others, use a Brown and Sharpe taper: 0.04167" (1.058418 mm) rise per inch length.
I played a new 1962 Conn 24i euphonium for 4 years in college. I do not recall the OEM mouthpiece, but my mouthpiece of choice at the time was a Bach 3 with a standard tenor trombone shank. The OEM adapter was the only way a tenor shank would fit and a bass trombone shank would not fit. I also played a Conn 72H bass trombone in H.S. which came with a Remington mouthpiece, my favored mouthpiece, a Bach 1½G, large shank, would not fit properly, and wobbled.
flotrb
Доверяй, но проверяй
(Trust, but verify)