As I mentioned earlier, Albert Kalmbach's 1943 version of this circuit used an ordinary resistor in place of the extra lamp. Lamps work much better in this circuit because the current that the lamp draws varies as the .55 power of voltage, not proportional to it as with a resistor (Ohm's law). So the voltage across the lamp increases almost as the square of the current. The number-53 lamp draws 120 milliamperes at 14 volts; so putting a number 57, which draws twice that, in parallel with the red lamp means that the red lamp gets only 1/3 the current that the green one does when they are in series. Because of the near-square-law behavior of the incandescent lamps, that means that the red lamp gets only about 1/7 the voltage of the green lamp, or about 1/8 of the total voltage. Furthermore, since an incandescent lamp puts out light proportional to the 3.5 power of voltage, the red lamp in that circumstance is only about 1/1000 as bright as the green one.
We could replace that number 57 lamp with a resistor having the same voltage/current ratio (which is its resistance) when the red lamp is off and get exactly the same performance. That would be about (14/8) /.08, or about 22 ohms. The problem comes when the train turns on the red lamp, in which case the resistor is dissipating 14^2/15, or 9 watts. The number 57 lamp, on the other hand, dissipates only about 3 watts when lit. (All of this assumes a 14-volt supply.)
So Kalmbach's resistor version certainly works. It just consumes a lot more power.
