Can any one please help me identify this object?

It could be a Victorian period cistern pull .

A brass fitting goes in the hole and this is connected via chain to the cistern lever .

Most commonly made of china , ivory or wood .

A slightly more posh one

 

It could also be the working end of a pestle .

Mortar and pestle

 

Of the two the pestle is the one.I had one like it.
The cistern pull has a hole all the way through it to secure the chain.
The pestle is smooth so it can grind.

 

It could be the marble handle of almost anything from an earlier time. Obviously the wooden part has rotted away. I would be looking for other pieces to see if you can't cobble some parts together and then get a better idea of what the greater object is. If you find something else don't forget to mark its location and its distance from the original object. Then you'll get a better idea of the size of the larger object that this marble handle is a part of.

 

And, yes, it does resemble a cistern pull. I actually looked at some online and they are usually connected to a metal fitting which is connected to a chain. I'd be sweeping the area in your garden with a metal detector. That is if you're still interested. Sometimes it's fun to do these little personal 'anthropology' projects.

 

It does not have the end wear expected on a pestle.

The thread does not look like a wood thread. Most brass tube is threaded with 26 tpi. What is the pitch of the thread ?

If marble, the hole would be drilled and tapped, then a bolt in a lathe would hold the article while the profile was cut and polished.

 

And even if it was wood, there should probably still be a brass or copper fitting. That's why he should go back in with a metal detector. Any mystery is a good mystery.