Use a drill to make a hole in one end of the ¼" (6mm) dowel.
Keep the wrapping snug and continue coiling it around until you have about a 12" (30cm) coil. Snip the wire where it went into the hole.
Working directly off of the 19-gauge spool of wire, insert the end into the hole and begin wrapping the wire around the dowel.
Remove the coil from the dowel. Use your hands to flatten and slightly spread the coil.