Short wave diathermy test kit or ultra-sound test kit?? Purely a guess.

I suspect that anything that "unfathomable" must be to do with physiotherapy.......

There is also a big bakelite handle that the "probes" plug into. The mains input is via a lamp bayonet fitting

The item in question is therapy device which works in the same way a plasma globe works (also seen in every B-movie science fiction film). These devices were made when doctors/scientists/quaks where initially obsessed with the healing properties of electrical currents. Of course these devices never really did any good, but also didn't do any harm. They are seen as collectors items in certain circles especially in full working order and complete sets. Hope this info is of interest.

Interesting.

Are those glass "probes" solid ... or are they filled with something?

I can't quite make out what the controls legends are.

What are we talking about here? Mains voltage?

And what does that middle control say:- Pulse (or Peak?) and Stream?

I guess that the extra-safe (?) bayonet lamp connection indicates "home use" (as in:- "don't try this at home folks")!

A Collectors' Item? Best get it on eBay, then!

The tubes are hollow and filled with low pressure gas usually helium or neon at the connection end there will be terminal which is supplied with a high frequency alternating current. When the glass probe is touched, an arc passes through the gas to complete a circuit. The gas enables us to see the arc. There is also a small 'tingley' arc at the connection between skin and glass. This is the so called 'therapy' for which the machine is designed for. this 'therapy arc also generates a small amount of ozone, the smell of which is quite distinctive.
full description is available here:
Wikipedia

Something for the antiques fair then. It is mains into a coil and condenser (too old to be a capacitor) then a tuned circuit looking item in the hand piece. Don't think I'll risk plugging it in as the insulation is failing on the inside but could easily be repaired. The controls even though looking like pots are just on off switches so you either get it all up you or half of it up you as Corp Jones would say

Some of these were called "violet Ray" treatment units as the glass applicators glow blue/violet colour when activated. I have one similar unit myself.

They are also popular with those who like to "experiment" sexually as apparently they tingle and give quite a nice sensation.
Robert
And I did say apparently - this is not from experience!!