Thanks, everyone. I did read JT's article, but thought that my cuttings were rotting and that it was spreading toward the main branch. That's why I posted the request for help. But, upon further examination, I find that it's just that--dying tips, which I have cut back, as recommended.
:lol: about placing your cutting in a narrow neck container and having the break it in order to get the root mass out. I had my cuttings rooting in a water filled vase, which was sitting on the fireplace hearth behind another potted plant (beside a sunny window). When I pulled it forward to examine it closely, I was shocked to find that some of the roots are close to an inch long already. One of the cuttings grew the long roots with only a few nubs.
The other has lots of nubbies and only 1 long root. Anyway, it looks like it's time to transplant them all to moist soil.
all for your help and encouragement.