I have a mid 70's Gitane 10 speed road bike and I am trying to fix the brakes myself. The old cable snapped. I bought a new cable and installed it. The brake provided no stopping power. Even when the cable is quite tense, the right pad does not make contact with the wheel. Could the problem be related to the casing on the outside of the cable? I don't know what it is called but does it need to be a certain length? And is it an important part of the braking mechanism?