This was my grandfather’s and have no idea what it is only that it is some piece of physics equipment!
The main black cylinder doesn’t seem like it wants to rotate but not sure if it should?
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It looks like an induction coil with the make and break device at the bottom and a switch right at the bottom. If you connect it up to an accumulator, be very, very careful as the output between the two balls, when separate, could be lethal. Also the electrical insulation elsewhere may be poor and you might get a shock just by touching the switch.
Use with very great care and preferably have somebody who knows about such devices with you.
It is a spark radio transmitter.
The first working radios.
Video: https://www.youtube.com/watch?v=YSf93g0heUA Pics: https://www.google.com/search?q=spark+radio+transmitter&source=lnms&tbm=isch&sa=X&ved=0ahUKEwi-68m5vJjfAhXMx1kKHVuUASQQ_AUIDygC&biw=1920&bih=930
This one looks awfully similar and might give you some help finding out model and such:
Remember 300 baud modems that you put the handset into? This was the top of the line once upon a time too. It's why we have "SOS" in our language rather than relying upon a simple "Oh God, we need help!"
And if Tesla'd ever realized be was using Morgan's money to succcessfully invent radio transmission rather than failing at wireless power transmission, we'd've never called these "Marconi Spark Gap Transmitters"... but he didn't.