Marble busts

[Milliepede]

I too would say perhaps the bust maker knew him or his family enough to make his bust. 

By the way why is it called a bust when it is of a head?  Serious question. 

[heywood]

I agree with what has been said already and add that looking up the sculptor and another piece of his work, that subject had died before the date of the first exhibition. There is an explanation that the date given is the date when the work was first exhibited rather than completed.
Could that have happened with your ancestor?

[Jillity]

Yes, it's Robert Carlisle Williams.  He was president of the Royal College of Surgeons from 1856 to 1857.  He was then elected to the GMC.  In June 1860 he was in London where he delivered an important lecture.  He finished the lecture and went back to his hotel room and there he collapsed and died.  He was only 55 years old and it was a shock to everyone.  A bust was commissioned after his death and it stands in the entrance hall of the RCSI in Dublin. 
I don't have any family photos from Dublin at all.  Most of my family on that side were barristers but my great grandfather broke with tradition and went off to England become an engineer.  His sister went with him.  My mother knew very little about her grandparents as they died before she was born.  She had no idea they were so learned.  It's a shame she isn't alive today to find out more of her family history.  Up until recently I thought they were all tinkers.
What I've done is to send a copy of the photo to some students who do clever things with Photoshop.  I've asked if they can tidy up the photo, remove the whiskers and cloak and make it look more lifelike.  It should be interesting if they take up the challenge.

[Mike in Cumbria]

Why would you want to remove his whiskers?

[Mike in Cumbria]

I've asked if they can tidy up the photo, remove the whiskers and cloak and make it look more lifelike.  It should be interesting if they take up the challenge.

If you can save a higher resolution scan and post it on the photo restoration board here, I can guarantee that you'll get a range of interesting results.

[ThrelfallYorky]

? As already said, why would you wish to tidy him up? And in any case, the genius image manipulators on here would do a really good job - for love.
Have you thought of writing to the RCA in Dublin, or whatever, and asking if they have any photos in their archive that they could let you have a copy of? If he had sifficient aminence to have a bust made in his honour, then surely they'd have images?
Millipede, I've absolutely no idea why it'd be called a "bust" - I know Victorian ladies at times referred to their bosom area as their "bust", thinking it was more ladylike, I suppose, - I shall spend hours now trying to find out why the term developed.....

[Mike in Cumbria]

? As already said, why would you wish to tidy him up? And in any case, the genius image manipulators on here would do a really good job - for love.
Have you thought of writing to the RCA in Dublin, or whatever, and asking if they have any photos in their archive that they could let you have a copy of? If he had sifficient aminence to have a bust made in his honour, then surely they'd have images?
Millipede, I've absolutely no idea why it'd be called a "bust" - I know Victorian ladies at times referred to their bosom area as their "bust", thinking it was more ladylike, I suppose, - I shall spend hours now trying to find out why the term developed.....

Bust comes from the latin bustum, meaning grave, tomb or funeral pyre, and presumably became associated with the grave ornaments.

[Jillity]

The reason I want the image tidied up is because it has flashes of light glinting across it. 
I have absolutely no photos of that side  of the family except for a few of my grandfather.  I can see the chin is similar but it's hard to tell with all those whiskers.  My grandfather was clean shaven.  There is also an aunt who had a similar nose.  I would love to see just one photo pf one of my ancestors from Ireland but the marble bust is the nearest thing I've got. 
The archivist at the RCSI took the photo for me but she could find no trace of any photos or a portrait.  There are loads of oil paintings in the building and they are all catalogued. 
You could look at Wikipedia to find out about busts. https://en.wikipedia.org/wiki/Bust_(sculpture)