I was just informed by Shopsmith that their bandsaw manufactured in 1984
cannot be serviced with new tires, after I ordered what were supposed to
be replacements.

"The very old Bandsaw did have a ribbed wheel. I asked our Service Repair
tech and he assured me that the tires we sell will work on the ribbed
wheel. The surface area to hold the adhesive is a little less, but the tire
will hold firm."

The Shopsmith bandsaw was manufactured in 1984.

Seems to me that putting a non-ribbed tire on a ribbed wheel could cause
problems, besides possible lack of adhesion.
....The rubber can move down into the ribs warping the outer surface of the
tire.
....The tension guide wont work properly due to a different outer diameter
of the tires on the wheels.

But since there are no other sources for Shopsmith bandsaw tires, I guess
we will have to cope.