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Frank Reed.  You ask for suggestions for the use of the eBay listing:  Here’s my sixpenneth.

A look at this dealer’s ‘Shop’ shows that he is a general dealer in antiquities made more interesting by the name or event they’re associated with or their curiosity value.  Much of the descriptive background to the listing can be got from five minutes Googling.  However, further Googling shows Edward Troughton was one of the foremost instrument makers, including astronomical instruments in the UK in the late 18^th early 19^th century.  He was particularly interested in the geometry of the circle in respect of his transit circles and their associated dividing engines and wrote papers about it mathshistory.st-andrews.ac.uk/Biographies/Troughton/.

Such instruments would need to be marked and read to great accuracy.  We also read that he didn’t make telescopes because he was colour blind (??? Explanation required).  Therefore, this might have led him to use scales on the circles of his instruments as the preferred method of obtaining the required accuracy.  Such scales require a certain amount of practice to read, which might not be present in his undoubtedly wealthy customers or potential customers. 

Therefore, I suggest that this is a demonstrating/teaching device kept in his shop or given as part of the toolkit with one of his measuring circles.  It could also be set up prior to an observing session and given to the assistant who was going to set up the actual circle prior to a set of readings.  Usual caveat.  I’m probably completely wrong.  DaveP