Charlotte Gibson told the Evening News that her grandad is “very caring and thoughtful” and “still goes round to neighbours to see if they need milk or bread or offer to clean their windows.”
He enjoys travelling by bus but he sticks to his routine and he’s “always glad to get home again and get settled”.
William has been missing since Tuesday when he was last seen at Greggs in the Kirkgate around 4pm.
Police have increased the number of officers working on the inquiry as temperatures drop.
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Charlotte said: “It’s been hard for the family. We have a small but very close family and he’s very much at the centre of it. There’s five grandchildren who have Christmas cards for him and starting to wonder where’s grandpa?
“I just really want to find him and know where he is now.”
Police in Edinburgh have thanked the public for alerting them to possible sightings and asks that they continue to get in touch.
CI David Robertson said: “I am gravely concerned for William. We have seen freezing temperatures and with snow forecast for the weekend it is imperative that we do everything we can to find him.
“I am increasing the number of officers working on this inquiry and I would urge everyone to keep sharing William’s photo and description and please call if you may have seen him at any time since Tuesday afternoon.
“It is still very possible that he has taken shelter from the cold and so if you have not already checked your shed or garage, please do so.”
Charlotte added: “I would just urge people to check their sheds, their gardens ... or check the man in the bus queue.”
If you think you have seen William since Tuesday contact Police Scotland on 101 quoting incident 3338 of 11th December.