Thanks to all who have replied - this helps me understand the basic idea. I sure wish I had known about grabbing that dolphin striker before re-righting the catamaran three times in a storm, but hey, you aren't supposed to be confronted with a flash thunderstorm your second time out.
I am beginning to think that my righting lines may be installed correctly.
I don't have my boat here, but I just drew two rough pictures of how the righting lines look from underneath and from beside the boat. On the bottom, there is a pulley arrangement that allows me to pull the line out in the back, moving the line from one side to the other [ see my attachment, which you can click on at the left of this posted message ]. The front is relatively stable.
When the cat flips, I can definitely reach the line from the bottom, but the line from the sides may be out of reach [ see attachment on my reply to this message ].
Do these drawings look correct? If so, how am I supposed to use this kind of line?