Where does the extra wire connect on my new furnace blower motor?
I'm assuming the grey colored motor is the new one and the rusty one is the old. In your old configuration the capacitor connected between the AC neutral (white) and the brown wire. In your new motor the white still needs to connect to your AC neutral. However, your new motor has two brown wires to connect to the capacitor, and any connection between it and AC common (if it has one) is internal to the motor. So whatever the white wire connected to on your old motor is where the white wire on your new motor should connect to. (I'm not sure if the diagram indicates that the wire in question is white, purple, or yellow; or a wire with white, purple, and yellow stripes. Your pictures don't show the actual wires.)