I don’t know why this did not come up the other day.
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Edit: Friday 1/22/2010 @ 4:40 pm
Thank you Paul for the additional details.
The large wrapped coil on the back of the speaker is an
electromagnet, not a permanent magnet.
The testing procedures I outlined below are still valid.

If an audio output tube is missing, you may hear something.
The 2 audio output tubes on the 62-1101 schematic are set up as a push-pull amplifier driving the audio output transformer.

From the 62-1101 schematic; here is the tube list.
There is a good chance the 62-1100 uses the same tubes

1 tube 5Y3G = rectifier

2 tubes 6F6G = Audio output tubes

1 tube 6H6 = 2nd det.

2 tubes 6J5G = tuning indicator & balancing exciter

2 tubes 6J7G = 1st audio & 1st det.

2 tubes 6U7G = IF and RF

Compare this tube list with what is on your radio.
This question is going to vote in 5 hours and I will not be able to add to my answer.
Feel free to email me, link below:
http://answers.yahoo.com/my/profile;_ylt=AtYz4OpIqAyRYTpGpJE3wpzty6IX;_ylv=3?show=arAcdUdgaa&preview=true
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Edit, 9 hours after I answered your question.
I looked at the first schematic I gave you and it is not a complete schematic.

I looked at a model 62-1101 , It has 4 pages.
On page 4, which is the last page of the down load,
after you rotate the page to the right.
On the bottom right side is the power supply and speaker wiring diagram.

The speaker electromagnet is shown as:
SPK. FIELD
960 ohms

The Voice coil is shown to be 1.5 ohms

This is all you need to reconnect the 4 wires from the speaker to the chassis socket.
The model numbers are different, but this schematic should be close enough to help.
I will leave the rest of my answer intact.
Here is the new link to a 62-1101 schematic.
follow the directions when you get there, to either view or down load it.
I would download and print it if you do decide to take your radio to a shop.
http://www.nostalgiaair.org/Resources/257/M0011257.htm

Original answer is below.
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Hello Paul.
I have one question to ask about your radio speaker.

Does it have a permanent magnetic on the back? If not, what I think you have is old enough to have an electromagnetic speaker magnet.

I am going on memory here.
The electromagnet magnet on the speaker is part of the radio power supply.
It is operated by the B+ voltage of around 300 volts DC.

I do not know how much you know about electricity/ electronics.

Do you have a volt/ ohm meter?
If not you can purchase one at some place like Radio Shack for around $30.00 US.

You can test the chassis socket to see if there is somewhere around 200 to 300 volts DC. between two of the pins.

I think the 5th pin in the chassis socket is only for the plug alignment.
Looking at the back/ under side of the chassis will tell you.

The radio needs to be turned on to do this test.
Be careful as the B+ voltage of around 300 volts DC is dangerous.
These two pins/ wires would connect to the electromagnet on the back of the speaker.

To determine what the 4 wires coming out of the speaker are, you need to do a ohm/ resistance test on those 4 wires.

Between 2 of the wires, you will have an ohm reading of maybe 8 to 16 ohms. The new schematic shows 1.5 ohms
These are the voice coil.

Between the other 2 wires, you will have an ohm reading that is higher, maybe 100 to 200 ohms or more.
The new schematic shows 960 ohms
These will go the electromagnet on the back of the speaker.

If I was there and could look at the wiring under the chassis, it would be no problem to figure it out.

Back to the safety issue and my lack of how much you know about electronics, your best bet would be to take the radio to an electronics repair shop and have them look at it.

This from memory from about 30 years ago.

I will do some research to find a schematic and get back to you.
Best of luck.
Wingman

Edit, A safety quote, the source is below the quote.

"Every day that you work on tub-type radios could be your last. There have been documented incidences of knowledgeable, but careless, individuals being KILLED by electrocution while working on tube-type radios. Those of use who have survived shocks from a 400-V plate supply will not forget it. A jolt from B+ left me feeling so weak that I thought I would have to lie down."

This is the 8th paragraph down at this website:
http://enginova.com/Antique_Radios.htm

I found a schematic for your radio, follow the directions
when you get there, to either view or down load it.
I would download and print it if you do decide to take your radio to a shop.
I do not have a printer and magnifying the schematic on my screen is not helping me to help you.

Nostalgia Air Online Antique and Vintage Radio References Free online schematics, manuals, tube data, references and more! In loving memory of my father …
http://www.nostalgiaair.org/Resources/256/M0011256.htm

I hope that is enough information for you.

Wingman