Bridge arm floor lamps have a swinging arm that extends out from the vertical base of the lamp. This makes them ideal for use as reading lamps, since you can move the light source close to you without having to move the entire lamp. If you have a favorite old bridge arm lamp whose wiring is showing signs of wear and decay, you don't have to consign it to the trash heap. The wiring in bridge arm lamps can be replaced rather easily with a small investment of time--an ideal job for the home handyman.
Unplug the lamp. Never attempt to work on a live electrical circuit. Remove the lamp shade and the bulb.
Detach the bulb socket from the bridge arm of the lamp. This is usually held in place with a nut at the base of the socket. Turn the nut counterclockwise with your fingers or with an adjustable wrench if necessary to loosen it. When the bolt is loosened, the bulb socket will be free, held in place only by the wires of the electrical cord in the lamp.
Loosen the two screws on the base of the bulb socket that the lamp cord of the lamp is connected to. Place the bulb socket off to the side for later reuse.
Tape the end of your new lamp cord to the end of the lamp cord you just disconnected from the bulb socket. Grasp the end of the lamp's cord with the electrical plug on it and carefully pull the cord out of the lamp. This will pull the new cord through the lamp, saving you the difficulty of fishing the new cord through by itself. Pull enough new cord through the lamp so that you have about 6 inches extending out the bulb socket end and enough to reach your electrical outlets at the base--usually about 6 to 8 feet is a good amount. Cut the new electrical cord to size when you've got the right amount at both ends, using a pair of wire cutters.
Remove 1/2 inch of insulation from both of the wires on both ends of the lamp cord, using your wire strippers.
Pull the cover off of your new electrical plug. Slide the cover over the end of the wire on the base end of the lamp. Loosen the two screws on the electrical plug. Slide the bare end of one of the lamp cord's wires under each of the screws. Tighten the screws to hold the wires in place. Slide the cover of the electrical plug onto the plug.
Slide the bare ends of the lamp cord at the bulb socket end of the lamp under the screws of the bulb socket, one wire to each screw. Tighten the screws to hold the wires in place.
Pull the lamp cord from the base end of the lamp to take up any slack on the bulb socket end. Attach the bulb socket to the bridge arm with the nut you loosened to remove the socket originally.