The top row in the photo shows finished rings and the bottom row shows the method used. Left: fusing Center: medium paste solder Right: medium chip/sheet solder Note: Use a smaller piece of chip solder than shown.
Fusing: Place the ring on a solderite board with the opening facing away from you. Because each of the rings will be textured, it is not necessary for the seams to be perfectly smooth. The ends just need to be fused or soldered together. To fuse, move the flame around one of the rings. Carefully heat the ring until the wire surface goes from shiny to dull to very shiny and slightly molten. The seam will start to fill in and fuse. Let the ring cool on the board. Flip it over. If the seam is not fully fused, repeat the process from that side. When the metal is almost molten, a good technique to use would be to heat and pull back, heat and pull back until the seam almost fuses. That way the seam will not separate, which means the open ring will have to be used for something else.The fuse will complete after the heat is removed.
Soldering: Place a small piece of hard solder of a small amount of paste solder under the seam and heat until the solder flows up through the seam. The placement in the photo is to show amounts only.
Pro Tip: If rings were made oval to solder or fuse the ends together, they must be rounded. Hoop, bezel, and ring mandrels are wonderful to have in your tool arsenal. Slip a misshapen ring on an appropriate mandrel and use a small rubber or plastic mallet to hammer the rings round again.