There is a preferred direction to the cables, and it is imperative that you get the same polarity of the magnets at the source and pre/amp end.
First, get a compass and find our which end of the cable attracts the 'north' end of the compass needle. This end will be the 'source' end, or in your case, the end that attaches to the outputs of the CD player. (I'm only 90% sure that this is how it goes. On later Ultra-Clear cables there is a directional arrow, which makes it much easier.)
Make sure that the 'south' end for both cables is at the CD player.
The small brass ring can alter the sound. If the ring/clamp is closer to the 'source', the sound is very slightly more detailed. With the ring/clamp towards the other end of the cable (closer to the pre/amp) the sound is slightly less detailed, but more 'full/rounded'.
The ring/clamp acts like the clamps on the older VD cables, in that apparently reduces micro-vibrations in the conductor. Don't clamp down too hard so as not to damage the cable.