This is an older tutorial, that I made once as a 'quick-shot' one, and posted in a discussion thread on MAIL. Now it's added here. It shows seamless joining of one chain into a ring, but can also be used to join two segments. I can not even remember the ring data I used there, but it was a massive chain, made from thick-wire Copper links, probably around 6 to 8AWG and roughly half an inch inner diameter. But it doesn't matter anyway, as at the moment you want to join JPL, you have already found a working ring size...
First, weave, until the last ring of the to be joined JPL chain has the same orientation as the first one. If you have two chain segments, simply orient them in a way, that the last ring of chain one, and the first one of the second chain segment have the same orientation AND layering scheme.
Then layer that last ring atop the first one, to continue the pattern.
Add the first connector ring; note that it has to be opened relatively wide to be able to set it at all; finally close it.
Setting the second (=final) connector ring is a straightforward affair, if you rotate the chain by 120 degrees, as you are used to when weaving the chain; and just follow the layering schematics - I show two slightly different images of this for clarification. Again, this connector ring has to be opened relatively wide. If you weave a tight JPL near the lower AR limit, you might be forced to close it halfways while setting to be able to continue fitting it in.
Then close that ring - the first image shows it not completely closed - and TADAAA!!! - a joined JPL3.
You can use that method for JPL5 (or higher JPLs) as well. There you need four connector rings (six, eight, or more if you really insist on doing that insane weave variants AND join them), but the method is straightforward and analogous. I must admit, that I never joined a higher JPL than JPL-7, but I know that the method works.
Have fun :)
-ZiLi-