[Ron Ramirez]

Well, Jim, it was good that you did not have any POW or POOF. Unfortunately, your resistance measurements tell the story - the high voltage winding of the power transformer is partially shorted out, and the primary of the audio output transformer is opening up.

So you know what you need to do.

At least you know your speaker is OK, so that is some good news.

Now to answer some of your other questions...

Yes I need a 10MFD 450 volt capacitor or filter (which term is more correct capacitor or filter?)

Electrolytic capacitor.

the layout of the schematic is confusing, in actual physical layout in the chassis the audio output transformer is really next to the main transformer and the Field Coil is next to or part of the speaker, BUT the schematic has the Audio Output Transformer next to the speaker and the field coil (Labeled Field Coil) next to the main transformer, why is the schematic like this, :

Again, schematics are sort of like road maps. However, unlike a conventional road map, a schematic diagram shows how everything is hooked up in a radio - it does not accurately reflect exactly how the wiring, parts, etc. are placed under the chassis. Once you gain experience in repairing radios, you will see that schematic diagrams are much, much easier to use than a pictorial of a set's under-chassis wiring - with a schematic, it is easier to see what each part is doing in each circuit of the radio.

Hang in there. You should be in the home stretch now; and with new transformers, hopefully that Philco will be playing Christmas music for you soon.