Here's a very good video that identifies and defines many anatomical terms that rose growers often use.

Here is a link that might be useful: Paul Zimmerman on Rose Anatomy

Cadence -- Bud eyes should be all along a cane, at any point where a leaf attaches to the stem. The bud eye is a tiny fleshy "bump" tucked between the cane and the leaf.

If there is a long length of stem, with no leaves at all, then you are correct that there are no bud eyes -- and so you don't want to cut the cane, in that area.

Is it possible for you to get a photo of these plants?

Jeri

I can't believe I am disagreeing with Jeri, but--the lower part of old canes used to have leaves, now don't, but they still have bud eyes. These are little bumps with smiley lines underneath where the leaf stem used to attach. If the canes are old and barky, you can often still make out the bumps.

Michael is right. Those are harder to spot.
I was thinking of a newer cane -- but of course, she's more likely describing older growth, yes?

Jeri

Oops . . . Terribly, terribly sorry for providing access to all the apparently erroneous and/or incomplete info contained in Paul Zimmerman's video . . .

Thanks everyone for all your help. Okay, I've got the bud-eye thing figured out. I really enjoyed Paul Zimmerman's video on 'The Anatomy of a Rose' - Once these rose bloom, I'll send a couple of photos to see if anyone can help me to identify what kind they are. Thanks again.