1970 Hercules 3spd

[JPKelley5]

All - After doing some research (CABE, Sheldon Brown) I'm still at a loss as to what tires will fit on this bike. I pulled a pair of dry-rotted 26x1 3/8 off the bike and attempted to replace them with a borrowed set of S-6 26 x 1 3/8 off a 42 Schwinn New World. Too big. What am I overlooking? The original Hercules wheels are stamped with Sturmey Archer 26 x 1 38. Thanks for the help.

 

[JPKelley5]

Update - Looks like the ISO is smaller on the English 3 spds. 590 vs 597 on the S-6. I suspect that is the issue.