John Rumm wrote:

I decided to go through the box of bits that I got with the ancient
lathe I was given. It seems like I have a lifetimes supply of cutters,
various face plates, a few widgets for fixing to stock and engaging
with same when turning stock between centres, plus the usual three and
four jaw chucks.

Now most of them I can make a stab at identifying, however there are a
couple of things there that I don't recognise. Here is one such:

http://www.internode.co.uk/temp/UnIDLatheObject1.JPG
http://www.internode.co.uk/temp/UnIDLatheObject2.JPG

Its probably about 2.5" by 1", and about 1/2" thick.

Any idea what one is supposed to do with it?

For carriage read cross-slide, looking closer at the pic, it may be for
parting off wood.
Don