Originally Posted by: river6109 
Soest,
Giving advice on electrical equipment such as main voltage can result in a disaster.
No electrician will give you advise over the phone or over the interent how to fix a transformer that has a main input voltage.
I'm somewhat surprised, we have restrictions about politics, religion and foul language but we don't have guidelines regarding help or request for electrical equipment such as main power transformers.
My advice is, don't touch it and get a new one.
although I have dismantled it previously and replaced cords, the inside reveals, the knob moves over a series of wires sideways and over years of operation these wires could be worn down.
by the time you've figured it all out it is noth worth it, value and safety wise.
You know the saying: curiosity killed the cat.
John
With John's very sound and wise advice in mind, I'll still try to answer your question.
This is probably your Trafo shown below. The Red knob on these will come off with the top cover, it can only be removed once the cover is off but the knob itself probably no need to remove.
There is a reason for the small silver rivets which is to dissuade the curious. I offer this advice only on the assumption that you are either experienced in electrical work, or will give the information to an experienced appliance service person or electrician to undertake for you - SERIOUSLY!!
Also be aware that the 278a Controller is now very old. ie most likely at LEAST c. 50+ years old so not only have you the issue with the speed control but also the mains flex is very likely deteriorated (internal insulation perished) and should also be replaced.
Couple that with it's relatively low power output and you can quickly see that this is the perfect time to consider replacement and perhaps (if the mains flex is ok) relegate this to being a lighting transformer.
But at the end of the day this forum is an information resource and having serviced a number of these myself I provide the following detail for its information value only;
And with that disclaimer out the way we shall proceed....
The rivets will need to be removed, either cut off or pulled through the holes with small side-cutters. The tabs which protrude through the base mnay be twisted also to secure the top and base together and will need to be gently straightened with flat ('duck-bill') pliers.
Then the top cover can be gently and slowly pried off the base - be careful as the wire for the speed control wiper will remain attached and it's only a short section of wire.
If you are lucky, the wiper may only have lost its pressure against the transformer windings in which case only a gentle bit of adjustment (bending), or in IBM-Speak, 'forming' to give additional pressure.
Failing that, the copper windings may have worn too far for reliable contact in which case repair is simply not an option. It would need re-winding of the core. These are done by machine under specific tension etc etc and impractical to even attempt repair and brings us right back to the 'time to replace it' option.
Hope this helps, and please, once again take this advice seriously - if you don't know what you are doing with main voltage, don't even try. It's just not worth the risk.
Kind regards
Steve
Melbourne
cookee_nz attached the following image(s):