Interconnects and shielding and what it does.

I just recently bought some Auditorium ICs, which I love, but Im a little confused still about which way to hook them up....waiting to hear back about this from my dealer about this in more detail, but from what I have gathered I am using these cable in reverse. The little one sheet that they came with says that the shielding is indicated with a longer shrink wrap on one end but does not say which side the shielding should be hooked up too.

Through a little experimenting I have decided with some enthusiasm that the way that sounds the best in my system is putting the shielded side on the source. So to make this clearer I put the the shielded end into my turntable then the unshielded into my phono pre then the same order from the phono pre to the amp. The other way around sounds a little brittle in comparison.

Is there anyone out there that can explain this to me how this should effect sound? Also is there any damage that could occur from using the shielded side incorrectly if I actually am doing this wrong?

Any help would to explain how this should be would be much appreciated. Thanks.
You will not cause any damage, regardless of the direction of the cable. as for why it sounds better with the shielded end at the source, I suspect its because you are preventing outside distortions from entering the cable at the source, and therefore not being carried through your system. Once a distortion enters the system, there is no way to remove it. Prevention is much more important than cure.
Think of it this way. In your turntable, you want a vibrationless bearing, not some plinth material that tries to absorb the vibration, which can never be completely accomplished. Same with your cables. Dont let outside distortion in, and you wont have to deal with it down the road.
Shield has to drain induced current to ground but we don't know the best, least inductive path without trying. In your case it is thru source. When path is less effective shielding becomes less effective. Induced interference affects purity of the sound. Since there is no separate shield pin it is connected to analog/signal ground (that most likely is connected thru capacitor to chassis/earth ground). I would think that connecting it to analog ground at the source where output impedance is low makes more sense than connecting it at the higher impedance input side but it is only a guess. The right side is one that sound better to you. You cannot damage anything.
Thank you guys so much for your responses. This would have been something that I just simply would have never considered if there were just the normal arrows on these cables, but i am really glad I did. This makes me want to go play around with my other interconnects and see if I couldn't get a better result trying out different combinations.
I've got you cables. Dealer told me to go the direction of the brand name writing. Right or wrong they sound great.
Try it both directions. If there is no noise then whatever sounds best. :)