Next I had the daunting task of how to safely splice the two wires together. I decided on using a "Western Union" type splice. It's an in-line type splice that allows for a strong mechanical and electrical connection. Here's how is goes...
STEP ONE: Hold the two wires to be joined at a 90 degree angle to one another. Make sure to twist the strands of each wire first before going to step two.
STEP TWO: Begin twisting clockwise with one hand and counter clockwise with the other. As you can see a nice twist is made between the two wires. They should be tight enough where they can't pull apart easily. Also, make sure to push down any strands that are sticking up. You don't want any strands poking through the tape or heat shink which will be added in a later step.
STEP THREE: To give the joint even more strength I soldered each one. I won't get into the in's and out's of soldering but there's lots of information on the net if you don't know how. Key is to heat the wire, not the solder. Keep the iron under the wire and when the wire is hot enough it will draw the solder into it. Just add enough solder to coat the wire, don't glob it on.
The finished soldered connection.
I originally was going to use heat shrink on each splice but after trying a couple test pieces I wasn't able to use the soldering iron and heat shrink in such a small joint. I ended up melting the heat shrink before I was done soldering. So,
crvz recommended using 3M's Super 33+ electrical tape. I can say this was a very wise move. After using cheap tape in the past I won't ever use anything else. This stuff is great!
STEP FOUR: Tape each soldered connection making sure no strands poke through the tape.
STEP FIVE: Once all the splices were taped, I bundled all three wires together and taped them together for some extra support.