Which is clearly marked on the old tyres? the 37-349, the 16 x 1 3/8 or both measurements? The ETRTO is the only one that will tell you for certain if the tires are made for a rim with the same BSD. There are at least three other possible BSD sizes that might be possible for a tire with 16 x 1 3/8 proudly shown on its carcass. 337mm, 335mm, 317mm. Though I don't know which may or may not have been produced in the last 20 years.