Everything I look at indicates a white and red wire for the connecting wires. Our thermostat is probably original to our home (1943). It has two wires. It is difficult to tell but it looks like one is a white wire and the other is black. I've tried looking on the internet for some info however I only see white & red wires mentioned. Should the black wire be connected to the rH terminal and the w connected to the w terminal?

That should work. The thermostat is just a switch, switching the power from one wire to another. On newer systems, the red is power from the transformer and is switched to the white, green and yellow as needed.

Everything I look at indicates a white and red wire for the connecting wires. Our thermostat is probably original to our home (1943). It has two wires. It is difficult to tell but it looks like one is a white wire and the other is black. I've tried looking on the internet for some info however I only see white & red wires mentioned. Should the black wire be connected to the rH terminal and the w connected to the w terminal?
Thanks. It works!