Hi again,
Would agree with Millmoor - the Diana Simpson at Drainie may be William's mother. At age 25 in 1851 she is unmarried and working as a servant.
Wondered if this chap was a possibility for William's father - John Davidson.
Aberdeenshire - Huntly - Nelson Street 1851 Census
MCPHERSON Alexander Head M M 33 Mason, Journeyman Inverness-shire - Laggan
MCPHERSON Margret Wife M F 33 Aberdeenshire - Forgue
MCPHERSON Ann Dau - F 2 Aberdeenshire - Huntly
MCPHERSON James Son - M 8m Aberdeenshire - Huntly
MCPHERSON Lachlan Brothr U M 31 Master Plasterer Inverness-shire - Laggan
FRASER Charles Grant Visitr U M 19 House Carpenter, Journeyman Banffshire - Rothiemay
DAVIDSON John Visitr U M 27 Blacksmith, Journeyman Morayshire - Fochabers
Fochabers was in Bellie Parish (don't know how familiar you are with the area

- I don't know it but I found out thanks to Google !)
Looby
