Tatting the chain around the other side of the bead, we come to the join. I opted to use the "Alligator Join". The core thread goes under the work, the auxiliary thread goes on top, (or reverse order if it looks better to you) and the tatting continues.
This photo shows the first half of of a double stitch just after the join. It is still loose in the photo to help you see it, but it needs to be pulled up tight.
Tatting continues around the beads.
This concludes my tutorial on a string of beaded mock rings. Have fun!