Good morning, Treddy, and Chris up in B. C. too;
I am impressed with the number of knowledgeable people who recognize that the Vivitar V1 Enlarger power supply is a regulated AC supply using a ferro-resonant regulating transformer. That transformer has three (3) windings where the winding with the black wires is the 120 VAC primary or input winding, the winding with the white wires is the regulated output lower voltage secondary winding, and the third or tertiary winding with the red and yellow wires is the regulating winding that works with the capacitor. The tertiary winding with the capacitor is the "resonant" part.
Others have already commented on the necessity for getting a replacement capacitor of the same value and AC voltage rating, although the AC voltage rating can be higher, but the value of the capacitor in ufd or Micro-Farads must be the same. The exact capacitor value is important. An AC voltage rated "motor starting" capacitor of the same value will work.
There are some other very simple ways that we can get around the death of the proprietary transformer if that has happened. One very simple way is to get a Sola type CV or CVS constant voltage transformer (there are some other brands also) with about a 90 Watt or 100 Watt rating, and replace the dead transformer and its capacitor in the power supply with just a simple low voltage transformer of about an 18 VAC at 5 Amperes rating. It may be called a "filament transformer." It will go between the black primary wires and the white secondary wires. When you plug the cable on the power supply into the external constant voltage transformer, you will move the voltage regulating function from the power supply out to the external constant voltage transformer, but the voltage lowering function stays in the power supply this way.
Yes, there may be a slight changing of the color temperature of the light with the possibly slightly different voltage, but it can be compensated in the filter pack if truly needed. Try some test prints in color and see how it looks to see if this is necessary. With black and white it will not be truly necessary.
Oddly enough, the V1 Enlarger is one of the very few things that Ponder and Best, or "Vivitar," actually did make in California.